A national laboratory of the U.S. Department of Energ y [615860]

A national laboratory of the U.S. Department of Energ y
Office of Energy Efficiency & Renewable Energ y
National Renewable Energy Laboratory
Innovation for Our Energy Future
Dynamics Modeling and Loads
Analysis of an Offshore
Floating Wind Turbine
J.M. Jonkman Technical Report
NREL/TP-500-41958
November 2007
NREL is operated by Midwest Research Institute ● Battelle Contract No. DE-AC36-99-GO10337

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by Midwest Research Institute • Battelle
Contract No. DE-AC36-99-GO10337 Technical Report
NREL/TP-500-41958
November 2007 Dynamics Modeling and Loads
Analysis of an Offshore
Floating Wind Turbine
J.M. Jonkman
Prepared under Task No. WER7.5001

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Acknowledgments
I would like to thank many individuals for the successful completion of this project. Without
their advice and help, I could not have completed a work of this scope.
First, I would like to thank my Ph.D. committee for evaluating this work: Professor Mark Balas,
formerly of the University of Colorado and now with the University of Wyoming; Professors Carlos Felippa and Lucy Pao of the Universi ty of Colorado; Dr. Michael Robinson of the
National Renewable Energy Laboratory; and Pr ofessor Paul Sclavounos of the Massachusetts
Institute of Technology. Special thanks go to my advisor, Professor Mark Balas, for his
guidance and support of this work, and to Profe ssor Paul Sclavounos, for educating me in marine
hydrodynamics.
Thank you to Dr. Robert Zueck and Dr. Paul Palo of the Naval Facilities Engineering Service
Center for giving me insight into the dynamics and modeling of mooring systems.
I would also like to thank Dr. Jon Erik Withee of the U.S. Navy for initiating the study of
offshore floating wind turbines at the Massachuse tts Institute of Technology, and Kwang Lee for
continuing in that effort and verifying the output of SWIM. I am also grateful to Libby Wayman
for modifying SWIM to output the frequency-dependent solutions of the radiation and diffraction problems, for developing a floating platform concept, and for providing me with data that I could use to validate my own models.
Thank you also to Torben Larsen of Risø Nati onal Laboratory and the Technical University of
Denmark for introducing me to the importance of the role that a variable blade-pitch-to-feather
control system can play in offshore floating wind turbines.
I would also like to thank Ian Edwards of ITI Energy for sponsoring the loads-analysis activities
and Professor Nigel Barltrop and Willem Vijfhuizen of the Universities of Glasgow and Strathclyde for developing the ITI Ener gy barge and mooring system concept.
Big thanks go to several of my colleagues at the National Renewable Energy Laboratory’s
National Wind Technology Center. I thank George Scott for processing the reference-site data
from the Waveclimate.com service, and Bonnie Jonkman for assisting me in developing the
scripts needed to generate the WAMIT
® geometric-data input files. I thank Marshall Buhl for
developing the scripts used to run the loads analys is and for assisting me in processing the loads-
analysis data. Thank you to Dr. Gunjit Bir for assisting me in examining the system instabilities and to Lee Jay Fingersh and Dr. Alan Wright for their guidance and advice in my controls-
development activities. Thanks also to Kathleen O’Dell, Rene Howard, Janie Homan, Bruce Green, and Bonnie Jonkman for editing this work to make it much more readable. Thank you
also to Walter Musial and Sandy Butterfield for leading the offshore wind energy program and to Dr. Robert Thresher and Dr. Michael Robinson for directing the National Wind Technology Center and for giving me the time and resources needed to work on this project.
I would like to thank my family and friends for their gracious support and encouragement
throughout this effort—I couldn’t have co mpleted the project without your help.
iii

This work was performed at the National Renewable Energy Laboratory in support of the U.S.
Department of Energy under contract num ber DE-AC36-99-GO10337 and in support of a
Cooperative Research and Development Ag reement (CRD-06-178) with ITI Energy.
iv

Acronyms and Abbreviations
Abbr. = abbreviation
ADAMS® = Automatic Dynamic Analysis of Mechanical Systems
ARGOSS = Advisory and Research Group on Geo Observation Systems and Services
A2AD = ADAMS-to-AeroDyn
BEM = blade-element / momentum
BVP = boundary-value problem
CM = center of mass
COB = center of bouyancy
DAC = disturbance-accommodating control
DLC = design load case DLL = dynamic link library DOE = U.S. Department of Energy DOF = degree of freedom DOWEC = Dutch Offshore Wind Energy Converter project
DU = Delft University
ECD = extreme coherent gust with direction change
ECN = Energy Research Center of the Netherlands
EOG = extreme operating gust equiripple = equalized-ripple ESS = extreme sea state ETM = extreme turbulence model EWM = turbulent extreme wind model EWS = extreme wind shear
FAST = Fatigue, Aerodynamics, Structures, and Turbulence
FEA = finite-element analysis
FFT = fast Fourier transform
F2T = frequency-to-time
GDW = generalized dynamic-wake
GE = General Electric
HAWT = horizontal-axis wind turbine IEA = International Energy Agency
IEC = International Electrotechnical Commission
JONSWAP = Joint North Sea Wave Project metocean = meteorological and oceanographic
MIMO = multiple-input, multiple-output
v

MIT = Massachusetts Institute of Technology
MSL = mean sea level
NACA = National Advisory Committee for Aeronautics
NASA = National Aeronautics and Space Administration NAME = Naval Architecture and Marine Engineering NFESC = Naval Facilities Engineering Service Center NREL = National Renewable Energy Laboratory NSS = normal sea state NTM = normal turbulence model NWTC = National Wind Technology Center
OCS = offshore continental shelf
OC3 = Offshore Code Comparison Collaborative O&G = oil and gas OWC = oscillating water column
PI = proportional-integral
PID = proportional-integral-derivative PSD = power spectral density PSF = partial safety factor
RAM = random access memory
RAO = response amplitude operator RECOFF = Recommendations for Design of Offshore Wind Turbines project
RNG = random-number generator
SAR = synthetic aperture radar
SDB = shallow-drafted barge SISO = single-input, single-output SML = SWIM-MOTION-LINES SVD = singular-value decomposition SWL = still water level
TFB = tower feedback
TLP = tension leg platform TMD = tuned-mass damper
UAE = Unsteady Aerodynamics Experiment VIV = vortex-induced vibration WAMIT
® = Wave Analysis at MIT
WGN = white Gaussian noise
WindPACT = Wind Partnerships for Advanced Component Technology project w.r.t. = with respect to
vi

Nomenclature
A = amplitude of a regular incident wave
Ad = discrete-time state matrix
ai = component of the undisturbed fluid-partic le acceleration in Morison’s equation in
the direction of the ith translational degree of freedom of the support platform
Aij = ( i,j) component of the impulsive hy drodynamic-added -mass matrix
rX Ea = three-component accelerati on vector in Kane’s equations of motion for the center
of mass (point Xr) of the rth system rigid body in the inertial frame (frame E)
ARadiation = added inertia (added mass) associated with hydrodynamic radiation in pitch
A0 = water-plane area of the support platform when it is in its undisplaced position
Aξ = amplitude of the platform-pitch oscillation
Bd = discrete-time input matrix
Bij = ( i,j) component of the hydrodynamic-damping matrix
BRadiation = damping associated with hydrodynamic radiation in pitch
BViscous = damping associated with hydr odynamic viscous drag in pitch
CA = normalized hydrodyna mic-added-mass coefficient in Morison’s equation
CB = coefficient of the static-friction drag between the seabed and a mooring line
CD = normalized viscous-drag coefficient in Morison’s equation
Cd = discrete-time output state matrix
CHydrostatic = hydrostatic restoring in pitch
Hydrostatic
ijC = ( i,j) component of the linear hydrostatic-r estoring matrix from the water-plane
area and the center of buoyancy
CLines = linearized hydrostatic restoring in pitch from all mooring lines
Lines
ijC = ( i,j) component of the linear restorin g matrix from all mooring lines
CM = normalized mass (inertia) coefficient in Morison’s equation
vii

Cx = effective damping in the equation of motion for the platform pitch in terms of the
translation of the hub
Cφ = effective damping in the equation of motion for the rotor-speed error
D = diameter of cylinder in Morison’s equation
Dc = effective diameter of a mooring line
Dd = discrete-time input transmission matrix
Platform
idF = ith component of the total external load acting on a differential element of cylinder
in Morison’s equation, other than those loads transmitted from the wind turbine
and the weight of the support platform
Viscous
idF = ith component of the viscous-drag load ac ting on a differential element of cylinder
in Morison’s equation
dz = length of a differential elemen t of cylinder in Morison’s equation
E[H s|Vhub] = expected value of the significant wave height conditioned on the mean hub-height
wind speed, based on the long-term joint-probability distribution of metocean parameters
EA = extensional stiffness of a mooring line
f
c = corner frequency
fi = component of the forcing function associated with the ith s y s t e m d e g r e e o f
freedom
Fi = generalized active force in Kane’s equations of motion associated with the ith
system degree of freedom
*
iF = generalized inertia force in Kane’s equations of motion associated with the ith
system degree of freedom
Hydro
iF = ith component of the total load on the s upport platform from the contribution of
hydrodynamic forcing, not in cluding impulsive added mass
Lines
iF = ith component of the total load on the suppor t platform from the contribution of all
mooring lines
Lines,0
iF = ith component of the total mooring line load acting on the support platform in its
undisplaced position
viii

Platform
iF = ith component of the total external load acting on the support platform, other than
those loads transmitted from the wind turbine and the weight of the support
platform
Viscous
iF = ith component of the total viscous-drag load acting on the support platform from
Morison’s equation
Waves
iF = ith component of the total excitation for ce on the support platform from incident
waves
rXF = three-component active-force vector in Kane’s equations of motion applied at the
center of mass (point Xr) of the rth system rigid body
g = gravitational acceleration constant
GK = gain-correction factor
h = water depth H
A = horizontal component of the effective tension in a mooring line at the anchor
HF = horizontal component of the effective te nsion in a mooring line at the fairlead
0
FH = starting value of H F used in the Newton-Raphson iteration during the initialization
of the mooring system module
rN EH& = three-component vector in Kane’s equa tions of motion representing the first time
derivative of the angular momentum of the rth system rigid body (body Nr) about
the body’s center of mass in the inertial frame (frame E)
Hs = significant wave height
Hs1 = significant wave height, based on a 3- h reference period, with a recurrence period
of 1 year
Hs50 = significant wave height, based on a 3- h reference period, with a recurrence period
of 50 years
IDrivetrain = drivetrain inertia cast to the low-speed shaft
IGen = generator inertia relative to the high-speed shaft
IMass = pitch inertia associated with wind turbine and barge mass
IRotor = rotor inertia
j = when not used as a subscript, this is the imaginary number, 1−
ix

k = wave number of an incident wave
KD = blade-pitch controller derivative gain
KI = blade-pitch controller integral gain
Ki = ith component of the time- and direction-de pendent incident-wave-excitation force
on the support platform per unit wave amplitude
Kij = ( i,j) component of the matrix of wave-rad iation-retardation ke rnels or impulse-
response functions of the radiation problem
KP = blade-pitch controller proportional gain
KPx = proportional gain in the tower-feedback control loop
Kx = effective stiffness in the equation of motion for the platform pitch in terms of the
translation of the hub
Kφ = effective stiffness in the equation of motion for the rotor-speed error
L = total unstretched length of a mooring line
LB = unstretched length of the portion of a mooring line resting on the seabed
LHH = hub height
Lij = ( i,j) component of the matrix of alterna tive formulations of the wave-radiation-
retardation kernels or impulse-response functions of the radiation problem
Mij = ( i,j) component of the body-mass (inertia) matrix
rNM = three-component active moment vector in Kane’s equations of motion applied to
the rth system rigid body (body Nr)
mr = mass of the rth system rigid body in Kane’s equations of motion
Mx = effective mass in the equation of motion for the platform pitch in terms of the
translation of the hub
Mφ = effective inertia (mass) in the equation of motion for the rotor-speed error
n = discrete-time -step counter
NGear = high-speed to low-speed gearbox ratio
P = mechanical power
P0 = rated mechanical power
x

Pθ∂∂ = sensitivity of the aerodynamic power to the rotor-collective blade-pitch angle
qj = system degree-of-freedom j (without the subscript, q represents the set of system
degrees of freedom)
jq& = first time derivative of system degree-of-freedom j (without the subscript, q
represents the set of first time derivatives of the system degrees of freedom) &
jq&& = second time derivative of system degree-of-freedom j (without the subscript, q
represents the set of second time derivatives of the system degrees of freedom) &&
s = unstretched arc distance along a mooring line from the anchor to a given point on
the line
1-SidedSζ = one-sided power spectral density of the wave elevation per unit time
2-SidedSζ = two-sided power spectral density of the wave elevation per unit time
t = simulation time
T = aerodynamic rotor thrust
TAero = aerodynamic torque in the low-speed shaft
Te = effective tension at a given point on a mooring line
TGen = generator torque in the high-speed shaft
Tp = peak spectral period
Ts = discrete-time step
T0 = aerodynamic rotor thrust at a linearization point
u = for the control-measurement filter, the unfiltered generator speed
u = for the system equations of motion, the set of wind turbine control inputs
U1 = first of two uniformly-distributed random numbers between zero and one
U2 = second of two uniformly-distributed random numbers between zero and one
V = rotor-disk-averaged wind speed
VA = vertical component of the effective tension in a mooring line at the anchor
VF = vertical component of the effective te nsion in a mooring line at the fairlead
xi

0
FV = starting value of V F used in the Newton-Raphson iteration during the initialization
of the mooring system module
Vhub = hub-height wind speed averaged over a given reference period
vi = component of the undisturbed fluid-partic le velocity in Morison’s equation in the
direction of the ith translational degree of free dom of the support platform
rXE
rv = three-component partial linear-velocity vector in Kane’s equations of motion for
the center of mass (point Xr) of the rth system rigid body in the inertial frame
(frame E)
Vin = cut-in wind speed
Vout = cut-out wind speed
Vr = rated wind speed
V0 = displaced volume of fluid when the s upport platform is in its undisplaced position
V1 = reference 10-min average wind speed with a recurrence period of 1 year
V50 = reference 10-min average wind speed with a recurrence period of 50 years
W = Fourier transform of a realization of a white Gaussian noise time-series process
with unit variance
x = for mooring systems, the horizontal dist ance between the anchor and a given point
on a mooring line
x = for the control-measurement filter, the filter state
x = for the platform-pitch damping problem, the translational displacement of the hub
x& = translational velocity of the hub
x&& = translational acceleration of the hub
xF = horizontal distance between the anchor and fairlead of a mooring line
Xi = ith component of the frequency- and dire ction-dependent complex incident-wave-
excitation force on the support plat form per unit wave amplitude
X,Y,Z = set of orthogonal axes making up an or iginal reference frame (when applied to the
support platform in particular, X,Y,Z represents the set of orthogonal axes of an
inertial reference frame fixed with respect to the mean location of the platform,
with the XY -plane designating the still water level and the Z-axis directed upward
xii

opposite gravity along the centerline of th e undeflected tower when the platform
is undisplaced)
x,y,z = set of orthogonal axes making up a tran sformed reference frame (when applied to
the support platform in particular, x,y,z represents the set of orthogonal axes of a
body-fixed reference frame within the platform, with the xy-plane designating the
still water level when the platform is undisplaced and the z-axis directed upward
along the centerline of the undeflected tower)
y = for the control-measurement filter, the filtered generator speed
z = for mooring systems, the vertical dist ance between the anchor and a given point
on a mooring line
zCOB = body-fixed vertical location of the cen ter of buoyancy of the support platform
(relative to the still water level and negative downward along the undeflected
tower centerline when the support plat form is in its undisplaced position)
zF = vertical distance between the anchor and fairlead of a mooring line
α = low-pass filter coefficient
β = incident-wave propagation heading direction
γ = peak shape parameter in the Joint North Sea Wave Project (JONSWAP) spectrum
Δζx = effective increase in the platform-pitch damping ratio
Δθ = small perturbation of the blade-p itch angles about their operating point
Δθ& = blade-pitch rate
ΔΩ = small perturbation of the low-speed sh aft rotational speed about the rated speed
ΔΩ& = low-speed shaft rotational acceleration
δij = ( i,j) component of the Kronecker-Delta func tion (i.e., identity matrix), equal to
unity when and zero when i=j ij≠
ζ = instantaneous elevation of incident waves
ζx = damping ratio of the response associat ed with the equation of motion for the
platform pitch in terms of the translation of the hub
ζφ = damping ratio of the response associat ed with the equation of motion for the
rotor-speed error
θ = for the blade-pitch controller, the full-span rotor-collective blade-pitch angle
xiii

θK = rotor-collective blade-pitch angle at which the pitch sensitivity has doubled from
its value at the rated operating point
θ1,θ2,θ3 = set of orthogonal rotations used to convert from an original to a transformed
reference frame (when applied to th e support platform in particular, θ1,θ2,θ3
represent the roll, pitch and yaw rotations of the platform about the axes of the
inertial reference frame)
λ0 = dimensionless catenary parameter used to determine the starting values in the
Newton-Raphson iteration durin g the initialization of the mooring system module
μc = mass of mooring line per unit length
ξ = platform-pitch angle (rotational displacement)
ξ& = platform-pitch rotational velocity
ξ&& = platform-pitch rotational acceleration
π = the ratio of a circle’s circumference to its diameter
ρ = water density
σ = scaling factor in the Joint North Sea Wave Project (JONSWAP) spectrum
2
ζσ = variance of the instantaneous elevation of incident waves
τ = dummy variable with the same units as the simulation time
φ = the integral of ϕ& with respect to time
ϕ& = small perturbation of the low-speed sh aft rotational speed about the rated speed
ϕ&& = low-speed shaft rotational acceleration
Ω = low-speed shaft rotational speed
Ω0 = rated low-speed shaft rotational speed
ω = for hydrodynamics, this is the freque ncy of incident waves or frequency of
oscillation of a particular mode of motion of the platform
ω = for mooring systems, this is the apparent weight of a line in fluid per unit length
of line
rNE
rω = three-component partial angular-velocity vector in Kane’s equations of motion for
the rth system rigid body (body Nr) in the inertial frame (frame E)
xiv

ωxn = natural frequency of the response associ ated with the equation of motion of the
platform pitch in terms of the translation of the hub
ωφn = natural frequency of the response associat ed with the equation of motion for the
rotor-speed error
xv

Executive Summary
The vast deepwater wind resource represents a po tential to use offshore floating wind turbines to
power much of the world with renewable energy . Many floating wind turbine concepts have
been proposed, but dynamics models, which account for the wind inflow, aerodynamics,
elasticity, and controls of the wind turbine, along with the incident waves, sea current,
hydrodynamics, and platform and mooring dynamic s of the floater, were needed to determine
their technical and economic feasibility.
This work presents the development of a comprehensive simulation tool for modeling the
coupled dynamic response of offshore floating wi nd turbines, the verification of the simulation
tool through model-to-model comparisons, and the application of the simulation tool to an integrated loads analysis for one of the promising system concepts.
A fully coupled aero-hydro-servo-elastic si mulation tool was deve loped with enough
sophistication to address the limitations of prev ious frequency- and time-domain studies and to
have the features required to perform loads an alyses for a variety of wind turbine, support
platform, and mooring system configurations. The simulation capability was tested using model-to-model comparisons. The favorable results
of all of the verification exer cises provided confidence to perform more thorough analyses.
The simulation tool was then applied in a pre liminary loads analysis of a wind turbine supported
by a barge with catenary moorings. A barge platform was chosen because of its simplicity in design, fabrication, and installation. The loads analysis aimed to characterize the dynamic
response and to identify potential loads and instabilities resulting from the dynamic couplings between the turbine and the floating barge in the presence of combined wind and wave excitation. The coupling between the wind turb ine response and the barge-pitch motion, in
particular, produced larger extreme loads in the floating turbine than experienced by an equivalent land-based turbine. Instabilities were also found in the system.
The influence of conventional wind turbine blade- pitch control actions on the pitch damping of
the floating turbine was also assessed. Design modifications for reduci ng the platform motions, improving the turbine response, and
eliminating the instabilities are suggested. These suggestions are aimed at obtaining cost-
effective designs that achieve favorable performance while maintaining structural integrity.
xvi

Table of Contents
Chapter 1 Introduction ………………………………………………………………………………………………….. 1
1.1 Background …………………………………………………………………………………………………………..1
1.2 Previous Research ………………………………………………………………………………………………….4
1.3 Objectives, Scope, and Outline ………………………………………………………………………………..6
Chapter 2 Development of Aero-Hydro-Servo-Elastic Simulation Capability ………………….. 8
2.1 Overview of Wind Turbine Aero-Servo-Elastic Modeling ………………………………………..10
2.2 Assumptions for the New Model Development ………………………………………………………..11
2.3 Support Platform Kinema tics and Kinetics Modeling……………………………………………….13
2.4 Support Platform Hydrodynamics Modeling ……………………………………………………………18
2.4.1 The True Linear Hydrodyna mic Model in the Time Domain……………………………..19
2.4.1.1 Diffraction Problem ……………………………………………………………………………..19
2.4.1.2 Hydrostatic Problem …………………………………………………………………………….25
2.4.1.3 Radiation Problem ……………………………………………………………………………….26
2.4.2 Comparison to Alterna tive Hydrodynamic Models …………………………………………..28
2.4.2.1 Frequency-Domain Representation ………………………………………………………..28
2.4.2.2 Morison’s Representation ……………………………………………………………………..32
2.4.3 HydroDyn Calculation Procedure Summary ……………………………………………………34
2.5 Mooring System Modeling ……………………………………………………………………………………35
2.6 Pulling It All Together ………………………………………………………………………………………….42
Chapter 3 Design Basis and Floating Wind Turbine Model …………………………………………… 45
3.1 NREL Offshore 5-MW Baseline Wind Turbine ……………………………………………………….45
3.1.1 Blade Structural Properties ……………………………………………………………………………48
3.1.2 Blade Aerodynamic Properties ………………………………………………………………………50
3.1.3 Hub and Nace lle Properties …………………………………………………………………………..55
3.1.4 Drivetrain Properties …………………………………………………………………………………….56
3.1.5 Tower Properties ………………………………………………………………………………………….56
3.1.6 Baseline Control System Properties ………………………………………………………………..57
3.1.6.1 Baseline Control-Measurement Filter ……………………………………………………..58
3.1.6.2 Baseline Generator-Torque Controller ……………………………………………………60
3.1.6.3 Baseline Blade-Pitch Controller …………………………………………………………….61
xvii

3.1.6.4 Baseline Blade-Pitch Actuator ……………………………………………………………….67
3.1.6.5 Summary of Baseline Control System Properties……………………………………..67
3.1.7 FAST with AeroDyn and ADAMS with AeroDyn Models ………………………………..68
3.1.8 Full-System Natural Frequenc ies and Steady-State Behavior …………………………….69
3.2 ITI Energy Barge …………………………………………………………………………………………………72
3.3 MIT / NREL Barge ………………………………………………………………………………………………74
3.4 Reference-Site Data ……………………………………………………………………………………………..75
Chapter 4 Verification of Simulation Capability …………………………………………………………… 79
4.1 Verification of the Hydrodynamics Module …………………………………………………………….79
4.1.1 Wave Elevation versus the Target Wave Spectrum …………………………………………..79
4.1.2 WAMIT Output / HydroDyn Input …………………………………………………………………80
4.1.3 Computation of Radiati on Impulse-Response Functions …………………………………..84
4.2 Verification of the Mooring System Module ……………………………………………………………84
4.2.1 Benchmark Problem ……………………………………………………………………………………..84
4.2.2 Nonlinear Force-Displacement Relationships ………………………………………………….86
4.3 Time Domain versus Frequency Domain Verification ………………………………………………87
4.3.1 Verification with Steady-State Response …………………………………………………………89
4.3.2 Verification with Stochastic Response ……………………………………………………………91
Chapter 5 Loads-An alysis Overview and Description …………………………………………………… 93
5.1 Design Load Cases ……………………………………………………………………………………………….93
5.2 Postprocessing and Pa rtial Safety Factors ……………………………………………………………..100
Chapter 6 Loads-Analysis Results and Discussion ………………………………………………………. 102
6.1 Normal Operation ………………………………………………………………………………………………102
6.1.1 Characterizing the Dynamic Response ………………………………………………………….103
6.1.2 Identifying Design-Driving Load Cases ………………………………………………………..105
6.1.3 Design-Driving Load Events ……………………………………………………………………….106
6.1.4 Comparing Land- and Sea-Based Loads ………………………………………………………..112
6.1.5 Drawing Conclusions about Responses in Normal Operation …………………………..115
6.2 Other Load Cases ……………………………………………………………………………………………….117
6.2.1 Tower Side-to-Side Instability of Land-Based Wind Turbine …………………………..118
6.2.2 Platform-Yaw Instability of Sea-Based Wind Turbine …………………………………….119
6.2.3 Excessive Barge Motions in Extreme Waves …………………………………………………121
xviii

Chapter 7 Influence of Conventional Control on Barge-Pitch Damping ………………………. 123
7.1 Overview of the Platform-Pitch-Damping Problem ………………………………………………..123
7.2 Influence of Conventional Wind Turbine Control Methodologies …………………………….127
7.2.1 Feedback of Tower-Top Acceleration …………………………………………………………..127
7.2.2 Active Pitch-to-Stall Speed-Control Regulation ……………………………………………..131
7.2.3 Detuning the Gains in the Pitch-to-Feather Controller …………………………………….137
7.3 Other Ways to Improve the Pitch Damping with Turbine Control …………………………….142
Chapter 8 Conclusions and Recommendations ……………………………………………………………. 144
References …………………………………………………………………………………………………………………. 148
Appendix A FAST Input Files for the 5-MW Wind Turbine ……………………………………….. 159
A.1 Primary Input File ……………………………………………………………………………………………..159
A.2 Blade Input File – NRELOffshrBsline5MW_Blade.dat ………………………………………….161
A.3 Tower Input File – NRELOffshrBsline5MW_Tower_ITIBarge4.dat ……………………….162
A.4 ADAMS Input File – NRELOffshrBsline5MW_ADAMSSpecific.dat ……………………..163
A.5 Linearization Input File – NRELOffshrBsline5MW_Linear.dat ………………………………164
Appendix B AeroDyn Input Files for the 5-MW Wind Turbine …………………………………… 165
B.1 Primary Input File – NRELOffshrBsline5MW_AeroDyn.ipt …………………………………..165
B.2 Tower Input File – NRELOffshrBsline5MW_AeroDyn_Tower.dat …………………………165
B.3 Airfoil-Data Input File – Cylinder1.dat …………………………………………………………………166
B.4 Airfoil-Data Input File – Cylinder2.dat …………………………………………………………………166
B.5 Airfoil-Data Input File – DU40_A17.dat ………………………………………………………………166
B.6 Airfoil-Data Input File – DU35_A17.dat ………………………………………………………………168
B.7 Airfoil-Data Input File – DU30_A17.dat ………………………………………………………………170
B.8 Airfoil-Data Input File – DU25_A17.dat ………………………………………………………………172
B.9 Airfoil-Data Input File – DU21_A17.dat ………………………………………………………………174
B.10 Airfoil-Data Input File – NACA64_A17.dat ……………………………………………………….176
Appendix C Source Code for the Baseline Turbine Control System DLL …………………….. 178
Appendix D Input Files for the ITI Energy Barge ……………………………………………………….. 185
D.1 FAST Platform / HydroDyn Input File …………………………………………………………………185
D.2 WAMIT Input File – CONFIG.WAM ………………………………………………………………….186
D.3 WAMIT Input File – Barge.POT …………………………………………………………………………186
xix

D.4 WAMIT Input File – Barge.FRC …………………………………………………………………………187
D.5 WAMIT Input File – Barge.GDF ………………………………………………………………………..187
D.6 WAMIT Output File – Barge.hst …………………………………………………………………………187
D.7 WAMIT Output File – Barge.1 ……………………………………………………………………………188
D.8 WAMIT Output File – Barge.3 ……………………………………………………………………………188
Appendix E Input Files for the MIT / NREL Barge …………………………………………………….. 197
E.1 FAST Platform / HydroDyn Input File …………………………………………………………………197
E.2 WAMIT Input File – CONFIG.WAM ………………………………………………………………….198
E.3 WAMIT Input File – Cylinder.POT ……………………………………………………………………..198
E.4 WAMIT Input File – Cylinder.FRC ……………………………………………………………………..198
E.5 WAMIT Input File – Cylinder.GDF …………………………………………………………………….199
E.6 WAMIT Output File – Cylinder.hst ……………………………………………………………………..199
E.7 WAMIT Output File – Cylinder.1 ………………………………………………………………………..199
E.8 WAMIT Output File – Cylinder.3 ………………………………………………………………………..200
Appendix F Extreme-Event Tables for Normal Operation ………………………………………….. 201
F.1 Land-Based Wind Turbine Loads …………………………………………………………………………201
F.2 Sea-Based Wind Turbine Loads …………………………………………………………………………..204
xx

List of Tables
Table 3-1. Gross Properties Chosen for the NREL 5-MW Baseline Wind Turbine ……………….. 47
Table 3-2. Distributed Bl ade Structural Properties ……………………………………………………………. 49
Table 3-3. Undistributed Bl ade Structural Properties ………………………………………………………… 50
Table 3-4. Distributed Blade Aerodynamic Properties ………………………………………………………. 51
Table 3-5. Nacelle and Hub Properties ……………………………………………………………………………. 55
Table 3-6. Drivetrain Properties …………………………………………………………………………………….. 56
Table 3-7. Distributed Tower Properties …………………………………………………………………………. 57
Table 3-8. Undistributed Tower Properties ……………………………………………………………………… 57
Table 3-9. Sensitivity of Aerodynamic Power to Blade Pitch in Region 3 …………………………… 64
Table 3-10. Baseline Cont rol System Properties ………………………………………………………………. 68
Table 3-11. Full-System Natural Frequencies in Hertz ……………………………………………………… 70
Table 3-12. Summary of ITI Energy Barge Properties ………………………………………………………. 73
Table 3-13. Summary of MIT / NREL Barge Properties ……………………………………………………. 74
Table 5-1. Summary of Selected Design Load Cases ………………………………………………………… 94
Table 5-2. Definition of Wind and Wave Models …………………………………………………………….. 95
Table 6-1. Extreme Events for the Blade 1 Root Moments – Land ……………………………………. 105
Table 6-2. Extreme Events for the Blade 1 Root Moments – Sea ……………………………………… 105
Table 6-3. Extreme Events for the Tower-Base Moments – Land …………………………………….. 105
Table 6-4. Extreme Events for the Tower-Base Moments – Sea ……………………………………….. 105
Table 7-1. Pitch-to-Feather Sensitivity of Aerodynamic Thrust to Wind Speed ………………….. 126
Table 7-2. Pitch-to-Feather Sensitivity of Aerodynamic Thrust to Blade Pitch …………………… 129
Table 7-3. Sensitivity of Aerodynamic Power to Blade Pitch (to Stall) ……………………………… 132
Table 7-4. Pitch-to-Stall Sensitivity of Aerodynamic Thrust to Wind Speed ……………………… 135
Table 7-5. Pitch-to-Stall Sensitivity of Aerodynamic Thrust to Blade Pitch ………………………. 137
xxi

List of Figures
Figure 1-1. Natural progression of substruc ture designs from shallow to deep water ……………… 3
Figure 1-2. Floating platform concepts for offshore wind turbines ……………………………………….. 4
Figure 2-1. Support platform degrees of freedom …………………………………………………………….. 14
Figure 2-2. Comparison between Pier son-Moskowitz and JONSWAP spectra …………………….. 24
Figure 2-3. Summary of the Hy droDyn calculation procedure …………………………………………… 35
Figure 2-4. Summary of my moorin g system module calculation procedure ………………………… 37
Figure 2-5. Mooring line in a local coordinate system ………………………………………………………. 38
Figure 2-6. Interfacing modules to achieve aero-hydro-servo-elastic simulation ………………….. 43
Figure 3-1. Corrected coefficients of the DU40 airfoil ………………………………………………………. 52
Figure 3-2. Corrected coefficients of the DU35 airfoil ………………………………………………………. 52
Figure 3-3. Corrected coefficients of the DU30 airfoil ………………………………………………………. 53
Figure 3-4. Corrected coefficients of the DU25 airfoil ………………………………………………………. 53
Figure 3-5. Corrected coefficients of the DU21 airfoil ………………………………………………………. 54
Figure 3-6. Corrected coefficients of the NACA64 airfoil …………………………………………………. 54
Figure 3-7. Bode plot of generator speed low-pass filter frequency response ……………………….. 59
Figure 3-8. Torque-versus-speed res ponse of the variable-speed controller …………………………. 61
Figure 3-9. Best-fit line of pitch sensitivity in Region 3 ……………………………………………………. 65
Figure 3-10. Baseline blade-pitch c ontrol system gain-scheduling law ……………………………….. 66
Figure 3-11. Flowchart of the baseline control system ………………………………………………………. 67
Figure 3-12. Steady-state responses as a function of wind speed ………………………………………… 71
Figure 3-13. Illustration of the 5-MW wind turbine on the ITI Energy barge ……………………….. 74
Figure 3-14. Reference-site location ……………………………………………………………………………….. 75
Figure 3-15. Normal sea state conditions at the reference site ……………………………………………. 77
Figure 4-1. PSD of wave elevati ons versus target wave spectrum ………………………………………. 80
Figure 4-2. Wave-elevation probability density ……………………………………………………………….. 81
Figure 4-3. Panel mesh of the ITI Energy barge used within WAMIT ………………………………… 82
Figure 4-4. Panel mesh of the ITI Energy barge used by NAME ………………………………………… 82
Figure 4-5. Hydrodynamic added mass and damping for the ITI Energy barge ……………………. 83
Figure 4-6. Radiation impulse-response functions for the ITI Energy barge ………………………… 85
Figure 4-7. Benchmark problem for a suspended cable …………………………………………………….. 86
xxii

Figure 4-8. Solution of the suspended-cable benchmark problem ………………………………………. 86
Figure 4-9. Force-displacement relations hips for the ITI Energy mooring system ………………… 87
Figure 4-10. RAO comparisons for the MIT / NREL barge ……………………………………………….. 90
Figure 4-11. Probability density comparisons for the MIT / NREL barge ……………………………. 92
Figure 6-1. Statistics from each simulation in DLC 1.1 …………………………………………………… 104
Figure 6-2. Time histories from se a-based simulation number 164 in DLC 1.1 ………………….. 108
Figure 6-3. Time histories from se a-based simulation number 101 in DLC 1.4 ………………….. 110
Figure 6-4. Sea-to-land ratios from DLCs 1.1, 1.3, 1.4, and 1.5 ……………………………………….. 113
Figure 6-5. Sea-to-land ratios for va riations in significant wave height ……………………………… 116
Figure 6-6. Time history of th e tower side-to-side instability …………………………………………… 119
Figure 6-7. Time history of the platform-yaw instability …………………………………………………. 121
Figure 7-1. Pitch-to-feathe r barge-pitch damping ratios …………………………………………………… 127
Figure 7-2. System responses with a nd without a tower-feedback control loop ………………….. 130
Figure 7-3. Steady-state pitch-to-sta ll responses as a function of wind speed …………………….. 133
Figure 7-4. Comparison of pitch-to-feat her and pitch-to-stall system responses …………………. 134
Figure 7-5. Pitch-to-feather and -stall barge-pitch damping ratios …………………………………….. 136
Figure 7-6. Detuned blade-pitch c ontrol system gain-scheduling law ……………………………….. 138
Figure 7-7. System responses with and without detuned blade-pitch control gains ……………… 139
Figure 7-8. Sea-to-land ratios with and without detuned blade-pitch control gains ……………… 141

xxiii

Chapter 1 Introduction
1.1 Background
Nonrenewable resources such as coal, natural gas, oil, and nuclear power are the primary sources
of energy for many parts of the world. Burning fossil fuels, however, is harmful to the
environment, and fossil fuel supplies are limited and subject to price volatility. And the safe storage and disposal of radio active waste, the potential for radioactive contamination from
accidents or sabotage, and the threat of nuclear pr oliferation are serious challenges to the success
of nuclear power. Renewable resources such as wind possess great potential because they are indigenous, nonpolluting, and inexhaustible.
Land-based wind power has been the world’s fastest growing energy source on a percentage
basis for more than a decade [ 99]. In the United States, most of the wind energy development
has taken place in the West and Midwest, where the wind is strong but the land is sparsely populated. The major barrier to increased deve lopment of this wind resource potential is
insufficient transmission-line capacity to majo r urban population (and load) centers near the
coastline [ 71].
To power coastal load centers, wind turbines can also be installed offshore. In Europe, where
vacant land is scarce and vast shallow-water wind resources are available, more than 900 MW of
offshore wind energy capacity has been installed in and around the North and Baltic seas [ 72].
Although offshore wind turbines are not currently in use outside Europe, worldwide interest is growing because the global offshore wind resour ce is abundant. The U.S. potential ranks second
only to China [ 70]. For instance, the wind resource potential at 5 to 50 nautical miles off the
U.S. coast is estimated to be more than the total currently installed electricity-generating capacity of the United States (more than 900,000 MW when accounting for exclusions), and much of this
offshore potential lies close to major coastal urban populations [ 99]. Additional advantages of
installing wind energy offshore include the following [ 30,71]:
• The wind tends to blow more strongly and cons istently, with less turbulence intensity and
smaller shear at sea than on land.
• The size of an offshore wind turbine is not limited by road or rail logistical constraints if
it can be manufactured near the coastline.
• The visual and noise annoyances of wind turb ines can be avoided if the turbines are
installed a sufficient distance from shore.
• Vast expanses of uninterrupted open sea ar e available and the installations will not
occupy land, interfering with other land uses.
These advantages are offset by several disa dvantages of placing wind turbines offshore [ 30,71]:
• A higher capital investment is required for offshore wind turbines because of the costs associated with marinization of the turbine and the added complications of the
foundation, support structure, in stallation, and decommissioning.
1

• Offshore installations are less accessible than onshore installations, which raises the
operations and maintenance costs and possibly increases the downtime of the machines.
• Not only do offshore wind turbines experien ce environmental loading from the wind, but
they must also withstand other conditions, su ch as hydrodynamic loading from waves and
sea currents. As a result, the complexity of the design increases.
Much of the offshore wind resource potential in the United States, China, Japan, Norway, and
many other countries is available in water deep er than 30 m. In contrast, all the European
offshore wind turbines installed to date are on fi xed-bottom substructures. These turbines have
mostly been installed in water shallower than 20 m by driving monopiles into the seabed or by
relying on conventional concrete gravity bases. These technologies are not economically
feasible in deeper water. Instead, space-fr ame substructures, including tripods, quadpods, or
lattice frames (e.g., “jackets”), will be required to maintain the strength and stiffness requirements at the lowest possi ble cost. The Beatrice Wind Farm Demonstrator Project in the
North Sea near Scotland, where two 5-MW wind turb ines are being installed on a jacket structure
in 45 m of water, is a good example of this technology.
1 At some depth, however, floating
support platforms will be the most economical. This natural progression is illustrated in Figure
1-1 [71]. Without performing a dynamic anal ysis, Musial, Butterfield, and Boone [ 70] have
demonstrated the economic potential of one floating platform design.
Numerous floating support platform configurat ions are possible for offshore wind turbines,
particularly considering the vari ety of mooring systems, tanks, and ballast options that are used
in the offshore oil and gas (O&G) industries. Figure 1-2 illustrates several of these concepts,
which are classified in terms of how the designs achieve static stability. The spar-buoy concept, which can be moored by catenary or taut lines, achieves stability by using ballast to lower the center of mass (CM) below the center of buoyancy (COB). The tension leg platform (TLP) achieves stability through the use of mooring-lin e tension brought about by excess buoyancy in
the tank. In the barge concept, the barge is generally moored by catenary lines and achieves stability through its water-plane area. Hybrid concepts, which use features from all three classes, are also a possibility [ 14].
Because the offshore O&G industries have demonstr ated the long-term survivability of offshore
floating structures, the technical feasibility of deve loping offshore floating wind turbines is not in
question. Developing cost-effective offshore floating wind turbine designs that are capable of penetrating the competitive energy marketplace, though, will require considerable thought and
analysis. Transferring the offshore O&G tech nology directly to the offshore wind industry
without adaptation would not be economical. Th ese economic challenges impart technological
challenges [ 14], which, in turn, must be addressed through conceptual design and analysis.
The International Electrotechnical Co mmission (IEC) 61400–1 design standard [ 33] specifies the
design requirements for land-based wind turbin es. The upcoming IEC 61400–3 design standard
[34] supplements the 61400–1 design standard with design requirements for sea-based wind
turbines. Both design standards require that an integrated loads analysis be performed when a machine is certified. Such analysis is also beneficial for conceptual design and analysis,

1 Web site: http://www.beatricewind.co.uk/home/default.asp
2

3 Ph.D. Defense
Shallow Water Transitional
DepthDeepwater
Floating
Offshore Offshore
Wind Wind
Technology Technology
DevelopmentDevelopment0 m–30 m
430 GW30 m–60 m
541 GW
60 m–900 m
1533 GWLand-Based
No exclusions assumed for resource estimatesCurrent Technology
Figure 1-1. Natural progression of substructure designs from shallow to deep water
allowing designers to conceptualize cost-effective wind turbines that achieve favorable
performance and maintain structural integrity.
Integrated loads analyses are carried out with comprehensive simulation tools called design
codes. For land-based wind turbine analysis, these design codes are labeled as “aero-servo-elastic” tools, meaning that they incorporate aerodynamic models, control system (servo) models, and structural-dynamic (elastic) models in a fully c oupled (integrated) simulation
environment. More precisely, these simulation tools incorporate sophis ticated models of both
turbulent- and deterministic-wind inflow; aerodynamic, gravitational, and inertial loading of the rotor, nacelle, and tower; elastic effects with in and between components and in the foundation;
and mechanical actuation and el ectrical responses of the generator and of the control and
protection systems.
In the offshore environment, additional loading is present, and additional dynamic behavior must
be considered. Wave-induced (diffraction) an d platform-induced (radiation) hydrodynamic
loads, which are the most apparent new sources of loading, impart new and difficult challenges
for wind turbine analysts. Additional offshore loads arise from the impact of floating debris or sea ice and from marine growth buildup on the s ubstructure. The analysis of offshore wind
turbines must also account for the dynamic coup ling between the motions of the support platform
3

Figure 1-2. Floating platform concepts for offshore wind turbines
and the wind turbine, as well as for the dynamic characterization of the mooring system for
compliant floating platforms.
1.2 Previous Research
In recent years, a variety of wind turbine aero-se rvo-elastic simulation tools have been expanded
to include the additional loading and responses representative of fixed-bottom offshore support
structures [ 4,15,19,52,61,77,97]. For the hydrodynamic-loading calculations, all of these codes
use Morison’s equation [22,74]. The incident-wave kinematics are determined using an
appropriate wave spectrum together with linear Airy wave theory for irregular seas or one of the various forms of nonlinear stream-function wave theo ry for extreme regular seas. The effects of
sea currents are also included. Morison’s represen tation, which is most valid for slender vertical
surface-piercing cylinders that extend to the sea floor, accounts for the relative kinematics
between the fluid and substructure motions, in cluding added mass, incident-wave inertia, and
viscous drag. It ignores the potential effects of free-surface memory and atypical added-mass-induced couplings between modes of motion in the radiation problem [ 16,76], and takes
advantage of G. I. Taylor’s long-wavelength approximation [ 16,76,85] to simplify the diffraction
problem. These neglections and approximations inherent in Morison’s representation limit its
4

applicability for analyzing many of the proposed support platform concepts for offshore floating
wind turbines.
A number of studies have also assessed the preliminary design of offshore floating wind
turbines. Many of these studies used linear frequency-domain analysis, which is commonly
employed in the offshore O&G industrie s. For example, Bulder et al [ 13] used linear frequency-
domain hydrodynamics techniques to find th e response amplitude operators (RAOs) and
amplitude standard deviations of the six rigid- body modes of motion for the support platform of
a tri-floater design for a 5-MW wind turbine. Lee [ 59] used a similar process to analyze a TLP
design and a taut-leg spar-buoy design fo r a 1.5-MW wind turbine. Wayman, Sclavounos,
Butterfield, Musial, and I [ 100,101] also used a similar process to analyze multiple TLP designs
and a shallow-drafted barge (SDB) design for a 5-MW wind turbine. Most recently, through
frequency-domain analysis, Vijfhuizen [ 98] designed a barge for a 5-MW wind turbine, which
was also a platform for an oscillating water column (OWC) wave-energy device. In these studies, the attributes of the wind turbine were included by augmenting the body-mass matrix with the mass properties of the turbine. The hydrodynamic-damping and -restoring matrices were also augmented with damping and restor ing contributions from rotor aerodynamics and
gyroscopics. Additionally, the linearized rest oring properties of the mooring system were
derived about a mean offset di splacement of the support platform caused by the aerodynamic
thrust on the rotor. The elasticity of the wind turbine was ignored. All of the studies demonstrated the technical feasibility of offshore floating wind turbines by showing that, through proper design, the natural frequencies of the fl oating support platform could be placed where
there was little energy in the wave spectrum to ensure that the overall dynamic response was minimized.
One limitation of these linear frequency-domain an alyses is that they cannot capture the
nonlinear dynamic characteristics and transient events that are important considerations in wind
turbine analysis. Several other offshore floati ng wind turbine studies have addressed this
limitation. Using what they termed a “state -domain” technique, He nderson and Patel [ 31] used
RAOs to prescribe the motions of a 700-kW wind turbine to determine the effect that platform motions have on turbine fatigue loads. They showed that platform motions have little effect on power capture and rotor loads; instead, these were dominated by the aerodynamics of the rotor.
They also showed, though, that platform motions have a substantial effect on the nacelle and
tower loads, which are dominated by inertia. As a result, the tower would have to be strengthened if the platform motions could not be reduced. The same conclusions were drawn
independently by Fulton, Malcolm, and Moroz [ 23] and by Withee [ 103]. These researchers
used different time-domain aero-servo-elastic wind turbine simulators that had been adapted to include the effects of platform motion and hydrodynamic loading of TLP designs for a 5-MW and 1.5-MW wind turbine, respectively. In a more recent analyses, Nielsen, Hanson, and Skaare [75,87] and Larsen and Hanson [ 57] drew similar conclusions. These researchers used a
combined aero-servo-elastic, hydrodynamic, and mooring program to design a deep-drafted spar buoy (called “Hywind”) to support a 5-MW wind turbine and develop its corresponding control system. This study, in particular, was important because the computer program simulations were verified by the response of a scaled-down model in a wave tank experiment . Finally, Zambrano,
MacCready, Kiceniuk, Roddier, and Cermelli [ 105,106] demonstrated the technical (but not
economic) feasibility of smaller floating wind turbines. They used a time-domain model to determine the support platform motions and moor ing tensions for a semi submersible platform
5

that supports three wind turbines of either 90 kW or 225 kW each and a TLP that supports a
single 1-kW turbine.
These studies have other limitations that must also be addressed. For instance, the time-domain
dynamics models employed by Fulton, Malcolm, and Moroz [ 23], and Withee [ 103] used
Morison’s equation to compute the hydrodynamic loading on the TLPs, which, as I mentioned
earlier, ignores potentially importa nt hydrodynamic effects. Although the hydrodynamics model
was more sophisticated in the time-domain dynamics program employed by Zambrano,
MacCready, Kiceniuk, Roddier, and Cermelli [ 105,106], their aerodynamics and structural-
dynamics models were unsophisticated, consisting only of a single horizontal drag force for the aerodynamics model and the six rigid-body modes of motion of the support platform for the full-system structural-dynamics model. Also, the concept analyzed by Nielsen, Hanson, and Skaare
[75,87] and Larsen and Hanson [ 57] had such a large draft (120 m) that it would be difficult to
construct and be deployab le only at sites with very deep water. Moreover, the findings and
conclusions drawn by all of the researchers mentioned in this section must be verified through a rigorous loads analysis.
1.3 Objectives, Scope, and Outline
In light of the limitations of the research stud ies described in the last section, I set three
objectives for my work: (1) develop a comprehens ive simulation tool that can model the coupled
dynamic response of offshore floating wind turbines, (2) verify the simulation capability through
model-to-model comparisons, and (3) apply the simulation tool in an integrated loads analysis for one of the promising floating support platform concepts.
My first objective addresses the foremost problem with the prior research studies—that the
dynamic models developed previously were not gene ral enough to allow analysis of a variety of
support platform configurations and were also limited in their capability for the configurations they could model. My model development activities also address the primary need dictated by the upcoming international design standard [ 34] for offshore wind turbines and fulfill the leading
recommendation from the study by Fulton, Malcolm, and Moroz [ 23] about the design of a
semisubmersible platform and anchor foundation system for wind turbine support. My offshore
floating wind turbine simulation tool was develope d with enough sophistication to address the
limitations of the previous time- and frequency-domain studies. In addition, it has the features required to perform an integrated loads analysis for a variety of wind turbine, support platform,
and mooring system configurations. The simula tion tool I developed is a fully coupled aero-
hydro-servo-elastic model based in the time domain. By “aero-hydro-servo-elastic,” I mean that aero-servo-elastic models and hydrodynamic models are incorporated in the fully coupled simulation environment. The “fully coupled” natu re of this capability is important for possible
follow-on design optimization projects, which would be difficult to carry out without taking the
integrated dynamic response into account. I de scribe the development of this simulation
capability in Chapter 2 . I have previously published some of this material in papers coauthored
with Sclavounos [ 40] and Buhl [ 41].
Chapter 3 presents the input data used for the mode l verification exercises and loads analyses
discussed in the subsequent chapters. These da ta include the specifications of a 5-MW wind
turbine, of two floating platforms, and of envir onmental conditions at a re ference site. Although
6

I developed the specifications of the wind turbine, I did not develop the basic designs of the two
floating support platforms used in this work. Butterfield, Musial, Scott, and I have submitted the
material in Chapter 3 for publication [ 42] and Buhl and I have already summarized parts of the
information [ 41,43].
In fulfillment of my second objective, Chapter 4 presents a verification of the simulation
capability covered in Chapter 2 using the input data given in Chapter 3 . The verification
exercises were important because they gave me confidence in the simulation capability that led
me to pursue more thorough inve stigations into the dynamic be havior of offshore floating wind
turbines. Again, I have previously published some of this material in work with Buhl [ 41].
My third objective addresses the secondary prob lem with the previous research studies—that
their results were demonstrated through only a handful of simulations. To carry out my
integrated loads analysis, I applied the simulation capability using the analysis requirements
prescribed by the IEC design standards as my guide. Chapter 5 contains an overview and
description of the loads analysis, and Chapter 6 presents the analysis results. Buhl and I have
published some of this material elsewhere [ 41,43]. I ran loads analyses for a 5-MW wind turbine
supported both on land and offshore by a floating barg e with slack catenary moorings. The loads
analysis allowed me to characterize the dynamic re sponse of the land- and sea-based systems. In
addition, by comparing both responses, I was able to quantify the impact brought about by the
dynamic coupling between the turbine and the floa ting barge in the presence of combined wind
and wave loading. The results of comprehensive loads analyses for some of the other promising offshore floating wind turbine configur ations are left for future work.
My loads analysis quickly demonstrated that the pitching motion of the barge brought about load
excursions in the supported wind turbine that exceeded those experienced by the equivalent
turbine that was installed on land. One possibl e avenue for improving the response of the
floating wind turbine is to apply active wind turbine control. To this end, Chapter 7 addresses
the influence of conventional wind turbine cont rol methodologies to the pitch damping of the
floating wind turbine system analyzed in Chapter 6 . I have submitted some of this material for
publication [ 44].
In Chapter 8 , I summarize the work, present my conclusions, and suggest directions for further
research.
My work does not address system economics; manufacturing, installa tion, or decomissioning
considerations; or optimization of the floating wind turbine system or wind farm. Nonetheless,
the work I present here is fundamental to de termining the most technically attractive and
economically feasible floating wind turbine design as outlined in Section 1.1.
7

Chapter 2 Development of Aero-Hydro-Servo-Elastic Simulation
Capability
Limitations with previous time- and frequency-domain studies on offshore floating wind turbines
motivated me to develop simulation capability for modeling the fully coupled aero-hydro-servo-elastic response of such systems. In developing this capability, I found it beneficial to combine
the computational methodologies of the land-based wind turbine and of the offshore O&G
industries.
Over the past decade, the U.S. Department of Energy’s (DOE’s) National Renewable Energy
Laboratory (NREL),
1 has sponsored the development, verification, and validation of
comprehensive aero-servo-elastic simulators through the National Wind Technology Center
(NWTC).2 These simulators are capable of pred icting the coupled dynamic response and the
extreme and fatigue loads of land-based horizontal -axis wind turbines (HAWTs). The U.S. wind
industry relies on two primary desi gn codes: (1) FAST (Fatigue, Aerodynamics, Structures, and
Turbulence) [ 39] with AeroDyn [ 55,67] and (2) MSC.ADAMS® (Automatic Dynamic Analysis
of Mechanical Systems) with A2AD (ADAMS-to-AeroDyn) [ 20,54] and AeroDyn. FAST and
MSC.ADAMS are separate programs that can be run independently to model the structural-
dynamic response and control system behavior of HAWTs. FAST is a publicly available code
distributed3 by the NWTC that employs a combined modal and multibody structural-dynamics
formulation in the time domain. I wrote most of the code in its present form (while employed at NREL / NWTC), but I based much of it on pr evious development e fforts at Oregon State
University and the University of Utah. The more complex MSC.ADAMS code is a
commercially available and general-purpose code from MS C Software Corporation
4 that
employs a higher fidelity multibody-dynamics formulation in the time domain. It is adaptable for modeling wind turbines through the set of A2AD modules Windward Engineering LLC
5 and
I developed. This set of A2AD modules is distributed6 by the NWTC.
The complicated HAWT models possible with in MSC.ADAMS can be generated through a
preprocessor functionality built-into the simpler FA ST code. To enable the fully coupled aero-
servo-elastic modeling of wind turbines in the time domain, both FAST and MSC.ADAMS have been interfaced with the AeroDyn aerodynamic subroutine package for calculating wind turbine
aerodynamic forces. AeroDyn was devel oped by Windward Engineering LLC and is
distributed
7 by the NWTC. Note that I use the term “ADAMS” to mean “MSC.ADAMS with
A2AD” in this work.

1 Web site: http://www.nrel.gov/
2 Web site: http://www.nrel.gov/wind/
3 Web site: http://wind.nrel.gov/designcodes/simulators/fast/
4 Web site: http://www.mscsoftware.com
5 Web site: http://www.windwardengineering.com/
6 Web site: http://wind.nrel.gov/designcodes/simulators/adams2ad/
7 Web site: http://wind.nrel.gov/designcodes/simulators/aerodyn/
8

For the offshore O&G industries, the Center for Ocean Engineering at the Massachusetts
Institute of Technology (MIT)8 has sponsored the development, verification, and validation of
comprehensive hydrodynamic computer programs capable of analyzing the wave interaction and
dynamic responses of offshore floating platform s in both the frequency and time domains. SML
(SWIM-MOTION-LINES) [ 47,48,49,50] from MIT is a publicly available suite of computer
modules for determining the hydrodynamic prope rties and responses of floating structures
operating in wind, waves, and current in waters of moderate to great depth. SML’s SWIM
module [48] analytically solves the linear- and second-order frequency-domain hydrodynamic radiation and diffraction problems for platforms composed of simple geometry, such as arrays of
vertical surface-piercing cy linders. The MOTION module [ 49] finds solutions of the large-
amplitude, time-domain, slow-drift responses and the LINES module [ 50] determines the
nonlinear mooring-line, tether, and riser reactions with the platform. The computer program
WAMIT
® (Wave Analysis at MIT) [ 58], a commercially available product from WAMIT, Inc.,9
uses a three-dimensional numerical-panel method in the frequency domain to solve the linearized hydrodynamic radiation and di ffraction problems for the interaction of surface waves with
offshore platforms of arbitrary geometry.
This chapter presents my efforts to develop an upgrade of the land-based wind turbine simulation
tools, FAST with AeroDyn and ADAMS with AeroDyn, to include the additional dynamic
loading and motions representative of offshore floating systems. Also in this chapter, I discuss
how the SML and WAMIT codes are used in the overall solution.
Before I describe the additional formulations ne eded to incorporate offshore dynamic responses
within FAST with AeroDyn and ADAMS with Ae roDyn, I take a step back and outline the
general class of theories employed for modeling a wind turbine within the simulation tools (see
Section 2.1). Then, in Section 2.2, I discuss the assumptions inherent in, and the implications of,
the new formulations relating to floating suppor t platforms for wind turbines. The remaining
sections of this chapter cover the addition of support platform kinema tics and kinetics modeling
(see Section 2.3), the incorporation of support platform hydrodynamics modeling (Section 2.4),
and the inclusion of mooring system modeling (Section 2.5) into FAST and ADAMS. I then
summarize this information in Section 2.6.
I call my newly developed time-domain hydrodynamics module “HydroDyn” because it is to hydrodynamic loading what AeroDyn is to aerodynamic loading in the system.
I make extensive use of equations to describe the hydrodynamic and mooring system
formulations as they relate to floating s upport platforms for offshore wind turbines. For
conciseness and clarity, I have not included the derivations of these equations; it is the form of
the equations and the physics behind them that I want to emphasize. (Please refer to the
associated references for many of the derivations.) In this chapter, I also emphasize the distinctions between my model and others used in the offshore wind turbine industry. These
distinctions are important because the approach I have taken to implement offshore dynamics into wind turbine design codes is substantiall y different than the approach taken by other

8 Web site: http://oe.mit.edu/
9 Web site: http://www.wamit.com/
9

simulation specialists who have analyzed fi xed-bottom offshore turbine support structures
[4,15,19,52,61,77,97]. Finally, my approach is more comprehensive than that taken by others
who have performed preliminary dynamic analyses of floating wind turbines
[13,23,31,59,98,100,101,103,105,106]. I discuss these dissimilarities at greater length in this
chapter.
2.1 Overview of Wind Turbine Aero-Servo-Elastic Modeling
The FAST code is a nonlinear time-domain simulator that employs a combined modal- and
multibody-dynamics formulation. Although FAST has a limited number of structural degrees of
freedom (DOFs), it can model most common wind tu rbine configurations and control scenarios,
including three-bladed turbines with a rigid hub, two-bladed turbines with a rigid or teetering
hub, turbines with gearboxes or direct drives, tu rbines with induction generators or variable-
speed controllers, turbines with active blade-pitc h regulation or passive st all regulation, turbines
with active or passive nacelle-yaw control, and turbines with passive rotor or tail furling.
In FAST, flexibility in the blades and tower is characterized using a linear modal representation
that assumes small deflections within each member. The flexibility characteristics of these members are determined by specifying distributed stiffness and mass properties along the span of the members, and by prescribing their mode shapes as equivalent polynomials. FAST allows for two flapwise and one edgewise bending-mode DOFs per blade and two fore-aft and two side-to-
side bending-mode DOFs in the tower. Along wi th one variable generator speed DOF, torsional
flexibility in the drivetrain is modeled using a single-DOF equivalent linear-spring and -damper model in the low-speed shaft. The nacelle (or at least the load-bearing base plate of the nacelle)
and hub are modeled in FAST as rigid bodies with appropriate lumped ma ss and inertia terms.
All DOFs can be enabled or locked through switches, permitting one to easily increase or decrease the fidelity of the model. All DOF s except the blade and tower bending-mode DOFs
can exhibit large displacements without loss of accuracy. Time marching of the nonlinear
equations of motion is performed using a constant-time-step Adams-Bashforth-Adams-Moulton predictor-corrector integrati on scheme. More details can be found in other works [ 37,38,39].
Not only can FAST be used for time-domain simu lation, but it can also be used to generate
linearized representations of the complete nonlinear aero-elastic wind turbine model (not including the influence of the control system). This analysis capability is useful for developing linearized state matrices of a wind turbine “plant” to aid in the design and analysis of control systems. It is also useful for determining the full-system modes of an operating or stationary HAWT through the use of a simple eigenanalysi s. More information can be found elsewhere
[38,39].
The structural-dynamics model in ADAMS is mo re sophisticated than the one in FAST.
ADAMS is a nonlinear time-domain code that employs a general-purpose multibody-dynamics
formulation, which permits an almost unlimited numbe r of configurations and DOFs. It is not a
code specific to wind turbines and is routinely used by engineers in the automotive, aerospace, and robotics industries. ADAMS represents a mechanical system as a se ries of six-DOF rigid
bodies with lumped mass and inertia interconnected by joints (cons traints). Flexible members,
such as the blades and tower of a wind turbine, are modeled in ADAMS using a series of rigid bodies interconnected by multidimensional linear s tiffness and damping matrices (i.e., six-DOF
10

joints). As in FAST, the nacelle and hub are typically modeled using rigid bodies with lumped
mass and inertia prope rties. ADAMS incorporates a time-mar ching scheme similar to the one in
FAST, except that the ADAMS scheme incorporates a variable-time-step algorithm.
It is often necessary to use the more comp licated ADAMS code in place of FAST because
ADAMS has many features that FAST does not. These include torsional and extensional DOFs
in the blades and tower, geometric (mass and elastic offsets from the pitch axis) and material
(asymmetric composite ply lay-up) couplings in the blades and tower, built-in prebend in the blades, and actuator dynamics in the blade-pitc h controller, among others. I also find ADAMS
useful for verifing the dynamic-response pred ictions obtained from FAST when I add new
functionality to FAST, especially new DOFs. This is because the equations of motion in ADAMS are not defined by the user and beca use its dynamic-response predictions are well
verified (see Ref. [ 39] for more information).
Both FAST and ADAMS allow analysts to include control system logic for actively controlling nacelle yaw, generator torque, and blade pitc h, among other actuators. The controller outputs
can be based on inputs that can be developed fr om the feedback of any number of previously
calculated model states or other derived parameters (see Ref. [ 39] for more information).
Both FAST and ADAMS interface to the Ae roDyn aerodynamic subroutine package for
computing aerodynamic forces. This aerodynamic package models rotor aerodynamics using the classic quasi-steady blade-element / momentum (BEM) theory or a generalized dynamic-wake (GDW) model, both of which include the effects of axial and tangential (rotational) induction.
The BEM model uses tip and hub losses as character ized by Prandtl. Dy namic-stall behavior can
be included using the optional Beddoes-Leishman dynamic-stall model. The element motion and
position are included in the calculation of the instantaneous relative wind vector at each blade element, making the codes fully aero-servo-elas tic. More details can be found in Ref. [ 67].
2.2 Assumptions for the New Model Development
When adding models for floating wind turbine simulation; including the support platform kinematics, kinetics, a nd hydrodynamics, as well as the mooring system responses; I invoked a
number of assumptions in addition to those that were previously inherent in the land-based aero-servo-elastic simulation tools.
For the support platform kinematics and kinetics, I assumed that th e floating support platform is
represented well as a six-DOF rigid body with three small rotational displacements. As I discuss
in Section 2.3, the implications of the small-angle assump tion are not thought to be critical. Like
the load-bearing base plate of the wind turbine’ s nacelle, the support platform was modeled as a
rigid body because it is considered to be so strong and inflexible, at least in relation to the wind turbine’s blades and tower, that direct hydro-elastic effects are unimportant. Additionally, I assumed that the tower is rigidly cantilevered to the support platform. Also, the CM (not
including the wind turbine) and COB of the s upport platform were assumed to lie along the
centerline of the undeflected tower.
I had originally planned [ 40] to include mooring system behavior in my offshore upgrades of
FAST and ADAMS by interfacing the dynamic mooring system LINES module of SML.
11

Because I discovered that LINES is numerically unstable when modeling the slack catenary
mooring lines of interest in some of my anal yses, I developed my ow n quasi-static model for
mooring systems instead. I present the development of this model and the implications of its
quasi-static characteristic in Section 2.5.
My fundamental assumption in the developmen t of the HydroDyn hydrodynamics module was
linearization of the classical marine hydrod ynamics problem. In the field of marine
hydrodynamics, the assumption of linearity signifies many things, three of which I discuss next.
First, linearization of the hydrodynamics problem (i.e., linearization of the nonlinear kinematic
and dynamic free-surface boundary conditions) implies that the amplitudes of the incident waves
are much smaller than their wavelengths. This permits the use of the simplest incident-wave-
kinematics theory, which is known as Airy wave theory. This assumption necessarily precludes
me from being able to model steep or breaking waves and the resulting nonlinear wave-induced
“slap” and “slam” loading. Linearization is a reasonable assumption for most waves in deep water and for small-amplitude waves in shallow water. When waves become extreme or propagate toward shore in shallow water, howev er, higher-order wave kinematics theories are
required, but neglected in my model.
Second, linearization implies that the translati onal displacements of th e support platform are
small relative to the size of the body (i.e., the characteristic body length). In this way, the
hydrodynamics problem can be split into three separate and simpler problems: one for radiation, one for diffraction, and one for hydr ostatics. I discuss the details of these problems in Section
2.4. As is often misunderstood, linearity of the hy drodynamics problem does not imply that the
characteristic length of the support platform need s to be small relative to the wavelength of the
incident waves. When the characteristic length of the support platform is small relative to the
wavelength of the incident waves, the hydrodyn amic scattering problem (part of the diffraction
problem) can be greatly simplified, but I did not i nvoke this simplification in my analysis. I did,
however, simplify the diffraction problem by ignoring incident-wave directional spreading and by assuming that all irregular sea states were long-crested. In other words, I modeled irregular sea states (stochastic waves) as a summation of sinusoidal wave compone nts whose amplitude is
determined by a wave spectrum, each para llel and described by Airy wave theory.
Third, linearization suggests that one can ta ke advantage of the powerful technique of
superposition. I discuss how s uperposition relates to the hydr odynamics problems in Section 2.4.
I have augmented the linearized hydrodynamic s problem with the viscous-drag term from
Morison’s equation. I included this effect because it was relatively easy to add, it allowed me to incorporate the influence of sea current, and it can be an important source of hydrodynamic damping in some situations.
Naturally, linearization of the hydrodynamics problem implies that second- or higher-order
hydrodynamic effects are not accounted for in my model. Although this follows directly from
the definition of linearity, it is important to disc uss its implications. Second- or higher-order
nonlinear hydrodynamics models more properly account for the loading about the actual
instantaneous wetted surface of a floating body an d may be important when the support platform
motions are large relative to their characteristic lengths. For example, I neglected second-order
12

mean-drift forces in my hydrodynamics calculati ons even though they can be derived from the
linear hydrodynamics solution. Just like the wind-induced thrust loading on the turbine rotor or
sea-current-induced loading on the platform, mean-drift forces can bring about a mean offset of
the support platform in relation to its undisplaced position. And for compliant floating systems,
the mooring system resistance is often related nonlinearly to its displacement; thus, the effects of mean-drift forces on the mooring system loads and resistances may be important for some designs. Second-order slow-dri ft forces, which result from the difference among the components
of multiple incident waves of varying frequency, were also neglected in my linear formulation of the classical marine hydrodynamics problem. Mean- and slow-drift forces are sometimes important for wave-induced loading on support platforms with small drafts, large water-plane areas, and mooring system configurations that impose little resistance to surge and sway, such as in barge designs with catenary mooring lines . Likewise, second-order sum-frequency
excitations, which result from the summation among the components of multiple incident waves
of varying frequency, were also neglected in my linear problem. Second-order sum-frequency excitations are sometimes important when analyzin g the “ringing” behavior in support platforms
with mooring systems that impose a strong resistance to heave, such as in TLP designs.
In my models I also ignored the potential loading from vortex-induced vibration (VIV) caused by
sea currents. When the VIV frequency nears a natural frequency of the system, a resonance
phenomenon known as “lock-in” can occur. VIV is also known to be critical for the stability of some designs. The ancillary effect of the s ea current on the radiation and diffraction problems,
such as the Doppler-shifted frequency-of-encounter effect [ 22], was ignored as well.
Finally, I ignored the potential loading from floating debris or sea ice. Sea ice can be a significant source of loading if the support platfo rm is intended to be used where sea ice is
present. In the continental United States, this may be of particular concern when designing offshore wind turbine support platforms for installation in the Great Lakes.
Also note that the classical marine hydrod ynamics problem takes advantage of unsteady
potential-flow theory to derive the governing eq uations of fluid motion. This theory assumes
that the fluid is incompressible, inviscid, and subject only to conservative body forces (i.e.,
gravity), and that the flow is irrotational.
2.3 Support Platform Kinematics and Kinetics Modeling
The first step required in upgrading existing la nd-based wind turbine simulation tools to make
them useful for analyzing offshore systems is to introduce DOFs necessary for characterizing the
motion of the support platform. For floating system s, it is crucial that all six rigid-body modes
of motion of the support platform be included in the development. These include translational
surge, sway, and heave displacement DOFs, along with rotational roll, pitch, and yaw
displacement DOFs, as shown in Figure 2-1 . In this figure,
X,Y,Z represents the set of
orthogonal axes of an inertial reference frame fixed with respect to the mean location of the support platform, with the
XY-plane designating the still water level (SWL) and the Z-axis
directed upward opposite gravity along the center line of the undeflected tower when the support
platform is undisplaced.
13

Because most of the support
platforms that have been proposed for floating wind turbines are more or less axisymmetric, and because there is no hydrodynamic mechanism that will induce yaw moments on such floating bodies, one might question whether the support platform yaw-rotation DOF is necessary. The wind turbine, however, induces yaw moments that are primarily the result of (1) the aerodynamic loads on the rotor when a yaw error exists between the rotor axis and nominal wind direction; and (2) the spinning inertia of the rotor combined with pitching motion (whether from support platform pitching or tower deflection), which induces a gyroscopic yaw moment.
As implied by item (2), then, the
dynamic coupling between the motions of the support platform and the motions of the supported wind turbine are crucial in the development of the equations of motion. In fact, I use the term “fully coupled” throughout this work, partially to imply that the wind turbine’s response to wind and wave excitation is fully coupled through the stru ctural-dynamic response. I do not use the term
to imply that the wind-inflow and sea state conditions need to be correlated. I am not attempting to model the air-sea interface, which is a very complicated, multiphase fluid-flow problem.

Figure 2-1. Support pla tform degrees of freedom
Source: Modifed from Ref. [ 103]
In ADAMS, I obtained all the dynamic couplings between the motions of the support platform
and the motions of the supported wind turbine by simply introducing the six-DOF support platform rigid body in the ADAMS model. In FAST, however, I obtained these couplings by
introducing the six rigid-body support platform DOF s into the system’s equations of motion.
While rederiving the equations of motion, I incor porated all appropriate te rms in the derivations
of the kinematics expressions for the points and reference frames in the system. For example,
before I added the six support platform DOFs in FAST, the kinematics expressions for the
position, velocity, and acceleration vectors of a point in the nacelle depended only on the tower bending-mode and nacelle-yaw DOFs (because the tower-base reference frame was the inertial frame). Once the six support platform DOFs were added, the tower-base reference frame moves
with the support platform, and thus, the kinematic s expressions for a point in the nacelle also
depend on the support platform DOFs. Indeed, th e kinematics expressions for all of the points
and reference frames in the system are affected by the support platform DOFs.
14

With the assumption that all rotations of th e support platform are small, rotation sequence
becomes unimportant. Consequently, I could avoid all the complications of using Euler angles
(or the like), where the order of rotation is significant, when I derived and implemented the equations of motion in FAST. Take
x,y,z to be the axes of the reference frame resulting from a
transformation involving th ree orthogonal rotations ( θ1,θ2,θ3) about the axes of an original
reference frame X,Y,Z. Using the first-order small-angle a pproximations for the sine and cosine
functions, and neglecting terms of higher order in the Taylor series expansion, the standard
Euler-angle transformation [ 25] relating the original and transformed reference frames simplifies
to
32
31
21x 1X
y1 Y
z 1Zθθ
θθ
θθ− ⎧⎫ ⎡ ⎤ ⎧ ⎫
⎪⎪ ⎪ ⎪ ⎢≈−⎨⎬ ⎨ ⎬⎢⎪⎪ ⎪ ⎪⎢⎥− ⎩⎭ ⎣ ⎦ ⎩ ⎭
15()() ( )
()() ( )
()
()222
31 2 3 1 2 1×1
y
zθ θθθ θ θ θ⎧⎫−+ + + +⎪⎪=⎨⎬
⎪⎪222 222 222 2222 222 223 123 1 2 123 2 123 1 3 1231 123 23
222 222 222 222 222 222
123 123 123 123 123 12311 111
111θ θθθ θ θ θθθ θ θθθ θ θ θθθθ θθθθθ
θθθ θθθ θθθ θθθ θθθ θθθ++ + +++− − ++ + +++−+++++
++ +++ ++ +++ ++ +++
⎩⎭()
() ()() ()
()
() ()
()222 222 22222 222 223 11 2 3 2 3 1 2 312 1233
222 222 222 222 222 222
123 123 123 123 123 12311 11
111θθ θ θθθ θ θ θθθθθ θθθθ
θθθ θθθ θθθ θθθ θθθ θθθ++− ++ + +++−+ ++++
++ +++ ++ +++ ++ +++
222 222
21 2 3 1 3 1 2 3 1
222 222
123 12311
1θ θθθ θ θ θθθ θ
θθθ θθθ++ + +++− −
++ +++() ()
() ()222 222222 222123 2 3 123123 123
222 222 222 222
123 123 123 123X
Y
Z
111
11θθθ θ θ θθθθθθ θθθ
θθθ θθθ θθθ θθθ⎡ ⎤
⎢ ⎥
⎢ ⎥
⎢ ⎥
⎢ ⎥
⎩⎭ ⎢ ⎥
⎢ ⎥ ++ + +++−++ +++⎢ ⎥
⎢ ⎥ ++ +++ ++ +++⎢ ⎥ ⎣ ⎦⎧⎫⎢ ⎥⎪⎪⎢ ⎥⎨⎬
⎢ ⎥⎪⎪⎥
⎥
. (2-1)
In this equation, the approximation sign ( ≈) is used in place of an equal symbol (=) because the
resulting transformation ma trix is not orthonormal beyond first order when the small-angle
approximations are used. This implies that the tr ansformed reference frame is not made up of a
set of mutually orthogonal axes. (All transformation matrices relatin g sets of mutually
orthogonal axes must be orthonormal.) Because using axes that are not mutually orthogonal can
lead to inaccuracies that propagate in the dy namic-response calculati ons, I invoked a correction
to the transformation matrix in Eq. (2-1) to ensure that it remained orthonormal. From matrix
theory [ 32], I knew that the closest orthonormal matrix to a given matrix, in the sense of the
Frobenius norm,10 was [ U][V]T where [ U] and [ V] are the matrices of eigenvectors inherent in the
singular-value decomposition (SVD) of the given matrix and the symbol “T” represents a matrix
transpose. By performing these operations, th e correct transformation expression was found to
be
. (2-2) Showing that the transformation matrix in Eq. (2-2) is orthonormal beyond the first-order terms
is a trivial exercise. When applied to the support platform,
x,y,z represents the set of orthogonal axes of the body-
fixed reference frame within the support platform and θ1,θ2,θ3 are the roll, pitch, and yaw
rotations of the support platform about the axes of the inertial reference frame (i.e., X,Y,Z). The
origin of x,y,z is called the platform reference point a nd is the location in the platform about

10 The Frobenius norm, also known as the Euclidean norm, l2 norm, Schur norm, or Hilbert-Schmidt norm, of a real
n × n matrix [ A] is []nn
2
ij2
i1 j1A
===∑∑ a, where aij represents an element of [ A].

which the support platform DOFs are defined. It is also the point at which the external load on
the support platform is applied.
Similar labeling of x,y,z and X,Y,Z is used when applying Eq. (2-2) to relate a reference frame
that is oriented with an element of a deflected blade (or tower) to the reference frame fixed in the
root of the blade (or tower)—in this case the rotations are the flap, lag, and twist slopes of the blade (or tower) element.
In FAST, I have implemented Eq. (2-2) instead of Eq. (2-1) for all transformations relating the
support platform to the inertial fra me, all transformations relating the deflected tower elements to
the tower base, and all transformations relating the deflected blade elements to the root of the
blade. Although these results are not shown here, I have demonstrated that incorporating Eq. (2-2) in FAST instead of Eq. (2-1) leads to dynamic responses that are in much better agreement
with responses obtained from ADAMS, which uses Eu ler angles, especially as the magnitude of
the angles increases. The dynamic re sponses are more accurate when Eq. (2-2) is used in place
of Eq. (2-1) because such transformation matrices get multiplied in series when determining the
orientation of subsystems far along the load path away from the inertial frame, such as in a tower or blade element. Errors in a single transformation matrix are compounded when multiplied together. If the wind turbine were very rigid, the correction would not be necessary.
The transformation expression of Eq. (2-2) still loses considerable accuracy when any of the
angles greatly exceed 20°. This threshold, th ough, should be adequate for support platform
designs suitable for floating wind turbines because (1) the floating platform must be stable
enough to enable access for maintenance personne l at regular intervals; and (2) the energy
capture from the wind is proportional to the swept area of the rotor disk projected normal to the
wind direction. (This projected area greatly diminishes with increasing angular displacement of
the support platform, particularly in pitch.)
I used Kane’s dynamics [ 45] to derive the equations of motion used in FAST. By a direct result
of Newton’s laws of motion, Kane’s equations of motion for a simple holonomic system with
P
generalized coordinates (DOFs) can be stated as follows:
( )*
iiFF0i 1 , 2 , , P+= = K , (2-3)
where for a set of W rigid bodies characterized by reference frame Nr, mass, mr, and CM point
Xr, the generalized active forces, Fi, are
(W
i
r1) F i1 , 2 ,, P
==⋅ + ⋅ =∑rr r rXX N NEE
iivF ωM K , (2-4)
and the generalized inertia forces, *
iF, are
()( ) (W
*
ir
r1) F m
==⋅ −+ ⋅ − =∑rr r rXX N NEE E E
iiva ω H& K i1,2,,P. (2-5)
16

In these equations, it is assumed that for each rigid body (body Nr), the three-component active
force and moment vectors, rXF and , respectively, are applied at the CM location (point
Xr). The three-component accelera tion vector of the CM point Xr, is given by , and the first
time derivative of the angular momentum of rigid body Nr, about Xr, in the inertial frame (frame
E) is given by the three-component vector, rNM
rX Ea
rN EH&. The three-component vector quantities,
and , represent the partial linear velocities of CM point Xr and the partial angular velocities
of rigid body Nr in the inertial frame, respectively. The symbol “rXE
rv
rNE
rω
⋅” represents a vector dot
product.
Although it was a long and tedious process, I had no particular di fficulty in deriving the FAST
system’s equations of motion (which I do not present here). First, I derived kinematics
expressions for the position, velocity, and acceler ation vectors for all of the key points and
reference frames in the system, taking into acco unt all appropriate DOFs I described previously.
These derivations were manageable when expressing terms relative to an appropriate reference
frame, taking advantage of transformation relationships like Eq. (2-2) . For example, with the
tower assumed to be cantile vered to the support platform, it is fairly straightforward to write an
expression for the angular velocity of a tower element relative to the support platform. The
absolute angular velocity of the tower element is then just the vector sum of the angular velocity relative to the support platform and the angular ve locity of the support platform relative to the
inertial frame. The angular velocity of the support platform relative to the inertial frame, in turn,
is just the vector sum of the first time derivatives of the roll, pitch, and yaw DOFs.
Once I derived the kinematics expressions, I established the partial velocity vectors utilized by
Kane’s dynamics. These, along with expressions for the generalized active and inertia forces, established the kinetics and led systematically to the complete nonlinear time-domain equations of motion of the coupled wind turb ine and support platform system.
The kinetics expressions for the support platform included contributions from platform mass and
inertia, gravity, hydrodynamics, and the reacti on loads of the mooring system. I used an
implementation that assu med that the CM of the support platform (not including the wind
turbine) is located along the centerline of th e undeflected tower; a poi nt mass and all three
principal inertias of the support platform (roll, pitc h, and yaw) were included in this model. The
effects of marine-growth buildup on the support platform can then be modeled through a suitable adjustment of the platform mass and inertia.
Once derived, the complete nonlinear time-domai n equations of motion of the coupled wind
turbine and support platform system are of the general form:

()()ij j i M q,u,t q f q,q,u,t=&& & , (2-6)
where Mij is the ( i,j) component of the inertia mass matr ix, which depends nonlinearly on the set
of system DOFs ( q), control inputs ( u), and time ( t); is the second time derivative of DOF j;
and fi is the component of the forcing function associated with DOF i. The forcing function, fi,
depends nonlinearly on the set of system DOFs and their first time derivatives ( q and q
respectively), as well as the set of control inputs ( u) and time ( t), and is positive in the direction jq&&
&
17

of positive motion of DOF i. I am employing Einstein notation in Eq. (2-6) , in which it is
implied that when the same subscript appears in multiple variables in a single term, there is a
sum of all of the possible terms. In FAST, for example, subscripts i and j range from one to the
total number of DOFs in the model (i.e., up to 22 for a two-bladed floating wind turbine or up to
24 for a three-bladed floating wind turbine).
Naturally, when hydrodynamic loading is present on the support platform, hydrodynamic-
impedance forces—including the influence of added mass—are importa nt. The added-mass
components of these forces are present because the density of water is of the same order of
magnitude as the density of the materials that make up the primary structure. This is in contrast to aerodynamic loading on the wind turbine, in which one generally ignores the influence of
added mass because the density of air is much less than the density of the materials that make up the primary structure. To ensure, then, that the equations of motion were not implicit (i.e., I
wanted to avoid
fi depending on q), the total external load acting on the support platform (other
than those loads transmitted from the wind turbin e and the weight of the support platform) was
split into two components: an impulsi ve added-mass com ponent summing with Mij and the rest
of the load adding to fi. In other words, the total external load on the support platform, ,
was written as follows: &&
Platform
iF
, (2-7) Platform Hydro Lines
ii jj i F= A q F F−+ +&&i
where Aij is the ( i,j) component of the impulsive hydr odynamic-added-mass matrix to be
summed with Mij, Hydro
iF is the ith component of the applied hydrodynamic load on the support
platform associated with everything but Aij, and is the ith component of the applied load on
the support platform from the contribution of all mooring lines. I then included both Lines
iF
Hydro
iF and
with the rest of the forcing function, fi, in Eq. Lines
iF (2-6) . In Eq. (2-7), subscripts i and j range
from 1 to 6; one for each support platform DOF ( 1 = surge, 2 = sway, 3 = heave, 4 = roll, 5 =
pitch, 6 = yaw). I discuss the forms of th e hydrodynamic impul sive-added-mass and
hydrodynamic-forcing terms in Section 2.4, and the term associated with the mooring lines in
Section 2.5.
My implementation of the kinetic s was not specific to the dynamic response of offshore floating
systems. It can also be used as the basis for modeling land-based found ations and fixed-bottom
sea-based foundations. With any type of founda tion, the contribution to the kinetics expressions
from the mooring system must be replaced with contributions from soil added mass (if any),
elasticity, and damping. For land-based foundatio ns, the effects of hydrodynamic loading would
be ignored.
2.4 Support Platform Hydrodynamics Modeling
Hydrodynamics are included within computer simulation programs by incorporating a suitable
combination of incident-wave kinematics and hydrodynamic loading models. Hydrodynamic loads result from the integration of the dynamic pressure of the water over the wetted surface of a floating platform. These loads include contribu tions from inertia (added mass) and linear drag
18

(radiation), buoyancy (restoring), incident-wav e scattering (diffraction), sea current, and
nonlinear effects.
I discuss the true linear hydrodynamic-loading equations in the time domain in Section 2.4.1,
taking advantage of the assumptions outlined in Section 2.2. By “true linear hydrodynamic-
loading equations,” I mean that these equations satisfy the linearized governing boundary-value
problems (BVPs) exactly, without re striction on platform size, shape, or manner of motion (other
than those required for the linearization assumption to hold). In Section 2.4.2 I compare and
contrast these with alternative hydrodynamic formulations, which are routinely used in the
offshore industry but contain restri ctions that limit their direct application to the analysis of
offshore floating wind turbines. As I present in Sections 2.4.1 and 2.4.2, I have brought together
parts of all the formulations in developing my HydroDyn support platform hydrodynamics
module for offshore floating wind turbines. I su mmarize how these formulations are organized
within HydroDyn in Section 2.4.3.
2.4.1 The True Linear Hydrodynamic Model in the Time Domain
In linear hydrodynamics, the hydrodynamics problem can be split into three separate and simpler problems: one for radiation, one for diffraction, and one for hydrostatics [ 22,74]. The radiation
problem seeks to find the loads on a floating platform when the body is forced to oscillate in its various modes of motion and no incident surface waves are present. The resulting radiation loads are brought about as the body radiates wave s away from itself (i.e., it generates outgoing
waves) and include contributi ons from added mass and from wa ve-radiation damping. The
diffraction problem seeks to find the loads on a fl oating platform when the body is fixed at its
mean position (no motion) and incident surface waves are present and scattered by the body. The diffraction loads are the result of the undist urbed pressure field (Froude-Kriloff) and wave
scattering. The hydrostatics problem is elementa ry, but is nevertheless crucial in the overall
behavior of a floating platform.
In Section 2.3, I discussed how the total external load on the support platform of an offshore
floating wind turbine—other than those loads transmitted from the turbine itself—is in the form
of Eq. (2-7) . In the true linear hydrodynamics problem, the term
Hydro
iF in Eq. (2-7) is of the
form shown in Eq. (2-8) [ 16,76]. I discuss the terms of this equation separately in the
subsections that follow.
() ( )t
Hydro Waves Hydrostatic
ii 0 i 3 i jj i j j
0F Fg V C q K t q d ρδ =+ − −− ∫&τττ (2-8)
2.4.1.1 Diffraction Problem
The first term on the right-hand side of Eq. (2-8) , , represents the total excitation load on
the support platform from incident waves and is closely related to the wave elevation, ζ. As
background, Airy wave theory [Waves
iF
22,74] describes the kinematics of a regular waves, whose
periodic elevation is represente d as a sinusoid propagating at a single amplitude and frequency
(period) or wavelength. (Airy wave theory al so describes how the undisturbed fluid-particle
velocities and accelerations decay ex ponentially with depth—see Section 2.4.2.2.) Irregular or
19

random waves that represent various stochastic sea states are modeled as the summation or
superposition of multiple wave components, as de termined by an appropriate wave spectrum.
Expressions for ζ and are given by [Waves
iF 21]:
() () ()2-Sided j t
-1t= W 2S e d2ω
ζ ζ ωπ ωπ∞
∞∫ω (2-9)
and
() () () ()Waves 2-Sided j t
i
-1
i F t= W 2S X , e d2ω
ζωπω ω βπ∞
∞∫ω. (2-10)
Equations (2-9) and (2-10) are inverse Fourier transforms, where j is the imaginary number,
1−. represents the desired two-sided power spectral density (PSD) of the wave
elevation per unit time, or the two-sided wave spectrum, which depends on the frequency of the
incident waves, ω. 2-SidedSζ
() Wω represents the Fourier transform of a realization of a white Gaussian
noise (WGN) time-series process with zero mean and unit variance (i.e., the so-called “standard
normal distribution”). This realization is used to ensure that the individual wave components
have a random phase and that the instantaneous wave elevation is normally- (i.e., Gaussian-)
distributed with zero mean and with a variance, on average, equal to ()22 – S i d e d
-Sdζζσ ωω∞
∞=∫. The
same realization is used in the computation of the wave elevation and in the computation of the
incident-wave force. (iX,)ωβ is a complex-valued array that represents the wave-excitation
force on the support platform normalized per un it wave amplitude; the imaginary components
permit the force to be out of phase with the wave elevation. This force depends on the geometry
of the support platform and the frequenc y and direction of the incident wave, ω and β,
respectively, and I discuss it further in Section 2.4.2.1. I have made the incident-wave-
propagation heading direction, β, which is zero for waves propagating along the positive X-axis
of the inertial frame, and positive for positive rotations about the Z-axis, an input to the model.
This allows me to simulate conditions in whic h the wind and wave directions are not aligned.
In my HydroDyn module, the realization of th e WGN process is calculated using the Box-Muller
method [ 83], which considers not only a uniformly -distributed random phase, but also a
normally-distributed amplitude. The normally-distributed amplitude ensures that the resulting wave elevation is Gaussian-distributed, but causes the actual variance to vary among realizations.
This is why I refer to the variance of the resulting wave elevation as “on average” in the previous paragraph. (To ensure that the variance remains constant for every realization requires that one
consider only random phase variations among the individual wave components—but then the instantaneous wave elevation w ould only be Gaussian-distributed with an infinite number of
wave components.)
The Box-Muller method turns two independent and uniformly-distr ibuted random variates into
two unit-normal random variates stored as real and imaginary components (see Ref. [ 83]):
20

() () () () {}
() () (){}12 2
12 20f
W=2 l n U c o s 2 U j s i n 2 U f o r
2ln U c os 2 U js in 2 U for 0ω
ω ω πω πω ω
ωπ ω π ωω⎧=⎪⎪−+⎡⎤ ⎡ ⎤⎡ ⎤⎨⎣⎦ ⎣ ⎦⎣ ⎦⎪
⎪−− − − −⎡⎤ ⎡ ⎤ ⎡ ⎤⎣⎦ ⎣ ⎦ ⎣ ⎦⎩or 0
0>
<, (2-11)
where U1 and U2 are the two independent and uniformly -distributed random variates (random
numbers between zero and one) chosen for each positive-valued incident-wave frequency ( ω).
()Wω is set to zero at zero frequency to ensure that each WGN process, and resulting wave
elevation, has zero mean. The use of random vari ates requires that a seed be specified for the
pseudo-random number generator (RNG). I have made these seeds inputs to the HydroDyn
module.
Equation (2-10) for the incident-wave-excitation force is very similar to Eq. (2-9) for the
incident-wave elevation—the only difference is the inclusion of the normalized wave-excitation
force complex transfer function, . This follows directly from linearization of the diffraction
problem. Superposition of the di ffraction problem implies that (1) the magnitude of the wave-
excitation force from a single wave is linearly proportional to the wave amplitude and (2) the
wave-excitation force from multiple superimposed waves is the same as the sum of the wave-
excitation forces produced by each individual wave component. In the limit as the difference
between individual wave frequencies approaches zer o, this sum is replaced with the integral over
all incident-wave frequencie s, as exemplified by Eq. iX
(2-10) . These same properties can also be
seen, perhaps more clearly, when Eq. (2-10) is expressed in an alternative—but equivalent—
form. Equation (2-12) , which was derived by applying the basic properties of bilateral
transforms [ 66], shows this form:
() ( ) ()Waves
ii
-F t= K t d τζτ τ∞
∞−∫. (2-12)
In this equation, τ is a dummy variable with the same units as the simulation time, t, and the
time- and direction-dependent inci dent-wave-excitation force on th e support platform normalized
per unit wave amplitude, Ki, is given by
() ()jt
ii
-1Kt= X , e d2ωωβπ∞
∞∫ω. (2-13)
The integral over all frequency-dependent incident-wave-excitation forces from Eq. (2-10) has
been replaced in Eq. (2-12) with a convolution over all time-d ependent incident-wave-excitation
forces. Regardless of which formulation is used, the floating support platform should be
designed with minimal structure near the fre e surface to minimize the wave-excitation forces.
In HydroDyn, I have implemented Eq. (2-10) instead of Eq. (2-12) because the former requires
fewer calculations. I implemented the inverse Fourier transforms using computationally efficient fast Fourier transform (FFT) routines [ 92].
21

The incident-wave-excitation force given by Eq. (2-10) or Eq. (2-12) is independent of the
motion of the support platform. This demonstr ates how the diffraction problem has been
separated from the radiation problem and reveal s how the linearization assumptions would be
violated if the motions of th e support platform were large.
It follows that Eq. (2-9) for the wave elevation is valid onl y at the mean position of the support
platform. For other locations, Eq. (2-9) can be expanded to
() () ()() () ()jk X cos Y sin 2-Sided j t
-1t, X,Y = W 2 S e e d2ωββ ω
ζ ζ ωπ ωπ∞
−+⎡⎤⎣⎦
∞∫ω, (2-14)
where ( X,Y) are the coordinates in the inertial reference frame of a point on the SWL plane and
()kω is the wave number, which is 2π-times the number of waves per unit distance along the
wave-propagation direction, β. For water of depth h, the wave number is correlated to the
incident-wave frequency, ω, and the gravitational acceleration constant, g, by the implicit
dispersion relationship [ 22,74]:
() ()2
k tanh k hgωωω =⎡⎤⎣⎦. (2-15)
In HydroDyn, this implicit relationship is solved using the numerical approach adopted in the
SWIM module [ 48] of SML; that is, a high-order initial guess is used in conjunction with a
quadratic Newton’s method for the solution with an accuracy of seven significant digits using
only one iteration pass. This solution method is attr ibuted to Professor J. N. Newman of MIT. I
have implemented Eq. (2-14) in HydroDyn for animating the wave surface around the floating
platform.
Because the inverse Fourier transforms require a distinction between positive and negative
frequencies, the frequency-dependent terms in the previous equations have several characteristics
that ensure that the total wave-excitation force on the support platform is a real function of time.
The requirement for this is that the real compon ents of the integrands be an even function of
frequency and the imaginary components of the integrands be an odd function of frequency [ 91].
Thus, the realization of the WGN process has the property that ()(*WW ) ωω −= , where the
symbol “*” is used to denote the complex conjugate. The normalized wave-excitation force has
the same property: () ()*
iiX, = X ,ωβ ωβ − . Similarly, I set ()( k= k ) ωω −− to ensure that
. The relationship between the two-side d wave spectrum used in the inverse
Fourier transforms, , and the one-sided wave spectrum commonly used in ocean
engineering, , follows standard practice [() ( )*jk jkeeω−− −⎡=⎣ω⎤⎦
2-SidedSζ
1-SidedSζ 80]:
22

()()
()1-Sided
2-Sided
1-Sided1Sf or2S=1Sf or2ζ
ζ
ζωω
ω
ωω⎧≥⎪⎪⎨
⎪0
0 − <⎪⎩. (2-16)
Equation (2-16) ensures that the variance of the wave elevation, or the area under the PSD
curves, is the same for both the one – and two-sided spectra, as in
() ()2 2-Sided 1-Sided
-0Sd Sζζ ζ d σ ωω ωω∞∞
∞==∫∫.
In HydroDyn, I have included three options for pr escribing the wave spectrum. I have included
the Pierson-Moskowitz and the Joint North Sea Wave Project (JONSWAP) spectra as they are
defined by the IEC 61400–3 design standard [ 34], and I have included an option for a user-
prescribed site-specific wave spectrum. The Pierson-Moskowitz wave spectrum is routinely
used to describe the statistical properties of fully developed seas and the JONSWAP spectrum is routinely used in limited fetch situations [ 22]. From the IEC 61400–3 design standard, the one-
sided JONSWAP spectrum is defined as

() ()()2
pT
12exp 0.5
54
pp 1-Sided 2
spTT 15 5S = H T exp 1 0.287 ln21 6 2 42ω
π
σω
ζωωωγππ π⎧⎫⎡⎤⎪⎪ −⎢⎥⎪⎪⎢⎥−⎨⎬−− ⎢⎥⎪⎢⎥⎪⎣⎦⎩⎡⎤ ⎛⎞ ⎛⎞−−⎢⎥ ⎡ ⎤ ⎜⎟ ⎜⎟ ⎣⎦⎢⎥ ⎝⎠ ⎝⎠ ⎣⎦γ⎪
⎪⎭, (2-17)
where Hs is the significant wave height, Tp is the peak spectral period, and γ is the peak shape
parameter of a given irregular sea state, and σ is a scaling factor. The IEC 61400–3 design
standard recommends that the scaling factor and the peak shape parameter be derived from the
significant wave height and peak spectral period as follows:
()p
p20.07 forT
=20.09 forTπω
σωπω⎧≤⎪⎪⎨
⎪ >⎪⎩ (2-18)
and
p
s
p
ss
p
sT5 for 3.6
H
TT= exp 5.75 1.15 for 3.6 5
HH
T1f or
Hγ⎧≤ ⎪
⎪
⎪⎛⎞⎪ p
5− <≤ ⎜⎟⎨⎜⎟⎪⎝⎠
⎪⎪ >⎪⎩. (2-19)
23

In Eq. (2-19) , Hs and Tp must have units of meters and seconds, respectively.
When the peak shape parameter of Eq. (2-19) equals unity, the one-sided JOWNSWAP-spectrum
formulation of Eq. (2-17) reduces down to the one-sided Pierson-Moskowitz spectrum, as given
in Eq. (2-20) . This simplification occurs in all but the most extreme sea states. Figure 2-2
compares the Pierson-Moskowitz and JONSWAP spectra for an extreme sea state with a
significant wave height of 11.8 m and a peak spectral period of 15.5 s, which corresponds to a peak shape parameter of about 1.75 in the JONSWA P spectrum. For spectra with the same total
energy, the JONSWAP spectrum, in general, has a higher and narrower peak than the Pierson-Moskowitz spectrum.

()54
p 1-Sided 2
spTT 15 5S= H T e x p21 6 2 42ζωωωππ π−−
p⎡ ⎤ ⎛⎞ ⎛⎞−⎢ ⎥ ⎜⎟ ⎜⎟⎢ ⎥ ⎝⎠ ⎝⎠ ⎣ ⎦ (2-20)
I have implemented the one-sided JONSWAP spectrum formulation of Eq. (2-17) into
HydroDyn with only one modification—to avoid nonphysical wave forces at high frequencies
(i.e., at short wavelengths), I truncate the wave spectrum above a cutoff frequency. I have
implemented the method proposed by Massel [ 65], in which the cutoff frequency is chosen to be
proportional to the peak spectral frequency. I used a proportionality factor of 3.0 in all
simulations.
01020304050
0.0 0.2 0.4 0.6 0.8 1.0 1.2
Wave Frequency, rad/sWave Spectrum, m2/(rad/s)Pierson-Moskowitz
JONSWAP

Figure 2-2. Comparison between Pierson-Moskowitz and
JONSWAP spectra
24

2.4.1.2 Hydrostatic Problem
The second and third terms on the right-hand side of Eq. (2-8) combined, Hydrostatic
0i 3 i j jgVCρδ− q,
represent the load contribution from hydrostatics as I have implemented them in HydroDyn.
Here, ρ is the water density, g is the gravitational acceleration constant, V0 is the displaced
volume of fluid when the support plat form is in its undisplaced position, δi3 is the ( i,3)
component of the Kronecker-Delta f unction (i.e., identity matrix), and Hydrostatic
ijC is the ( i,j)
component of the linear hydrostatic-restoring matrix from the effects of water-plane area and the
COB. The hydrostatic loads are independent of the incident and outgoing waves from the
diffraction and radiation problems, respectively.
The first of these terms, 0i 3gVρδ, represents the buoyancy force from Archimedes’ principle;
that is, it is the force directed vertically upward and equal to the weight of the displaced fluid
when the support platform is in its undisplaced position. This term is nonzero only for the
vertical heave-displacement DOF of the support platform (DOF i3=) because the COB of the
platform is assumed to lie on the centerline of th e undeflected tower (or z-axis of the platform).
If this were not the case, the cross product of the buoyancy force with the vector position of the
COB would produce a hydrostatic moment about th e support platform refe rence point (i.e., the
origin of the platform DOFs). In the field of naval architecture and in the analysis of large
offshore O&G platforms, the term 0i 3gVρδ is not often found in the equations of motion because
it cancels with the weight in air of the floating body and the weight in water of the mooring
system. Because the location of the CM of the floating wind turbine continually changes as a result of wind turbine flexibility, however, it was important to separa te out the individual
contributions of gravity. These contributions are wind turbine and support platform weight,
weight in water of the mooring system, and b uoyancy. The weights of the wind turbine and
support platform are inherent in the
fi term of Eq. (2-6) .
The second of the hydrostatic terms, , represents the change in the hydrostatic force
and moment resulting from the effects of th e water-plane area and the COB as the support
platform is displaced. The wate r-plane area of the support platform when it is in its undisplaced
position, A0, affects the hydrostatic load because the displaced volume of the fluid changes with
changes in the support platform displacement ( qj). Similarly, the body-fixed vertical location of
the COB of the support platform, zCOB, affects the hydrostatic load because the vector position of
the COB also changes with plat form displacement and because the cross product of the buoyancy
force with the vector position of the COB produces a hydrostatic moment about the support platform reference point. (
zCOB is, in general, less than zero because the z-axis is directed upward
along the centerline of the undeflected tower.) The only nonzero components of Hydrostatic
ij j C− q
Hydrostatic
ijC are
(3,3), (4,4), (5,5), (3,5), and ( 5,3) when the body-fixed xz-plane of the submerged portion of the
support platform is a plane of symmetry [ 22]:
25

. (2-21) 0
0
0 00
A
Hydrostatic2ij0C O B
A
2
0C O B
AA000 0 0 0
000 0 0 0
00 g A 0 g x d A 0
C000 g y d A g V z 0 0
00 g x d A0 g x d A g V z 0
000 0 0 0ρρ
ρρ
ρρ⎡⎤
⎢⎥
⎢⎥
⎢⎥ −⎢⎥
⎢⎥=⎢⎥ +
⎢⎥
⎢⎥
⎢− +
⎢⎥
⎢⎥
⎣⎦∫∫
∫∫
∫∫ ∫∫ρ ⎥
If the body-fixed yz-plane of the submerged portion of the support platform is also a plane of
symmetry, the ( 3,5) and ( 5,3) components of Hydrostatic
ijC are also zero. Equation (2-21) clearly
demonstrates how hydrostatics provides restoring only for roll, pitch, and heave motions;
restoring in the other modes of motion must be realized by the mooring system. In classical
marine hydrostatics, the effects of body weight are often lumped with the effects of hydrostatics when defining the hydrostatic-restoring matrix; for example, when it is defined in terms of metacentric heights [ 22,74]. For the same reason given in the previous paragraph for the
0i 3gVρδ term appearing in the hydrostatic-loadi ng equations, though, it was important to
separate out the contributions of body weight and hydrostatic restorin g. So to reiterate, Hydrostatic
ijC
really is the hydrostatic contribution sole ly from the water-plane area and the COB.
2.4.1.3 Radiation Problem
The wave-radiation loads include contributions from hydrodynamic added mass and damping.
Because the radiation problem has been sepa rated from the diffraction problem, the wave-
radiation loads are independent of the incident waves.
In Eq. (2-7) , the impulsive hydrodyna mic-added-mass components, Aij, represent the force
mechanism proportional to the acceleration of th e support platform in th e time-domain radiation
problem. In particular, the ( i,j) component represents the hydrodyn amic force in the direction of
DOF i resulting from the integration (over the we tted surface of the support platform) of the
component of the outgoing-wave pressure fi eld induced by, and proportional to, a unit
acceleration of the jth DOF of the support platform. Like the body (inertia) mass matrix, the
impulsive hydrodynamic-added-mass matrix is symmetric. Unlike the inertia mass matrix, and depending on the shape of the support platform, the impulsive hydrodyn amic-added-mass matrix
may contain off-diagonal components that coupl e modes of motion that cannot be coupled
through body inertia.
The final term in Eq. (2-8) ,
() ( )t
ij j
0Ktqdτττ −−∫& , is a convolution integral representing the load
contribution from wave-radiation damping and also represents an additional contribution from
added mass that is not accounted for in Aij. In this expression, τ is a dummy variable with the
same units as the simulation time, t, and Kij is the ( i,j) component of the matrix known as the
wave-radiation-retardation kernel. In the radiation problem, the free surface brings about the
26

existence of memory effects, denoting that th e wave-radiation loads depend on the history of
motion for the support platform.
The meaning of the wave-radiation-retardation ke rnel is found by considering a unit impulse in
support platform velocity. Specifically, the ( i,j) component of the kernel, ()ijKt, represents the
hydrodynamic force at time t in the direction of DOF i resulting from a unit impulse in velocity
at time zero of DOF j. The wave-radiation-retardation kernel, consequently, is commonly
referred to as the impulse-response functions of the radiation problem. An impulse in support
platform velocity causes a for ce at all subsequent time because the resulting outgoing free-
surface waves induce a pressure field within the fluid domain that persists for as long as the
waves radiate away. As in Eq. (2-12) for the diffraction problem, th e convolution integral in the
radiation problem follows directly from the a ssumption of linearity. Superposition of the
radiation problem implies that if the support platform
experiences a succession of impulses, its response at any time is assumed to be the sum
of its responses to the individual impulses, each response being calculated with an
appropriate time lag from the instant of the corresponding impulse. These impulses can be considered as occurring closer and closer together, until finally one integrates the responses, rather than summing them [ 76, p. 33].
Using what I would label as “convolution by part s” (instead of “integration by parts”) and
assuming zero-valued initial conditions, the convoluti on integral in the radiation problem can be
rewritten as follows [ 102]:

() ( ) () ( )tt
ij j ij j
00Ktqd L tqdτττ τ ττ −− = −−∫∫&& & , (2-22)
where the convolution kernels, Kij and Lij, are related by
()()ij ijdKtLdt= t. (2-23)
Equation (2-22) highlights the elusive nature of the me mory effect in the radiation problem—that
both acceleration-dependent (added-mass) and velocity-dependent (damping) forces are captured by the convolution term. To minimize the wave -radiation loads, the floating support platform
should be designed with minimal structure near th e free surface, regardless of which formulation
of the convolution integral is applied. The m ooring system should also be designed to limit the
motion of the support platform. I discuss the impulsive hydrodynamic -added-mass matrix and
retardation kernels from the radi ation problem further in Section 2.4.2.
In the HydroDyn module, I have implemented a numerical convolution in the time domain to
capture the memory effect directly. I chose to implement the velocity formulation from the left-hand side of Eq. (2-22) because it is more convenient than the acceleration formulation from the
right-hand side. The latter would lead to an implicit formulation of the time-domain equations of
motion for the coupled wind turbine and support plat form system. As demonstrated in Section
4.1.3, the memory effect, in general, decays to zero after a certain amount of lapsed time.
27

Because of this, I have enabled HydroDyn to truncate the numerical co nvolution after a user-
specified amount of time. This allows for fa ster calculations of the memory effect.
2.4.2 Comparison to Alternative Hydrodynamic Models
I discused the true linear hydrodyn amic-loading equations in Section 2.4.1. Alternative
hydrodynamics formulations, however, are routinely used in the offshore industry. The two most
common alternatives are the frequency-domain representation and Morison’s representation.
2.4.2.1 Frequency-Domain Representation
The frequency-domain representation is most alig ned with how marine hy drodynamics is taught
in the classroom and presented in textbooks. For instance, the frequency-domain representation
is the hydrodynamics formulati on most emphasized in Refs. [ 22] and [ 74], which are popular
textbooks in ocean-engineering education. The pr esentation here summarizes these references.
In the time-domain representation of the frequency-domain problem, Eq. (2-7) for the total
external load acting on the support platform, , is replaced with Platform
iF
()() (){ } ()Platform j t Lines Hydrostatic
ii j j i i j i j j ij j F t= A q+ R eA X , e C C q B qωωω β⎡⎤ −− +⎣⎦&& &ω− , (2-24)
where A is the amplitude of a regular incident wave of frequency ω and direction β; is the
(i,j) component of the linear restoring matrix from all mooring lines (discussed in Section Lines
ijC
2.5);
and ()ijAω and ()ijBω are the ( i,j) components of the hydrodyn amic-added-mass and -damping
matrices, which are frequency dependent. Re{} denotes the real value of the argument; the only
complex-valued terms in Eq. (2-24) are the normalized wave-excitation force, , and the
harmonic exponential, iX
jteω.
The frequency-domain hydrodynamics problem make s use of the same assumptions used in the
true linear hydrodynamics formulation. There ar e additional requirements, though. The incident
wave must propagate at a single amplitude, freque ncy, and direction (i.e., the incident wave is a
regular wave), and the platform motions must be oscillatory at the same frequency as the incident wave. To reiterate this point, when Eq. (2-24) is incorporated in Eq. (2-6) , the resulting
differential equations are not true differential equations in the proper sense. This is because the
time-domain representation of the frequency-domain problem is valid only when the platform motions are oscillating at the same frequency as the incident wave (
ω). In other words, Eq.
(2-24) is valid only for the steady-state situation, a nd not for transient-response analysis. When
used within the system’s equations of motion, Eq. (2-24) also requires that all additional loading
in the system be linear in nature. This prevents me from being able to apply the frequency-domain hydrodynamics formulation to the direct analysis of offshore floating wind turbines—except under steady-state conditions—because nonlin ear characteristics and transient events are
important considerations for wind turbines. Nevert heless, others have applied this approach to
the preliminary analysis of several offshore floating wind turbine concepts [ 13,59,98,100,101].
The solution to the frequency-domain problem is generally given in terms of an RAO, which is the complex-valued amplitude of motion of a floating platform normalized per unit wave
28

amplitude. Imaginary components indicate that the response is out of phase with the wave
elevation. In the frequency-domain problem, the support platform’s response to irregular waves
can only be characterized statistically because the frequency-domain representation is not valid for transient analysis. Specifically, the motion of a linearized floating body will have a response
that is Gaussian-distributed when it is excited by a sea state with a Gaussian-distributed instantaneous wave elevation [ 85,101]. (Irregular sea states are, in general, Gaussian-
distributed.) The standard deviations of th e motion response are dictated by the Wiener-
Khinchine theorem.
Just as in the true linear hydrodynamics model, the radiation and the di ffraction problems can be
solved separately in the frequency-domain repres entation. In the radiation problem, six BVPs
are solved independently to find six velocity potentials, one for each mode of motion. By
substituting these velocity potentials into the lin earized unsteady form of Bernoulli’s equation,
the resulting pressures, when integrated over the wetted surface of the floating platform, yield the added-mass and dampin g matrices. Similarly, in the diffr action problem, two BVPs are solved
independently to find two velocity potentials, one for the incident wave and one for the scattered
wave. By applying Bernoulli’s equation and wetted surface integration again, one arrives at the normalized wave-excitation force.
The formulation for the radia tion and diffraction BVPs, and he nce the resulting hydrodynamic-
added-mass and -damping matrices,
Aij and Bij, and wave-excitation force, Xi, depend on
frequency, water depth, and sea current, as well as on the geometric shape of the support
platform, its proximity to the free surface, and its forward speed. Additionally, the wave-
excitation force depends on the heading direction of the incident waves.
The frequency dependence of the hydrodynamic-added-mass and -damping matrices is of a different nature than that of the wave-excita tion force. The frequency dependence of the
hydrodynamic-added-mass and -damping matrices means that the matrices depend on the
oscillation frequency of the par ticular mode of support platform motion. In contrast, the
frequency dependence of the wave-excitation fo rce means that the force depends on the
frequency of the incident wave. In Eq. (2-24) , however, both frequencies are identical because
the platform is assumed to oscillate at the same frequency as the incident wave.
Analytical solutions for the hydrodynamic-a dded-mass and -damping matrices and wave-
excitation force are available for bodies of simple geometry such as cylinders and spheres.
Usually, approximations are employed to find these analytical solutions. For example, if the
characteristic length of the body is small relative to the wavelength, G. I. Taylor’s long-wavelength approximation [ 85] can be used to simplify the diffraction problem. Morison’s
equation (discussed next in Section 2.4.2.2) uses G. I. Taylor’s long-wavelength approximation
[16,76,85] to simplify the diffraction problem for the case of slender vertical surface-piercing
cylinders. For bodies with complex geometrical su rfaces, like the hull of a ship, numerical-panel
method techniques are required.
Even though the frequency-domain formulation ca nnot be directly applied to the transient
analysis of offshore floating wind turbines, wh ere nonlinear effects, transient behavior, and
irregular sea states are important, the solution to the frequency-domain problem is valuable in
determining the parameters used in the true linear hydrodynamic-loading equations. For
29

instance, the solution to the frequency- (and direction-) dependent wave-excitation force,
(iX,)ωβ , is needed not only in the frequency-dom ain solution, but also in the time-domain
formulation of the linearized diffraction problem in Eq. (2-10) . Equally important is the
relationship between ()ijAω and ()ijBω from the frequency-domain solution and Aij and ()ijKt
from the time-domain formulation of the linearized radiation problem. By forcing a particular
mode of motion of the support platform to be sinusoidal in the true linear hydrodynamics
formulation, and comparing the resulting expression to the time-domain representation of the frequency-domain problem, Ref. [ 76] shows that

() () ( )ij ij ij
01A= A K t s i n tωω∞
−∫d tω (2-25)
and
() ( ) ( )ij ij
0B =K t c o s t d tω∞
∫ω . (2-26)
The Aij term on the right-hand side of Eq. (2-25) represents the impulsive hydrodynamic-added-
mass matrix from Eq. (2-7). Note that Eq. (2-26) is valid only when the ancillary effects of sea
current or forward speed are ignored in th e radiation problem (a s assumed, see Section 2.2);
though not given here, a slightly different expr ession exists when thes e effects are important.
Equations (2-25) and (2-26) highlight the interdependence between the hydrodynamic added
mass and damping. Section 2.4.1.3 alluded to their relationship, wh ich is discussed more in Ref.
[76].
Because the radiation-retardation kernel, ()ijKt, may be assumed to be of finite energy,
application of the Riemann-Lebesgue lemma to Eq. (2-26) reveals that the infinite-frequency
limit of ()ijBω is zero. Similarly, the infinite-frequency limit of Eq. (2-25) yields
()()ij ij ij A = lim A = A
ωω
→∞∞. (2-27)
Thus, the appropriate impulsive added-mass matrix to be used in the true linear hydrodynamic-
loading equations does not de pend on frequency, but is the infinite-frequency limit of the
frequency-dependent added-mass ma trix, represented here as ()ijA∞. This limit does, in
general, exist for three-dimensional bodies.
Through application of Fourier-transform techniques and Eq. (2-27) , Eqs. (2-25) and (2-26) can
be rearranged to show that
() () () ( )ij ij ij
02Kt= A A s i n tdωωπ∞
⎡⎤−− ∞⎣⎦∫ω ω (2-28a)
30

or
() () ( )ij ij
02Kt= B c o s td ωωπ∞
∫ω, ( 2-28b)
and from Eq. (2-23) in Section 2.4.1.3 that
() () () ( )ij ij ij
02Lt= A A c o s td ω ωπ∞
⎡⎤−∞⎣⎦∫ω (2-29a)
or
()()()ij
ij
0B2Lt= s i n tdωωωπω∞
∫. ( 2-29b)
As a corollary to the interdependence betwee n added mass and damping discussed previously,
Eqs. ( 2-28) and ( 2-29) show that the radiation-retardati on kernels depend on both added mass
and damping. Once the solution of the frequenc y-domain radiation problem has been found, any
of these expressions can be used to find the wave -radiation-retardation kernels to be used in the
true linear hydrodynamic-loadi ng equations. When the velocity form of the radiation
convolution is used, the sine transform of Eq. (2-28a) should be applied if the solution accuracy
for the frequency-dependent hydrodynamic-added-mass matrix is greater than the solution
accuracy for the frequency-dependent hydrodyna mic-damping matrix. Similarly, the cosine
transform of Eq. (2-28b) should be used if the solution accu racy for the frequency-dependent
hydrodynamic-damping matrix is greater than the solution accuracy for the frequency-dependent hydrodynamic-added-mass matrix. If the solution accuracy is the same for both matrices, Eq. (2-28b) is generally a better choice when the integrals are computed numerically because,
without a correction for truncati on error, the accuracy of Eq. (2-28a) is poor near
t = 0, where
()ijK0 is, in general, not zero [even though () sin 0 is]. Similar to the inverse Fourier
transforms, I have implemented the cosine transform of Eq. (2-28b) using a computationally
efficient FFT routine [ 92] in my HydroDyn module.
Because the frequency-domain approach is so of ten employed in analyses in the offshore O&G
industries, many computer codes are available for solving the frequency-domain hydrodynamics
problem. For instance, the SWIM module [ 48] of the SML computer package can be used to
analytically solve the frequency- domain problem for support platform s of simple geometry. For
platforms of more complicated surface geometry, the numerical-panel WAMIT code [ 58] can be
employed.
My hydrodynamics formulation in HydroDyn is applied identically regardless of how the
frequency-domain radiation and diffraction problems are solved. This is because I simply made
the frequency-dependent hydrodynamic-added-mass and -damping matrices ( Aij and Bij) and
wave-excitation force ( Xi) inputs to HydroDyn.
31

2.4.2.2 Morison’s Representation
Morison’s representation is widely used in the analysis of fixed-bottom offshore wind turbines
[4,15,19,52,61,77,97]. Though somewhat misapplied, it has also been used directly in the
analysis of offshore floating wind turbines [ 23,103 ]. Morison’s representation, in conjunction
with strip theory, can be used to compute the linear wave loads and nonlinear viscous-drag loads in a straightforward manner, mostly for slender vertical surface-piercing cylinders that extend to the sea floor. In hydrodynamic strip theory, as in BEM theory for wind turbine aerodynamics,
the structure is split into a number of elements or strips, where two-dimensional properties
(added-mass and viscous-drag coefficients in the case of Morison’s hydrodynamics) are used to
determine the overall three-dimensional loading on the structure [ 22].
The total external load acting on the support platform, in Eq.
Platform
iF (2-7) , is thus found by
integrating over the length of the cylinder the loads acting on each strip of the cylinder,
. In the relative form of Morison’s representation, Eq. Platform
idF (2-7) for the surge and sway
modes of motion ( i = 1 and 2) is replaced with Morison’s equation [ 22,74]:
() ()( ) ()
( ) () ( ) () ( )
()Viscous
i22
Platform
iA i A i
Di i
dF t ,zDDd F t , z=C d zq z 1 C d zat , 0 , 0 , z44
for i 1 or 21C Ddz v t,0,0,z q z v t,0,0,z q z2ππρρ
ρ⎛⎞ ⎛⎞−+ + ⎜⎟ ⎜⎟⎝⎠ ⎝⎠
=
+− − ⎡⎤⎣⎦&&
&&
144444444424444444443, (2-30a)
where D is the diameter of the cylinder, dz is the length of the differential strip of the cylinder,
CA and CD are the normalized hydrodynamic-added -mass and viscous-drag coefficients,
is the viscous-drag load acting on the strip of the cylinder, and vi and ai are the components of
the undisturbed fluid-particle velocity and acceleration in the direction of DOF i. (vi and ai,
including their arguments, are discussed below.) The symbol “|·|” denotes the magnitude of the
vector difference of v and q; it is implied in Eq. Viscous
idF
& (2-30a) that only the vector normal to the strip
of cylinder is included in this magnitude. The term 2Ddz4π⎛
⎜⎝⎠⎞
⎟ is the displaced volume of fluid
for the strip of the cylinder. The term ()Ddz is the frontal area for the strip of the cylinder.
Please note that Morison’s equation is often written in terms of the normalized mass (inertia)
coefficient, CM, in place of CA, where MAC= 1C+ .
Using strip theory, expressions similar to Eq. (2-30a) can be written for the roll and pitch
moments ( i = 4 and 5). Because a cylinder is axisymmetric, the yaw moment ( i = 6) is zero, and
because Morison’s equation is strictly valid onl y for bottom-mounted cylinders, the heave force
(i = 3) is also zero. These expressions are all given in Eq. (2-30b) :
32

()()
()Platform
2 Platform
i Platform
10f
dF t,z z for i 4dF t,z =dF t,z z for i 5
0fori3
ori6= ⎧
⎪− = ⎪⎨=⎪
⎪ = ⎩. ( 2-30b)
Consistent with Eq. (2-14) and Airy wave theory, the undistur bed fluid-particle velocity and
acceleration in the direction of DOF i, vi and ai, respectively, at point ( X,Y,Z) in the inertial
reference frame (where Z0≤) are, in the absence of sea currents
()()() ()() () () ()()
()jk X cos Y sin 2-Sided jt
1
-cosh k Z h cosvt , X , Y , Z = W 2 S e e d2 sinh k hωββ ω
ζω βωπω ωπ ω∞
−+⎡⎤⎣⎦
∞+⎡⎤⎣⎦
⎡⎤⎣⎦∫ω, (2-31a)
()()() ()() () () ()()
()jk X cos Y sin 2-Sided jt
2
-cosh k Z h sinvt , X , Y , Z = W 2 S e ed2 sinh k hωββ ω
ζω βωπω ωπ ω∞
−+⎡⎤⎣⎦
∞+⎡⎤⎣⎦
⎡⎤⎣⎦∫ω, ( 2-31b)
and
() () ()() () () ()()
()jk X cos Y sin 2-Sided jt
3
-sinh k Z h jvt , X , Y , Z = W 2 S e ed2 sinh k hωββ ω
ζωωπω ωπ ω∞
−+⎡⎤⎣⎦
∞+⎡⎤⎣⎦
⎡⎤⎣⎦∫ω ( 2-31c)
and
()()() ()() () () ()()
()jk X cos Y sin 2-Sided 2 j t
1
-cosh k Z h jcosat , X , Y , Z = W 2 S e e d2 sinh k hωββ ω
ζω βωπω ωπ ω∞
−+⎡⎤⎣⎦
∞+⎡⎤⎣⎦
⎡⎤⎣⎦∫ω, (2-32a)
()()() ()() () () ()()
()jk X cos Y sin 2-Sided 2 j t
2
-cosh k Z h jsinat , X , Y , Z = W 2 S e ed2 sinh k hωββ ω
ζω βωπω ωπ ω∞
−+⎡⎤⎣⎦
∞+⎡⎤⎣⎦
⎡⎤⎣⎦∫ω, ( 2-32b)
and
() () ()() () () ()()
()jk X cos Y sin 2-Sided 2 j t
3
-sinh k Z h 1at , X , Y , Z = W 2 S e ed2 sinh k hωββ ω
ζωωπω ωπ ω∞
−+⎡⎤⎣⎦
∞+⎡⎤ − ⎣⎦
⎡⎤⎣⎦∫ω. ( 2-32c)
By comparing Eq. ( 2-30) with the true linear hydrodynamic-loa ding equations, it can be seen that
Morison’s representation assumes that viscous drag dominates the damping such that wave-
radiation damping can be ignored. This assumption is valid only if the motions of the cylinder
are very small (i.e., it is most appropriate when the cylinder is bottom-mounted and very rigid).
The viscous-drag load is not part of the lin ear hydrodynamic-loading equations because the
viscous-drag load is proportional to the square of the relative velocity between the fluid particles and the platform. Nevertheless, I did augmen t the linear hydrodynamic-loading equations in
HydroDyn by including the nonlinear viscous-drag term from Morison’s equation. I include the
viscous-drag term by assigning an effective platform diameter (
D) and by integrating
over the draft of the support platform to find the total viscous-drag load, . I included this
effect because (1) it was relatively easy to add, (2 ) it allowed me to incorporate the influence of
sea current, and (3) it can be an important source of hydrodynamic damping in some situations.
To include the influence of sea current generated by winds, tides, and thermal gradients in Viscous
idF
Viscous
iF
33

HydroDyn, I have vectorally combined a steady, depth-varying current velocity with the surface-
wave-particle velocity [Eq. ( 2-31)] when computing the viscous-drag term from Morison’s
equation.
By comparing Eq. ( 2-30) with the true linear hydrodynamic-loading equations, it is also seen that
Morison’s representation ignores off-diagonal terms in the added-mass matrix other than those
that directly couple the motions between surge a nd pitch and sway and roll. It may do this
because a cylinder is axisymmetric, which ensures that there is no other added-mass-induced coupling between modes of motion. Morison’s re presentation also takes advantage of G. I.
Taylor’s long-wavelength approximation [ 16,76,85] to simplify the diffraction problem (i.e., the
cylinder must be slender). This appr oximation is how the second term in Eq. (2-30a) for the
wave-excitation force can be expressed in term s of the normalized added-mass coefficient and
the undisturbed fluid-particle ac celeration along the centerline of the cylinder. In the linear
hydrodynamics problem,
CA theoretically approaches unity ( ) in the infinite-frequency
limit. In practice, however, CA (or CM) and CD must be empirically determined and are
dependent on many factors, including Reynol d’s number, Keulegan-Carpenter number, and
surface roughness, among others. The assumptions inherent in Morison’ s representation explain
why it is applicable to the analysis of bo ttom-mounted monopile designs for offshore wind
turbines. The asumptions also explain why Mori son’s representation is not applicable for the
analysis of many of the proposed platform concepts for offshore floating wind turbines (except for the viscous-drag term). MC= 2
One useful feature of Morison’s equation, and strip theory in gene ral, is that the hydrodynamic
loading is written in terms of the undisturbed flui d-particle velocity and accelerations directly,
instead of velocity potentials, which are inhere nt in the hydrodynamic-added-mass and -damping
matrices and the wave-excitation force of the linear frequency-domain problem. This feature allows Morison’s equation and strip theory to ta ke advantage of nonlinear wave- and sea-current
kinematics models. Nonlinear wave theories account better fo r the mass transport, wave
breaking, shoaling, reflection, transmission, and other nonlinear characteristics of real surface
waves. Various forms of nonlinear stream-function wave theory—including Dean’s theory, Fenton’s theory, and Boussinesq theory—are the mo st widely used when these characteristics are
required [ 17]. Researchers have also developed a new nonlinear wave-kinematics model that
does not require the solution to the nonlinear potential-flow free-surface BVP [ 86]. This new
model can be used as input to an extended Mori son formulation to evaluate the wave loads on
slender vertical cylinders in steep and random shallow-water waves.
2.4.3 HydroDyn Calculation Procedure Summary
The presentation of a variety of hydrodynamics form ulations creates a virtua l forest of concepts
and formulas. In Sections 2.4.1 and 2.4.2, I investigated each tree in detail as I made my way
through that forest, but sometimes “it’s hard to see the forest for the trees.” To help you see that
forest, Figure 2-3 draws together the information I have presented.
In summary, HydroDyn accounts for
• Linear hydrostatic restoring
• Nonlinear viscous drag from incident-wave kinematics, sea currents, and platform motion
34

Time-Domain Hydrodynamics ( H ydroDyn )
Wave Spectrum
& DirectionRadiation Kernel
Incident-Wave
Excitation
Plat form
Mot ionsHydrod ynamic
For cing
Lo adsAdded-Ma ss Matrix
(Radiation Problem)Damping Matrix
(Radiation Problem)
Impu lsive
Added Mass Restoring Matrix
(Hydrostatic Problem)Wave-Excitation Force
(Diffraction Problem)
White G aussian
No iseInfinite-Freq.
LimitCosine
Transform
Inverse FFTBox-Muller
MethodSeed for
RNGPlatform
Geometry
Sea
CurrentTime
ConvolutionBuoyancy
Calculation
Sum ForcesMemory
EffectBuoy ancy
Morison’s
EquationViscous
DragFrequency-Domain Radiation / Diffraction
Hydrodynamics Preprocessor (SWIM or WAMIT )
Incid ent-Wave
Kin ematics

Figure 2-3. Summary of the HydroDyn calculation procedure
• Added-mass and damping cont ributions from linear wave radiation, including free-
surface memory effects
• Incident-wave excitation from linear diffra ction in regular or irregular seas.
Just as aerodynamic loads depend on the shape of the rotor-blade airfoils, hydrodynamic loads
depend on the support platform’s geometry. To th is end, I developed HydroDyn such that the
hydrodynamic coefficients for platforms of arbitrary shape are imported from SWIM, WAMIT, or an equivalent hydr odynamic preprocessor.
HydroDyn does not account for the effects of nonlinear steep and / or breaking waves, VIV, and loading from sea ice. It also does not account for the second-order effect s of intermittent wetting
and mean-drift, slow-drift, and sum-frequency excitation.
2.5 Mooring System Modeling
Mooring systems are used as a means of sta tion-keeping—holding a floating platform against
wind, waves, and current. In some support platform de signs, such as in a TLP, they are also used
as a means of establishing stability. A mooring system is made up of a number of cables that are attached to the floating support pl atform at fairlead connections, with the opposite ends anchored
to the seabed. Cables can be made up of chain, steel, and / or synthetic fibers and are often a
segmented combination of these materials. Restraining forces at the fairleads are established
35

through tension in the mooring lines. This tension depends on the buoyancy of the support
platform, the cable weight in water, the elasticity in the cable, viscous-separation effects, and the geometrical layout of the mooring system. As the fairleads move with the support platform in
response to unsteady environmental loading, the re straining forces at the fairleads change with
the changing cable tension. This means that the mooring system has an effective compliance
[22].
If the mooring system compliance were inherently linear and mooring inertia and damping were
ignored, the total load on the support platform from the contribution of all mooring lines, ,
from Eq. Lines
iF
(2-7) , would be
Lines Lines,0 Lines
ii i j j F =F C q− , (2-33)
where is the ( i,j) component of the linearized restoring matrix from all mooring lines [as
included in Eq. Lines
ijC
(2-24) ] and is the ith component of the total mooring system load acting
on the support platform in its undisplaced position. For catenary mooring lines,
represents the pre-tension at the fairleads from th e weight of the cable not resting on the seafloor
in water. If the catenary lines were neutrally buoyant, would be zero. For taut mooring
lines, is the result of pre-tension in the mooring lines from excess buoyancy in the tank
when the support platform is undisplaced, including the contribution of the weight of the cable in
water. is the combined result of the elastic stiffness of the mooring lines and the effective
geometric stiffness brought about by the weight of the cables in water, depending on the layout
of the mooring system. Lines,0
iF
Lines,0
iF
Lines,0
iF
Lines,0
iF
Lines
ijC
In general, however, the mooring system dynamics are not linear in nature; instead,
nonlinearities are generally evident in the force-displacement relationships. The mooring dynamics also often include nonlinear hysteresis effects, where energy is dissipated as the lines oscillate with the support pl atform around its mean position.
Because I discovered that the dynamic LINES module [ 50] of SML was unsuitable for my
general use, I developed my ow n quasi-static module to simulate the nonlinear restoring loads
from the mooring system of floating platforms. Instead of interfacing with LINES, I have
interfaced my mooring system module to FAST and ADAMS.
My module can model an array of homogenous taut or slack catenary mooring lines. It accounts
for the apparent weight in fluid, elastic stretchin g, and seabed friction of each line, but neglects
the individual line bending stiffness. But because my quasi-static module is fully coupled with
FAST and ADAMS, it also accounts for the nonlin ear geometric restoration of the complete
mooring system. By “quasi-static,” I mean th at with the fairlead positions known for a given
platform displacement at any instant in time, my mooring system module solves for the tensions within, and configuration of, each mooring line by assuming that each cable is in static equilibrium at that instant. Using the tensions and additional loading on the platform from hydrodynamics and loading on the turbine from aerodynamics, FAST or ADAMS then solves the dynamic equations of motion for the accelerations of the rest of the system (platform, tower,
36

nacelle, and blades). Next, FAST or ADAMS in tegrates in time to obtain new platform and
fairlead positions at the next time step, repeating this process.
Clearly, this quasi-static approach also ignores the inertia and damping of the mooring system,
which may or may not be important in various situ ations. To justify using this approach, I used
the system-mass data presented in Chapter 3 to calculate that the mass of a typical mooring
system is 8% of the combined mass of a typi cal wind turbine and floating support platform.
According to conversations with Dr. R. Zueck of the Naval Facilities Engineering Service Center
(NFESC), about one-quarter of the inertia of a mooring system is important to the dynamic
response of a floating platform. One-quarter of 8% is only 2%, which ju stifies ignoring mooring
system inertia in the analyses for these turbin e / platform configurations. Ignoring mooring
system damping is also a conservative approach.
Figure 2-4 presents a layout of the calculation pro cedures in my quasi-static mooring system
module. Each line of the mooring system is analyzed independently. The user must specify the
fairlead locations of each mooring line relative (and fixed) to the support platform and the anchor locations of each mooring line relative (and fixed) to the inertial reference frame (i.e., the seabed). For each mooring line, the total unstretched length,
L, apparent weight in fluid per unit
length, ω, extensional stiffness, EA, and coefficient of seabed static-friction drag, CB, must also
be assigned. Because a mooring line is buoyant, ω is related to the mass of the line per unit
length, μc, by
2
c
cDg4πωμρ⎛
=−⎜⎜⎝⎠⎞
⎟⎟, (2-34)
FxFzLωEABC
( )F FF B xF H , V , L , , E A , C ω =
( )FF Fz FH, V, L ,, E A ω =
FHFV
AH AV ()xs()zs()eTs

Figure 2-4. Summary of my mooring system module calculation procedure
37

where ρ is the water density, g is the gravitational acceleration constant, and Dc is the effective
diameter of the mooring line. Because I have limited the model to simulating only homogenous
mooring lines, I handle multisegment lines (i.e., chain plus wire plus chain segments in series) by
using an equivalent line with weighted-average values of the weight and stiffness (weighted based on the unstretched lengths of each segment).
Each mooring line is analyzed in a local coordinate system that originates at the anchor. The
local
z-axis of this coordinate system is vertical and the local x-axis is directed horizontally from
the anchor to the instantane ous position of the fairlead. Figure 2-5 illustrates a typical line.
When the mooring system module is called fo r a given support platform displacement, the
module first transforms each fairlead position from the global frame to this local system to
determine its location relative to the anchor, xF and zF.

Figure 2-5. Mooring line in a local coordinate system
I took advantage of the analytical formulation fo r an elastic cable suspended between two points,
hanging under its own weight (in fluid). I deri ved this analytical formulation following a
procedure similar to that presented in Ref. [ 22], which I do not give here for brevity. (The
derivation was not exactly the same because Ref. [ 22] did not account for seabed interaction nor
did it account for taut lines where the angle of the line at the anchor was nonzero). The derivation required the assumption that the extensional stiffness of the mooring line,
EA, was
much greater than the hydrostatic pressure at all locations along the line.
In the local coordinate system, the analytical formulation is given in terms of two nonlinear
equations in two unknowns—the unknowns are the hor izontal and vertical components of the
effective tension in the mooring line at the fairlead, HF and VF, respectively. (The effective
tension is defined as the actual cable [wall] tens ion plus the hydrostatic pressure.) When no
portion of the line rests on the seabed, the analytical formulation is as follows:
38

()22
FF F F F
FF F
FF F F
FHV V V L V LxH , V= l n 1 l n 1HH H H
HL
EAωω
ω⎧⎫⎡⎤ ⎡⎛⎞ ⎛ ⎞ −− ⎪⎪⎢⎥ ⎢ ++ − ++⎨⎬ ⎜⎟ ⎜ ⎟⎢⎥ ⎢⎝⎠ ⎝ ⎠ ⎪⎪⎣⎦ ⎣ ⎩⎭
+⎤
⎥
⎥
⎦ (2-35a)
and
()222
FF F
FF F F
FFHV V L 1zH , V= 1 1 V LL
H HE Aω ω
ω⎡⎤⎛⎞ ⎛ ⎞ ⎛ −⎢⎥+− + + −⎜⎟ ⎜ ⎟ ⎜⎢⎥ ⎝⎠ ⎝⎠ ⎝ ⎠⎣⎦2⎞
⎟. ( 2-35b)
Equivalent formulations of Eq. ( 2-35) are sometimes cited in terms of the inverse of the
hyperbolic sine; that is:
()()21ln x 1 x sinh x−++ = . (2-36)
The first terms on the right-hand side of Eq. ( 2-35) characterize the arc length of the catenary,
projected on the x- and z-axes. (Even taut mooring lines have a catenary-shaped sag.) The
second terms on the right-hand side of Eq. ( 2-35) represent the horizontal and vertical stretching
of the mooring line.
The analytical formulation of two equations in two unknowns is different when a portion of the
mooring line adjacent to the anchor rests on the seabed:
()2
FF F F F
FF F
FF
2
B F FF FF
BBVH V V H LxH , V= L l n 1HH E A
C V VH VHL LM AX L2EA C Cωω
ω
ωω ω ω ω⎡⎤⎛⎞⎢⎥ −+ ++ + ⎜⎟⎢⎥⎝⎠⎣⎦
⎡⎤ ⎛⎞ ⎛ ⎛⎞+ −− +−− −−⎢⎥ ⎜⎟ ⎜ ⎜⎟⎝⎠⎢⎥ ⎝⎠ ⎝ ⎣⎦,0⎞
⎟
⎠ (2-37a)
and
()222
FF F
FF F F
FFHV V L 1zH , V= 1 1 V LL
H HE Aω ω
ω⎡⎤⎛⎞ ⎛ ⎞ ⎛ −⎢⎥+− + + −⎜⎟ ⎜ ⎟ ⎜⎢⎥ ⎝⎠ ⎝⎠ ⎝ ⎠⎣⎦2⎞
⎟. ( 2-37b)
The first two terms on the right-hand side of Eq. (2-37a) combine to represent the unstretched
portion of the mooring line resting on the seabed, LB:
F
BVLLω=− . (2-38)
In Eq. ( 2-35), LB is zero.
39

The last term on the right-hand side of Eq. (2-37a), which involves CB, corresponds to the
stretched portion of the m ooring line resting on the seabed that is affected by static friction. The
seabed static friction was modeled simply as a drag force per unit length of CBω. The MAX
function is needed to handle cases with and wit hout tension at the anchor. Specifically, the
resultant is zero when the anchor tension is positive; that is, the seabed friction is too weak to
overcome the horizontal tension in the mooring line. Conversely, the resultant of the MAX
function is nonzero when the anchor tension is zer o. This happens when a section of cable lying
on the seabed is long enough to ensure that the seabed friction entirely overcomes the horizontal tension in the mooring line.
The remaining terms in Eq. ( 2-37) are similar in form to, and typify the same information as, the
terms in Eq. ( 2-35). They are simpler than the terms in Eq. ( 2-35), though, because a slack
catenary is always tangent to the seabed at the point of touchdown.
My mooring system module uses a Newton-Raph son iteration scheme to solve nonlinear Eqs.
(2-35) and ( 2-37) for the fairlead effective tension (
HF and VF,), given the line properties ( L, ω,
EA, and CB) and the fairlead position relative to the anchor ( xF and zF). The Jacobian in the
Newton-Raphson iteration was implemented with the analytical partial derivatives of Eqs. ( 2-35)
and ( 2-37). My mooring system module determines which of Eqs. ( 2-35) or (2-37) must be used
as part of the solution process. The equations were implemented in a slightly different form than
shown to avoid numerical problems (e.g., a division by zero when CB is zero-valued).
My mooring system module uses the values of HF and VF from the previous time step as the
initial guess in the next iterati on of Newton-Raphson. As the m odel is being initialized, I used
the starting values, 0
FH and 0
FV, documented by Peyrot and Goulois in Ref. [ 79]:
0 F
F
0xH2ω
λ= (2-39a)
and
()0 F
F
0zV2 tanhω
λL⎡ ⎤= + ⎢ ⎥
⎣ ⎦, ( 2-39b)
where the dimensionless catenary parameter, λ0, depends on the initial configuration of the
mooring line:
F
22
0
22
F
2
F1,000,000 for x 0
=0 . 2 f o r x z L
Lz3 1 otherwisexλ⎧
⎪=⎪
⎪
F F+≥ ⎨
⎪⎛⎞−⎪−⎜⎟⎪⎝⎠⎩. (2-40)
40

Note that Eqs. ( 2-39) and (2-40) are slightly different from those given in Ref. [ 79] because my
analytical formulati on and notation differs.
Once the effective tension at the fairlead has b een found, determining the horizontal and vertical
components of the effective tension in the mooring line at the anchor, HA and VA, respectively, is
simple. (The blue arrows depicting HA and VA in Figure 2-5 are the horizontal and vertical
components of the effective line tension at the anchor—they are not the reaction forces at the
anchor.) From a balance of external forces on a mooring line, one can easily verify that
AFH H= (2-41a)
and
AFVV Lω=− , ( 2-41b)
when no portion of the line rests on the seabed, and
( )AF B B H MAX H C L ,0 ω =− (2-42a)
and
AV0=, ( 2-42b)
when a portion of the line does rest on the seab ed. Although they do not affect the dynamic
response of the floating wind turbine system, the an chor effective tensions are computed by my
mooring system module and become available outputs from the simulation.
Next, my mooring system module solves for the configuration of, and eff ective tensions within,
the mooring line. Again, the values of these parameters do not affect the dynamic response of
the floating wind turbine system, but they are available outputs from the simulation. When no
portion of the mooring line rests on the seabed, th e equations for the horizontal and vertical
distances between the anchor and a given point on the line, x and z, and the equation for the
effective tension in the line at that point, Te, are as follows:
()22
F AA A A
FF F FF H Vs Vs V V Hxs= l n 1 l n 1s
H HH Hωω
ω⎧⎫⎡⎤ ⎡⎛⎞ ⎛ ⎞ ++⎪⎪⎢⎥ ⎢ ++ − ++ + ⎨⎬ ⎜⎟ ⎜ ⎟⎢⎥ ⎢⎝⎠ ⎝ ⎠ ⎪⎪⎣⎦ ⎣ ⎩⎭EA⎤
⎥
⎥
⎦, (2-43a)
()222
FA A
A
FFHV s V 1zs= 1 1 V ss
H HE A 2ω ω
ω⎡⎤⎛⎞⎛ ⎞ ⎛ +⎢⎥+− + + +⎜⎟⎜ ⎟ ⎜⎢⎥ ⎝⎠ ⎝⎠⎝ ⎠⎣⎦⎞
⎟, ( 2-43b)
and
() ( )2 2
eF ATs =H + V s ω+ , (2-44)
41

where s is the unstretched arc distance along the mooring line from the anchor to the given point.
The similarity between Eqs. ( 2-43) and ( 2-35) should be apparent. Similar to Eq. ( 2-37), the
equations with seabed interaction are more onerous:

()
() ()F
B
B
2 F
B
BB F
B B
BFF
BB
BB
2
BB FF
B
FF
2 BF F
BB B
BBHsfC
Hs2 L sC CHor0sL
s for L s L2EA C HHLM A X L , 0CCxs=
sL sL HH sLl n 1HH E A
CH HL L MAX L ,02EA C Cω
ω ω
ω
ωω
ωω
ω
ω
ωω≤≤ −
⎡⎤⎛⎞−−⎢⎥⎜⎟
⎝⎠⎢⎥+−⎢⎥⎛⎞ ⎛ ⎞⎢⎥+− −⎜⎟ ⎜ ⎟⎢⎥⎝⎠ ⎝ ⎠⎣⎦
⎡⎤−− ⎛⎞⎢⎥++ + +⎜⎟⎢⎥⎝⎠⎣⎦
⎛⎞ ⎛ ⎞+− + − − ⎜⎟ ⎜⎝⎠ ⎝ ⎠B for L s L⎧
⎪
⎪
⎪
⎪
⎪
⎪
⎪
⎪⎪⎨
⎪
⎪
⎪
⎪ ≤≤
⎪⎡⎤⎪⎢⎥ ⎟⎪⎣⎦⎪
⎪⎩≤≤
, (2-45a)
() () ()B
2 2
BB F
B
F0f
zs= sL sL Hln 1 1 for L s LH2 EAωω
ω≤≤ ⎧
⎪⎪⎡⎤−−⎛⎞ ⎨⎢⎥+− + ≤⎜⎟ ⎪⎢⎥⎝⎠ ⎪⎣⎦⎩or0sL
≤, ( 2-45b)
and
()() ( )
()()F BB
e 22
FB BB MAX H C s L ,0 for 0 s L
Ts =
H sL f o r L sLω
ω⎧ +− ≤ ≤⎪⎨
+−≤ ⎪⎩≤. (2-46)
As shown in Figure 2-4 , the final calculation in my quasi-static mooring system module is a
computation of the total load on the support from the contribution of all mooring lines; that is,
from Eq. Lines
iF (2-7) . This mooring system-restoring load is found by first transforming each
fairlead tension from its local mooring line coordinate system to the global frame, then summing
up the tensions from all lines.
2.6 Pulling It All Together
Limitations of previous time- and frequency-domain studies on offshore floating wind turbines
motivated my development of simulation tools capable of modeling the fully coupled aero-hydro-servo-elastic response of such systems. I have developed this capability by leveraging the computational methodologies and analysis tools of the onshore wind turbine and offshore O&G
industries. The onshore wind-industry-accept ed aero-servo-elastic turbine simulation
capabilities of FAST [ 39] with AeroDyn [ 55,67] and MSC.ADAMS with A2AD [ 20,54] and
AeroDyn have been interfaced with the external hydrodynamic wave-body interaction programs SWIM [ 48] and WAMIT [ 58], which are commonly employed in the offshore O&G industry. I
42

established the interfaces among these simulati on capabilities by developing modules for treating
time-domain hydrodynamics (HydroDyn) and quasi-static mooring system responses. Figure 2-6
summarizes the modules and their interfaces.
Turbulent-wind inflow is prescribed by the external computer program TurbSim [ 36], and
deterministic-wind infl ow (not shown in Figure 2-6 ) is prescribed by the external computer
program IECWind [ 56]. FAST with AeroDyn and ADAMS with AeroDyn account for the
applied aerodynamic and gravitational loads, the be havior of the control and protection systems,
and the structural dynamics of the wind turbine. The latter contribution includes the elasticity of
the rotor, drivetrain, and tower, along with the newly added dynamic coupling between the
motions of the support platform and the motions of the wind turbine.11 Nonlinear restoring loads
from the mooring system are obtained from a qua si-static mooring line module that accounts for
the elastic stretching of an array of homogenous taut or slack catenary lines with seabed interaction. HydroDyn is a module that comput es the applied hydrodynamic loads in the time
domain, as summarized in Section 2.4.3.
By interfacing these modules as described, fu lly coupled time-domain aer o-hydro-servo-elastic
simulation of offshore floating wind turbines is achieved. This capability is crucial for analyzing the dynamic response from combined wind and wave loading because both can affect the
motions, loads, and power production of the system . The generality of each module also ensures

Figure 2-6. Interfacing modules to achieve aero-hydro-servo-elastic simulation

11 FAST and ADAMS are separate programs that can be run independently to model the structural-dynamic
response and control system behavior of wind turbines. FAST employs a combined modal and multibody structural-
dynamics formulation, whereas ADAMS employs a higher fidelity multibody formulation. They have both been
interfaced with AeroDyn to enable the full aer o-servo-elastic modeling of wind turbines.
43

that the overall simulation tool is universal e nough to analyze a variety of wind turbine, support
platform, and mooring system configurations. Moreover, the same simulation tools can still be
used to model land-based wind turbines by di sabling the hydrodynamic and mooring system
modules.
44

Chapter 3 Design Basis and Floating Wind Turbine Model
To obtain useful information from this and othe r concept studies aimed at assessing offshore
wind technology suitable in the deep waters off the U.S. offshore continental shelf (OCS) and
other offshore sites worldwide, use of realistic and standardized input da ta is required. This
chapter summarizes the input da ta developed and used in th e simulation code verification
exercises and in the integrated loads analyses presented in subsequent chapters. A large
collection of input data is needed, including detailed specifications of the wind turbine and
support platform, along with a design basis. A de sign basis consists of analysis methods (see
Chapter 2 ); a collection of applicable design st andards (i.e., IEC); and the site-specific
meteorological and oceanographic (metocean) parameters at a reference site.
In this work, I developed the turbine specificati ons of what is now called the “NREL offshore 5-
MW baseline wind turbine,” as presented in Section 3.1. Although I put together the
specifications of this wind turbine, I did not de velop the basic designs of the two floating support
platforms used in this work. Instead, I used two platforms that were developed by others through
partnerships with NREL. Both platforms were developed specifically to support the NREL
offshore 5-MW baseline wind turbine. The fi rst platform, which I summarize in Section 3.2, was
a barge with slack catenary moorings from a company called ITI Energy1 [98]. The second
platform, summarized in Section 3.3, was a barge with a spread-mooring system developed at
MIT through a contract with NREL [ 100,101]. Barge concepts were chosen because of their
simplicity in design, fabrication, and installation. For the loads analyses, ITI Energy selected a
location in the northern North Sea as the reference site from which to obtain metocean data.
These data are described in Section 3.4.
3.1 NREL Offshore 5-MW Baseline Wind Turbine
This section documents the specifications of NREL’s offshore 5-MW baseline wind turbine and
the rationale behind its development. My objective was to establish the detailed specifications of a large wind turbine that is representative of typical utility-scale land- and sea-based
multimegawatt turbines.
Before establishing the deta iled specifications, however, we
2 had to choose the basic size and
power rating of the machine. Because of the large portion of system costs in the support
structure of a deepwater wind system, we unders tood from the outset that if a deepwater wind
system is to be cost-effective, each individual wind turbine must be rated at 5 MW or higher
[70].3 Ratings considered for the baseline ranged from 5 MW to 20 MW. We decided that the
baseline should be 5 MW because it has precedence:

1 Web site: http://www.itienergy.com/
2 My NREL colleagues, W. N. Musial and S. Butterfield, assisted me in selecting some of the basic specifications of
this offshore turbine. To acknowledge this support, I use “we” in place of “I” and “our” in place of “my” where
appropriate.
3 A single 5-MW wind turbine can supply enough energy annually to power 1,250 average American homes.
45

• Feasible floater configurations for offs hore wind turbines scoped out by Musial,
Butterfield, and Boone [ 70] were based on the assumption of a 5-MW unit.
• Unpublished DOE offshore cost studies were based on a rotor diameter of 128 m, which
is a size representative of a 5- to 6-MW wind turbine.
• The land-based Wind Partnerships for Adva nced Component Technology (WindPACT)
series of studies, considered wind turbine systems rated up to 5 MW [ 64,73,88].
• The Recommendations for Design of Offs hore Wind Turbines project (known as
RECOFF) based its conceptual design calcula tions on a wind turbine with a 5-MW rating
[93].
• The Dutch Offshore Wind Energy Converter (DOWEC) project based its conceptual
design calculations on a wind turbine with a 6-MW rating [ 24,51,60].
• At the time of this writing, the largest wind turbine prototypes in the world—the Multibrid M5000 [ 18,68,69] and the REpower 5M [ 62,81,82]—each had a 5-MW rating.
I gathered the publicly available inform ation on the Multibrid M5000 and REpower 5M
prototype wind turbines. And because detailed information on these machines was unavailable, I
also used the publicly available properties from the conceptual models used in the WindPACT, RECOFF, and DOWEC projects. These models contained much greater detail than was
available about the prototypes. I then created a composite from th ese models, extracting the best
available and most representative specifications.
The Multibrid M5000 machine has a significantly higher tip speed than typical onshore wind
turbines and a lower tower-top mass than would be expected from scaling laws previously
developed in one of th e WindPACT studies [88]. In contrast, the REpower 5M machine has
properties that are more “expected” and “conventi onal.” For this reason, we decided to use the
specifications of the REpower 5M machine as the target specifications
4 for our baseline model.
The wind turbine used in the DOWEC project had a slightly higher rating than the rating of the
REpower 5M machine, but many of the other basic properties of the DOWEC turbine matched
the REpower 5M machine very well. In fact, the DOWEC turbine matched many of the properties of the REpower 5M machine better than the turbine properties derived for the
WindPACT and RECOFF studies.
5 As a result of these similarities, I made the heaviest use of
data from the DOWEC study in my developmen t of the NREL offshore 5-MW baseline wind
turbine.
The REpower 5M machine has a rotor radius of about 63 m. Wanting the same radius and the
lowest reasonable hub height possible to minimize the overturning moment acting on a floating

4 Note that I established the target specifications using information about the REpower 5M machine that was
published in January 2005 [ , ]. Some of the information presented in Refs. [81] and [ ] disagrees with more
recently published information. For example, the published nacelle and rotor masses of the REpower 5M are higher in the more recent publications. 8182 82
5 This was probably because the REpower 5M prototype utilized blades provided by LM Glasfiber [62], a company
that helped establish the structural properties of the blades used in the DOWEC study.
46

support platform, we decided that the hub height for the baseline wind turbine should be 90 m.
This would give a 15-m air gap between the blade tips at their lowest point when the wind
turbine is undeflected and an estimated extreme 50- year individual wave height of 30 m (i.e., 15-
m amplitude). The additional gross propertie s we chose for the NREL 5-MW baseline wind
turbine, most of which are identical to those of the REpower 5M, are given in Table 3-1 . The
(x,y,z) coordinates of the overall CM location of the wind turbine are indicated in a tower-base
coordinate system, which originates along the tower centerline at ground or mean sea level
(MSL). The x-axis of this coordinate system is directed nominally downwind, the y-axis is
directed transverse to the nominal wind direction, and the z-axis is directed vertically from the
tower base to the yaw bearing.
Table 3-1. Gross Properties Chosen for the NREL 5-MW Baseline
Wind Turbine
Rating 5 MW
Rotor Orientation, Configuration Upwind, 3 Blades
Control Variable Speed, Collective Pitch
Drivetrain High Speed, Multiple-Stage Gearbox
Rotor, Hub Diameter 126 m, 3 m
Hub Height 90 m
Cut-In, Rated, Cut-Out Wind Speed 3 m/s, 11.4 m/s, 25 m/s
Cut-In, Rated Rotor Speed 6.9 rpm, 12.1 rpm
Rated Tip Speed 80 m/s
Overhang, Shaft Tilt, Precone 5 m, 5ș, 2.5ș
Rotor Mass 110,000 kg
Nacelle Mass 240,000 kg
Tower Mass 347,460 kg
Coordinate Location of Overall CM (-0.2 m, 0.0 m, 64.0 m)
The actual REpower 5M wind turbine uses blades with built-in prebend as a means of increasing tower clearance without a large rotor overhang. Because, as I mentioned in Section 2.1, the
FAST code cannot support blades with built-in prebend, I chose a 2.5°-upwind precone in the
baseline wind turbine to represent the smaller amount of precone and larg er amount of prebend
that are built into the actual REpower 5M machine.
The rotor diameter indicated in Table 3-1 ignores the effect of blade precone, which reduces the
actual diameter and swept area. The exact rotor diameter in the turbine specifications (assuming
that the blades are undeflect ed) is actually (126 m) ×
cos(2.5°) = 125.88 m and the actual swept
area is (π/4) × (125.88 m)2 = 12,445.3 m2.
I present other information about this model as follows:
• The blade structural properties in Section 3.1.1
• The blade aerodynamic properties in Section 3.1.2
• The hub and nacelle pr operties in Section 3.1.3
• The drivetrain properties in Section 3.1.4
• The tower properties in Section 3.1.5
47

• The baseline control system properties in Section 3.1.6
• The aero-servo-elastic FAST with AeroDyn and ADAMS with AeroDyn models of the
wind turbine in Section 3.1.7
• The basic responses of the land-based versi on of the wind turbine, including its full-
system natural frequencies and steady-state behavior in Section 3.1.8.
Although I summarize much of this information6 for conciseness and clarity, Section 3.1.6
contains a high level of deta il about the development of the wind turbine’s baseline control
system. These details are fundamental to the controls work presented in Chapter 7 .
Beyond its application to this work, the NREL offshore 5-MW baseline wind turbine has been
used to establish the reference specifications for a number of research projects supported by the
U.S. DOE’s Wind & Hydropower Technologies Program [ 1,23,84,100,101 ]. In addition, the
integrated European Union UpWind research program7 and the International Energy Agency
(IEA) Wind Annex XXIII Subtask 28 Offshore Code Comparis on Collaboration (OC3) [ 78] have
adopted the NREL offshore 5-MW baseline wind tu rbine as their referenc e model. The model
has been, and will likely continue to be, used as a reference by research teams throughout the
world to standardize baseline offshore wind turbine specifications and to quantify the benefits of
advanced land- and sea-base d wind energy technologies.
3.1.1 Blade Structural Properties
The NREL offshore 5-MW baseline wind turbine has three blades. I based the distributed blade
structural properties of each blade on the struct ural properties of the 62.6-m-long LM Glasfiber
blade used in the DOWEC study (using th e data given in Appendix A of Ref. [ 60]). Because the
blades in the DOWEC study were 1.1 m longer than the 61.5-m-long LM Glasfiber blades [ 62]
used on the actual REpower 5M machine, I trunca ted the 62.6-m blades at 61.5-m span to obtain
the structural properties of the NREL 5-MW baselin e blades (I found the structural properties at
the blade tip by interpolating between the 61.2- m and 61.7-m stations given in Appendix A of
Ref. [ 60]). Table 3-2 lists the resulting properties.
The entries in the first column of Table 3-2 , labeled “Radius,” are the spanwise locations along
the blade-pitch axis relative to the rotor center (apex). “BlFract” is the fractional distance along
the blade-pitch axis from the root (0.0) to the tip (1.0). I located the blade root 1.5 m along the
pitch axis from the rotor center, equivale nt to half the hub diameter listed in Table 3-1 .
“AeroCent” is the name of a FAST input parameter. The FAST code assumes that the blade-pitch axis passes through each airfoil section at 25% chord. By definition, then, the quantity
(AeroCent − 0.25) is the fractional distance to the aerodynamic center from the blade-pitch axis

6 Note that some of the turbine properties are presented with a large number (>4) of significant figures. Most of
these were carried over from the turbine properties documented in the DOWEC study [ , , ]—I did not truncate
their precision to maintain consistency with the original data source. 245160
7 Web site: http://www.upwind.eu/default.aspx
8 Web site: http://www.ieawind.org/Annex%20XXIII/Subtask2.html
48

Table 3-2. Distributed Blade Structural Properties
Radius BlFract AeroCent StrcTwst BMassDen FlpStff EdgStff GJStff EAStff Alpha FlpIner EdgIner PrecrvRef PreswpRef FlpcgOf EdgcgOf FlpEAOf EdgEAO f
(m) (-) (-) (ș) (kg/m) (N•m2)( N • m2)( N • m2) (N) (-) (kg•m) (kg•m) (m) (m) (m) (m) (m) (m)
1.50 0.00000 0.25000 13.308 678.935 18110.00E+6 18113.60E+6 5564.40E+6 9729.48E+6 0.0 972.86 973.04 0.0 0.0 0.0 0.00017 0.0 0.0
1.70 0.00325 0.25000 13.308 678.935 18110.00E+6 18113.60E+6 5564.40E+6 9729.48E+6 0.0 972.86 973.04 0.0 0.0 0.0 0.00017 0.0 0.0
2.70 0.01951 0.24951 13.308 773.363 19424.90E+6 19558.60E+6 5431.59E+6 10789.50E+6 0.0 1091.52 1066.38 0.0 0.0 0.0 -0.02309 0.0 0.03.70 0.03577 0.24510 13.308 740.550 17455.90E+6 19497.80E+6 4993.98E+6 10067.23E+6 0.0 966.09 1047.36 0.0 0.0 0.0 0.00344 0.0 0.04.70 0.05203 0.23284 13.308 740.042 15287.40E+6 19788.80E+6 4666.59E+6 9867.78E+6 0.0 873.81 1099.75 0.0 0.0 0.0 0.04345 0.0 0.05.70 0.06829 0.22059 13.308 592.496 10782.40E+6 14858.50E+6 3474.71E+6 7607.86E+6 0.0 648.55 873.02 0.0 0.0 0.0 0.05893 0.0 0.06.70 0.08455 0.20833 13.308 450.275 7229.72E+6 10220.60E+6 2323.54E+6 5491.26E+6 0.0 456.76 641.49 0.0 0.0 0.0 0.06494 0.0 0.0
7.70 0.10081 0.19608 13.308 424.054 6309.54E+6 9144.70E+6 1907.87E+6 4971.30E+6 0.0 400.53 593.73 0.0 0.0 0.0 0.07718 0.0 0.0
8.70 0.11707 0.18382 13.308 400.638 5528.36E+6 8063.16E+6 1570.36E+6 4493.95E+6 0.0 351.61 547.18 0.0 0.0 0.0 0.08394 0.0 0.0
9.70 0.13335 0.17156 13.308 382.062 4980.06E+6 6884.44E+6 1158.26E+6 4034.80E+6 0.0 316.12 490.84 0.0 0.0 0.0 0.10174 0.0 0.0
10.70 0.14959 0.15931 13.308 399.655 4936.84E+6 7009.18E+6 1002.12E+6 4037.29E+6 0.0 303.60 503.86 0.0 0.0 0.0 0.10758 0.0 0.0
11.70 0.16585 0.14706 13.308 426.321 4691.66E+6 7167.68E+6 855.90E+6 4169.72E+6 0.0 289.24 544.70 0.0 0.0 0.0 0.15829 0.0 0.0
12.70 0.18211 0.13481 13.181 416.820 3949.46E+6 7271.66E+6 672.27E+6 4082.35E+6 0.0 246.57 569.90 0.0 0.0 0.0 0.22235 0.0 0.013.70 0.19837 0.12500 12.848 406.186 3386.52E+6 7081.70E+6 547.49E+6 4085.97E+6 0.0 215.91 601.28 0.0 0.0 0.0 0.30756 0.0 0.014.70 0.21465 0.12500 12.192 381.420 2933.74E+6 6244.53E+6 448.84E+6 3668.34E+6 0.0 187.11 546.56 0.0 0.0 0.0 0.30386 0.0 0.015.70 0.23089 0.12500 11.561 352.822 2568.96E+6 5048.96E+6 335.92E+6 3147.76E+6 0.0 160.84 468.71 0.0 0.0 0.0 0.26519 0.0 0.016.70 0.24715 0.12500 11.072 349.477 2388.65E+6 4948.49E+6 311.35E+6 3011.58E+6 0.0 148.56 453.76 0.0 0.0 0.0 0.25941 0.0 0.017.70 0.26341 0.12500 10.792 346.538 2271.99E+6 4808.02E+6 291.94E+6 2882.62E+6 0.0 140.30 436.22 0.0 0.0 0.0 0.25007 0.0 0.019.70 0.29595 0.12500 10.232 339.333 2050.05E+6 4501.40E+6 261.00E+6 2613.97E+6 0.0 124.61 398.18 0.0 0.0 0.0 0.23155 0.0 0.021.70 0.32846 0.12500 9.672 330.004 1828.25E+6 4244.07E+6 228.82E+6 2357.48E+6 0.0 109.42 362.08 0.0 0.0 0.0 0.20382 0.0 0.023.70 0.36098 0.12500 9.110 321.990 1588.71E+6 3995.28E+6 200.75E+6 2146.86E+6 0.0 94.36 335.01 0.0 0.0 0.0 0.19934 0.0 0.025.70 0.39350 0.12500 8.534 313.820 1361.93E+6 3750.76E+6 174.38E+6 1944.09E+6 0.0 80.24 308.57 0.0 0.0 0.0 0.19323 0.0 0.027.70 0.42602 0.12500 7.932 294.734 1102.38E+6 3447.14E+6 144.47E+6 1632.70E+6 0.0 62.67 263.87 0.0 0.0 0.0 0.14994 0.0 0.029.70 0.45855 0.12500 7.321 287.120 875.80E+6 3139.07E+6 119.98E+6 1432.40E+6 0.0 49.42 237.06 0.0 0.0 0.0 0.15421 0.0 0.031.70 0.49106 0.12500 6.711 263.343 681.30E+6 2734.24E+6 81.19E+6 1168.76E+6 0.0 37.34 196.41 0.0 0.0 0.0 0.13252 0.0 0.0
33.70 0.52358 0.12500 6.122 253.207 534.72E+6 2554.87E+6 69.09E+6 1047.43E+6 0.0 29.14 180.34 0.0 0.0 0.0 0.13313 0.0 0.0
35.70 0.55610 0.12500 5.546 241.666 408.90E+6 2334.03E+6 57.45E+6 922.95E+6 0.0 22.16 162.43 0.0 0.0 0.0 0.14035 0.0 0.0
37.70 0.58862 0.12500 4.971 220.638 314.54E+6 1828.73E+6 45.92E+6 760.82E+6 0.0 17.33 134.83 0.0 0.0 0.0 0.13950 0.0 0.0
39.70 0.62115 0.12500 4.401 200.293 238.63E+6 1584.10E+6 35.98E+6 648.03E+6 0.0 13.30 116.30 0.0 0.0 0.0 0.15134 0.0 0.0
41.70 0.65366 0.12500 3.834 179.404 175.88E+6 1323.36E+6 27.44E+6 539.70E+6 0.0 9.96 97.98 0.0 0.0 0.0 0.17418 0.0 0.0
43.70 0.68618 0.12500 3.332 165.094 126.01E+6 1183.68E+6 20.90E+6 531.15E+6 0.0 7.30 98.93 0.0 0.0 0.0 0.24922 0.0 0.0
45.70 0.71870 0.12500 2.890 154.411 107.26E+6 1020.16E+6 18.54E+6 460.01E+6 0.0 6.22 85.78 0.0 0.0 0.0 0.26022 0.0 0.0
47.70 0.75122 0.12500 2.503 138.935 90.88E+6 797.81E+6 16.28E+6 375.75E+6 0.0 5.19 69.96 0.0 0.0 0.0 0.22554 0.0 0.049.70 0.78376 0.12500 2.116 129.555 76.31E+6 709.61E+6 14.53E+6 328.89E+6 0.0 4.36 61.41 0.0 0.0 0.0 0.22795 0.0 0.051.70 0.81626 0.12500 1.730 107.264 61.05E+6 518.19E+6 9.07E+6 244.04E+6 0.0 3.36 45.44 0.0 0.0 0.0 0.20600 0.0 0.053.70 0.84878 0.12500 1.342 98.776 49.48E+6 454.87E+6 8.06E+6 211.60E+6 0.0 2.75 39.57 0.0 0.0 0.0 0.21662 0.0 0.055.70 0.88130 0.12500 0.954 90.248 39.36E+6 395.12E+6 7.08E+6 181.52E+6 0.0 2.21 34.09 0.0 0.0 0.0 0.22784 0.0 0.056.70 0.89756 0.12500 0.760 83.001 34.67E+6 353.72E+6 6.09E+6 160.25E+6 0.0 1.93 30.12 0.0 0.0 0.0 0.23124 0.0 0.057.70 0.91382 0.12500 0.574 72.906 30.41E+6 304.73E+6 5.75E+6 109.23E+6 0.0 1.69 20.15 0.0 0.0 0.0 0.14826 0.0 0.058.70 0.93008 0.12500 0.404 68.772 26.52E+6 281.42E+6 5.33E+6 100.08E+6 0.0 1.49 18.53 0.0 0.0 0.0 0.15346 0.0 0.059.20 0.93821 0.12500 0.319 66.264 23.84E+6 261.71E+6 4.94E+6 92.24E+6 0.0 1.34 17.11 0.0 0.0 0.0 0.15382 0.0 0.059.70 0.94636 0.12500 0.253 59.340 19.63E+6 158.81E+6 4.24E+6 63.23E+6 0.0 1.10 11.55 0.0 0.0 0.0 0.09470 0.0 0.060.20 0.95447 0.12500 0.216 55.914 16.00E+6 137.88E+6 3.66E+6 53.32E+6 0.0 0.89 9.77 0.0 0.0 0.0 0.09018 0.0 0.060.70 0.96260 0.12500 0.178 52.484 12.83E+6 118.79E+6 3.13E+6 44.53E+6 0.0 0.71 8.19 0.0 0.0 0.0 0.08561 0.0 0.061.20 0.97073 0.12500 0.140 49.114 10.08E+6 101.63E+6 2.64E+6 36.90E+6 0.0 0.56 6.82 0.0 0.0 0.0 0.08035 0.0 0.061.70 0.97886 0.12500 0.101 45.818 7.55E+6 85.07E+6 2.17E+6 29.92E+6 0.0 0.42 5.57 0.0 0.0 0.0 0.07096 0.0 0.0
62.20 0.98699 0.12500 0.062 41.669 4.60E+6 64.26E+6 1.58E+6 21.31E+6 0.0 0.25 4.01 0.0 0.0 0.0 0.05424 0.0 0.0
62.70 0.99512 0.12500 0.023 11.453 0.25E+6 6.61E+6 0.25E+6 4.85E+6 0.0 0.04 0.94 0.0 0.0 0.0 0.05387 0.0 0.063.00 1.00000 0.12500 0.000 10.319 0.17E+6 5.01E+6 0.19E+6 3.53E+6 0.0 0.02 0.68 0.0 0.0 0.0 0.05181 0.0 0.0
along the chordline, positive toward the trailing edge. Thus, at the root (i.e., BlFract = 0.0),
AeroCent = 0.25 means that the aerodynamic center lies on the blade-pitch axis [because (0.25 −
0.25) = 0.0], and at the tip (i.e., BlFract = 1.0), AeroCent = 0.125 means that the aerodynamic
center lies 0.125 chordlengths toward the leadi ng edge from the blade-pitch axis [because (0.125
− 0.25) = −0.125].
The flapwise and edgewise section stiffness and inertia values, “FlpStff,” “EdgStff,” “FlpIner,”
and “EdgIner” in Table 3-2 , are given about the principal struct ural axes of each cross section as
oriented by the structural-twist angle, “StrcTwst.” The values of the structural twist were assumed to be identical to the aerodynamic twist discussed in Section 3.1.2.
“GJStff” represents the values of the blade torsion stiffness. Because the DOWEC blade data did not contain extensional stiffness information, I estimated the blad e extensional stiffness values—
“EAStff” in Table 3-2 —to be 10
7 times the average mass moment of inertia at each blade station.
This came from a rule of thumb derived from the data available in the WindPACT rotor design
study [ 64], but the exact values are not important because of the low rotational speed of the rotor.
The edgewise CM offset values, “EdgcgOf,” are the distances in meters along the chordline from
the blade-pitch axis to the CM of the blade sec tion, positive toward the trailing edge. I neglected
the insignificant values of the flapwise CM offsets, “FlpcgOf,” and flapwise and edgewise elastic offsets, “FlpEAOf” and “EdgEAOf,” given in Appendix A of Ref. [ 60]. Instead, I assumed that
they were zero as shown in Table 3-2 .
The distributed blade section mass per un it length values, “BMassDen,” given in Table 3-2 are
the values documented in Appendix A of Ref. [ 60]. I increased these by 4.536% in the model to
49

scale the overall (integrated) blade mass to 17,740 kg, which was the nominal mass of the blades
in the REpower 5M prototype. In my baseline specifications, the nominal second mass moment of inertia, nominal first mass moment of inertia, and the nominal radial CM location of each blade are 11,776,047 kg
•m2, 363,231 kg •m, and 20.475 m with respect to (w.r.t.) the blade root,
respectively.
I specified a structural-damping ratio of 0.477465% critical in all modes of the isolated blade,
which corresponds to the 3% logarithmic decrement used in the DOWEC study from page 20 of Ref. [ 51].
Table 3-3 summarizes the undistributed blade structural properties discussed in this section.
Table 3-3. Undistributed Blade Structural Properties
Length (w.r.t. Root Along Preconed Axis) 61.5 m
Mass Scaling Factor 4.536 %
Overall (Integrated) Mass 17,740 kg
Second Mass Moment of Inertia (w.r.t. Root) 11,776,047 kg•m2
First Mass Moment of Inertia (w.r.t. Root) 363,231 kg•m
CM Location (w.r.t. Root along Preconed Axis) 20.475 m
Structural-Damping Ratio (All Modes) 0.477465 %
3.1.2 Blade Aerodynamic Properties
Similar to the blade structural properties, I based the blade aerodynamic properties of the NREL 5-MW baseline wind turbine on the DOWEC blades (u sing the data described in Table 1 on page
13 of Ref. [ 51] and in Appendix A of Ref. [ 60]). I set the FAST and ADAMS models to use 17
blade elements for integration of the aerodynamic and structural forces. To better capture the large structural gradients at the blade root and the large aerodynamic gradients at the blade tip, the 3 inboard and 3 outboard elements are two-thirds the size of the 11 equally spaced midspan elements. Table 3-4 gives the aerodynamic properties at the blade nodes, which are located at
the center of the blade elements.
The blade node locations, labeled as “RNodes” in Table 3-4 , are directed along the blade-pitch
axis from the rotor center (apex) to the blade cross sections. The element lengths, “DRNodes,”
sum to the total blade length of 61.5 m indicated in Table 3-3 . The aerodynamic twist,
“AeroTwst,” as given in Table 3-4 , are offset by −0.09182° from the values provided in
Appendix A of Ref. [ 60] to ensure that the zero-twist reference location is at the blade tip.
Integrating the chord distribution along the blade span reveals that the rotor solidity is roughly 5.16%.
As indicated in Table 3-4 , I incorporated eight unique airfoil-data tables for the NREL offshore
5-MW baseline wind turbine. The two innermost airfoil tables represent cylinders with drag
coefficients of 0.50 (Cylinder1.dat) and 0.35 (Cylinder2.dat) and no lift. I created the remaining
six airfoil tables by making corrections for thre e-dimensional behavior to the two-dimensional
airfoil-data coefficients of the six airfoils used in the DOWEC study (as detailed in Appendix A
50

Table 3-4. Distributed Blade Aerodynamic Properties
Node RNodes AeroTwst DRNodes Chord Airfoil Table
(-) (m) (ș) (m) (m) (-)
1 2.8667 13.308 2.7333 3.542 Cylinder1.dat
2 5.6000 13.308 2.7333 3.854 Cylinder1.dat
3 8.3333 13.308 2.7333 4.167 Cylinder2.dat
4 11.7500 13.308 4.1000 4.557 DU40_A17.dat
5 15.8500 11.480 4.1000 4.652 DU35_A17.dat
6 19.9500 10.162 4.1000 4.458 DU35_A17.dat
7 24.0500 9.011 4.1000 4.249 DU30_A17.dat
8 28.1500 7.795 4.1000 4.007 DU25_A17.dat
9 32.2500 6.544 4.1000 3.748 DU25_A17.dat
10 36.3500 5.361 4.1000 3.502 DU21_A17.dat
11 40.4500 4.188 4.1000 3.256 DU21_A17.dat
12 44.5500 3.125 4.1000 3.010 NACA64_A17.dat
13 48.6500 2.319 4.1000 2.764 NACA64_A17.dat
14 52.7500 1.526 4.1000 2.518 NACA64_A17.dat
15 56.1667 0.863 2.7333 2.313 NACA64_A17.dat
16 58.9000 0.370 2.7333 2.086 NACA64_A17.dat
17 61.6333 0.106 2.7333 1.419 NACA64_A17.dat
of Ref. [ 51]).9 In these airfoil tables, “DU” refers to Delft University and “NACA” refers to the
National Advisory Committee for Aerona utics. I used AirfoilPrep v2.0 [ 28] to “tailor” these
airfoil data. I first corrected the lift and drag coefficients for rotational stall delay using the Selig
and Eggars method for 0° to 90° angles of attack. I then corrected the drag coefficients using the
Viterna method for 0° to 90° angles of attack a ssuming an aspect ratio of 17. Finally, I estimated
the Beddoes-Leishman dynamic-stall hysteresis parameters. I made no corrections to the DOWEC-supplied pitching-moment coefficients. The resulting three-dimensionally corrected airfoil-data coefficients are illustrated graphically in Figure 3-1 through Figure 3-6 . The
numerical values are documented in the Aero Dyn airfoil-data input files that make up Appendix
B.

9 C. Lindenburg of the Energy Research Center of the Netherlands (ECN) provided numerical values for these
coefficients.
51

-1.5-1.0-0.50.00.51.01.52.02.5
-180 -150 -120 -90 -60 -30 0 30 60 90 120 150 180
Angle of Attack, °Lift
Drag
Pitching-Moment

Figure 3-1. Corrected coefficients of the DU40 airfoil

-1.5-1.0-0.50.00.51.01.52.02.5
-180 -150 -120 -90 -60 -30 0 30 60 90 120 150 180
Angle of Attack, °Lift
Drag
Pitching-Moment

Figure 3-2. Corrected coefficients of the DU35 airfoil
52

-1.5-1.0-0.50.00.51.01.52.02.5
-180 -150 -120 -90 -60 -30 0 30 60 90 120 150 180
Angle of Attack, °Lift
Drag
Pitching-Moment

Figure 3-3. Corrected coefficients of the DU30 airfoil

-1.5-1.0-0.50.00.51.01.52.02.5
-180 -150 -120 -90 -60 -30 0 30 60 90 120 150 180
Angle of Attack, °Lift
Drag
Pitching-Moment

Figure 3-4. Corrected coefficients of the DU25 airfoil

53

-1.5-1.0-0.50.00.51.01.52.02.5
-180 -150 -120 -90 -60 -30 0 30 60 90 120 150 180
Angle of Attack, °Lift
Drag
Pitching-Moment

Figure 3-5. Corrected coefficients of the DU21 airfoil

-1.5-1.0-0.50.00.51.01.52.02.5
-180 -150 -120 -90 -60 -30 0 30 60 90 120 150 180
Angle of Attack, °Lift
Drag
Pitching-Moment

Figure 3-6. Corrected coefficients of the NACA64 airfoil

54

3.1.3 Hub and Nacelle Properties
As indicated in Table 3-1 , I located the hub of the NREL 5-MW baseline wind turbine 5 m
upwind of the tower centerline at an elevation of 90 m above the ground when the system is
undeflected. I also specified the same vertical distance from the tower top to the hub height used
by the DOWEC study—that is, 2.4 m (as specified in Table 6 on page 26 of Ref. [ 51]).
Consequently, the elevation of the yaw bearing above ground or MSL is 87.6 m. With a shaft tilt
of 5°, this made the distance directed along th e shaft from the hub center to the yaw axis 5.01910
m and the vertical distance along the yaw axis from the tower top to the shaft 1.96256 m. The
distance directed along the shaft from the hub cente r to the main bearing was taken to be 1.912 m
(from Table 6 on page 26 of Ref. [ 51]).
I specified the hub mass to be 56,780 kg like in the REpower 5M, and I located its CM at the hub center. The hub inertia about the shaft, taken to be 115,926 kg
•m2, was found by assuming that
the hub casting is a thin spherical shell with a radius of 1.75 m (this is 0.25 m longer than the actual hub radius because the nacelle height of the DOWEC turbine was 3.5 m, based on the data
in Table 6 on page 26 of Ref. [ 51]).
I specified the nacelle mass to be 240,000 kg like in the REpower 5M and I located its CM 1.9 m
downwind of the yaw axis like in the DOWEC turbine (from Table 7 on page 27 of Ref. [ 51])
and 1.75 m above the yaw bearing, which was half the height of the DOWEC turbine’s nacelle (from Table 6 on page 26 of Ref. [ 51]). The nacelle inertia about the yaw axis was taken to be
2,607,890 kg
•m2. I chose this to be equivalent to th e DOWEC turbine’s nacelle inertia about its
nacelle CM, but translated to the yaw axis using the parallel-axis theorem with the nacelle mass and downwind distance to the nacelle CM.
I took the nacelle-yaw actuator to have a natural frequency of 3 Hz, which is roughly equivalent
to the highest full-system natural frequency in the FAST model (see Section 3.1.8), and a
damping ratio of 2% critical. This resulted in an equivalent nacelle-yaw-actuator linear-spring
constant of 9,028,320,000 N
•m/rad and an equivalent nace lle-yaw-actuator linear-damping
constant of 19,160,000 N •m/(rad/s). The nominal nacelle-yaw rate was chosen to be the same as
that for the DOWEC 6-MW turbine, or 0.3°/s (from page 27 of Ref. [ 51]).
Table 3-5 summarizes the nacelle and hub proper ties discussed in this section.
Table 3-5. Nacelle and Hub Properties
Elevation of Yaw Bearing above Ground 87.6 m
Vertical Distance along Yaw Axis from Yaw Bearing to Shaft 1.96256 m
Distance along Shaft from Hub Center to Yaw Axis 5.01910 m
Distance along Shaft from Hub Center to Main Bearing 1.912 m
Hub Mass 56,780 kg
Hub Inertia about Low-Speed Shaft 115,926 kg•m2
Nacelle Mass 240,000 kg
Nacelle Inertia about Yaw Axis 2,607,890 kg•m2
Nacelle CM Location Downwind of Yaw Axis 1.9 m
Nacelle CM Location above Yaw Bearing 1.75 m
Equivalent Nacelle-Yaw-Actuator Linear-Spring Constant 9,028,320,000 N•m/rad
Equivalent Nacelle-Yaw-Actuator Linear-Damping Constant 19,160,000 N•m/(rad/s)
Nominal Nacelle-Yaw Rate 0.3 ș/s
55

3.1.4 Drivetrain Properties
I specified the NREL 5-MW baseline wind turbine to have the same rated rotor speed (12.1 rpm),
rated generator speed (1173.7 rpm), and gearbox ratio (97:1) as the REpower 5M machine. The
gearbox was assumed be a typical multiple-stage gearbox but with no frictional losses—a
requirement of the preprocessor functionality in FAST for creating ADAMS models [ 39]. The
electrical efficiency of the generator was taken to be 94.4%. This was chosen to be roughly the
same as the total mechanical-to-electrical conversion loss used by the DOWEC turbine at rated power—that is, the DOWEC turbine had about 0.35 MW of power loss at about 6.25 MW of
aerodynamic power (from Figure 15, page 24 of Ref. [ 51]). The generator inertia about the high-
speed shaft was taken to be 534.116 kg
•m2, which is the same equivalent low-speed shaft
generator inertia used in the DOWEC study (i.e., 5,025,500 kg •m2 from page 36 of Ref. [ 51]).
The driveshaft was taken to have the same natural frequency as the RECOFF turbine model and a structural-damping ratio—associated with the free-free mode of a drivetrain composed of a rigid generator and rigid rotor—of 5% critical. Th is resulted in an equivalent driveshaft linear-
spring constant of 867,637,000 N
•m/rad and a linear-damping constant of 6,215,000 N •m/(rad/s).
The high-speed shaft brake was assumed to have the same ratio of maximum brake torque to maximum generator torque and the same time lag as used in the DOWEC study (from page 29 of
Ref. [ 51]). This resulted in a fully deployed high-speed shaft brake torque of 28,116.2 N
•m and
a time lag of 0.6 s. This time lag is the amount of time it takes for the brake to fully engage once
deployed. The FAST and ADAMS models employ a simple linear ramp from nothing to full
braking over the 0.6-s period.
Table 3-6 summarizes the drivetrain proper ties discussed in this section.
Table 3-6. Drivetrain Properties
Rated Rotor Speed 12.1 rpm
Rated Generator Speed 1173.7 rpm
Gearbox Ratio 97 :1
Electrical Generator Efficiency 94.4 %
Generator Inertia about High-Speed Shaft 534.116 kg•m2
Equivalent Drive-Shaft Torsional-Spring Constant 867,637,000 N•m/rad
Equivalent Drive-Shaft Torsional-Damping Constant 6,215,000 N•m/(rad/s)
Fully-Deployed High-Speed Shaft Brake Torque 28,116.2 N•m
High-Speed Shaft Brake Time Constant 0.6 s
3.1.5 Tower Properties
I based the distributed tower properties of th e NREL 5-MW baseline wind turbine on the base
diameter (6 m) and thickness (0.027 m), top diameter (3.87 m) and thickness (0.019 m), and
effective mechanical steel properties of the tower used in the DOWEC study (as given in Table 9
on page 31 of Ref. [ 51]). The Young’s modulus was taken to be 210 GPa, the shear modulus
was taken to be 80.8 GPa, and the effective de nsity of the steel was taken to be 8,500 kg/m3. The
density of 8,500 kg/m3 was meant to be an increase above steel’s typical value of 7,850 kg/m3 to
account for paint, bolts, welds, and flanges that ar e not accounted for in the tower thickness data.
The radius and thickness of the tower were assumed to be linearly tapered from the tower base to
56

tower top. Because the REpower 5M machine had a larger tower-top mass than the DOWEC
wind turbine, I scaled up the thickness of the tower relative to the values given earlier in this
paragraph to strengthen the tower. I chose an increase of 30% to ensure that the first fore-aft and side-to-side tower frequencies were placed between the one- and three-per-rev frequencies throughout the operational range of the wind turbine in a Campbell diagram. Table 3-7 gives the
resulting distributed tower properties.
Table 3-7. Distributed Tower Properties
Elevation HtFract TMassDen TwFAStif TwSSStif TwGJStif TwEAStif TwFAIner TwSSIner TwFAcgOf TwSScgOf
(m) (-) (kg/m) (N•m2)( N • m2)( N • m2) (N) (kg•m) (kg•m) (m) (m)
0.00 0.0 5590.87 614.34E+9 614.34E+9 472.75E+9 138.13E+9 24866.3 24866.3 0.0 0.0
8.76 0.1 5232.43 534.82E+9 534.82E+9 411.56E+9 129.27E+9 21647.5 21647.5 0.0 0.0
17.52 0.2 4885.76 463.27E+9 463.27E+9 356.50E+9 120.71E+9 18751.3 18751.3 0.0 0.0
26.28 0.3 4550.87 399.13E+9 399.13E+9 307.14E+9 112.43E+9 16155.3 16155.3 0.0 0.0
35.04 0.4 4227.75 341.88E+9 341.88E+9 263.09E+9 104.45E+9 13838.1 13838.1 0.0 0.0
43.80 0.5 3916.41 291.01E+9 291.01E+9 223.94E+9 96.76E+9 11779.0 11779.0 0.0 0.0
52.56 0.6 3616.83 246.03E+9 246.03E+9 189.32E+9 89.36E+9 9958.2 9958.2 0.0 0.0
61.32 0.7 3329.03 206.46E+9 206.46E+9 158.87E+9 82.25E+9 8356.6 8356.6 0.0 0.0
70.08 0.8 3053.01 171.85E+9 171.85E+9 132.24E+9 75.43E+9 6955.9 6955.9 0.0 0.0
78.84 0.9 2788.75 141.78E+9 141.78E+9 109.10E+9 68.90E+9 5738.6 5738.6 0.0 0.0
87.60 1.0 2536.27 115.82E+9 115.82E+9 89.13E+9 62.66E+9 4688.0 4688.0 0.0 0.0
The entries in the first column, “Elevation,” are the vertical locations along the tower centerline
relative to the tower base. “HtFract” is the fractional height along the tower centerline from the tower base (0.0) to the tower top (1.0). The rest of columns are similar to those described for the
distributed blade prope rties presented in Table 3-2 .
The resulting overall (integrated) tower mass is 347,460 kg and is centered at 38.234 m along the
tower centerline above the ground. This result follo ws directly from the overall tower height of
87.6 m.
I specified a structural-damping ratio of 1% criti cal in all modes of the isolated tower (without
the rotor-nacelle assembly mass present), which corresponds to the values used in the DOWEC
study (from page 21 of Ref. [ 51]).
Table 3-8 summarizes the undistributed tower properties discussed in this section.
Table 3-8. Undistributed Towe rProperties
Height above Ground 87.6 m
Overall (Integrated) Mass 347,460 kg
CM Location (w.r.t. Ground along Tower Centerline) 38.234 m
Structural-Damping Ratio (All Modes) 1 %
3.1.6 Baseline Control System Properties
For the NREL 5-MW baseline wind turbine, I chose a conventional variable-speed, variable blade-pitch-to-feather configuration. In such wind turbines, the conventional approach for controlling power-production operation relies on the design of two basic control systems: a generator-torque controller and a full-span roto r-collective blade-pitch controller. The two
control systems are designed to work independent ly, for the most part, in the below-rated and
above-rated wind-speed range, respectively. The goal of the generator-torque controller is to
57

maximize power capture below the rated operation point. The goal of the blade-pitch controller
is to regulate generator speed above the rated operation point.
I based the baseline control system for the NREL 5-MW wind turbine on this conventional
design approach. I did not establish add itional control actions for nonpower-production
operations, such as control actions for normal start-up sequences, normal shutdown sequences,
and safety and protection functions. Nor did I de velop control actions to regulate the nacelle-
yaw angle because all of the normal power-produ ction simulations I modeled were per the IEC
design standards [ 33,34]. The standards designate small nacelle-yaw errors for these simulations
(with the exception that the IEC extreme coherent gust with direction change [ECD] load case expects large yaw errors). The nacelle-yaw control system is generally neglected within aero-servo-elastic simulation because its response is sl ow enough that it does not generally contribute
to large extreme loads or fatigue damage.
I describe the development of my baseline control system next, including the control-
measurement filter (Section 3.1.6.1), the generator-torque controller (Section 3.1.6.2), the blade-
pitch controller (Section 3.1.6.3), and the blade-pitch actuator (Section 3.1.6.4). Section 3.1.6.5
shows how these systems are put together in the overall integrated control system.
3.1.6.1 Baseline Control-Measurement Filter
As is typical in utility-scale multimegawatt wind turbines, both the generator-torque and blade-
pitch controllers use the generator speed measurem ent as the sole feedback input. To mitigate
high-frequency excitation of the control systems, I filtered the generator speed measurement for both the torque and pitch controllers using a recursive, single-pole low-pass filter with exponential smoothing [ 89]. The discrete-time recursion (difference) equation for this filter is

[]()[][] yn 1 un yn 1 αα=−+ −, (3-1)
with
sc 2T feπα−= , (3-2)
where y is the filtered generator speed (output measurement), u is the unfiltered generator speed
(input), α is the low-pass filter coefficient, n is the discrete-time-step counter, Ts is the discrete
time step, and fc is the corner frequency.
By defining the filter state,
[][] xny n 1=−, (3-3a)
or
[][] xn1 y n+= , ( 3-3b)
one can derive a discrete-time state- space representation of this filter:
58

[][][]
[] [] []dd
ddxn1 A x n B u n
ynC x nD u n+= +
=+, (3-4)
where dAα= is the discrete-time state matrix, dB1α=− is the discrete- time input matrix,
dCα= is the discrete-time output state matrix, and dD1α=− is the discrete-time input
transmission matrix.
The state-space representation of Eq. (3-4) is useful for converting the filter into other forms,
such as transfer-function form or frequency-response form [ 91].
I set the corner frequency (the -3 dB point in Figure 3-7 ) of the low-pass filter to be roughly one-
quarter of the blade’s first edgewi se natural frequency (see Section 3.1.8) or 0.25 Hz. For a
discrete time step of 0.0125 s, th e frequency response of the resulting filter is shown in the Bode
plot of Figure 3-7. I chose the recursive, single-pole filter for its simplicity in implementation and effectiveness in
the time domain. The drawbacks to this filter are its gentle roll-off in the stop band (-6 dB/octave) and the magnitude and nonlinear ity of its phase la g in the pass band [ 89]. I
considered other linear low-pass filters, such as Butterworth, Chebyshev, Elliptic, and Bessel filters because of their inherent advantages relative to the chosen filter. Like the chosen filter, a Butterworth filter has a frequency response that is flat in the pass band, but the Butterworth filter
offers steeper roll-off in the stop band. Chebyshe v filters offer even steeper roll-off in the stop
band at the expense of equalized -ripple (equiripple) in the pass ba nd (Type 1) or stop band (Type
-18-15-12-9-6-30
0.01 0.10 1.00
Frequency, HzMagnitude, dB
-90-75-60-45-30-150
0.01 0.10 1.00
Frequency, HzPhase, ˚

Figure 3-7. Bode plot of generator speed low-pass filter frequency response
59

2), respectively. Elliptic filters offer the steepest roll-off of any linear filter, but have equiripple
in both the pass and stop bands. Bessel filters offe r the flattest group delay (linear phase lag) in
the pass band. I designed and tested examples of each of these other low-pass filter types, considering state-space representations of up to f ourth order (four states). None were found to
give superior performance in the overall system response, however, so they did not warrant the
added complexity of implementation.
3.1.6.2 Baseline Generator-Torque Controller
I computed the generator torque as a tabulated function of the filtered generator speed, incorporating five control regions: 1, 1½, 2, 2½, and 3. Region 1 is a control region before cut-in
wind speed, where the generator torque is zero and no power is extracted from the wind; instead,
the wind is used to accelerate the rotor for start-up . Region 2 is a control region for optimizing
power capture. Here, the generator torque is proportional to the square of the filtered generator speed to maintain a constant (optimal) tip-speed ratio. In Region 3, the generator power is held constant so that the generator torque is inve rsely proportional to the filtered generator speed.
Region 1½, a start-up region, is a linear transition between Regions 1 and 2. This region is used to place a lower limit on the generator speed to limit the wind turbine’s operational speed range. Region 2½ is a linear transition between Regions 2 and 3 with a torque slope corresponding to
the slope of an induction machine. Region 2½ is typically needed (as is the case for my 5-MW turbine) to limit tip speed (and hence noise emissions) at rated power.
I found the peak of the power coefficient as a function of the tip-speed ratio and blade-pitch
surface by running FAST with AeroDyn simula tions at a number of given rotor speeds and a
number of given rotor-collective blade-pitch angles at a fixed wind speed of 8 m/s. From these
simulations, I found that the peak power coeffici ent of 0.482 occured at a tip-speed ratio of 7.55
and a rotor-collective blade-pitch angle of 0.0 ˚. With the 97:1 gearbox ratio, this resulted in an
optimal constant of proportionality of 0.0255764 N
•m/rpm2 in the Region 2 control law. With
the rated generator speed of 1173.7 rpm, rate d electric power of 5 MW, and a generator
efficiency of 94.4%, the rated mechanical power is 5.296610 MW and the rated generator torque
is 43,093.55 N •m. I defined Region 1½ to span the ra nge of generator speeds between 670 rpm
and 30% above this value (or 871 rpm). The minimum generator speed of 670 rpm corresponds
to the minimum rotor speed of 6.9 rpm used by the actual REpower 5M machine [ 81]. I took the
transitional generator speed between Regions 2½ a nd 3 to be 99% of the rated generator speed,
or 1,161.963 rpm. The generator-slip percentage in Region 2½ was taken to be 10%, in
accordance with the value used in the DOWEC study (see page 24 of Ref. [ 51]). Figure 3-8
shows the resulting generator-torque versus generator speed response curve.
Because of the high intrinsic structural damping of the drivetrain, I did not need to incorporate a
control loop for damping drivetrain torsiona l vibration in my baseline generator-torque
controller. I did, however, place a conditional statement on the generator-torque controller so that the torque
would be computed as if it were in Region 3—r egardless of the generator speed—whenever the
previous blade-pitch-angle command was 1ș or gr eater. This results in improved output power
quality (fewer dips below rated) at the expense of short-term overloading of the generator and
the gearbox. To avoid this excessive overloading , I saturated the torque to a maximum of 10%
60

010,00020,00030,00040,00050,000
0 200 400 600 800 1,000 1,200 1,400
Generator Speed, rpmGenerator Torque, N•mOptimal
Variable-Speed ControllerRegion 1 1½ 2 2½ ► 3

Figure 3-8. Torque-versus-speed response of the variable-speed controller
above rated, or 47,402.91 N •m. I also imposed a torque rate limit of 15,000 N •m/s. In Region 3,
the blade-pitch control system takes over.
3.1.6.3 Baseline Blade-Pitch Controller
In Region 3, I computed the full-span rotor-collective blade-pitch-angle commands using gain-
scheduled proportional-integral (PI) control on the speed error between the filtered generator speed and the rated generator speed (1173.7 rpm).
I designed the blade-pitch control system using a simple single-DOF model of the wind turbine.
Because the goal of the blade-pitch control system is to regulate the generator speed, this DOF is the angular rotation of the shaft. To compute the required control gains, it is beneficial to examine the equation of motion of this single-DOF system. From a simple free-body diagram of
the drivetrain, the equation of motion is

() ()2
Aero Gear Gen Rotor Gear Gen 0 DrivetraindTN T I N I IdtΩΔΩ ΔΩ −= + + = &, (3-5)
where TAero is the low-speed shaft aerodynamic torque, TGen is the high-speed shaft generator
torque, NGear is the high-speed to low-speed gearbox ratio, IDrivetrain is the drivetrain inertia cast to
the low-speed shaft, IRotor is the rotor inertia, IGen is the generator inertia relative to the high-
speed shaft, is the rated low-speed shaft rotational speed, 0Ω ΔΩ is the small perturbation of
low-speed shaft rotational speed about the rated speed, ΔΩ& is the low-speed shaft rotational
acceleration, and t is the simulation time.
61

Because the generator-torque controller maintains constant generator power in Region 3, the
generator torque in Region 3 is inversel y proportional to the generator speed (see Figure 3-8 ), or
()0
Gen Gear
GearPTNNΩΩ= , (3-6)
where P0 is the rated mechanical power and Ω is the low-speed shaft rotational speed.
Similarly, assuming negligible variation of aerodynamic torque with rotor speed, the aerodynamic torque in Region 3 is

()()0
Aero
0P,TθΩθΩ= , (3-7)
where P is the mechanical power and θ is the full-span rotor-collective blade-pitch angle.
Using a first-order Taylor series expansion of Eqs. (3-6) and (3-7) , one can see that
00
Gen 2
Gear 0 Gear 0PPTNNΔΩΩΩ≈− (3-8)
and
0
Aero
00P 1PT ΔθΩΩθ∂⎛⎞≈+ ⎜⎟∂⎝⎠, (3-9)
where is a small perturbation of the blade-pitc h angles about their operating point. With
proportional-integral-derivative (PID) control, this is related to the rotor-speed perturbations by Δθ
, (3-10) t
P Gear I Gear D Gear
0KN K N d t KNΔθ ΔΩ ΔΩ ΔΩ =+ + ∫&
where KP, KI, and KD are the blade-pitch controller proportional, integral, and derivative gains,
respectively.
By setting ϕΔΩ=& , combining the above expressions, a nd simplifying, the equation of motion
for the rotor-speed error becomes
0
Drivetrain Gear D Gear P Gear I 2
00 0 0
MC KP 1P 1P 1PI NK NK NK 0
ϕϕ ϕϕϕΩθ Ωθ Ω Ωθ⎡⎤ ⎡ ⎤ ⎡ ∂∂ ∂⎛⎞ ⎛⎞ ⎛⎞+− + − − + − =⎢⎥ ⎢ ⎥ ⎢ ⎜⎟ ⎜⎟ ⎜⎟∂∂ ∂⎝⎠ ⎝⎠ ⎝⎠ ⎣⎦ ⎣ ⎦ ⎣&& &
144444244444 3 14444 4244443 14442444 3ϕ⎤
⎥⎦. (3-11)
One can see that the idealized PID-controlled rotor-speed error will respond as a second-order
system with the natural frequency, ωφn, and damping ratio, ζφ, equal to
62

nK
Mϕ
ϕ
ϕω= (3-12)
and

nCC
2M 2K Mϕ
ϕϕ
ϕϕ ϕϕζω== . (3-13)
In an active pitch-to-feather wind turbine, the sensitivity of aerodynamic power to the rotor-
collective blade-pitch angle, Pθ∂∂ , is negative in Region 3. With positive control gains, then,
the derivative term acts to increase the effectiv e inertia of the drivetra in, the proportional term
adds damping, and the integral term adds restor ing. Also, because the generator torque drops
with increasing speed error (to maintain constant power) in Region 3, one can see that the
generator-torque controller introduces a negative damping in the speed error response [indicated
by the 2
00PΩ− term in Eq. (3-11) ]. This negative damping must be compensated by the
proportional term in the blade-pitch controller.
In the design of the blade-pitch controller, Ref. [ 29] recommends neglecting the derivative gain,
ignoring the negative damping from the generator-t orque controller, and aiming for the response
characteristics given by ωφn = 0.6 rad/s and ζφ = 0.6 to 0.7. This specification leads to direct
expressions for choosing appropriate PI gains once the sensitivity of aerodynamic power to
rotor-collective blade pitch, Pθ∂∂ , is known:
Drivetrain 0 n
P
Gear2IKPNϕϕΩζω
θ=∂⎛⎞−⎜⎟∂⎝⎠ (3-14)
and
2
Drivetrain 0 n
I
GearIKPNϕΩω
θ=∂⎛⎞−⎜⎟∂⎝⎠. (3-15)
The blade-pitch sensitivity, Pθ∂∂ , is an aerodynamic property of the rotor that depends on the
wind speed, rotor speed, and blade-pitch angle. I calculated it for the NREL offshore 5-MW
baseline wind turbine by performing a linearization analysis in FAST with AeroDyn at a number
of given, steady, and uniform wind speeds; at the rated rotor speed (0Ω = 12.1 rpm); and at the
corresponding blade-pitch angles that produce the rated mechanical power ( P0 = 5.296610 MW).
The linearization analysis involves perturbing th e rotor-collective blade-pitch angle at each
operating point and measuring the resulting variation in aerodynamic power. Within FAST, the
partial derivative is computed using the central -difference-perturbation numerical technique. I
created a slightly customized copy of FAST with AeroDyn so that the linearization procedure would invoke the frozen-wake assumption, in which the induced wake velocities are held
63

constant while the blade-pitch angle is perturbed. This gives a more accurate linearization for
heavily loaded rotors (i.e., for operating points in Region 3 closest to rated). Table 3-9 presents
the results.
Table 3-9. Sensitivity of Aerodynamic Power to Blade
Pitch in Region 3
Wind Speed Rotor Speed Pitch Angle ∂P/∂θ
(m/s) (rpm) (ș) (watt/rad)
11.4 – Rated 12.1 0.00 -28.24E+6
12.0 12.1 3.83 -43.73E+6
13.0 12.1 6.60 -51.66E+6
14.0 12.1 8.70 -58.44E+6
15.0 12.1 10.45 -64.44E+6
16.0 12.1 12.06 -70.46E+6
17.0 12.1 13.54 -76.53E+6
18.0 12.1 14.92 -83.94E+6
19.0 12.1 16.23 -90.67E+6
20.0 12.1 17.47 -94.71E+6
21.0 12.1 18.70 -99.04E+6
22.0 12.1 19.94 -105.90E+6
23.0 12.1 21.18 -114.30E+6
24.0 12.1 22.35 -120.20E+6
25.0 12.1 23.47 -125.30E+6
As Table 3-9 shows, the sensitivity of aerodynamic power to rotor-collective blade pitch varies
considerably over Region 3, so constant PI gains are not adequate for effective speed control.
The pitch sensitivity, though, varies nearly linearly with blade-pitch angle:
()
(
KP0P0θθθθθθ θ∂⎡⎤=⎢⎥∂∂)P⎡ ⎤ ∂=+⎢⎥ =⎢ ⎥∂∂ ⎣ ⎦ ⎢⎥
⎣⎦ (3-16a)
or

()
K11
P P01θθθθ θ=∂ ⎛⎞ ∂=+⎜⎟∂∂ ⎝⎠, ( 3-16b)
where (P0θθ∂=∂) is the pitch sensitivity at rated and θK is the blade-pitch angle at which the
pitch sensitivity has doubled from its value at the rated operating point; that is,
() (KPP2 θθ θθθ∂∂)0 ===∂∂. (3-17)
64

On the right-hand side of Eq. (3-16a) , the first and second terms in square brackets represent the
slope and intercept of the best-fit line, respectively. I computed this regression for the NREL 5-
MW baseline wind turbine and present the results in Figure 3-9.
-140E+6-120E+6-100E+6-80E+6-60E+6-40E+6-20E+6000E+0
0 5 10 15 20
Rotor-Collective Blade-Pitch Angle, șPitch Sensitivity, watt/radOriginal Data
Best-Fit Line0E+6
∂P/∂θ(θ=0ș) = -25.52E+6 watt/rad
θk = 6.302336ș

Figure 3-9. Best-fit line of pitch sensitivity in Region 3
The linear relation between pitch sensitivity and blade-pitch angle presents a simple technique
for implementing gain scheduling base d on blade-pitch angle; that is,
()
()()Drivetrain 0 n
P
Gear2IKPN0ϕϕΩζωGK θ θ
θθ=∂⎡⎤−=⎢⎥∂⎣⎦ (3-18)
and
()
()()2
Drivetrain 0 n
I
GearIKPN0ϕΩωGK θ θ
θθ=∂⎡⎤−=⎢⎥∂⎣⎦, (3-19)
where ()GKθ is the dimensionless gain-correction factor (from Ref. [ 29]), which is dependent
on the blade-pitch angle:
65

()
K1GK
1θθ
θ=
+. (3-20)
In my implementation of the gain-scheduled PI blade-pitch controller, I used the blade-pitch
angle from the previous controller time step to calculate the gain-correction factor at the next
time step.
Using the properties for the baseline wind turbin e and the recommended response characteristics
from Ref. [ 29], the resulting gains are KP(θ = 0ș) = 0.01882681 s, KI(θ = 0ș) = 0.008068634, and
KD = 0.0 s2. Figure 3-10 presents the gains at other blad e-pitch angles, along with the gain-
correction factor. I used the upper limit of the recommended damping ratio range, ζφ = 0.7, to
compensate for neglecting negative damping from the generator-torque controller in the
determination of KP.
Unfortunately, the simple gain-scheduling law derived in this section for the proportional and integral gains cannot retain c onsistent response characteristic s (i.e., constant values of
ωφn and
ζφ) across all of Region 3 when applied to the deriva tive gain. I, nevertheless, considered adding
a derivative term by selecting a nd testing a range of gains, but none were found to give better
performance in the overall system response. Inst ead, the baseline control system uses the gains
derived previously in this sec tion (without the derivative term).
I set the blade-pitch rate limit to 8°/s in absolute value. This is speculated to be the blade-pitch
rate limit of conven tional 5-MW machines based on General Electric (GE) Wind’s long-blade
test program. I also set the minimum and maximum blade-pitch settings to 0° and 90°,
0.00.20.40.60.81.0
0 5 10 15 20
Rotor-Collective Blade-Pitch Angle, șGain-Correction Factor
0.0000.0050.0100.0150.0200.025
Proportional and Integral GainsGain-Correction Factor, –
Proportional Gain, s
Integral Gain, –

Figure 3-10. Baseline blade-pitch control system gain-scheduling law
66

respectively. The lower limit is the set blade pitch for maximizing power in Region 2, as
described in Section 3.1.6.2. The upper limit is very close to the fully feathered blade pitch for
neutral torque. I saturated the integral term in the PI controller between these limits to ensure a fast response in the transitions between Regions 2 and 3.
3.1.6.4 Baseline Blade-Pitch Actuator
Because of limitations in the FAST code, the FAST model does not include any blade-pitch
actuator dynamic effects. Blade-pitch actuator dynamics are, however, needed in ADAMS. To
enable successful comparisons between the FA ST and ADAMS response predictions I present in
subsequent chapters, I found it beneficial to reduc e the effect of the blad e-pitch actuator response
in ADAMS. Consequently, I designed the blade-pitch actuator in the ADAMS model with a very high natural frequency of 30 Hz, which is higher than the highest full-system natural frequency in the FAST model (see Section 3.1.8), and a damping ratio of 2% critical. This
resulted in an equivalent blade-pitch actuator linear-spring constant of 971,350,000 N
•m/rad and
an equivalent blade-pitch actuato r linear-damping constant of 206,000 N •m/(rad/s).
3.1.6.5 Summary of Baseline Control System Properties
I implemented the NREL offshore 5-MW wind turbine’s baseline control system as an external dynamic link library (DLL) in the style of Garrad Hassan’s
BLADED wind turbine software
package [ 5]. Appendix C contains the source code for this DLL, and Figure 3-11 presents a

Figure 3-11. Flowchart of the baseline control system
67

flowchart of the overall integrated control system calculations. Table 3-10 summarizes the
baseline generator-torque and blade-pitch control proper ties I discussed earlier in this section.
Table 3-10. Baseline Control System Properties
Corner Frequency of Generator-Speed Low-Pass Filter 0.25 Hz
Peak Power Coefficient 0.482
Tip-Speed Ratio at Peak Power Coefficient 7.55
Rotor-Collective Blade-Pitch Angle at Peak Power Coefficient 0.0 ș
Generator-Torque Constant in Region 2 0.0255764 N•m/rpm2
Rated Mechanical Power 5.296610 MW
Rated Generator Torque 43,093.55 N•m
Transitional Generator Speed between Regions 1 and 1½ 670 rpm
Transitional Generator Speed between Regions 1½ and 2 871 rpm
Transitional Generator Speed between Regions 2½ and 3 1,161.963 rpm
Generator Slip Percentage in Region 2½ 10 %
Minimum Blade Pitch for Ensuring Region 3 Torque 1 ș
Maximum Generator Torque 47,402.91 N•m
Maximum Generator Torque Rate 15,000 N•m/s
Proportional Gain at Minimum Blade-Pitch Setting 0.01882681 s
Integral Gain at Minimum Blade-Pitch Setting 0.008068634
Blade-Pitch Angle at which the Rotor Power Has Doubled 6.302336 ș
Minimum Blade-Pitch Setting 0 ș
Maximum Blade-Pitch Setting 90 ș
Maximum Absolute Blade Pitch Rate 8 ș/s
Equivalent Blade-Pitch-Actuator Linear-Spring Constant 971,350,000 N•m/rad
Equivalent Blade-Pitch-Actuator Linear-Damping Constant 206,000 N•m/rad/s
3.1.7 FAST with AeroDyn and ADAMS with AeroDyn Models
Using the turbine properties described previously in this section, I put together models of the
NREL offshore 5-MW baseline wind turbine within FAST [ 39] with AeroDyn [ 55,67]. The
input files for these models are given in Appendix A and Appendix B , for version (v) 6.10a-jmj
of FAST and v12.60i-pjm of AeroDyn, respectively. I then generated the higher fidelity
ADAMS models through the preprocessor fu nctionality built into the FAST code.
The input files in Appendix A are for the FAST model of the NREL offshore 5-MW baseline
wind turbine mounted on the ITI Energy barge. Th e input files for other versions of the model,
such as that for the equivalent land-based ve rsion, required only a few minor changes. These
include changes to input parame ters “PtfmModel” and “PtfmFile,” which identify the type and
properties of the support platform, and modifications to the prescribed mode shapes in the tower
input file, “TwrFile.”
Although most of the input-parameter specifications in Appendix A and Appendix B are self-
explanatory, the specifications of the prescribed mode shapes needed by FAST to characterize
the flexibility of the blades and tower (see Section 2.1) deserve a special explanation. The
required mode shapes depend on the member’s boundary conditions. For the blade modes, I
used v2.22 of the Modes program [ 6] to derive the equivalent pol ynomial representations of the
blade mode shapes needed by FAST. The Modes program calculates the mode shapes of rotating
blades, assuming that a blade mode shape is unaffected by its coupling with other system modes
of motion. This is a common assumption in wind turbine analysis. For the tower modes,
68

however, there is a great deal of coupling with the rotor motions, and in floating systems, there is
coupling with the platform motions as well. Taking these factors into account, I used the
linearization functionality of the full-system ADAMS model to obtain the tower modes for both the floating systems and their equivalent land-based counterparts. In other words, I built an ADAMS model of the coupled wind turbine and s upport platform system, enabled all system
DOFs, and linearized the model. Then I passed a best-fit polynomial through the resulting tower mode shapes to get the equivalent polynomial re presentations of the tower mode shapes needed
by FAST.
Not including platform motions, the FAST model of the land-based version of the NREL 5-MW
baseline wind turbine incorporates 16 DOFs as follows:
• Two flapwise and one edgewise bending-mode DOFs for each of the three blades
• One variable-generator speed DOF and one driveshaft torsional DOF
• One nacelle-yaw-actuator DOF
• Two fore-aft and two side-to-side bending-mode DOFs in the tower.
Not including platform motion, the higher fide lity ADAMS model of the land-based version of
the wind turbine incorporates 378 DOFs as follows:
• One hundred and two DOFs in each of the thr ee blades, including fl apwise and edgewise
shear and bending, torsion, and extension DOFs
• One blade-pitch actuator DOF in each of the three blades
• One variable-generator speed DOF and one driveshaft torsional DOF
• One nacelle-yaw actuator DOF
• Sixty-six DOFs in the tower, including fore -aft and side-to-side shear and bending,
torsion, and extension DOFs.
The support platform motions in the sea-base d versions of the NREL 5-MW baseline wind
turbine add six DOFs per model.
I specified a constant time step of 0.0125 s in FAST’s fixed-step-size time-integration scheme
and a maximum step size of 0.0125 s in ADAMS’ variable-step-size time integrator. I had
AeroDyn perform aerodynamic calculations ever y other structural time step (i.e., 0.025 s) to
ensure that there were at least 200-azimuth-step computations per revolution at 12 rpm. Data
were output at 20 Hz or every fourth structural time step. I made these time steps as large as
possible to ensure numerical stability and suitable output resolution across a range of operating conditions.
3.1.8 Full-System Natural Frequencie s and Steady-State Behavior
Up to now in this section, I have summarized the specifications of NREL’s 5-MW baseline wind
turbine. To provide a cursory overview of the overall system behavior of the equivalent land-
based turbine, I calculated the full-system na tural frequencies and the steady-state response of
the system as a function of wind speed.
69

I obtained the full-system natural frequencie s with both the FAST model and the ADAMS
model. In FAST, I calculated the natural fre quencies by performing an eigenanalysis on the
first-order state matrix created from a linearization analysis. In ADAMS, I obtained the
frequencies by invoking a “LINEAR/EIGENSOL” command, which linearizes the complete ADAMS model and computes eigendata. To avoid the rigid-body drivetrain mode, the analyses
considered the wind turbine in a stationary condi tion with the high-speed shaft brake engaged.
The blades were pitched to their minimum set poi nt (0ș), but aerodynamic damping was ignored.
Table 3-11 lists results for the first 13 full-system natural frequencies.
Table 3-11. Full-System Natural Frequencies in Hertz
Mode Description FAST ADAMS
1 1st Tower Fore-Aft 0.3240 0.3195
2 1st Tower Side-to-Side 0.3120 0.3164
3 1st Drivetrain Torsion 0.6205 0.6094
4 1st Blade Asymmetric Flapwise Yaw 0.6664 0.6296
5 1st Blade Asymmetric Flapwise Pitch 0.6675 0.66866 1st Blade Collective Flap 0.6993 0.7019
7 1st Blade Asymmetric Edgewise Pitch 1.0793 1.07408 1st Blade Asymmetric Edgewise Yaw 1.0898 1.08779 2nd Blade Asymmetric Flapwise Yaw 1.9337 1.650710 2nd Blade Asymmetric Flapwise Pitch 1.9223 1.855811 2nd Blade Collective Flap 2.0205 1.9601
12 2nd Tower Fore-Aft 2.9003 2.8590
13 2nd Tower Side-to-Side 2.9361 2.9408

The agreement between FAST and ADAMS is quite good. The biggest differences exist in the
predictions of the blades’ second asymmetric flapwise yaw and pitch modes. By “yaw” and
“pitch” I mean that these blade asymmetric modes couple with the na celle-yaw and nacelle-
pitching motions, respectively. Because of the offsets of the blade section CM from the pitch
axis, higher-order modes, and tower-torsion DO Fs—which are available in ADAMS, but not in
FAST—ADAMS predicts lower natural frequen cies in these modes than FAST does.
Bir and I have published [ 2] a much more exhaustive eigenanalysis for the NREL 5-MW
baseline wind turbine. The referenced public ation documents the natural frequencies and
damping ratios of the land- and sea-based versions of the 5-MW turbine across a range of operating conditions.
I obtained the steady-state response of the land-ba sed 5-MW baseline wind turbine by running a
series of FAST with AeroDyn simulations at a number of given, steady, and uniform wind
speeds. The simulations lengths were long enough to ensure that all transient behavior had died
out; I then recorded the steady-state output values. I ran the simulations using the BEM wake
option of AeroDyn and with all available and relevant land-based DOFs enabled. Figure 3-12
shows the results for several output para meters, which are defined as follows:
• “GenSpeed” represents the rotational speed of the generator (high-speed shaft).
• “RotPwr” and “GenPwr” represent the mechanical power within the rotor and the electrical output of the generator, respectively.
70

01,0002,0003,0004,0005,0006,000
3456789 1 0 1 1 1 2 1 3 1 4 1 5 1 6 1 7 1 8 1 9 2 0 2 1 2 2 2 3 2 4 2 5
Wind Speed, m/sGenSpeed, rpm
RotPwr, kW
GenPwr, kW
RotThrust, kN
RotTorq, kN·mRegion 1½ 2 2½ 3

05101520253035404550
3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
Wind Speed, m/sRotSpeed, rpm
BlPitch1, ș
GenTq, kN·m
TSR, -Region 1½ 2 2½ 3

-2-10123456
3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
Wind Speed, m/sOoPDefl1, m
IPDefl1, m
TTDspFA, m
TTDspSS, mRegion 1½ 2 2½ 3

Figure 3-12. Steady-state responses as a function of wind speed
71

• “RotThrust” represents the rotor thrust.
• “RotTorq” represents the mechanical torque in the low-speed shaft.
• “RotSpeed” represents the rotational speed of the rotor (low-speed shaft).
• “BlPitch1” represents the pitch angle of Blade 1.
• “GenTq” represents the electrical torque of the generator.
• “TSR” represents the tip-speed ratio.
• “OoPDefl1” and “IPDefl1” represent the out-o f-plane and in-plane tip deflections of
Blade 1 relative to the undeflected blade-pitch axis.
• “TTDspFA” and “TTDspSS” represent the fore -aft and side-to-side deflection of the
tower top relative to the centerline of the undeflected tower.
As planned, the generator and rotor speeds increase linearly with wind speed in Region 2 to
maintain constant tip-speed ra tio and optimal wind-power conversion efficiency. Similarly, the
generator and rotor powers and generator and ro tor torques increase dramatically with wind
speed in Region 2, increasing cubically and quadratically, respectively. Above rated, the generator and rotor powers are held constant by regulating to a fixed speed with active blade-pitch control. The out-of-plane tip deflection of the reference blade (Blade 1) reaches a
maximum at the rated operating poi nt before dropping again. This response characteristic is the
result of the peak in rotor thrust at rated. Th is peak is typical of variable generator speed
variable blade-pitch-to-feather wind turbines because of the transition that occurs in the control system at rated between the active generator-tor que and the active blade-pitch control regions.
This peak in response is also visible, though le ss pronounced, in the in-plane tip deflection of the
reference blade and the towe r-top fore-aft displacement.
Start-up transient behavior is an artifact of the computational analysis. To mitigate this behavior, I used the steady-state values of the ro tor speed and blade-pitch angles found in Figure 3-12 as
initial conditions in many of the simulations presented in subsequent chapters.
3.2 ITI Energy Barge
For some of the simulation code ve rification exercises presented in Chapter 4 and for the sea-
based loads analysis presented in Chapter 5 and Chapter 6 , I modeled the NREL 5-MW baseline
wind turbine mounted on a floating barge from ITI Energy. I used a preliminary barge concept
developed by W. Vijfhuizen under the direction of Professor N. Barltrop of the Department of
Naval Architecture and Marine Engineering ( NAME) at the Universities of Glasgow and
Strathclyde
1 through a contract with ITI Energy. Not only is the barge intended to support the 5-
MW wind turbine, but it is also a platform for an OWC wave-power device. To ensure that the
simplest possible manufacturing techniques can be used in its fabrication, the barge is square and the wave energy is extracted from a square moon pool located at the center of the barge, which
allows the OWC to be installed within the wind turbine’s tower. The barge is ballasted with
seawater to achieve a reasonable draft, which is not so shallow that it is susceptible to incessant

1 Web site: http://www.na-me.ac.uk/
72

wave slamming. To prevent it from drifting, the platform is moored by a system of eight
catenary lines. Two of these lines emanate from each corner of the bottom of the barge such that
they would be 45° apart at the corner.
I provide some details of the ITI Energy barge and mooring system in Table 3-12 and illustrate
the concept with an image generated using ADAMS in Figure 3-13. The concept is documented
in much greater detail in Ref. [ 98].2 Appendix D contains the FAST platform input file, which
includes the input parameters related to the support platform, HydroDyn, and the mooring
system; the WAMIT input files; and a portion of the WAMIT output files (some of the data are removed to save space). Additi onally, some of the WAMIT input and output data are plotted in
Chapter 4 .
The capabilities of my aero-hydro-servo-elastic simulation tools do not permit me to model an OWC wave-power device or its associated poten tial for energy extraction. Instead, I modeled
the hydrodynamics of the barge by assuming th at the moon pool was covered by a fixed plate
located just below the free surface. Section 4.1.2 explains this assumption in more detail.

2 Note that some of the properties given in disagree with the data published in Ref. [98] because I used
an updated design. For example, the published freeboard of 4 m in Ref. [98] was increased to 6 m after wave tank
testing at NAME demonstrated that more freeboard would be beneficial to the system’s response. This changed the CM location and inertias slightly. In addition, Ref. [ ] used a simple linearized representation of the mooring
system. Professor N. Barltrop developed the more deta iled mooring system documented in after Ref.
[98] was published. Table 3-12
Table 3-12Table 3-12. Summary of ITI Energy Barge P
roperties
Size (W×L×H) 40 m × 40 m × 10 m
Moon pool (W×L×H) 10 m × 10 m × 10 m
Draft, Freeboard 4 m, 6 m
Water Displacement 6,000 m3
Mass, Including Ballast 5,452,000 kg
CM Location below SWL 0.281768 m
Roll Inertia about CM 726,900,000 kg•m2
Pitch Inertia about CM 726,900,000 kg•m2
Yaw Inertia about CM 1,453,900,000 kg•m2
Anchor (Water) Depth 150 m
Separation between Opposing Anchors 773.8 m
Unstretched Line Length 473.3 m
Neutral Line Length Resting on Seabed 250 m
Line Diameter 0.0809 m
Line Mass Density 130.4 kg/m
Line Extensional Stiffness 589,000,000 N
98
73

Figure 3-13. Illustration of the 5-MW wind
turbine on the ITI Energy barge
3.3 MIT / NREL Barge
Under the direction of Professor P. D. Scla vounos of MIT, E. N. Wayman also developed
preliminary concepts of several floating platforms for the NREL offshore 5-MW baseline wind
turbine. One of her designs was named the MIT / NREL SDB. I also mounted the 5-MW baseline wind turbine on this floating platform for some of the simulation code verification exercises presented in Chapter 4 . (I did not, however, carry out a comprehensive loads analysis
for this concept.) The MIT / NREL SDB is a cylindrical barge and has a spread-mooring system with four pairs of taut lines that radiate outward. I list some of the barge data in and provide the FAST platform input file, the WAMIT input files, and a portion of the WAMIT output files in Appendix E . This concept is documented in much greater detail in Refs. [ 100] and [ 101].
Table 3-13. Summary of MIT / NREL Barge Properties
Diameter, Height 36 m, 9.5 m
Draft, Freeboard 5 m, 4.5 m
5,089 m3 Water Displacement
Mass, Including Ballast 4,519,150 kg
CM Location below SWL 3.88238 m
390,147,000 kg•m2 Roll Iner tia about CM
390,147,000 kg•m2 Pitch Inertia about CM
750,866,000 kg•m2 Yaw Inertia about CM
Anchor (Water) Depth 200 m
Separation between Opposing Anchors 436 m
Unstretched Line Length 279.3 m
Neutral Line Length Resting on Seabed 0 m
Line Diameter 0.127 m
Line Mass Density 116.0 kg/m
Line Extensional Stiffness 1,500,000,000 N
74

3.4 Reference-Site Data
The IEC 61400–3 design standard [ 34] requires that a loads analys is be based on site-specific
external conditions. At the request of ITI Ener gy, the location of the former Stevenson Weather
Station was selected as the reference site for wh ich to obtain environmental (metocean) data for
the loads analyses (presented in Chapter 5 and Chapter 6 ). This site is located at 61ș 20 ′ N
latitude, 0ș 0 ′ E longitude on the prime meridian northeast of the Shetland Islands, which are
northeast of Scotland. Figure 3-14 illustrates this
location with an image courtesy of Google Earth.3
This reference site was chosen for its fairly extreme
wind and wave conditions, with the implication that if the results of the loads analysis are favorable, the floating wind turbine system under consideration will be applicable at almost any site around the world.
ITI Energy requested that I use data from a
Waverider buoy that collected short-term wave
statistics at this site from February 1973 to February 1976. Because this data set did not contain wind-speed information, however, it was not directly applicable to the loads analysis, which requires joint wind and wave data. Instead, NREL purchased wind and wave data at the reference site through the
online Waveclimate.com service
4 that is run by the
Advisory and Research Group on Geo Observati on Systems and Services (ARGOSS) in the
Netherlands.5 The Waveclimate.com service hosts a worldwide database of wind and wave
climate information based on a combination of measurements and a global hindcast model. The measured data come from a composite of radar altimeter, radar scatterometer, and imaging radar (synthetic aperture radar [SAR]) observa tions, taken from 1985 to present. The
Waveclimate.com database has been validated and calibrated with measurements from surface buoys, though not specifically at the chosen refe rence site. The model is based on the third-
generation ocean wind-wave model WaveWatch III [ 94], which solves the spectral-action,
density-balance equation for wave -number-direction spectra. Although I do not show any of the
comparisons here, the wave data obtained through the Waveclimate.com service agreed quite well with the wave statistics available from the former Waverider buoy. This gave me confidence in the accuracy of the Waveclimate.com product.

Figure 3-14. Reference-site location
The Waveclimate.com service uses a grid spacing of 1ș latitude by 1ș longitude in the vicinity of the reference site. We
6 chose the cell with grid boundaries of 61ș to 62ș N latitude, 0ș to 1ș E

3 Web site: http://earth.google.com/
4 Web site: http://www.waveclimate.com/
5 Web site: http://www.argoss.nl/
6 My NREL colleague, G. N. Scott, assisted me with pr ocessing the data from the Waveclimate.com service. To
acknowledge this support, I use “we” in place of “I” where appropriate in this section.
75

longitude. NREL purchased two sets of data for this cell. The first data set consisted of an
estimate of the long-term joint- probability distribution of wind sp eed, significant wave height,
and mean wave period. The second data set was a prediction of the extreme significant wave
heights for various return periods.
The joint-probability distributi on was provided in terms of 37,992 samples, each based on a 3-h
reference (averaging) period, representing a total of about 13 years of da ta. The samples were
grouped in bins with a wind-speed width of 2 knots (1.029 m/s), a significant-wave-height width
of 1 m, and a mean-wave-period width of 1 s. The reference elevation for the wind-speed data
was 10 m above the MSL. To adjust these data to the turbine’s hub height of 90 m, we assumed
a vertical power-law shear exponent7 of 0.14. In addition, we scaled all of the wind-speed bins
by a factor of (90 m/10 m)0.14 = 1.360, resulting in an altered bin width of 1.399 m/s for the hub-
height wind speed, Vhub. We also converted the mean wave-period data to peak spectral period,
Tp. By assuming that the wave conditions were represented by the modified Pierson-Moskowitz
spectrum [ 22], all of the wave-period bins were scaled by a factor of 1.408, resulting in an
altered bin width of 1.408 s. The data of signifi cant wave height, Hs, did not require adjustment.
The resolution of the resulting long-term joint-probability distribution does not entirely conform to the maximum bin widths of 2 m/s, 0.5 m, and 0.5 s required by the IEC 61400–3 design standard [ 34]. I did, however, consider the resolution to be adequate because the loads analysis
presented in Chapter 5 and Chapter 6 is preliminary in nature. Similarly, I found it acceptable to
base the joint-probability distribution on a 3-h reference period instead of the 1-h period required by the 61400–3 design standard. This is because the marginal long-term probability distributions
of significant wave height and peak spectra l period do not depend on the averaging period, and
because one can assume that the marginal long-term probability distribution of mean wind speed is independent of the averaging period for periods in the range of 10 min to 3 h [ 34].
Using the long-term joint-probability distribution, we characterized the expected value of the
significant wave height,
E[H s|Vhub], as well as the range of associated peak spectral periods,
conditioned on the mean hub-height wind speed from cut-in to cut-out. Figure 3-15 illustrates
these data. As shown, the expected value of the significant wave height increases with the mean hub-height wind speed that it is cond itioned on—from about 1.6 m at cut-in,
Vin = 3 m/s, to about
5.9 m at cut-out, Vout = 25 m/s. The peak spectral periods have a median that increases and a
range that tends to decrease with the expected significant wave heights they are associated with, from about 12.7 ± 5.6 s at 1.6 m, to about 15.5 ± 4.2 s at 5.9 m.
The Waveclimate.com service’s extreme-value analysis yielded predictions of the extreme
significant wave heights at the reference site fo r various return periods. The associated wind-
and wave-period information wa s not available, however, so we relied on assumptions and
estimates to specify them. Although the 61400–3 design standard [ 34] requires that the extreme
individual wave heights be estimated at the reference site, I did not assess them because I did not

7 The vertical power-law profile is () ( )r
rZVZ VZZα⎛⎞=⎜⎟
⎝⎠, where V(Z) is the wind speed at height Z above the ground
(or above the mean sea level), Z r is a reference height, and α is the power-law exponent.
76

0510152025
3579 1 1 1 3 1 5 1 7 1 9 2 1 2 3 2Hub-Height Wind Speed, m/s5Expected Significant Wave Height, m Peak Spectral Period Range, s

Figure 3-15. Normal sea state conditions at the reference site
use regular, periodic waves in the preliminary loads analysis. Instead, I relied on irregular sea
states as described in Chapter 5 .
Based on a 3-h reference period, the significant wa ve height with a recurrence period of 1 year,
Hs1, was predicted by the Waveclima te.com service to be 10.8 m. The service also predicted the
significant wave height with a recurrence period of 50 years, Hs50, to be 13.8 m. From data
available in the joint-probability distribution, we estimated that the range of peak spectral periods
associated with the 1-year recurrence of si gnificant wave height would be 15.5 to 19.7 s.
Because 50-year recurrence data do not exist in the 13-year record of joint-probability statistics, we had to extrapolate to estimate the range of peak spectral periods associated with the 50-year recurrence of significant wave height. By th is extrapolation, we es timated a range of 18.5 to
19.9 s. I assumed that the extreme wind speeds at the reference site conformed to those
prescribed by wind turbine class I from the IEC 61400–1 design standard [ 33]. Based on this
assumption and a 10-min averaging period, th e reference hub-height wind speed with a
recurrence period of 1 year,
V1, was prescribed to be 40 m/s a nd the reference hub-height wind
speed with a recurrence period of 50 years, V50, was prescribed to be 50 m/s.
The water depth at the reference site is roughly 160 m; however, I analyzed the sea-based loads presented in Chapter 5 and Chapter 6 with a depth of 150 m (as indicated in Table 3-12 for the
ITI Energy barge).
I did not quantify several other commonly assessed environmental conditi ons at the reference
site, again because the loads analysis was preliminary. For some of the unquantified conditions,
I assumed typical values. I did not assess— nor does the loads analysis account for—the
potential loading from sea ice; marine growth; corrosion; wake effects from neighboring wind
turbines in a wind farm; earthquakes; variations in water levels from astronomical tides and
storm surges; and sea currents generated by wi nd, tides, storm surges, atmospheric-pressure
variations, and near-shore waves (i.e., surf curren ts). I did not assess the soil conditions at the
reference site because my mooring system module assumes that the anchor locations of each
77

mooring line are fixed to the inertial frame at the seabed. I assumed standard values of 1.225
kg/m3 for the air density and 1,025 kg/m3 for the water density. As dictated by the 61400–3
design standard [ 34], I assumed a vertical power-law shea r exponent of 0.14 for all normal wind
conditions and 0.11 in extreme 1- and 50-year wi nd conditions. Similarly, I did not assess the
ambient turbulence standard deviation from site data, or from estimations derived from the
surface roughness according to the Charnock ex pression. Instead, I assumed that the wind
turbulence at the reference site conformed to the models prescribed by wind turbine turbulence-category B from the 61400–1 design standard. I also did not assess the correlation of wind and wave direction, opting instead to use the guidance of the 61400–3 design standard (see Chapter
5). I ignored wave directional spreading and used long-crested waves for all sea states. Finally,
I did not prescribe a site-specific wave spectrum, but opted instead to use the JONSWAP spectrum defined in Section 2.4.1.1. All these assumptions and omissions will need to be
addressed in more detailed follo w-on loads-analysis projects.
78

Chapter 4 Verification of Simulation Capability
The aero-servo-elastic capabilities of FAST with AeroDyn and ADAMS with AeroDyn have
been well verified and validated in previous studies [ 7,8,9,12,37,38,63]. But because my
hydrodynamics and mooring system modules are novel, they must be verified to ensure that the
response predictions from the fully coupled aero-hy dro-servo-elastic capab ility are accurate. In
all, I performed seven verification studies to test the accuracy of the new features: three for the
hydrodynamics module (Section 4.1), two for the mooring system module (Section 4.2), and two
for the complete system (Section 4.3). The last pair of verification exercises compared the
results from my time-domain simulation tool with the results from a frequency-domain model. As I discuss in this chapter, the results of all the verification exercises were favorable. This gave me confidence to pursue more thorough investig ations into the dynamic behavior of offshore
floating wind turbines in Chapter 5 and Chapter 6 .
Additionally, though not explicitly documente d here, the resulting dynamics from the newly
added support platform DOFs in FAST agree well with ADAMS. I furnish some examples of this in Chapter 6 .
I used model-to-model comparisons for all thes e verification exercises. The fully coupled
simulation tool will be validated later, onc e experimental data are made available.
4.1 Verification of the Hydrodynamics Module
I performed three verification tests to check Hy droDyn’s hydrodynamics module. First, as
presented in Section 4.1.1, I verified that the PSD of the wave-elevation time series computed by
HydroDyn matched the target JONSWAP spectrum prescribed by HydroDyn’s wave-spectrum
input parameters. Second, I verified that the ou tput from WAMIT, which is used as input to
HydroDyn, is similar to that generated by a different radiation / diffracti on solver (see Section
4.1.2). Third, I verified that the radiation im pulse-response functions computed within my
hydrodynamics module were the same as those computed with WAMIT’s stand-alone frequency-
to-time (F2T) conversion utility [ 58]. I present these results in Section 4.1.3.
4.1.1 Wave Elevation versus the Target Wave Spectrum
Irregular sea states (stochastic waves) are modeled in HydroDyn by the inverse Fourier transform of Eq. (2-9) , which represents the superposition of a large number of periodic and
parallel wave components. The amplitudes of these wave components, on average, are
determined by the prescribed wave spectrum. I say, “on average,” because randomness comes in through the realization of the WGN process. That process considers not only a uniformly-
distributed random phase, but a normally-dist ributed amplitude as well (see Section 2.4.1.1). In
HydroDyn, Eq. (2-9) is implemented using a computationally efficient FFT routine [ 92].
I ran a simple test to check that I implemented these mathematical relationships correctly in HydroDyn. I computed four wave-elevation time series, each determined with the Pierson-Moskowitz wave spectrum [see Eq. (2-20) ] given by a significant wave height,
Hs, of 5.49 m and
a peak spectral period, Tp, of 14.656 s or a peak spectral frequency of about 0.429 rad/s. [This
79

spectrum is equivalent to a JONSWAP spectrum with the default value (unity) of the peak shape
parameter given by Eq. (2-19) ]. Each wave-elevation time series was 10,000 s long (i.e., just shy
of 3 h each) and was differentiated throug h the choice of dissimilar random seeds.
I then computed the PSD of each wave-elevation record, and compared each to the target wave
spectrum determined by the given spectral parameters. Figure 4-1 shows the results. To
minimize scatter, I grouped the discrete-frequency PSD data of Figure 4-1 in bins of width 0.001
Hz (about 0.00628 rad/s). Because of the normally -distributed amplitudes provided by the WGN
process, however, there is still a fair amount of scatter in the PSD of each individual run. But the
average of the four PSDs, as indicated by the series labeled “Run Average” in Figure 4-1 , is
approaching the target spectrum nicely. This out come would improve by averaging the results of
many more simulations.
024681012
0.0 0.2 0.4 0.6 0.8 1.0 1.2
Wave Frequency, rad/sWave Spectrum, m2/(rad/s)Run 1
Run 2
Run 3
Run 4
Run Average
Target

Figure 4-1. PSD of wave elevations versus target wave spectrum
I also calculated the probability density for the aggregate composite of the wave-elevation
records computed by, and output from, HydroDyn. As expected, this histogram is Gaussian-distributed with a mean of zero and a st andard deviation (for this test case) of
Hs/4 = 1.37 m.
The result is shown with the corresponding pr obability density function derived from a zero-
valued mean and a standard deviation of 1.37 m in Figure 4-2.
4.1.2 WAMIT Output / HydroDyn Input
As I described in Chapter 2 , I used WAMIT [ 58] as a preprocessor for generating the
hydrodynamic-added-mass and -damping matrices, ()ijAω and ()ijBω, and wave-excitation
force, (iX,)ωβ , which are inputs to HydroDyn. WAMIT uses the three-dimensional numerical-
panel method to solve the linearized hydrodyna mic radiation and diffraction problems for the
80

0.00.10.20.30.4
-6 -4 -2 0 2 4
Wave Elevation, mProbability Density, 1/mHydroDyn Output
Gaussian Distribution

Figure 4-2. Wave-eleva tion probability density
interaction of surface waves with offshore plat forms in the frequency domain. WAMIT ignores
the effects of sea current or forward speed on th e radiation and diffraction problems, as well as
higher-order effects.
Because the hydrodynamic solution my simulation tool generates is only as good as the
hydrodynamic inputs, verifying the acceptability of the WAMIT results is beneficial. Consequently, I ran a test to ensure that the WAMIT output I generated is similar to that calculated by a different radiation / diffraction solver. Data used by NAME at the Universities of Glasgow and Strathclyde when devising the ITI Energy barge described in Section 3.2 were
available for this comparison. NAME used a custom-made linear hydrodynamic radiation and
diffraction solver with capabilities similar to, but independent of, WAMIT.
In WAMIT, I modeled the barge with two geom etric planes of symmetry with 2,400 rectangular
panels within a quarter of the body. Consistent with linear theory, I needed to mesh only the
wetted portion of the body in its undisplaced position. Figure 4-3 shows the panel mesh with
both symmetries. To avoid accounting for the OWC in the WAMIT analysis, I covered the moon pool with a fixed plate located 0.01 m below th e free surface. In an attempt by NAME to
model the OWC, they considered that the plate was free to move relative to the barge. Figure
4-4 shows the panel mesh for NAME’s analysis.
To improve the accuracy of the WAMIT results , I chose to override three default settings,
choosing instead to (1) integrate the logarithmic singularity analytically, (2) solve the linear
system of equations using a direct solver, and (3 ) remove the effects of irregular frequencies by
automatically projecting the body panels to the free surface. These settings were necessary
because some panels are located in a plane near the free surface, the barge has a large water-plane area, and subsequent analysis required high-frequency results. The barge was analyzed in its undisplaced position with infinite water depth in both codes. The hydrodynamic-added-mass and -damping matrices were compared in all si x rigid-body modes of motion of the barge (in the
matrix subscripts,
1 = surge, 2 = sway, 3 = heave, 4 = roll, 5 = pitch, 6 = yaw), resulting in 6 × 6
81

matrices at each frequency. Because NAME
considerd the plate to be a separate body, their resulting matrices at each frequency were of the size 12 × 12. To assist in the comparison, though, NAME reduced these down to 6 × 6 matrices via postprocessing. The hydrodynamic wave-excitation force was not considered in this test.
Figure 4-5 shows the results in a side-by-side
comparison. All data are dimensional as
indicated. Only the upper triangular matrix elements are shown because the hydrodynamic-added-mass and -dampi ng matrices are
symmetric in the absence of sea current or forward speed [ 22,74]. Also, because of the barge’s symmetries, the surge-surge elements of the
frequency-dependent added-ma ss and damping matrices,
A11 and B11, are identical to the sway-
sway elements, A22 and B22. Similarly, the roll-roll elements, A44 and B44, are identical to the
pitch-pitch elements, A55 and B55. Other matrix elements not shown are zero-valued or very
close to being zero-valued.
Figure 4-3. Panel mesh of the ITI Energy barge used within WAMIT

Figure 4-4. Panel mesh of the ITI Energy barge
used by NAME
In Figure 4-5 , the WAMIT results are given in even increments of frequency. The NAME
results are given in even increments of period, so re solution is lost at the higher frequencies. As
expected, all matrix elements peak out at some intermediate frequency and level out at higher frequencies. Additionally, the zero- and infi nite-frequency limits of all elements of the
82

0E+610E+620E+630E+640E+6
01234
Frequency, rad/sForce-Translation Modes, kgA11 WAMIT
A22 WAMIT
A33 WAMIT
A11 NAME
A22 NAME
A33 NAME
0E+62E+64E+66E+68E+6
01234
Frequency, rad/sForce-Translation Modes, kg/sB11 WAMIT
B22 WAMIT
B33 WAMIT
B11 NAME
B22 NAME
B33 NAME

0E+85E+810E+815E+820E+8
0123 40E+82E+84E+86E+88E+8
01234
Frequency, rad/sMoment-Rotation Modes, kg·m2/sA44 WAMIT B44 WAMIT
hydrodynamic-damping matrix are zero ( not all shown), as required by theory [ 22,74]. The
comparisons between the output of WAMIT and th e results of NAME generally agree very well
and demonstrate that WAMIT is an acceptable code for generating the hydrodynamic inputs
needed by my simulation tool. The biggest discrepancies are in the heave-heave elements of the
frequency-dependent added-ma ss and damping matrices, A33 and B33. I believe that these
differences are artifacts of the dissimilar numerical solutions employed by WAMIT and NAME’s radiation / diffraction solver. The diff erences are not large, however, and I do not
believe they are crucial to the accu racy of my hydrodynamics solution. Frequency, rad/sMoment-Rotation Modes, kg·m2 A55 WAMIT B55 WAMIT
A66 WAMIT B66 WAMIT
A44 NAME B44 NAME
A55 NAME B55 NAME
A66 NAME B66 NAME

-30E+6-20E+6-10E+60E+610E+620E+630E+6
01234
Frequency, rad/sFrc-Rot & Mom-Trans Modes, kg·mA15 WAMIT
A24 WAMIT
A15 NAME
A24 NAME
-30E+6-20E+6-10E+60E+610E+620E+630E+6
01234
Frequency, rad/sFrc-Rot & Mom-Trans Modes, kg·m/sB15 WAMIT
B24 WAMIT
B15 NAME
B24 NAME

Figure 4-5. Hydrodynamic added mass and damping for the ITI Energy barge
83

4.1.3 Computation of Radiati on Impulse-Response Functions
The radiation “memory effect” is captured in HydroDyn’s hydrodynamics module through the
convolution integral of Eq. (2-8) . As described in Section 2.4.1.3, the kernel, ()ijKt, in this
convolution integral is commonly referred to as the impulse-response functions of the radiation
problem. Section 2.4.2.1 described how the radiation impul se-response functions can be found
from the solution of the frequency-domain radiati on problem. In HydroDyn specifically, these
functions are found using the cosine transfor m of the frequency-dependent hydrodynamic-
damping matrix, as given in Eq. (2-28b) , using a computationally efficient FFT routine [ 92]. As
in the verification of the wave-eleva tion computation presented in Section 4.1.1, verifying that
this cosine transform was impleme nted correctly is advantageous.
I performed this verification by testing that the radiation impulse-res ponse functions computed
within HydroDyn are the same as those com puted by WAMIT’s stand-alone F2T conversion
utility. I implemented the cosine transform w ithin HydroDyn, as opposed to having HydroDyn
read in the output of WAMIT’s F2T utility, because many of the other computer codes available
to solve the frequency-domain hydrodynamics problem, such as the SWIM module [ 48] of SML,
do not contain the F2T conversion functionality. In this test, I used the WAMIT output of the
frequency-dependent hydrodynamic-damping matrix for the ITI Energy barge from the previously presented verification test.
Because the comparison between the F2T results and my own is so good (i.e., the results are
essentially identical), I present only one set of results in Figure 4-6 . As before, all data are
dimensional as indicated, and because of the symm etries of the barge, the surge-surge elements
are identical to the sway-sway elements, and the roll-roll elements are identical to the pitch-pitch
elements. Most of the response decays to ze ro after about 20 s (as shown) and has all but
vanished at 60 s (not shown). Consequently, to sp eed up the calculations of the memory effect in
my simulation tool, I generally truncate the numerical convolution after 60 s of memory.
4.2 Verification of the Mooring System Module
I performed two verification tests to check my qu asi-static mooring system module. First, as
presented in Section 4.2.1, I verified that my mooring system module correctly solves a classic
benchmark problem for the static equilibrium of a suspended- cable mechanism. Second, as
presented in Section 4.2.2, I verified that the nonlinear force-displacement relationships for a
mooring system in surge, as computed by my module, were the same as those calculated by an
independent analysis performed by NAME.
4.2.1 Benchmark Problem
A classic test problem [ 95] for checking the accuracy of a mooring system program is that of a
horizontally suspended cable with one support free to slide laterally. Figure 4-7 illustrates this
problem. For a cable of an unstretched length of
L = 200, a weight per unit length of ω = 0.1, an
extensional stiffness of EA = 105, and a horizontal load (equivalent to the horizontal tension at
the fairlead) of HF = 5.77 applied at the free end (the fairlead), the theoretical static-equilibrium
solution is for a horizontal span of xF = 152.2 and a vertical sag of 58.0. (No units are specified
for any parameter in Ref. [ 95]; instead, consistent units were assumed.)
84

-4E+6-2E+60E+62E+64E+6
0 5 10 15 20
Time, sForce-Translation Modes,
kg/s2K11
K22
K33

-6E+8-3E+80E+83E+86E+8
0 5 10 15 20
Time, sMoment-Rotation Modes,
kg·m2/s2K44
K55
K66

-20E+6-10E+60E+610E+620E+6
0 5 10 15 20
Time, sFrc-Rot & Mom-Trans Modes,
kg·m/s2K15
K24

Figure 4-6. Radiation impulse-response functions for the ITI Energy barge
This benchmark problem involves finding a static-equilibrium position of the fairlead. I tested
my mooring system module (in the form without seabed interaction) by solving this problem
through time integration of the nonlinear equations of motion. The platform, where the fairlead
attaches, was given one horizontal -translation DOF and a small, inconsequential mass. A small
amount of linear damping was added to the motion to ensure that it eventually settled out. I then
ran the time-marching solver until the solution se ttled out and converged. I had to solve the
85

Figure 4-7. Benchmark problem for a suspended cable
static-equilibrium problem in this way because my mooring system module is interfaced to
FAST and ADAMS, both of which operate in th e time domain. If my mooring system module
was implemented correctly, the horizontal span a nd vertical sag should settle out at the correct
solution regardless of the lateral offset chosen as an initial c ondition for the DOF. Indeed, this is
exactly what happens.
Figure 4-8 shows the time-series solution of the horizontal span (displacement) when the fairlead
was positioned to the left of the anchor at time zero, at a lateral offset of −100. FAST and
ADAMS gave identical results. The solution is seen to converge to the correct result after about
120 s. Other initial conditions showed s imilar behavior with the same result.
-1500150300
0 2 55 07 5 1 00
Simulation Time, sHorizontal DisplacementAnalytical Solution
125FAST
ADAMS

Figure 4-8. Solution of the suspended-cable benchmark problem
4.2.2 Nonlinear Force-Displacement Relationships
Nonlinearities are evident in the force-displacement relationships of most mooring systems.
Because these nonlinearities may be important in the dynamic response of offshore floating wind
turbines, I must check to ensure that my quasi-static mooring system module is computing them correctly.
NAME used a custom-made mooring analysis progr am to develop the mooring system for the
ITI Energy barge described in Section 3.2. NAME’s program accounts for homogenous taut or
catenary lines with horizontal (but not vertical) elastic stretching . A portion of a line may rest on
the seabed in NAME’s mooring program, but the program does not account for seabed friction.
Even though NAME’s program has fewer capabilitie s than the mooring system module I have
developed, comparing my response with NAME’s en abled me to verify my analysis module in
the form with seabed interaction.
86

The layout of the mooring system for the ITI Energy barge, which consists of eight catenary
lines, was discussed in Section 3.2. In this verification test, how ever, I modified the layout to
make the mooring lines parallel to the sides of the barge because this is the only way NAME’s program could model it. With this modification, each pair of lines is 90ș apart at the corner and
opposing lines are parallel to each other. NAME computed the force-disp lacement relationships
for surge motions of the barge for each line indepe ndently as well as opposing lines jointly. To
reproduce NAME’s results, I built a model of th e barge and mooring system in ADAMS and
translated the barge in surge through a time-mar ching simulation. This time-dependent motion
of the barge does not affect the results of my analysis because the mooring lines are treated quasi-statically in my module.
As in previous verification tests, the results from this exercise compared very well. Because the
agreement is so good (i.e., the results are esse ntially identical), again, only my results are
presented, as shown in Figure 4-9 . There is a horizontal tension of about 100 kN in each line
when the barge is in its neutral position. The force-displacement curve for opposing lines, which
represents the net horizontal restraining force on the barge, remains fairly linear between +20 m and −20 m of surge motion. Beyond a surge displacement of about 40 m, the resistance of the
mooring system increases dramatically. At 50 m of surge displacement, the horizontal tension in
each line is greater than 1,000 kN.
-2,00002,0004,0006,0008,000
-60 -40 -20 0 20 40
Platform Surge, mTension / Force, kNHorizontal Tension of Upwind Line
Horizontal Tension of Downwind Line
Net Horizontal Restraining Force on Barge

Figure 4-9. Force-displacement relationships for the ITI Energy mooring system
4.3 Time Domain versus Fre quency Domain Verification
Because my fully coupled aero-hydro-servo-elastic simulation tool is the first of its kind to be
developed, finding independent model results to use for verification is difficult. The time-
domain models that others have previously deve loped and used to analyze offshore floating wind
turbines were either not rigorous enough to yi eld sufficient verification data or were unavailable
for my use [ 23,31,57,75 ,87,103,105,106]. Many of the previous studies related to offshore
floating wind turbines used frequency-domain models [ 13,59,98,100,101]. I can use the results
of a frequency-domain analysis to verify my simulation tool because the hydrodynamic theory in my module was derived from the time-domain representation of the frequency-domain problem (see Section 2.4.2.1). I present two such verifications here.
87

Frequency-domain solutions describe the sinusoi dal steady-state response of a platform to
incident waves that propagate at a single amplitu de, frequency, and direction. As discussed in
Section 2.4.2.1, the solution to the frequency-domain pr oblem is generally given in terms of
RAOs, which are the complex-valued amplitudes of motions for each DOF of the support
platform, normalized per unit of wave amplitude. In a time-domain model, the sinusoidal steady-state response of a floatin g platform can be found by introducing regular, periodic waves
as forcing functions, and simulating in time long enough to ensure all transient behavior has died
out. As a first verification of my fully coupled model, we
1 used such time-series simulations to
back out the RAOs at discrete incident-wave fre quencies, and repeated the process to find the
RAOs at each desired frequency. For this verification test, we used Wayman’s frequency-domain results for the MIT / NREL SDB (see Ref. [ 101]).
As I also discussed in Section 2.4.2.1, the response of a floating platfo rm to stochastic sea states
in the frequency-domain problem can only be characterized statistically because the frequency-domain representation is not valid for transient analysis. Specifically, the motion of a linearized floating body will have a response that is Gaussian -distributed when it is excited by a sea state
with a Gaussian-distributed wave elevation. Th e standard deviations of the motion response are
dictated by the Wiener-Khinchine theorem [ 85,101]. In a time-domain model, the distributions
of the motion response can be ascertained by postp rocessing the output of a series of simulations
that are long enough to ensure the the results are statistically reliable. (The process can be repeated to find the distributions at each desired sea state.) We used this procedure as a second
verification of my fully coupled, time- domain model, again using Wayman’s [ 101] frequency-
domain results for the MIT / NREL SDB for comparison.
For these verification tests, we used the NREL offshore 5-MW baseline wind turbine described
in Section 3.1 installed on the MIT / NREL barge (SDB) described in Section 3.3. I chose this
configuration and Wayman’s [ 101] frequency-domain results because that was the only
configuration and the only study documented with enough information for me to build a system
model and compare results for all six platform modes of motion. Wayman used WAMIT to compute the frequency- domain hydrodynamic pr operties of the MIT /
NREL SDB and modeled the spread-moor ing system described in Section 3.3 with linear
restoring only in the surge and sway DOFs. Wayman used the LINES module [ 50] of SML to
find linear restoring coefficients of 4,000 kN/m. The attributes of the wind turbine were
included in Wayman’s linearized system model by augmenting the body-mass matrix with the
mass properties of the turbine and by augmenti ng the hydrodynamic-damping and -restoring
matrices with damping and rest oring contributions from rotor aerodynamics and gyroscopics.
Wayman ignored the elasticity of the wind turbine and considered only the six rigid-body modes of the barge [ 101].

1 My NREL colleague, M. L. Buhl, Jr., assisted me in running my simulation tool and plotting the results presented
in Section 4.3. To acknowledge this support, I use “we” in place of “I” and “our” in place of “my” where
appropriate.
88

4.3.1 Verification with Stea dy-State Response
For this comparison, I constructed a FAST with AeroDyn and HydroDyn model of the NREL
offshore 5-MW baseline wind turbine installed on the MIT / NREL barge. To ensure reasonable
similarity to Wayman’s model and to isolate the behavior of the hydrodynamics and mooring system, I modeled the turbine without any control system (i.e., using constant rotor speed and
fixed blade pitch) or any modes of motion othe r than the six rigid-body DOFs of the floating
support platform. For environmental conditi ons, a constant unsheared 11.2-m/s wind (as
Wayman used) and regular periodic waves of unit amplitude (a peak-to-peak height of 2 m) were used. Both the wind and waves were codirec tional and aligned with the surge coordinate.
When we first attempted to run the time-domain simulations, I modeled the spread-mooring system with my quasi-static mooring system module interfaced to FAST. We soon discovered,
however, that the nonlinear restoring of the sp read-mooring system prohibited the response from
ever reaching a sinusoidal stead y-state condition, which eliminated any possibility of backing out
the RAOs. To get around this, I decided to re move the interface to my mooring module, and
instead, modeled the mooring system as Wayman did with linear restoring coefficients (in surge and sway only). As a consequence, the results presented next are not useful for verifying my
time-domain implementation of the mooring system module. They are, though, still useful for verifying the time-domain implementa tion of my hydrodynamics module.
With the linearized mooring system model, we ran a series of 2,000-s simulations to give them time to reach a periodic steady stat e. Even after all that time, the platform motion was still not
perfectly sinusoidal for the sway, roll, and yaw re sponses. We ran 10 simulations and varied the
discrete frequency of the incident waves from 0.1 5 to 1.05 rad/s in even increments. Using the
last cycle from each simulation, we computed th e amplitudes of the oscillations for the three
translational and three rotational platform resp onses. Because the incident waves were unit
amplitude, these response amplitude s are equivalent to the magnitudes of the RAOs. For the
rotational responses, we normalized the RAOs by the platform radius (18 m), as Wayman did [101]. We added our results to the nondimensiona l RAO plots that Wayman had generated. In
these tests, we did not compare the phases of the response.
As shown in Figure 4-10 , our time-domain predictions closely mimic those from Wayman’s
frequency-domain analysis for the platform-surge and -heave modes. This gave me confidence
that my time-domain implementation of the platform hydrodynamics was correct. The platform-
pitch curves seem to have a similar character, but portions differ in both magnitude and frequency. The other three parameters—sway, ro ll, and yaw—have such small responses that
comparison is difficult. Because the oscillations of these modes had not become completely sinusoidal after 2,000 s, we question whether those comparisons are meaningful. Even though there is no excitation of the platform-yaw mode from aerodynamics or hydrodynamics in this configuration, the yaw response is nonzero because the spinning inertia of the rotor, combined
with the pitching motion of the plat form, induces a gyroscopic yaw moment.
89

Frequency Domain Time Domain
012345
0.00 .51 .01 .52
Frequency, rad/sBarge-Surge RAO
.0
012345
0.0 0.5 1.0 1.5 2.0
Frequency, rad/sBarge-Roll RAO

012345
0.00 .51 .01 .5
Frequency, rad/sBarge-Sway RAO
I believe that the differences in the pitch RAO are caused by the variation between my model
and Wayman’s for the aerodynamic damping in pitch. Wayman showed that the platform
damping in pitch is completely dominated by rotor aerodynamics, not by wave radiation (see Appendix A.1 of Ref. [ 101]). This is not true for the other modes of motion, such as surge and
heave. In Wayman’s analysis, the aerodynamic damping in barge pitch was constant (it was derived by using FAST with AeroDyn to lineariz e the rotor aerodynamic thrust about the mean
pitch orientation of the platform). In my mode l, the aerodynamic damping in barge pitch varies
as the turbine oscillates against and with the wind. 2.0
012345
0.0 0.5 1.0 1.5 2.0
Frequency, rad/sBarge-Pitch RAO

012345
0.00 .51 .01 .5
Frequency, rad/sBarge-Heave RAO
2.0
012345
0.00 .51 .01 .52 .0
Frequency, rad/sBarge-Yaw RAO

Figure 4-10. RAO comparisons for the MIT / NREL barge
90

4.3.2 Verification with Stochastic Response
To verify the stochastic response, I built three FAST with AeroDyn and HydroDyn models of the
NREL offshore 5-MW baseline wind turbine installed on the MIT / NREL barge. The first was
the same one used in the RAO comparison: it had a rigid turbine, no control system, and a
linearized form of the mooring system in surge and sway. For the second model, I replaced the linearized mooring line model with the standard interface between FAST and my quasi-static mooring system module. To see how well these simpler models agreed with higher fidelity
simulations, in the third model I replaced the rigid turbine with a fully flexible one and enabled the variable-speed generator-torque and blade-pitch control systems.
The published results [ 101] of Wayman’s frequency-domain stud y included mean and standard
deviations of the Gaussian-distributed responses at a variety of sea states, wind speeds, and water depths. I chose to compare all three of my mode ls with only one of these cases. The case I
chose used winds roughly at rated (11.2 m/s), a water depth of 200 m, and the same wave
conditions considered in my test of the wave-elevation time series (see Section 4.1.1). We used
steady unsheared winds in the first two models, but for the third model with an active control system, we used turbulent and sheared winds, w ith a mean hub-height speed of 11.2 m/s and IEC
category B turbulence [ 33]. As before, the wind and waves we re codirectional and aligned with
the surge coordinate.
For each model, we computed the probability densities for the output of all but the first 30 s of a
series of four 10,000-s simulations (i.e., just shy of 3 h each), which used different random seeds
for the stochastic waves (just as in Section 4.1.1). We constructed an aggregate of the four cases
before computing the probability densities. We plotted our resulting histograms against the normal probability density functions derived from the means and standard deviations of Wayman’s frequency-domain analysis [ 101].
2
Figure 4-11 presents the comparison between our time-domain results and Wayman’s frequency-
domain results. Because the differences between th e results of my second and third models were
much smaller than the changes brought about by the switch to nonlinear mooring lines, the figure shows only the results from the first and third m odels. As with the RAOs, the surge and heave
predictions from my model with the linearized mooring lines agree very well. The spread for the pitch response is narrower for our simulation with the linearized mooring system than it is in
Wayman’s predictions. This is consistent with what the pitch RAO comparison showed in
Figure 4-10—that is, Wayman’s RAO was greater at 0.429 rad/s than the magnitude predicted by
my model.

2 Note that I had to make one correction to Wayman’s results published in Ref. [101]. I discovered that when
Wayman computed the standard deviations of motion for the rotational modes of the platform, the results were
incorrectly dimensionalized. To correct for this mistake, all of the standard deviations of motion presented for the
rotational modes in Ref. [101] must be scaled up by a factor of 180π to reach the values Wayman meant to
publish. The results presented here account for this correction.
91

Rigid, Linear Moorings
Flexible, Controls, Nonlinear Moorings
Frequency Domain
0.00.10.20.30.4
-8 -4 0 4
Platform Surge, mProbability Density, 1/mș
0.00.20.40.60.8
-40 -20 0 20
Platform Roll, șProbability Density, 1/ș

05101520
-8 -4 0 4
Platform Sway, mProbability Density, 1/m
0.000.050.100.150.20
-20 -10 0 10
Platform Pitch, șProbability Density, 1/ș

0.00.20.40.6
-6 -3 0 3
Platform Heave, mProbability Density, 1/m
0.00.20.40.6
-30 -15 0 15
Platform Yaw, șProbability Density, 1/ș

Figure 4-11. Probability density comparisons for the MIT / NREL barge
After introducing the nonlinear mooring system module into the FAST simulations, the mean
surge, pitch, and heave responses decreased considerably (see Figure 4-11 ). This is because
once the lines go taut, the stiffness increases dramatically and the mooring system essentially acts as a four-bar linkage. This keeps the platfo rm from rising as high or from traveling as far
downwind. The thrust on the rotor tries to pitc h the turbine downwind, but the higher tensioned
upwind mooring lines prevent the upwind end of th e barge from lifting so far out of the water;
the platform, in turn, is pushed slightly upwind. Because there is more coupling in the system in
the higher fidelity model, the spread of values for the sway, roll, and yaw is also much greater than in the simpler model.
92

Chapter 5 Loads-Analysis Overview and Description
I ran two preliminary sets of loads analyses. The first was for the NREL offshore 5-MW
baseline wind turbine installed on land. Its a im was to establish the response of the baseline
wind turbine without the effects of hydrodynamic loading or platform motion. The second loads
analysis was for the same wind turbine mounted offshore on the floating ITI Energy barge. I
used the same wind turbine control system in both analyses. Using the same turbine model (identical from the blade tip to the tower base ) and control system in both the on- and offshore
load sets has precedent because the design process prescribed in the IEC 61400–3 design
standard [ 34] endorses deriving a sea-based wind turbin e design from that of a land-based wind
turbine.
Ultimately, for the wind turbine installed on the floating barge, design modifications will have to
be made to ensure that favorable performance is achieved and structural integrity is maintained. Indeed, my loads analysis is just the first step in an iterative design process. And by starting with the simplest concept (i.e., an onshore wind turb ine mounted atop an offshore barge), one can
avoid unnecessary complication in the final design. Even though I ran only one step in the iterative process in this work, comparing the res ponse of the floating system to the response of
the turbine installed on land allowed me to quantify the impact brought about by the dynamic couplings between the turbine and floating barg e in the presence of combined wind and wave
loading. This comparison point outs where modifi cations must be made to arrive at a suitable
design for the floating system. Such design modifications will have to be addressed through additional loads-analysis iterati ons in subsequent projects.
I used the IEC 61400–1 design standard [ 33] for land-based turbines and the IEC 61400–3
design standard [ 34] for sea-based turbines as guides for my preliminary loads analysis. The
61400–3 design standard is still in draft form, and discussion about it s design requirement
prescriptions continues. Moreove r, the 61400–3 design standard explic itly states that “the design
requirements specified in this standard are not necessarily sufficient to ensure the engineering
integrity of floating offshore wind turbines” [ 34, p. 7]. For the purposes of my preliminary loads
analysis (which is principally a feasibility study), however, I assumed that the stated design
requirements were sufficient. I made no attempt to identify other possible platform-specific
design conditions.
In Section 5.1, I present an overview and description of the simulations run in the land- and sea-
based loads analyses. Section 5.2 then discusses how we
1 processed the loads-analysis data.
Chapter 6 presents the results of the loads analyses.
5.1 Design Load Cases
Loads analysis involves verifying the structural in tegrity of a wind turbine by running a series of
design load cases (DLCs) to determine the extreme (ultimate) and fatigue loads (i.e., forces and

1 My NREL colleague, M. L. Buhl, Jr., developed the scri pts used to run the loads an alyses and assisted me in
processing the loads-analysis data. To acknowledge this support, I use “we” in place of “I” and “our” in place of
“my” where appropriate in Chapter 5.
93

moments) expected over the lifetime of the machine. The loads are examined within the primary
members of the wind turbine, including the blad es, drivetrain, nacelle, and tower, and for the
floating system, the mooring lines. The required DL Cs cover essential desi gn-driving situations
such as normal operating conditions, start-up ev ents, shutdown events, and parked or idling
states, together with appropriate normal and extreme external conditions and likely fault scenarios.
Each IEC design standard prescribes numerous DLCs. For this preliminary loads analysis, I did
not consider it necessary to run all the DLCs prescribed by the design standards; instead, I used a subset, eliminating the fatigue-type DLCs and processing only the anticipated ultimate loads. This omission follows from standard design pr actice for land-based and fixed-bottom sea-based
wind turbines in which the structure is configured to survive ultimate loads before it is checked for fatigue [ 96]. Because fatigue behavior often governs the design of wind turbines, however,
the effect of platform motion on wind turbine fatigue damage will have to be assessed by processing the omitted fatigue-type DLCs in a subsequent project.
As described in Section 3.1.6, the control system for the reference turbine does not include logic
for start-up or shutdown sequences, so I eliminated the 3.x, 4.x, and 5.x DLCs defined in the
design standards. I do, however, consider shutdo wns that follow fault scenarios in DLC 2.x. I
also ignored the 8.x cases, which relate to transport, assembly, maintenance, and repair. The four DLCs I omitted may have governed the ultimate loading of some historical wind turbines, but I believe omitting them was reasonable because, from my experience with land-based turbines, they have not dominated the ultimate loads.
The remaining ultimate-type DLCs included the fo llowing design situations: power production,
DLC 1.x; power production with occurrence of fault, DLC 2.x; parked (idling), DLC 6.x; and
parked with fault, DLC 7.x. Table 5-1 summarizes the DLCs I selected. In this table, the DLCs
are indicated for each design situation by thei r associated wind conditions, wave conditions, and
operational behavior of the control system, fault scenarios, and other events. For the land-based cases, I disregarded the wave conditions and cantile vered the base of the tower to the ground.
Table 5-1. Summary of Selected Design Load Cases
DLC Controls / Events Load
Model Speed Model Height Direction Factor
1.1 NTM Vin < V hub < Vout NSS Hs = E[H s|Vhub]β = 0ș Normal operation 1.25*1.2
1.3 ETM Vin < Vhub < Vout NSS Hs = E[Hs|Vhub]β = 0ș Normal operation 1.35
1.4 ECD Vhub = Vr, Vr±2m/s NSS Hs = E[H s|Vhub]β = 0ș Normal operation; ± ∆ wind dir'n. 1.35
1.5 EWS Vin < V hub < Vout NSS Hs = E[H s|Vhub]β = 0ș Normal operation; ± ∆ ver. & hor. shr. 1.35
1.6a NTM Vin < V hub < Vout ESS Hs = 1.09* Hs50β = 0ș Normal operation 1.35
2.1 NTM Vhub = Vr, Vout NSS Hs = E[H s|Vhub]β = 0ș Pitch runaway → Shutdown 1.35
2.3 EOG Vhub = Vr, Vr±2m/s, Vout NSS Hs = E[H s|Vhub]β = 0ș Loss of load → Shutdown 1.10
6.1a EWM Vhub = 0.95* V50 ESS Hs = 1.09* Hs50β = 0ș, ±30ș Yaw = 0ș, ±8ș 1.35
6.2a EWM Vhub = 0.95* V50 ESS Hs = 1.09* Hs50β = 0ș, ±30ș Loss of grid → -180ș < Yaw < 180ș 1.10
6.3a EWM Vhub = 0.95* V1 ESS Hs = 1.09* Hs1β = 0ș, ±30ș Yaw = 0ș, ±20ș 1.35
7.1a EWM Vhub = 0.95* V1 ESS Hs = 1.09* Hs1β = 0ș, ±30ș Seized blade; Yaw = 0ș, ±8ș 1.106) Parked (Idling)
7) Parked (Idling) and FaultWinds Waves
1) Power Production
2) Power Production Plus Occurrence of Fault
94

The wind and wave models are defined in Table 5-2 for readers who are unfamiliar with the IEC
terminology.
In general, the 61400–3 sea-based design stan dard is a superset of the 61400–1 land-based
design standard. When the two IEC design sta ndards differed in details, I chose to use the
specifications of the 61400–3 design standard for both my land- and sea-based loads analyses.
This allowed me to compare the results fairly. For example, the normal wind profile that is used
in both the deterministic- and tur bulent-wind models should consist of a vertical power-law shear
exponent of 0.2 for land-based wind turbines according to the 61400–1 design standard and a
value of 0.14 for sea-based turbines according to the 61400–3 design standar d. To facilitate the
response comparisons, I decided to use 0.14 for both.
Table 5-2. Definition of Wind and Wave Models
Abbr. Definition Description
ECD Extreme Coherent Gust with
Direction ChangeThis deterministic-wind model consists of an unsheared gust superimposed on a uniform
wind profile with a vertical power-law shear exponent of 0.14. The gust rises to 15 m/s over a 10-s period. Occurring concurrently, the wind direction changes inversely
proportional to the given hub-height wind speed. Both positive and negative direction
changes are considered.
EOG Extreme Operating Gust This deterministic-wind model consists of an unsheared gust superimposed on a uniform
wind profile with a vertical power-law shear exponent of 0.14. Over a 10.5-s transient, the gust first dips, rises to a maximum, then dips again before disappearing. Its magnitude depends on the wind-turbine class (IB in this project) and increases with the
given hub-height wind speed.
ESS Extreme Sea State This irregular sea state is similar to the NSS but uses a JONSWAP spectrum that is
derived from 1- and 50-year return values of the significant wave height and peak
spectral period. Like the NSS, the sea state is modeled as a summation of sinusoidal
wave components whose amplitude is determined by the wave spectrum, each parallel
(long-crested) and described by Airy wave theory.
ETM Extreme Turbulence Model This model is similar to the NTM but consists of full-field 3-component stochastic winds
with a higher turbulence standard deviation, based on the wind-turbine class (IB in this project) and increases with the given hub-height wind speed. Like the NTM, the full-field turbulence is superimposed on a normal wind profile with a vertical power-law shear
exponent of 0.14.
EWM Turbulent Extreme Wind
ModelThis model consists of full-field 3-component stochastic winds with a turbulence standard
deviation of 0.11 times the 10-min average wind speed at hub height, plus 0.2 m/s for 1-h
–
long simulations. The full-field turbulence is superimposed on a wind profile with a vertical power-law shear exponent of 0.11.
EWS Extreme Wind Shear This deterministic-wind model consists of a linear shear superimposed on a uniform wind
profile with a vertical power-law shear exponent of 0.14. Over a 12-s transient, the shear
rises to a maximum, then decreases again before disappearing. Its magnitude depends
on the wind turbine turbulence category (B in this project) and increases with the given hub-height wind speed. Positive and negative vertical and horizontal shears are
considered independently.
NSS Normal Sea State This irregular sea state is modeled as a summation of sinusoidal wave components
whose amplitude is determined by the wave spectrum, each parallel (long-crested) and
described by Airy wave theory. The sea state is derived from the JONSWAP spectrum,
whose formulation is based on the given values of the significant wave height and peak
spectral period. The JONSWAP spectrum reduces down to the Pierson-Moskowitz spectrum in all but the most extreme sea states.
NTM Normal Turbulence Model This model consists of full-field 3-component stochastic winds with a turbulence standard
deviation given by the 90% quantile, based on the wind turbine turbulence category (B in
this project) and increases with the given hub-height wind speed. The full-field
turbulence is superimposed on a wind profile with a vertical power-law shear exponent of 0.14.

95

The 61400–3 design standard specifies subsidiary cases for the DLCs involving extreme waves
of 1- or 50-year recurrence because it is genera lly difficult to account for both the irregularity
and nonlinearity of the extreme waves simultaneously within simulation. This, in turn, follows
from the fact that models for nonlinear irregular wave kinematics are not common in engineering usage. The subsidiary DLCs involve analysis w ith (a) turbulent winds a nd stochastic sea states
used in conjunction with full-system flexibility and dynamics, or (b and c) steady winds and deterministic nonlinear design waves used in conjunction with a quasi-steady computation with appropriate corrections for dyna mic amplification. (The letters “a,” “b,” and “c” refer to
subcases used in the 61400–3 design standard.) I chose the former method as indicated by the
“a” in DLCs 1.6a, 6.1a, 6.2a, 6.3a, and 7.1a because it is not possible to model nonlinear waves
in my simulation tool, which is based on the linearized radiation and diffraction method (see
Chapter 2 ).
I ran all load-case simulations for both the land – and sea-based turbine configurations using
FAST [ 39] v6.10a-jmj with AeroDyn [ 55,67] v12.60i-pjm and HydroDyn. I also reran some of
the simulations in MSC.ADAMS v2005.2.0 with A2AD [ 20,54] v12.21a-jmj, AeroDyn v12.60i-
pjm, and HydroDyn to verify the responses pred icted by FAST. (Unless otherwise specified, all
results presented in this work were produced by FAST.) All simulati ons were run with all
appropriate and available DOFs enabled. In FAST, these included—for the wind turbine—two flapwise and one edgewise bending-mode DOFs per blade, one drivetrain torsion DOF, one variable generator speed DOF, one nacelle-yaw DOF, and two fore-aft and two side-to-side
tower bending-mode DOFs. For the floating system, three translational (surge, sway, and heave) and three rotational (roll, pitch, and yaw) DOFs were enabled for the platform.
In my loads analyses, I made a couple of smal l modifications to the properties of the NREL
offshore 5-MW baseline wind turbine documented in Section 3.1 and to the FAST model given in Appendix A . (These modifications are include d in the simulations presented in Chapter 5 and
Chapter 6 , but not in those presented in Chapter 3 , Chapter 4 , and Chapter 7 .) To account for
manufacturing variability, all loads-analysis simulations included a mass imbalance in the rotor, which instigates a once-per-rev excitation of the system when the rotor is spinning. I implemented the rotor-mass imbalance by making one blade 0.5% heavier and one blade 0.5%
lighter than the mass of the nominal (reference) blade. This is the same way in which a mass imbalance was applied in the DOWEC st udy (as given on page 19 of Ref. [ 51]). I did not model
an aerodynamic imbalance (such as different blad e-pitch angles or twist distributions) because
AeroDyn does not currently have that capability. All loads-analysis simulations also incorporated a blade structural -damping ratio of 2.5% critical, which is a higher amount of
damping than the 0.477465% value mentioned in Section 3.1.1 and used in the DOWEC study
(from page 20 of Ref. [ 51]). In my experience, the higher number is more representative.
For the power-production cases with and without faults, DLCs 1.x and 2.x, I used the quasi-
steady BEM axial-induction model with the Beddoes-Leishman dynamic-stall model in
AeroDyn. I chose the BEM induction model ov er AeroDyn’s GDW induction model because
the latter is not suitable when the turbulent-wake state is approached (particularly at low wind speeds) [ 67]. I did not wish to see a change in re sponse at the wind speed where I would have
had to switch between the different models. Similarly, I chose the axial-induction model over
AeroDyn’s option for a combination of axial- and tangential- (rotati onal-) induction models
because the tangential-induction model is not num erically stable at all rotor speeds under
96

consideration (particularly the low rotor speeds du ring a shutdown event). In addition, I disabled
both the BEM induction model and the dynamic-sta ll model in AeroDyn for DLCs 6.x and 7.1a,
relying instead on simple lookup-table aerodynamics with geometric angles of attack. I made
this choice because the BEM and dynamic-stall models are not applicable in parked (idling)
cases, particularly at the very hi gh post-stall angles of attack.
The generator-torque and blade-pitch control syst ems are operating properly and the turbine is
producing power normally in DLCs 1.x and prior to the fault in DLCs 2.x. In DLCs 6.x and 7.x,
the control system is disabled. Instead, the rotor is idling in these DLCs with no generator or brake reaction torques, and all blades are fully feathered to the maximum pitch setting of 90ș (exception: one blade is seized at the minimum set point in DLC 7.1a—see the next paragraph).
As described in Section 3.1.6, the control system for the 5-MW baseline wind turbine does not
include logic for the active control of nacelle yaw. In all DLCs, then, I secured the nacelle at given yaw angles with a spring and damper to represent compliance in the yaw drive. I describe the given nacelle-yaw angles in the following discussion of wind conditions.
For DLCs 2.x and 7.x, which involve fault conditi ons, the IEC design standards require choosing
faults with the worst consequences. I chos e common design-driving faults based on my
experience with other land-based wind turbine lo ads analyses. For DLC 2.1, I simulated a fault
in the rotor-collective blade-pitch control syst em where one blade ignores its command and runs
away to the minimum set point of 0ș at the full pitch rate of 8ș/s. I assumed that the turbine’s
protection system detects this fault in this situation by simulating a shutdown of the turbine. The shutdown is initiated after a 0.2-s delay (to account for the time it takes the protection system to detect the fault and take action) by feathering the other two blades at full pitch rate to the maximum pitch setting of 90ș. For DLC 2.3, I simu lated a fault where the load is lost, implying
that the generator reaction torque is zero. In this situation, I again assumed that the turbine’s
protection system detects the fault and shuts down the turbine by feathering all blades after a 0.2-s delay at full pitch rate to the maximum pitc h setting. For DLC 7.1a, I simulated the fault
condition where one blade is seized at the minim um set point (i.e., flat into the wind) while
idling with the other two blades fully feathered.
The hub-height wind speeds,
Vhub, considered within each DLC are listed in Table 5-1 . In the
turbulent-wind models (ETM, EWM, and NTM), Vhub represents the average hub-height wind
speed over a simulation. In the determin istic-wind models (ECD, EOG, and ECD), Vhub
represents the steady wind speed at hub height in the absence of the transient gust. For the cases
where a wind-speed range is indicated from cut-in to cut-out, Vin < Vhub < Vout, I used a set of
simulations with discrete values of Vhub centered within bins of 2 m/s width (i.e., discrete values
of 4, 6, …, 24 m/s). This resolution came from guidance in the IEC design standards. Even
though the design standards recommend that DL C 2.1 be analyzed at all wind speeds between
cut-in and cut-out, I chose to analyze this load case only at the rated ( Vr) and cut-out ( Vout) wind
speeds, again based on my experience that they produce the highest loads. The extreme wind
conditions were considered with the 1- and 50-ye ar recurrence values of the mean reference hub-
height wind speed, V1 and V50, respectively, as shown in Table 5-1 .
We generated the turbulent full-field thre e-component wind conditions with TurbSim [ 36] v1.20.
We used the Kaimal wind spectrum because Turb Sim does not have the capability of generating
turbulent-wind inflow with th e IEC-recommended Mann model [ 33]. (The IEC design standards
97

also allow for the use of the Kaimal wind spectrum.) We generated the deterministic-wind
conditions with a customized copy of IECWind [ 56] v5.00. We had to customize IECWind so
that it would generate wind inflow with a vertic al power-law shear exponent of 0.14 because it
was originally developed only for the 61400–1 design standard.
All winds were generated with a mean wind directi on and a vertical inclination of the mean flow
angle of 0ș, except in DLC 1.4 where the wind direc tion departs from 0ș during the gust. In our
simulations, a mean wind direction of 0ș implies th at the rotor is aligned properly with the wind
when the platform and nacelle are not displaced. For the power-production cases with and
without faults, I aligned the rotor with the wind at the start of the simulation by securing the nacelle-yaw angle at 0ș. For the parked (idling) cases, I also included nonzero-mean nacelle-yaw
misalignments as directed by the design standards and indicated by the yaw specifications in Table 5-1 . DLC 6.2a considers the full range of nacelle-yaw misalignments, −180ș < Yaw <
180ș, because of an assumed inability of the nace lle-yaw controller to align the rotor with the
wind when electrical power is unavailable because the grid is lost. To cover the range of yaw misalignments in this case, I used a set of simulations with discrete nacelle-yaw angles in increments of 20° (i.e., discrete values of −160ș, −140ș, …, 180ș).
Per the guidance of the 61400–3 design standard (and as shown in Table 5-1 ), all normal
irregular sea states (NSS) were considered with a significant wave height,
Hs, given by the
expected value conditioned on the re levant mean hub-height wind speed, E[H s|Vhub], and based
on the long-term joint-probability distribution of me tocean parameters at the reference site (see
Section 3.3). The range of peak spectral periods asso ciated with each expected significant wave
height, Tp, was split uniformly into three bins and was considered in the loads analysis by
running three sets of simulati ons with discrete values of Tp centered within those bins. The
extreme stochastic sea states (ESS) were consider ed with the 1- or 50-year recurrence values of
the significant wave height, Hs1 and Hs50, respectively. I used Hs50 as a conservative estimate for
the severe 50-year significant wave heights conditioned on the relevant mean hub-height wind
speeds in DLC 1.6a. I did this because I did not have the opportunity to compute the latter
values, which must be determined by extrapolating the appropriate site-specific metocean data such that the combination of the significant wave height and wind speed has a recurrence period of 50 years. This practice again follows the guidance of the 61400–3 design standard. As in the
normal wind conditions, I ran three sets of simulations with discrete values of
Tp in the extreme
sea states to represent the range of wave peak spectral periods associated with Hs1. But, in the
simulations with extreme sea states using Hs50, I only used one value of Tp (the midpoint in the
range) because the reference-site data included only a very small range of associated peak spectral periods.
I considered wave propagation to be codire ctional with the winds in DLCs 1.x and 2.x,
β = 0ș,
except in DLC 1.4 where the wind direction departs from the wave direction during the gust. For
the parked (idling) cases, I also included wave misalignments as directed by the 61400–3 design
standard and indicated by the β specifications in Table 5-1 . The design standard requires one to
consider wind and wave misalignments of up to 30° before reducing the severity of the sea state,
so in DLCs 6.x and 7.1a I considered three wave heading directions, one aligned with the wind
and two misaligned with the wind by ±30°.
98

The design standards specify the minimum quantity and length of each simulation in each load
case. More than one simulation is required for each pair of turbulent-wind and stochastic-wave conditions to obtain statistically reliable results. The simulations at each pair of turbulent-wind
and stochastic-wave conditions were differentiated by choosing varying seeds in their respective pseudo-random number generators. I paired the wind and wave seeds so that when
n seeds were
required, I ran n total simulations instead of all n2 combinations of the two seeds.
For D LCs 1.1 and 1.3, the 61400–3 design standard requires that six 10-min simulations2 be run
at each wind and wave condition, diffe rentiated with variations in the wind and wave seeds. For
DLCs 1.4 and 1.5, the design standard requires six 1-min simulations at each wind and wave
condition, differentiated with variations in the wave seed (t he deterministic-w ind models do not
require random seeds to be specified). For DL C 2.1, the design standard requires twelve 10-min
simulations at each wind and wave condition, differ entiated with variations in the wind and wave
seeds. For DLC 2.3, the design standard require s six 1-min simulations at each wind and wave
condition, differentiated with varia tions in the wave seed and the time at which the load is lost
relative to the gust. Finally, for cases with extreme sea states—DLCs 1.6a, 6.x, and 7.1a—the design standard requires six 1-h simulations at each wind, wa ve, and nacelle-yaw condition,
differentiated with variations in th e wind and wave seeds. In this last group of DLCs, a factor of
1.09 is needed to scale the 1- and 50-year recurr ence values of significant wave heights that
correspond to a 3-h reference period to the 1-h leng th of the simulation. Similarly, a factor of
0.95 is needed to scale the 1- and 50-year recu rrence values of the 10-min average wind speeds
to the 1-h length of the simulation. Thes e scale factors also come from the 61400–3 design
standard.
For the power-production cases with and without faults, I initialized the rotor speed and blade-
pitch angles based on the given mean hub-height wind speed for each simulation to mitigate the
start-up transient behavior, which is an artifact of the computational analysis. I initialized the rotor speed and blade-pitch angles to the values they would trim to in the land-based wind turbine (see Section 3.1.8), based on the action of the control system if the given wind speeds
were steady and uniform. Nevertheless, I added 30 s to the required simulation times before outputting simulation data to eliminate any remaining start-up transient behavior that may have spuriously affected my loads predictions. Thus, I actually ran the 1-min simulations for 90 s, and
so on. All of the transient gusts, shears, and direction changes in the de terministic-wind models
were initiated 60 s into the simulation (i.e., 30 s after the end of the 30-s start-up transient). The blade-pitch control system faults in DLC 2.1 were also initiated 60 s into the simulation. The loss of load in DLC 2.3 was initiated at varyin g times during the 10.5-s gust, depending on the
random seed.
Accounting for all of the combinations of wind conditions, wave conditions, and control
scenarios, together with the number of required seeds, I ran a total of 2,190 separate sea-based
simulations and 452 separate land- based simulations in my loads analysis. To manage the
quantity and variety of simulations, we develo ped and utilized custom-made scripts written in
Perl and the Windows batch command language. Using scripts greatly reduced the chance of

2 For all simulations ran for less than 1 h, I generated wave -elevation records based on 1 h to ensure that I captured
an appropriate frequency content.
99

mistakes (and eliminated a great deal of tedium). The main Perl script used an input file to
specify which of the aforementioned DLCs would be run and with what specific parameters.
This script was developed to pr ocess all the cases sequentially on one computer, or in parallel
using the job-queuing utility known as Condor,3 which permits one to distribute a set of
simulations among all idle computers on a ne twork. We used the sequential method only for
debugging. Using Condor on the 45 to 60 availa ble networked processors at NREL / NWTC
enabled me to run most of the DLC simulations for each loads analysis overnight. (If I had had
to run them all sequentially on a single computer , it would have taken just over three weeks of
processing time per loads analysis!)
5.2 Postprocessing and Partial Safety Factors
In addition to examining the time-series output from simulations, we processed all of the loads-
analysis data using the postprocessing computer program Crunch [ 11] v3.00.00, called with
another custom-made Windows batch script. We processed each DLC separately in Crunch
because the processing requirements varied by DLC and because Crunch ca nnot process files of
different lengths. Because of memory restrictio ns, we had to run Crunch on a 64-bit server with
16 GB of random access memory (RAM) to hold the biggest DLC data set in memory all at the
same time. We processed the loads data with Crunch in two different ways. First, we had
Crunch compute the statistics (i.e.; minimum, m ean, and maximum value; standard deviation;
skewness; and kurtosis) of each output parameter for each simulation in each DLC. These data enabled me to characterize the dynamic respons e of the land- and sea-based systems under the
influence of the wind conditions, wave conditions, and control scenarios pertinent to each DLC.
Second, we had Crunch generate extreme-event ta bles for each DLC. These tables list the
extreme minimum and maximum loads for a group of similar output parameters, along with the associated values of the other parameters that occur when the extreme load is reached. The tables also list the specific simulation that triggered the extreme loads and the times at which they occurred, as well other information that may be relevant to the event, such as instantaneous hub-height wind speed and wave elevation.
As Crunch read in the simulation output for the ex treme-event processing, we had it apply partial
safety factors (PSFs) to the blade tip-to-tower clearance outputs, to the internal loads in the wind
turbine, and for the floating system, to the tensions in the mooring lines. We did not apply the PSFs to other output parameters, including the blade-tip and tower-top deflections; the floating
platform displacements; and the control actions such as the generator-torque and power output, and the blade-pitch angles. The PSFs for loads, as specified in the IEC design standards, varied by DLC, and I document them in the last column of Table 5-1 . In addition, an extra factor of 1.2
is stated for DLC 1.1. The IEC design standard s require that the ultima te loads predicted under
normal operation with normal wind-turbulence a nd stochastic-wave cond itions be based on the
statistical extrapolation of the load response. To eliminate this extra step, I decided to use a rule
of thumb resulting from experience with other land-based loads-analysis exercises. From my and others’ experiences, the extrapolation typically increases the predicted ultimate load by 20%. This factor is further justified by the example extrapolation given in Appendix F of the 61400–1 design standard [ 33]. So I increased the normal 1.25 load PSF for DLC 1.1 by 20%, to a value of

3 Web site: http://www.cs.wisc.edu/condor/
100

1.5. I did not, however, increase the load PSF for the calculation of the blade tip-to-tower
clearance outputs in DLC 1.1 as per the design standard, which says that one should not
extrapolate deflections.
According to the IEC 61400–1 design standard [ 33], the PSFs for loads “take account of possible
unfavorable deviations / uncertainties of the load from the characteristic value [and] uncertainties
in the loading model.” We applied the PSFs to the loads in our extreme-event processing to enable a useful comparison of the loads between the DLCs. In other words, it is necessary to weight each DLC properly when determinin g the DLC that causes the overall ultimate
(maximum) load because loads from abnormal design situations, which are less likely to occur,
should be given a lower weighting (and are given a lower load PSF) than normal loads that are
more likely to occur. To obtain the global extremes across all DLCs, we combined all of the extreme-event tables from each DLC using a slightly customized copy of the Perl script CombEEv [ 10] v1.20. We had to customize CombEEv so that it would not only generate the
global extreme-event tables, but also the absolute extremes for each output parameter (i.e., the absolute maximum value of the minima and maxima). I used the absolute extremes for each output parameter to compare the la nd- and sea-based loads results.
The IEC design standards also document PSFs for materials and consequenc es of failure. I did
not apply these, however, because they are the same across all load cases. This means that they will cancel out in the comparison. I also made no attempt to compare the load predictions to the
material or buckling strengths of the individual components.
101

Chapter 6 Loads-Analysis Results and Discussion
I ran loads analyses for extreme (ultimate) loads using the simulation capability documented in
Chapter 2 ; the properties of the wind turbine, floating ITI Energy barge, and reference site
described in Chapter 3 ; and the load-case conditions and procedures explained in Chapter 5 . I
now present the results of this analysis. Because of the sheer volume of results, which includes more than 100 GB of data, I cannot present them all. Instead, I focus on results that are
characteristic of the overall system responses.
My loads analysis helped to identify problems with both the land- and sea-based system
configurations. I discovered a side-to-side instability in the tower of the idling land-based wind turbine when we
1 were processing the loads-analysis data for DLC 6.2a. In the sea-based
system, I discovered an instability in the yaw motion of the floating platform that manifested itself in the fault conditions of DLCs 2.1 and 7.1a. Finally, I determined that the floating barge
system is susceptible to excessive platform-pitching motion in large and / or steep waves, especially in extreme waves such as those occurring during 1- and 50-year events in DLCs 1.6a,
6.x, and 7.1a. These design problems all led to unreasonable loading of the wind turbine, which
dominated the final predictions in ultimate loads.
To gain insight into the dynamic behavior of the onshore and floating systems and to enable a
fair comparison between the two systems, I split the results into groups and present each group
separately. In Section 6.1, I present the land- and sea-based results for DLCs 1.1, 1.3, 1.4, and
1.5, which consider the wind turbine in normal ope ration with a variety of external wind and
wave conditions, not including extreme 1- or 50- year events. These results embody the response
of the systems unencumbered by the aforementione d design problems. I then present (Section
6.2) the findings from the other load cases, DLCs 1.6a, 2.x, 6.x, and 7.1a, which are concerned
with the wind turbine when it is experiencing a fault, when it is idling, and / or when it is being excited by 1- and 50-year wind and wave conditions. My presen tation of this latter group of
DLCs includes a description of the ensuing design problems and possible mitigation measures.
6.1 Normal Operation
I processed the loads-analysis results from the normal operation cases to characterize the
dynamic response of the land- and sea-based systems (Section 6.1.1); to identify the design-
driving conditions and quantify the resulting ultimate loads (Sections 6.1.2 and 6.1.3,
respectively); and to measure the impact of installing the wind turbine on the ITI Energy barge
(Section 6.1.4). Section 6.1.5 draws conclusions from this analysis.

1 My NREL colleague, M. L. Buhl, Jr., assisted me in processing the loads-analysis data. Another NREL colleague,
Dr. G. S. Bir, assisted me in examining the instabilities. To acknowledge this support, I use “we” in place of “I” and
“our” in place of “my” where appropriate in this chapter.
102

6.1.1 Characterizing the Dynamic Response
Figure 6-1 presents the minimum, mean, and maximum values from each simulation in DLC 1.1
for several output parameters. These values are not scaled by the PSFs for loads described in
Section 5.2. The statistics from both the land- and sea-ba sed systems are presented side by side.
The results for the floating system are further gr ouped by the peak spectral period of the incident
waves in each sea state.
The mean values (indicated by the middle dots) of all parameters are very similar between land
and sea, except for the mean value of the platfo rm pitch, which is zero for the land-based wind
turbine because its tower is cantilevered to the gro und at its base. The mean values also correlate
well with the steady-state responses presented in Figure 3-12 . As in Figure 3-12, the mean value
of the rotor speed in Figure 6-1 increases linearly with mean hub-height wind speed below rated
(11.4 m/s) to maintain constant tip-speed ratio and optimal wind-power conversion efficiency.
Similarly, the mean generator power and rotor tor que increase dramatically with wind speed up
to rated, increasing cubically and quadratically, respectively. Above rated, the mean generator
power is held constant by regulating to a fixed speed with active blade-pitch control and a generator torque that is inversely proportional to the generator speed. The mean values of the out-of-plane tip deflection and root-bending mome nt of the reference blade (Blade 1) reach a
maximum at the rated operating poi nt before dropping again. This response characteristic is the
result of a peak in rotor thrust at rated (not shown in Figure 6-1 , but seen in Figure 3-12 ). This
peak in response is also visible, though less pr onounced, in the mean values of the platform
pitch, tower-top fore-aft displacement, and tower-base fore-aft bending moment.
The mean values are similar between land and sea, but Figure 6-1 shows that the excursions of
the minimum and maximum values (indicated by the lower and upper horizontal dashes,
respectively) in the sea-based results are much larger. The widest spread between the minimum and maximum values in the land-based simulations occurs in the generator power parameter just
above rated. This is a result of the large diff erence in control actions when switching between
Regions 2 and 3 while operating in turbulen t winds near optimal wind-power conversion
efficiency. The excursions of minimum and maximum values for all parameters in the sea-based simulations, however, increase with wind speed. More precisely, they increase with the pitch motion of the floating platform, which increases w ith wind speed. This is because the barge has
a natural tendency to move with the surface waves and because the expected value of the
significant wave height increases with wind speed, as shown in Figure 3-15 . The pitching of the
barge causes large variations in the generator power and rotor speed, which may lead to a loss of energy capture and an increase in aeroacoustic emissions. The pitching of the barge also causes large load excursions—more so for the tower-bas e loads than for the loads in the blades and
drivetrain—because the floating system acts as an inverted pendulum, with the largest effect
from inertia loading nearest the pivot point. The magnitudes of the minimum and maximum loads in the floating system are largest with sea states derived from large significant wave heights and from peak spectral periods in the rang e of 10 to 15 s. The wave-period range of 10
to 15 s is particularly dominant because the resulting waves are more likely to excite the rigid-body—turbine plus barge—pitch mode. That mode has a natural frequency of about 0.0863 Hz, which equates to a natural period of about 11.6 s. So even though the expected significant wave height is lower at a mean hub-height wind speed of 22 m/s than at 24 m/s, the loads in the
103

Land Sea, 5 s < Tp < 10 s Sea, 10 s < Tp < 15 s Sea, 15 s <Tp < 20 s

-30-20-100102030
3579 1 1 1 3 1 5 1 7 1 9 2 1 2 3 2 5
Hub-Height Wind Speed, m/sPlatform Pitch, ș
01,0002,0003,0004,0005,0006,000
3 5 7 9 11 13 15 17 19 21 23 25Hub-Height Wind Speed, m/sGenerator Power, kW

0510152025
3579 1 1 1 3 1 5 1 7 1 9 2 1 2 3 2 5Hub-Height Wind Speed, m/sRotor Speed, rpm
-2,00002,0004,0006,0008,000
3 5 7 9 1 11 31 51 71 92 12 32 5
Hub-Height Wind Speed, m/sRotor Torque, kN·m

-15-10-5051015
3 5 7 9 11 13 15 17 19 21 23 25
Hub-Height Wind Speed, m/sBlade 1 Out-of-Plane Tip Deflection, m
-30,000-20,000-10,000010,00020,00030,000
3 5 7 9 11 13 15 17 19 21 23 25Hub-Height Wind Speed, m/sBlade 1 Out-of-Plane Root Bending
Moment, kN·m

-4-2024
3579 1 1 1 3 1 5 1 7 1 9 2 1 2 3 2 5Hub-Height Wind Speed, m/sTower-Top Fore-Aft Displacement, m
-800,000-400,0000400,000800,000
3 5 7 9 11 13 15 17 19 21 23 25
Hub-Height Wind Speed, m/sTower-Base Fore-Aft Bending
Moment, kN·m

Figure 6-1. Statistics from each simulation in DLC 1.1
floating system are higher at 22 m/s than at 24 m/s, where the wave periods are higher (but
outside the critical wave-period range).
104

Similar statistical trends exist for both the land- and sea-based system responses in DLC 1.3 (not
shown). The only difference is that some of the output parameters, pa rticularly for the land-
based wind turbine, have slightly larger load excursions that result from increased turbulence in the wind inflow.
6.1.2 Identifying Design-Driving Load Cases
I identified the design-driving load conditions and quantified the resulting ultimate loads by
examining the extreme-event tables. We generated 21 tables for the land-based loads and 32 tables for the sea-based loads. Each table cont ains a distinct group of similar output parameters,
such as the internal loads in the blades, drivetrain, nacelle, and tower, and for the floating system, tensions in the mooring lines. The extreme events for the root moments of the reference blade (Blade 1) in the land- and sea-based analyses are presented in Table 6-1 and Table 6-2 ,
respectively. The extreme events for the tower-base moments in the land- and sea-based analyses are presented in Table 6-3 and Table 6-4 , respectively. All of the extreme-event tables
we generated for both the land- and sea- based loads analyses are contained in Appendix F .
Table 6-1. Extreme Events for the Blade 1 Root Moments – Land

Table 6-2. Extreme Events for the Blade 1 Root Moments – Sea

Table 6-3. Extreme Events for the Tower-Base Moments – Land

Table 6-4. Extreme Events for the Tower-Base Moments – Sea
105

The extreme-event tables record
• The extreme minimum and maximum loads (the shaded values on the block diagonal) for
each parameter (identified in the first column)
• The name of the simulation output file that triggered the extreme load (third column)
• The time at which the extreme load was reached (last column)
• The associated values of the other parameters that occur when the extreme load is
reached (off-diagonal values).
The loads data have all been weighted using the PSFs for loads described in Section 5.2. In an
actual turbine design, these loads data would be fed into a finite-element analysis (FEA) program to determine the detailed stress distributions within individua l turbine components, such as the
blades, hub, shaft, and tower. I did not perform this extra step, however, because my project is
only a conceptual and feasibility study.
In the parameter names for the blade-root moment tables, “Mxc1,” “Myc1,” and “Mzc1” refer to
the internal moments about the
x-, y-, and z-axes of the coordinate sy stem of Blade 1, which is
fixed in the hub so as not to rotate with the pitch control motion of the blade. The x-axis of this
coordinate system is dire cted nominally downwind, the y-axis is located in the plane of rotation,
and the z-axis is directed from the hub to the tip of Blade 1. (Reference [ 39] illustrates this
coordinate system and others related to the analyzed loads.) The parameters, then, correspond to
the in-plane bending moment, the out-of-plane bending moment, and the pitching (torsion)
moment at the root of Blade 1, respectively. In the parameter names for the tower base, “Mxt,”
“Myt,” and “Mzt” refer to the internal moments about the x-, y-, and z-axes of the tower-base
coordinate system. The x-axis of this coordinate system is directed nominally downwind, the y-
axis is directed transverse to the nominal wind direction, and the z-axis is directed vertically from
the tower base to the yaw bearing. The parame ters correspond to the roll (side-to-side) bending
moment, the pitch (fore-aft) bending moment, and the yaw (torsion) moment at the tower base,
respectively. The file names list the DLC, the simulation number, the land or sea basis, the wind and wave conditions, and th e random-seed identifier.
For the wind turbine installed on land, Table 6-1 shows that DLCs 1.3 and 1.4 drive most of the
extreme root moments in Blade 1 and Table 6-3 shows that DLC 1.3 produces all of the extreme
moments in the base of the tower. In contrast, Table 6-2 and Table 6-4 show that DLC 1.1 plays
more of a role in triggering the ultimate loads for the wind turbine mounted on the barge. In particular, the sea-ba sed simulation numbered 164 in DL C 1.1 generates (1) the minimum and
maximum out-of-plane bending moments in the root of Blade 1, (2) the maximum pitching moment in the root of Blade 1, (3) the minimum and maximum pitch bending moments in the tower base, and (4) the maximum yaw moment in the tower base—all within a 7-s period of time (i.e., from time 256 to 263 s).
6.1.3 Design-Driving Load Events
To determine the exact sequence of events and the physics behind the dynamic response that led
to the extreme load of each output parameter, I examined the time-series output from each of the
dominant simulations identified by the extreme-event tables.
106

Figure 6-2 presents a portion of the time history for several output paramete rs from the sea-based
simulation numbered 164 in DLC 1.1. Results from independent FAST with AeroDyn and
HydroDyn and ADAMS with AeroDyn and HydroDyn runs are shown side by side. As
indicated within the associated file name in Table 6-2 and Table 6-4 , this particular simulation
has a random-seed identifier of 01, stochastic winds with a mean hub-height wind speed of 22 m/s, and irregular waves with a significant wave height of 4.7 m and a peak spectral period of
13.4 s.
The parameter names in Figure 6-2 that have not been previously defined earlier in this chapter
are as follows:
• “WindVxi” represents the instantaneous nominally downwind component of the wind
speed at the undeflected hub location.
• “WaveElev” represents the instantaneous wave elevation relative to the SWL at the origin
of the undisplaced platform.
• “PtfmPitch” represents the instantaneous pitch angle of the platform (barge).
• “GenPwr” represents the instantaneous electrical output of the generator.
• “RotSpeed” represents the instantaneous rotati onal speed of the rotor (low-speed shaft).
• “RotTorq” represents the instantaneous mechanical torque in the low-speed shaft.
The response of the floating system during the first half of the time histories in Figure 6-2 is
characteristic of its response in many other simulations. The incident waves cause the barge to
pitch back and forth. The ensuing motion in the supported wind turbine causes all the other parameters to exhibit the same oscillatory behavior. Moreover, the pitching causes a large translation of the wind turbine’s nacelle, which results in an oscillating inflow to the rotor. As the platform pitches downwind (positive slope), the rotor’s relative wind speed decreases, causing the applied aerodynamic torque to drop. The control system responds by driving the
blade-pitch angles to zero (not shown). As the aerodynamic torque drops, there is a mismatch with the generator torque, so the rotor speed decreases as well. (The reverse is true when pitching upwind.) The rotor speed exhibits much more variation than one would see in a land-
based wind turbine. (The rotor torque shown in Figure 6-2 equals the difference between the
applied aerodynamic torque and the rotor-inertia acceleration or deceleration by d’Alembert’s principle [ 25], which is why the phase of the response may not follow intuition.)
107

010203040WindVxi,
m/sFAST ADAMS
-4-2024WaveElev,
m
-40-2002040PtfmPitch,
ș
02,0004,0006,0008,000GenPwr,
kW
0102030RotSpeed,
rpm
-2,00002,0004,0006,0008,000RotTorq,
kN·m
-40,000-20,000020,00040,000RootMyc1,
kN·m
-800,000-400,0000400,000800,000
100 150 200 250 300 Simulation Time, sTwrBsMyt,
kN·m

Figure 6-2. Time histories from sea-based simulation number 164 in DLC 1.1
108

During the second half of the time history in Figure 6-2 , the response of the floating system
changes considerably. As shown, a series of large incident waves begins to impinge on the
barge. These waves have a height of around 7 m and propagate near the barge-pitch natural
frequency of 0.0863 Hz. Concurrent with these wa ves are sustained hub-height winds near cut-
out (25 m/s) that are then followed by a gust to 30 m/s. These wind and wave conditions bring
about excessive pitch motion of the barge that le ads to large loads in the blades and tower and
large excursions in the rotor-speed and generato r power output, as well as extreme values in the
rotor-thrust, tower-top-displacement, and nacelle-acceleration output parameters (not all shown).
In fact, this one series of events drives one-quarter of the extreme values for all of the most relevant output parameters . The loads plotted in Figure 6-2 are not scaled by the PSFs, which is
why the extreme values of the blade-root out -of-plane and tower-base pitch bending moments
seen in the FAST time histories do not exactly match the values listed in the extreme-event tables shown earlier.
There are differences between the FAST and ADAMS predictions in Figure 6-2 , mostly after the
series of events that trigger the largest loads. I believe that these differences are caused by the
greater structural fidelity of the ADAMS simulato r, which includes torsion and mass offsets in
the blade model that are not accounted for in FAST . A clear consequence of these differences is
that the blade-pitch angles are smaller for ADAMS than for FAST because the control system in
FAST must compensate for the lack of blade twist. This difference is visible in the simulation
results I present next.
By ex amining Table 6-1 and the other extreme-event tables presented in Appendix F , I
discovered that DLC 1.4 drives the extreme out-o f-plane blade-tip deflec tions and several blade
loads in both the land- and sea-based system configurations. Figure 6-3 presents a portion of the
time history for several output parameters during the sea-based simulation of this design-driving
event. Again, results from independent FAST with AeroDyn and HydroDyn and ADAMS with
AeroDyn and HydroDyn runs are shown side by side and the data are not scaled by the PSFs for loads.
Of the parameter names not previously defi ned above or earlier in this chapter,
• “BlPitch1” represents the instantaneous pitch angle of Blade 1.
• “OoPDefl1” and “IPDefl1” represent the in stantaneous out-of-plane and in-plane tip
deflections of Blade 1 relative to the undeflected blade-pitch axis.
• “NcIMUTAxs” represents the instantaneous acceleration of the inertial measurement
unit, which is located in the nacelle at, and aligned with the centerline of, the main low-
speed shaft bearing.
• “PtfmYaw” represents the instantaneous yaw angle of the platform (barge).
109

02,0004,0006,0008,000GenPwr,
kWFAST ADAMS
Start of Event
0510152025BlPitch1,
ș
05101520RotSpeed,
rpm
-1001020OoPDefl1,
m
-4-2024IPDefl1,
m
-4-2024NcIMUTAxs ,
m/sec2
-10-505PtfmYaw,
ș
-15,000015,00030,000
30 40 50 60 70 80 90
Simulation Time, sRootMyc1,
kN·m

Figur e 6-3. Time histories from sea-based simulation number 101 in DLC 1.4
110

This particular simulation is numbered 101 and has a random-seed identifier of 04, a steady hub-
height wind speed of 13.4 m/s (2 m/s above rated) before the ECD event, and irregular waves
with a significant wave height of 2.7 m and a peak spectral period of 12.7 s. Before the ECD event, which starts at 60 s, the barge oscillates in pitch, again because of the impinging surface waves. This is seen in Figure 6-3 through the oscillatory effect on the out-of-plane blade-tip
deflection and root-bending moment, the nacelle fore-aft acceleration, the rotor speed, and the
blade-pitch angle. The blade-pitch angle varies depending on the action of the control system
responding to the oscillating rotor speed, which in turn is a result of the oscillating wind inflow relative to the rotor. In an interesting result, even when the hub-height wind speed is above rated
and steady, there are still short periods of below-rated operation where power is lost.
The ECD event starts at 60 s and takes 10 s to reach the 15 m/s increase in wind speed and the
concurrent 54ș change in wind direction. The wi nd direction shifts to the left when looking
downwind. As shown in Figure 6-3 , the escalation in wind speed from the gust generates a rise
in the rotor speed and an increase in the blade-pitch angle as the control system tries to compensate. But the change in wind direction produces a large nacelle-yaw error that eventually causes the wind speed relative to the rotor to drop. This, in turn, causes the rotor speed and blade-pitch angle to decrease. The maximum out-o f-plane tip deflection (of nearly 14 m!) occurs
after this series of events, when the blade is pointing horizontally into the wind just after the blade-pitch angle reaches its 0ș minimum set point. The condition where this occurs is severest for the blade deflections and loads because the blade is flat into the wind during that time. Although the extreme out-of-plane bending moment at the root of Blade 1 is higher in DLC 1.1, this series of events in DLC 1.4 brings a bout the maximum out-of-plane bending moment in
Blade 1 at 50% span (not shown in Figure 6-3 , but included in Appendix F.2). The ECD event
also perturbs the yaw angle of the barge. After th e event is over, the barge begins to yaw slightly
into the wind. There is still about a 50ș nacelle-yaw error at 90 s into the simulation, but the mooring lines eventually restrain the platform from yawing any farther.
Of all the different hub-height wind speeds I ran s imulations for in DLC 1.4, the simulations at a
wind speed of 2 m/s above rated led to the larg est out-of-plane blade-tip deflections in the
floating turbine. This wind speed was associated with the highest wave heights and the resulting
barge-pitch motion exacerbated an existing problem. In the wind turbine installed on land, the DLC 1.4 simulations run at rated wind speed ge nerated the largest out-of-plane blade-tip
deflections and bending moments.
For the land-based wind turbine, DLC 1.3 played a significant role in driving many of the
extreme values of the most relevant output parameters not driven by DLC 1.4. Although I do not
present any of the time histories, DLC 1.3, with its extreme wind turbulence, was particularly
dominant because the resulting wind inflow contained many drastic jumps or drops in wind speed. These wind speed changes generated ultimate loads because the control system could not react fast enough. Jumps in wind speed from below to above rated, or from above to below
rated, created particularly large deflections and loads because of the peak in thrust at rated. Large variations in wind speed near cut-out were also problematic.
The wind turbine mounted on the floating barge was more affected by the waves than the wind.
Consequently, DLC 1.1 in the sea-based analysis, which has the higher effective PSF for loads, dominated the loads results more than DLC 1.3, whic h has higher levels of wind turbulence. In
111

other words, higher PSF for loads were more impor tant than higher levels of wind turbulence.
For example, the maximum magnitude of acceleration in the nacelle at the main shaft bearing
was 10.1 m/s2 (just over 1 g) in the floating turbine, as driven by large waves in DLC 1.1, but
only 1.4 m/s2 in the land-based turbine, as driven by extreme wind turbulence in DLC 1.3.
The only loads in the floating system that appeared to be driven more by wind than waves were the tensions in the mooring lines. The tensions, particularly at the anchors and the fairleads of the upwind mooring lines, were driven by simulati ons involving sustained winds at or near rated
wind speed. This is because sustained winds at ra ted generate the highest sustained rotor-thrust
forces, which push the barge far downwind (i.e., a large surge displacement), and tug on the
upwind mooring lines. Even at maximum tension, though, there was enough slack in the mooring lines to keep them from pulling upward on the anchors. This result means that inexpensive anchors could be used.
In relation to DLCs 1.1, 1.3, and 1.4, DLC 1.5, which considers transient wind-shear events, did
not play a significant role in driving ultimate loads in either the land- or sea-based wind turbine
systems.
6.1.4 Comparing Land- and Sea-Based Loads
We took the absolute extreme values of each para meter (i.e., the absolute maximum values of the
minima and maxima, from the block diagonals of the extreme-event tables) of the sea-based
analysis of DLCs 1.1, 1.3, 1.4, and 1.5 and divided th em by the corresponding absolute extremes
of the land-based analysis. The resulting dimensionless ratios quantify the impact of installing the NREL 5-MW baseline wind turbine on the floating ITI Energy barge. I present the ratios for many of the parameters in Figure 6-4 . A ratio of unity (indicated by the dashed horizontal line)
would imply that the absolute extreme is una ffected by the dynamic couplings between the
turbine and the floating barge in the presence of combined wind and wave loading. Ratios greater than unity imply an increase in load or response that may have to be addressed by
modifying the system design in subsequent analysis iterations.
The chart in the upper-left corner of Figure 6-4 presents the sea-to-land ratios for the absolute
extremes of the generator power, generator torque , generator (high-speed shaft) speed, and rotor
(low-speed shaft) speed. The sea-to-land ratio of the generator torque is unity because the
variable-speed control system, which is identi cal in the land and sea analyses, places a limit on
the torque command to avoid excessive overloading of the genera tor and gearbox (see Section
3.1.6.2). Nevertheless, greater generator power excursions are seen in the sea-based system because of the increased excursions in generator speed. This may have to be addressed in the floating wind turbine to avoid generator burnout. The sea-to-land ratios of the generator and rotor speed are identical because the high- and lo w-speed shafts are directly coupled through the
gearbox. The rotor-speed excursions in the floati ng wind turbine are 60% higher than those seen
in the turbine installed on land. These excursions are the result of the oscillatory wind inflow
relative to the rotor from the pitching motion of the barge, as discussed earlier. They will most assuredly lead to an increase in aeroacoustic em issions from the rotor, which may or may not be
important offshore.
112

012345
GenPwr GenTq GenSpeed RotSpeedRatio of Sea to Land
012345
OoPDefl1 IPDefl1 TTDspFA TTDspSSRatio of Sea to Land
5.6

012345
RootFMxy1 RootFzc1 RootMMxy1 RootMzc1Ratio of Sea to Land
012345
RotThrust LSSGagFMyz RotTorq LSSGagMMyzRatio of Sea to Land

012345
YawBrFMxy YawBrFzp YawBrMMxy YawBrMzpRatio of Sea to Land
5.2
012345
TwrBsFMxy TwrBsFzt TwrBsMMxy TwrBsMztRatio of Sea to Land
6.06.4

Figure 6-4. Sea-to-land ratios from DLCs 1.1, 1.3, 1.4, and 1.5
The chart in the upper-right corner of Figure 6-4 presents the sea-to-land ratios for the absolute
extremes of the out-of-plane and in-plane tip defl ections of Blade 1 and the fore-aft and side-to-
side displacements of the tower top (i.e., yaw bearing). The sea-to-land ratio for the tower-top
fore-aft displacement exceeds the upper bound of 5 placed on the ordinate, which is why its
value of 5.6 is listed. This ratio is much larger than the sea-to-land ratio of the out-of-plane
blade-tip deflection again because of the inverted-p endulum effect discussed earlier. The larger
excursions of in-plane blade-tip deflection in the sea-based system are the result of faster rotor rotational accelerations, corresponding with the el evated excursions in rotor speed. The tower
side-to-side displacements are larger in the floating wind turbine because larger yaw errors are present between the nominal wind direction and the rotor axis. These, in turn, come from the yaw motion of the barge. That motion is excited by a gyroscopic yaw moment resulting from the
113

spinning inertia of the rotor in combination with the pitching motion of the barge. Larger yaw
motions are permissible because of the yaw compliance of the mooring system.
The remaining four charts in Figure 6-4 , from the middle-left to the lower-right corner, present
the sea-to-land ratios for the absolute extremes of the forces and moments in the root of Blade 1,
in the low-speed shaft at the main bearing, in the yaw bearing, and in the tower base,
respectively. In the parameter names, “FMxy” refers to the magnitude of the internal shear force in the transverse
x- and y-plane of the various coordinate sy stems. These were found by taking
the vector sum of the shear forces along the x- and y-axes. Similarly, “MMxy” refers to the
magnitude of the internal bendi ng moment in the transverse x- and y-plane of the various
coordinate systems, calculated by taking the vector sum of the bending moments about the x- and
y-axes. We computed the maximum values of the vector sums as opposed to the more
conservative calculation of the vector sums of the maximum values. The remaining parameters
refer to the axial forces along, and the torsion moments about, the primary axis of the members.
The sea-to-land ratios of the internal shear force and bending moment magnitudes, in general, increase as one follows the load path from the blade tip, through the drivetrain and nacelle, to the tower base. This increase in relative loading between the sea- and land-based systems results
again from the inverted-pendulum eff ect in the floating wind turbine; that is, there is more effect
of loading from inertia farther down the load path. The axial forces in the blades are increased in
the floating wind turbine relative to the onshore turbine because of the centripetal effect from
elevated excursions in rotor speed . The axial forces at the yaw bearing and tower base are larger
in the floating system than in the onshore system because of the heave motion of the barge as it follows the up and down elevation of the waves. The sea-to-land ratio of the rotor thrust,
“RotThrust,” is large because it is computed not as the applied aerodynamic thrust, but as the internal force within the low-speed shaft, which by d’Alembert’s principle [ 25] is the difference
between the applied thrust and the fore-aft rotor-i nertia acceleration or deceleration. The inertia
effect itself is large again because of the barge-pitch motion. To withstand the increased loading for the wind turbine mounted on the floating barge, the tower will certainly have to be strengthened, and the blades and drivetrain may have to be as well.
Of course, all the results presented so far were derived from the environmental conditions at the
chosen reference site. As I discussed in Section 3.3, we chose this reference site for its fairly
extreme wind and wave conditions, with the implication that if the results of the loads analysis
are favorable, the floating wind turbine system under consideration will be applicable at almost any site around the world. The loads-analysis results indicate, however, that without design
modifications, there is the potential for loads in the floating wind turbine that are much larger (up
to 6.4 times as large at the tower base, as indicated in Figure 6-4 ) than what would be seen in an
equivalent onshore wind turbine. Because of this , it is beneficial to examine whether or not the
existing concept, without modifica tion, may be better suited at a site where conditions are less
severe.
I studied the effect of the choice in reference site by rerunning the sea-based loads analysis with
varying environmental conditions. Instead of choosing different locations to reobtain metocean
data, I took a simpler approach and obtained vary ing environmental conditions by modifying the
existing data from the chosen reference site. I chose to adjust only the data of significant wave height because the size of the waves was the key parameter that led to the excessive pitching of
114

the barge and subsequent loading of the floating wind turbine. I did not modify the wind-speed
data because I wanted to maintain a fair comparison to the results from the land-based wind
turbine, which is unaffected by wave conditions . Neither did I modify the wave-period data
because the range of wave periods considered are typical of sites around the world and because I did not want to adversely affect the wave steepne ss. (The wave steepness is related to the wave
height and wavelength, the latter of which is dictated by the wave frequency or period.) I
adjusted the data of significant wave height by scaling down the magnitude of each data sample provided by the Waveclimate.com service, which corresponds to scaling consistently across all
other conditions. I chose wave-height scaling factors of 75%, 50%, 25%, and 0%. For example, with a wave-height scaling factor of 50%, the expected value of the significant wave height would increase with the mean hub-height wind sp eed that it is conditioned on, from about 0.8 m
(instead of 1.6 m) at cut-in to about 3.0 m (inste ad of 5.9 m) at cut-out (the original data are
plotted in Figure 3-15 ). A wave-height scaling factor of 0% represents still water with no
incident surface waves (but outgoing waves can still be generated by wave radiation).
I reran the sea-based loads analysis with the reference-site data adjusted by each wave-height scaling factor. Figure 6-5 presents the sea-to-land ratios for the absolute extremes from the rerun
loads analysis of DLCs 1.1, 1.3, 1.4, and 1.5. The leftmost ratios of each parameter, labeled
“100% – Original,” correspond to the ratios presented in Figure 6-4 , which result from the
original reference-site data. The remaining ratios of each pa rameter correspond with decreasing
severity in the wave conditions, from left to right.
For most parameters, the sea-to-land ratios decline rapidly at first, then drop off more slowly
with decreasing severity in the wave conditions. So, interestingly, the response is nonlinear even though the hydrodynamic model is primarily base d on linear radiation and diffraction theory (see
Section 2.4). This implies that other nonlinear features of the model—such as aerodynamic
loading, turbine dynamics, and control actions—are affecting the response. Moreover, even in
still water, the wind turbine mounted on the barge experiences higher loading than the turbine
that is installed on land. In fact, the absolute extreme magnitude of the internal bending moment at the base of the tower is still 60% higher for the floating wind turbine in still water than for the turbine on land. This implies that the barge pitches because of the wind inflow as well as wave
excitation. Nevertheless, the results show that the potential loads in the floating wind turbine
will be considerably less at a sheltered site than at a site in the open ocean.
6.1.5 Drawing Conclusions about Responses in Normal Operation
To summarize the results presented in this sectio n, the pitching motion of the barge brings about
load excursions in the supported wind turbine that exceeds those experi enced by the turbine
when it is installed on land. The load excursi ons are worse in the tower than in the blades
because of the increased effect of inertia from the barge-pitch motion. To arrive at a technically feasible concept, the design will need to be modified, except possibly at the most sheltered of sites. This is not surprising, however, because I made no attempt to minimize the motions of the
floating platform in this analysis, which was the first step of the design-iteration process outlined
in the beginning of Chapter 5 .
Two forms of design modifications are possible. First, the turbine, especially the tower, could be
strengthened to enable it to withstand the increased loading. However, this approach may not be
115

100% – Original 75% 50% 25% 0% – Still Water
012345
GenPwr GenTq GenSpeed RotSpeedRatio of Sea to Land
012345
OoPDefl1 IPDefl1 TTDspFA TTDspSSRatio of Sea to Land
5.6

012345
RootFMxy1 RootFzc1 RootMMxy1 RootMzc1Ratio of Sea to Land
012345
RotThrust LSSGagFMyz RotTorq LSSGagMMyzRatio of Sea to Land

012345
YawBrFMxy YawBrFzp YawBrMMxy YawBrMzpRatio of Sea to Land
5.2
012345
TwrBsFMxy TwrBsFzt TwrBsMMxy TwrBsMztRatio of Sea to Land
6.06.4

Figure 6-5. Sea-to-land ratios for va riations in significant wave height
cost-effective even though the wind turbine in an offshore floating system represents a smaller
fraction of the total installed cost than in an onshore system. Second, design alterations may be
able to improve the response of the floating sy stem to diminish the increases in loading.
One possible approach to improving the response of the floating system is to add design features that will increase damping to stabilize the barge-pitch motion. In ITI Energy’s original concept, not only is the barge designed to support the NREL offshore 5-MW baseline wind turbine, but it is also a platform for an OWC wave-power device. Unfortunately, I could not model the OWC
device with my current simulation tool, as described in Sections 3.2 and 4.1.2. But if positioned
suitably and controlled properly, the OWC may be able to introduce damping of the barge-pitch
motion while extracting wave energy. This concept is currently being researched through
116

analytical modeling and wave-tank testing at NAME at the Universities of Glasgow and
Strathclyde [ 98]. Other actuator opportunities include gyro actuators, used commonly for system
stabilization in aerospace and spacecraft appli cations, or hydrodynamic thrusters, used
commonly for station-keeping in naval architecture.
To dampen the barge-pitch motion, it may also be possible to develop a wind turbine control
system that relies on the conventional wind turbin e actuation of blade pitch, generator torque,
and nacelle yaw. In Chapter 7 , I present the results of my analysis examining the influence of
conventional blade-pitch contro l systems on the pitch damping of the wind turbine—plus
floating barge—system.
Beyond active control, a simpler solution for improving the barge-pitch damping may be to
introduce passive damping devices into the underlyi ng design. Tuned-mass dampers (TMDs) are
frequently employed in skyscrapers to dampen wind-induced vibrations. Similarly, a TMD
could be placed at the top of the wind turbine’s tower; when tuned at the natural period of the
rigid-body—turbine plus barge—pitch mode, such a system could dampen pitching (and rolling)
motion dramatically. It may also be possible to dampen the barge rotational motions with the equivalent of passive an ti-roll stabilizers installed within or on top of the barge. (Anti-roll
stabilizers, which are commonly installed on ships, act like TMDs, but are made of water-filled U-tube tanks [ 22].) The platform’s hydrodynamic radia tion damping and viscous drag could also
be increased by incorporating damping orifices in the planform of the barge or horizontal
damping plates and / or bilge keels positioned below the free surface.
Instead of trying to improve the barge-pitch damping, it may be better to add DOFs in or
between the floating platform and the wind turbine to eliminate the direct coupling between the motions of the platform and the turbine. For example, articulated joints could be installed in the
floating platform, as in th e Versabuoy offshore system,
2 or between the wind turbine’s tower and
nacelle, as in the Wind Eagle turbine [ 46].
Finally, the easiest solution may be to modify the geometry of the floating platform or the layout
of the mooring system, or both, to reduce the barge’s natural pitch motion. This would,
consequently, minimize the impact on the su pported wind turbine. Possibilities include
streamlining the shape of the barge to allow surface waves to more easily pass by (i.e., as in a spar-buoy concept), shifting the CM closer to the COB through ballast (i.e., as in a spar-buoy
concept), or introducing ta uter mooring lines (i.e., as in a TLP concept).
6.2 Other Load Cases
As mentioned in this chapter’s introduction, I identified problems with both the land- and sea-
based system configurations when we processed the loads-analysis results for DLCs 1.6a, 2.x,
6.x, and 7.1a. These DLCs are concerned with the wind turbine when it is experiencing a fault,
when it is idling, and / or when it is being exc ited by 1- and 50-year wind and wave conditions. I
describe these problems in more detail here, but because the loads resulting from the problems were unreasonable, I do not quantify them. I al so discuss potential design modifications that
may be used to correct the problems.

2 Web site: http://www.vbuoy.com/index.html
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Section 6.2.1 describes the tower side-to-side instability of the land-based wind turbine, Section
6.2.2 describes the platform-yaw instability of the sea-based wind turbine, and Section 6.2.3
describes the susceptibility of the barge to excessive motions in extreme waves. All of these
results are based on the loads-analysis data. Though not presented here, we have also analyzed the instabilities using linear system models and obtained consistent results (see Ref. [ 2]).
DLC 2.3 considers an extreme operating wind gust concurrent with a loss of load. I did not
include the results for this case in Section 6.1 because of the way I split the results into
meaningful groups. Because DLC 2.3 did not cause problems in either the land- or sea-based
wind turbine systems—relative to DLCs 1.6a, 2.1, 6.x, and 7.1a—I do not discuss any of the results from DLC 2.3 in this work.
6.2.1 Tower Side-to-Side Instability of Land-Based Wind Turbine
The first problem I discovered was a side-to-side instability in the tower of the wind turbine installed on land. This instability was identified when we were analyzing the loads predicted by land-based DLC 6.2a. The instability occurs when the turbine is idling with all blades fully
feathered to the maximum pitch setting of 90ș, bu t only when the rotor is positioned at certain
azimuth angles and is misaligned with the mean wind direction by 20ș to 40ș on either side of 0ș. (DLC 6.2a considers the full range of yaw misalignments because of an assumed inability of the nacelle-yaw controller to align the rotor with the wind when electrical power is unavailable
because the grid is lost.) DLC 6.2a required me to analyze this situation with extreme 50-year
wind conditions,
V50 = 50 m/s. After more study, though, we discovered that the instability is
predicted at much lower wind speeds, as low as a mean hub-height wind speed of 25 m/s. The
instability is more severe, however, at the higher wind speeds. The instability leads to excessive limit-cycle oscillations in the tower-top side-to-si de displacement and the tower-base side-to-side
(roll) bending moment. The oscillations occur at about 0.32 Hz, which corresponds with the
natural frequency of the first side-to- side bending mode of the tower (see Table 3-11 ).
In the sea-based simulations of DLC 6.2a, it is difficult to distinguish an instability from the excessive barge motions generated by the extrem e 50-year wave conditions (described as the
third problem in Section 6.2.3 below). To eliminate the excessive barge motions, we reanalyzed
the floating wind turbine with all of the specifications of DLC 6.2a except the 50-year wave conditions, which we replaced with s till water. In this situation, the instability is nonexistent; in
a fascinating finding, the barge compliance actually helps to eradicate the side-to-side instability in the land-based tower, at least when no incident surface waves are present. In other words, the tower is prevented from going unstable because of the barge’s compliance in still water.
The reason for the instability in the land-based turbine is almost certainly because the amount of
structural damping in the first side-to-side bending mode of th e tower is exceeded by the amount
of energy the rotor absorbs within the critical range of rotor-azimuth and nacelle-yaw-error
angles. This probably results from the range of wind-inflow angles of attack on the blades during those conditions. It is difficult to determine what causes what, though, because of the classic chicken-and-egg problem: Which comes first? The oscillation in angles of attack or the
instability? It is also difficult to determine if the predicted instability is physical or an artifact of
my analysis. As described in Section 5.1, I ran this DLC without AeroDyn’s induction or
dynamic-stall models enabled because they are not applicable in this idling case, particularly at
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very high post-stall angles of attack. Examining the time histories of the angles of attack might
be worthwhile for determining if the simple lookup-table aerodyn amic methods that I used are
adequate in this situation. The examination might also allow one to determine if other aerodynamic theories are more appropriate and w ould predict different behavior. But I did not
consider this action necessary in this preliminary analysis.
Nevertheless, the information I do know about the tower side-to-side instability of the land-based
wind turbine suggests two possible remedies that ma y be pursued if the problem is real instead of
virtual. First, it may be possible to modify the shape of the airfoils in the blades to reduce the amount of energy absorption at th e problematic angles of attack.
3 A second possibility is to
apply a fail-safe brake to park the rotor in extreme winds and to keep it away from the critical azimuth positions. The downside to this second so lution is that it may cause excessive wear on
the brake and become a source of routine maintenance. In the time history presented in Figure
6-6, however, I show that this solution does work. The figure shows the results of two separate
FAST simulations. The first simulation consid ered the onshore wind turbine idling with all
blades fully feathered in steady uniform 50-m/ s winds and a nacelle-yaw error of 30ș. The
second simulation used the same set of conditions, but at 150 s into the simulation, we applied a high-speed shaft brake. Before the brake is engaged, the responses predicted by the two simulations are identical. After the brake is engaged, the amplitude of the limit-cycle oscillation in the tower-top side-to-side displacement is reduced significantly. (The cycles are very close together and difficult to discern because the frequency of about 0.32 Hz is small for the range of
simulation times considered on the abscissa.)
-4-2024
0 100 200 300 400 500 600
Simulation Time, sTower Top Side-to-Side
Displacement, mNo Brake
BrakeBrake Engaged

Figure 6-6. Time history of the tower side-to-side instability
6.2.2 Platform-Yaw Instability of Sea-Based Wind Turbine
The second problem I discovered was a yaw instability in the barge of the floating wind turbine.
The instability occurs when the rotor is idling with a fault, where one blade (the faulted blade) is
seized at the minimum pitch set point of 0ș and the other two blades are fully feathered to the
maximum pitch setting of 90ș. We identified this instability during analysis of the loads predicted by sea-based DLCs 2.1 and 7.1a. In DLC 2.1, which consid ers normal wind and wave

3 Even though the NREL 5-MW baseline wind turbine model is heavily based on the publicly available
specifications of the REpower 5M prototype wind turbine, there is no reason to conclude that the REpower 5M
machine has a tower side-to-side instability. The airfoil properties (which influence the instability) of the NREL 5-
MW baseline wind turbine are likely very different from those of the REpower 5M turbine.
119

conditions, the instability occurs after the protection system has detected the blade-pitch fault
and shut down the turbine. The instability is more severe in DLC 7.1a , which required me to
analyze this fault condition under extreme 1-year wind and wave conditions with misalignments in the mean wind and wave directions of ±8ș and ±30ș, respectively. After more study, however, we discovered that the instability is predicted by my simulation tool regardless of the yaw misalignment and also in still water. The instability is caused by a coupling of the barge-yaw motion with the azimuthal motion of the seized blade, and leads to excessive limit-cycle oscillations in the barge-yaw displacement. This , in turn, may cause a knotting of the mooring
lines (although my simulation tool cannot model lin e-to-line interference), excessive loading of
the wind turbine from the ensuing dynamics, or both. The oscillations occur at about 0.02 Hz, which corresponds with the natural frequency of the rigid-body—turbine plus barge—yaw mode.
The i dling-plus-fault condition does not cause a problem in the land-based wind turbine because
it has very little yaw compliance. This conditio n may cause problems, however, that are more
pronounced in floating spar-buoy or TLP concepts than in the floating barge because the former concepts are likely to be more compliant in yaw because smaller moment arms are available to resist yaw moments. In the floating barge, the yaw instability may also be less severe than my simulation tool predicts because my model considers hydrodynamic damping in yaw only from wave radiation (i.e., potential flow), which is negligible at the yaw mode natural frequency (see
B66 in Figure 4-5 at about 0.02 Hz = 0.1257 rad/s). In actuality, hydrodynamic viscous damping
in yaw may be more dominant. Hydrodynam ic viscous damping in yaw comes from vortex
shedding off the corners of the barge and skin fri ction, neither of which are accounted for in my
model (Morison’s equation considers viscous drag only in surge, sway, roll, and pitch—see
Section 2.4.2.2). It may be worthwhile to try to quantify the viscous-drag contributions through
wave-tank tests for the vortex-shedding drag an d / or ship-resistance formulas for the skin-
friction drag to see if they provide enough damping to eliminate the yaw instability. But, as in our investigation of the tower side -to-side instability, I did not consider this action necessary at
this time.
As in the tower side-to-side instability, several pathways may be pursued to eliminate the yaw
instability of the barge if the problem is real instead of virtual. Possibilities include
• Supplementing the existing yaw damping by installing damping plates below the free
surface
• Increasing the yaw stiffness by adding a so -called “crowfoot” at the connection between
each mooring line and the barge
• Applying a fail-safe shaft brake to park the rotor when shutdown
• Reducing the pitch angle of the fully feathered blades to generate a low, but persistent,
aerodynamic torque that will produce a slow roll of the rotor while idling.
The latter two solutions would prevent the sei zed blade from coupling with the platform-yaw
motion. Again, we tested the brake approach with FAST simulations and present the results in
Figure 6-7 . The first simulation considered the floating wind turbine idling with one blade flat
into the wind (faulted) and with steady uniform 40-m/s winds and no incident surface waves
(still water). The second simulation used the sa me set of conditions, but at 100 s into the
simulation, we applied a high-speed shaft brake. Before the brake is engaged, the responses
120

-180-90090180
0 100 200 300 400 500 600
Simulation Time, sPlatform Yaw,
șNo Brake
Brake
Brake Engaged

Figure 6-7. Time history of the platform- yaw instability
predicted by the two simulations are identical. After the brake is engaged, the limit-cycle
oscillation in the barge-yaw displacement is eliminated.
6.2.3 Excessive Barge Motions in Extreme Waves
The final problem I discovered through my load s analysis was that the floating barge is
susceptible to excessive motions when the incident waves are large and / or steep, such as during extreme 1- or 50-year wave conditions. This is especially true with the harsh conditions that occur at the chosen reference site. The problems exist whether the wind turbine is idling, as in
DLCs 6.x and 7.1a, or producing power, as in DLC 1.6a. The response is worse, however, in the idling turbine because the operating turbine introduces more aerodynamic damping. The
response is also worse in the 50-year wave co nditions than in the 1-year conditions. The
problems in DLCs 1.6a or 6.x are not relate d to a system instability because the problems
disappear in simulations where the extreme wave conditions are exchanged with still water.
The problematic motions usually occur in a series of stages. First, the barge begins to pitch back
and forth as it moves with the incident surface waves. The large pitching motion leads to
excessive deflections in the blades and tower of the wind turbine. When the blades deflect
asymmetrically because of variations in the rotor-aximuth angle, turbulence in the wind, or misalignment of the waves from the barge’s planes of symmetry, the barge gets excited in other modes of motion, such as roll and yaw.
4 The overall result is excessive deflections and loading
throughout the entire system, from the blades to th e moorings. The problem is so bad that even
though the blade tips of the undeflected or undisplaced floating turbine are positioned 30 m
above the SWL (see Section 3.1), the system gets jostled so severely that the blade tips pass
below the free surface in many of the DLC simulations involving 1- and 50-year wave conditions.
All of the simulations exhibiting this problem co ntain waves and responses that most assuredly
violate linear hydrodynamic radiation and diffracti on theory, and my simulation tool is invalid in

4 This response shows the importance of the fully coupled dynamics solution, demonstrating that the motions of the
support platform are coupled with the motions of the wind turbine. The simulations in Section 6.1 demonstrate that
the wind turbine excites the floating platform yaw motions through the rotor’s gyroscopic effect. The simulations in DLCs 6.x and 7.1a, however, show that asymmetric deflections in the wind turbine also contribute to excitation of
the platform motions. (The coupling between the wind turbine and floating platform motions is not the result of
rotor gyroscopics because the rotor is idling—not spinning—in these DLCs.)
121

these situations. It is unclear, however, whether the “real” responses would fare better or worse.
This is simply a fundamental limitation with my analysis, if not with most other computational
capabilities available in the offshore O&G industry today. To get around these limitations, wave-tank testing of a scaled model under equiva lent conditions is required. This work has
already been initiated at NAME at the Universities of Glasgow and Strathclyde [ 98].
More likely than not, unless the barge is installed only at sheltered sites, modifications to the system design will be required to eliminate the vulnerability of the barge to extreme waves. The design modifications listed in Section 6.1.5 will help to solve this problem, except those
modifications that involve activ e wind turbine control (which are not applicable to an idling
turbine), or active control of other actuators (which cannot always be relied on during extreme
events). I plan to examine many of these design modifications in subsequent projects.
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Chapter 7 Influence of Conventional Control on Barge-Pitch
Damping
Chapter 6 showed that the pitching motion of the ITI Energy barge brings about load excursions
in the supported wind turbine that exceed those th e turbine experiences when it is installed on
land. One possible approach to improving the response of the floating system is to incorporate
design features that will increase damping to stabilize the barge-pitch motion. Damping can be tailored through passive design features and ac tive control. The NREL offshore 5-MW baseline
wind turbine I developed and used in the land – and sea-based loads analyses relied on a
conventional variable-speed, variable blade- pitch-to-feather control system (see Section 3.1.6).
A consequence of conventional pitc h-to-feather control of wind turbines, though, is that steady-
state rotor thrust is reduced with increasing wind speed above rated (see Figure 3-12 ). As
pointed out by Nielsen, Hanson, and Skaare in Ref. [ 75, p. 673], “this effect may introduce
negative damping in the system that may lead to large resonant motions of [a] floating wind
turbine.” As the loads-analysis results of Chapter 6 demonstrate, it is important that the damping
of the barge-pitch mode be positive and kept as large as possible.
Section 7.2 addresses the influence of conventional wind turbine c ontrol methodologies to the
pitch damping of the floating wind turbine system analyzed in Chapter 6 . In this work, my aim
was to modify the baseline control system of the NREL 5-MW turbine to improve the pitch
damping of the ITI Energy barge. Moreover, I wanted to make these improvements using
conventional wind turbine control t echniques to establish a modified baseline with which I could
compare more advanced or unconve ntional control scenarios. Even though I performed this
work specifically for the NREL baseline wind turbine and the ITI Energy barge, the analysis
process is valid for other concepts in which fl oating platforms support wind turbines controlled
by blade pitch. Section 7.3 qualitatively discusses other potential methods for improving the
damping performance using wind turbine control.
First, however, it is important to describe the barge-pitch damping problem in more detail.
Section 7.1 presents more details and a quantification of the problem.
7.1 Overview of the Platform-Pitch-Damping Problem
The barge-pitch damping problem can be analyzed by considering the rigid-body platform-pitch
mode as a single DOF. The equation of motion for this simple model is
() ( ) ( ) Mass Radiation Radiation Viscous Hydrostatic Lines HH I AB B C Cξξ ++ + ++ = && & L Tξ , (7-1)
where ξ is the platform-pitch angle (i.e., rotational displacement), ξ& is the platform-pitch
rotational velocity, ξ&& is the platform-pitch rotational acceleration, IMass is the pitch inertia
associated with wind turbine and barge mass, ARadiation is the added in ertia (added mass)
associated with hydrodynamic radiation in pitch, BRadiation is the damping associated with
hydrodynamic radiation in pitch, BViscous is the linearized damping associated with hydrodynamic
viscous drag in pitch, CHydrostatic is the hydrostatic restoring in pitch, CLines is the linearized
123

hydrostatic restoring in pitch from all mooring lines, T is the aerodynamic rotor thrust, and LHH is
the hub height (i.e., rotor-thrust moment arm).
Thoug h not directly evident from Eq. (7-1), the aerodynamic rotor thrust also contributes to the
platform-pitch damping. To consider its effect, it is convenient to state the equation of motion in
terms of the translational motion of the hub instead of the pitching motion of the platform. For small pitch angles, the translational displacement of the hub,
x, is linearly related to the platform-
pitch angle by
HH xLξ= . (7-2)
Like the blade-pitch sensitivity discussed in Section 3.1.6.3, the aerodynamic rotor thrust
depends on the wind speed, rotor speed, and blade-pitch angle. To be clear, its dependence on
the wind speed is actually a dependence on the relative wind speed at the hub because the hub can move in this simple model of the platform-pitch mode. If the hub translation varies slowly, the wake of the rotor will respond to changes in hub speed just as it does to changes in wind speed. Considering variations in aerodynamic rotor thrust only with hub speed, a first-order
Taylor series expansion gives

0TTT xV∂=−∂&, (7-3)
where T0 is the aerodynamic rotor thrust at a linearization point and V is the rotor-disk-averaged
wind speed.
The negative sign appears in Eq. (7-3) because, from Figure 2-1 , positive platform-pitch angles
correspond to downwind translati onal displacements of the hub, resulting in a reduction of the
relative wind speed. By combining Eqs. (7-1) through (7-3) and simplifying, the equation of
motion of the platform-pitch mode stated in terms of the translational motion of the hub becomes

xx xHydrostatic Lines Mass Radiation Radiation Viscous
0 22 2
HH HH HH
MC KCC IA B B Tx xLL V L+ ⎛⎞ ⎛ ⎞ ⎛++ ∂++ + ⎜⎟ ⎜ ⎟ ⎜∂ ⎝⎠ ⎝ ⎠ ⎝&& &
1442443 1444 424444 31 4 4 42444 3xT⎞=⎟
⎠. (7-4)
As in the PID-controlled rotor-speed error, one can see that the isolated rigid-body platform-
pitch DOF will respond as a second-order system with the natural frequency, ωxn, and damping
ratio, ζx, equal to
x
xn
xK
Mω= (7-5)
and
x
x
x xC
2K Mζ= . (7-6)
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Most of the terms in the effective mass, damping, and stiffness coefficients in Eq. (7-4) are easy
to quantify. In particular, the terms related to the effective mass and stiffness, including the
added inertia (added mass) in pitch and the linea rized pitch restoring of the mooring system, are
easily computed from a linearization analysis in FAST with HydroDyn. This linearization analysis resulted in a platform-pitch natural frequency for the ITI Energy barge with the NREL 5-MW baseline wind turbine of
ωxn = 0.5420 rad/s = 0.0863 Hz.1
Two terms in Eq. (7-4) , the damping associated with hydrodynamic radiation in pitch, BRadiation ,
and the thrust sensitivity to wind speed, TV∂∂, are more difficult to quantify. The former is
problematic because the hydrodynamic wave-radiation loads in the true linear hydrodynamic-loading expressions are actually described by a convolution integral (see Section 2.4.1.3), which
is used to capture the wave-radiation memory eff ect. This convolution term is not convenient in
this analysis or in the design of modern contro l systems. For use in controls engineering, for
instance, Ref. [ 53] describes a method of converting the convolution term to state-space form by
adding “radiation memory states.” To get around this complication in this analysis, however, I
neglected the memory effect and approximated
BRadiation as the amount of linear radiation
damping at the platform-pitch natural frequency, ωxn (i.e., BRadiation ≈ 0.86E+8 kg •m2/s from
Figure 4-5 ). This choice is consistent with the linear time-domain representation of the
frequency-domain problem described in Section 2.4.2.1.
The thrust sensitivity to wind speed, TV∂∂, can be computed in multiple ways. One way
would be to estimate this sensitivity (at each wind speed) as the slope of the steady-state thrust versus wind-speed response discussed in Section 3.1.8 and presented in Figure 3-12 . (Because
the aerodynamic rotor thrust depends on wind speed , among other factors, the thrust sensitivity
to wind speed depends on wind speed as well.) This way of computing the thrust sensitivity to wind speed characterizes the sensitivity of an ideal closed-loop blade-pitch speed-regulation
system. I say “ideal” because a real blade-pitch control system (see Section 3.1.6.3) responds to
rotor-speed error (not variations in wind speed) and because the steady-state speed is constant
with wind speed throughout Region 3 where the rotor-speed control system functions (again, see
Figure 3-12 ).
A second way of estimating the thrust sensitiv ity to wind speed would be to perform a
linearization analysis in FAST with AeroDyn. FAST with AeroDyn could be used to compute
TV∂∂ at each of a number of given, steady, and uniform wind speeds and at the associated
rotor speeds and blade-pitch angles from the stea dy-state response. This would be accomplished

1 This frequency falls in the range of typical sea states, which have peak spectral periods in the range of 5 to 20 s
(see ) corresponding to frequencies in the range of 0.05 to 0.2 Hz (i.e., 0.314 to 1.257 rad/s). The barge
will tend to oscillate at the excitation frequency of the incident waves, but the motions will be most severe when the wave-excitation frequency is at or near the barge’s natural frequency. If the barge were to oscillate at its natural
frequency with a pitch amplitude of A
ξ, the amplitude of the hub translational velocity would be Figure 3-15
HH xnALξω and the
amplitude of the hub translational acceleration would be 2
HH xnALξω. For Aξ = 5ș, this translates into hub velocity and
acceleration amplitudes of about 4.26 m/s and 2.31 m/s2 = 0.24 g’s, respectively; for Aξ = 10ș, this translates into hub
velocity and acceleration amplitudes of about 8.51 m/s and 4.61 m/s2 = 0.47 g’s, respectively. At these amplitudes,
the wind turbine control system will continuously switch between below- and above-rated control regions, except at
the very lowest and highest mean hub-height wind speeds.
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by perturbing the wind speed at each operating po int and measuring the variation in the resulting
aerodynamic thrust (using the sa me process described in Section 3.1.6.3 for computing the
aerodynamic power sensitivity to blade-pitch angle). This way of computing the thrust
sensitivity to wind speed characterizes the sensitiv ity of an open-loop system because the blade-
pitch angle is not varied with the perturbations in wind speed.
I calculated TV∂∂ using both methods and show the results in Table 7-1 . I found the slope of
the steady-state thrust versus wind-speed response in the ideal closed-loop method from the
central-difference approximation of the derivative using the two wind speeds on either side of
each given wind speed. This is why I did not estimate the slope at the cut-in and cut-out wind
speeds. The magnitude of this slope is largest near rated, where the slope changes sign. In the open-loop method, the thrust sens itivity increases with wind speed below rated and remains flat
and positive above rated.
Using these thrust sensitivities to wind speed and other properties of the ITI Energy barge with
the NREL 5MW baseline wind turbine, I estimated the barge-pitch damping ratios according to
Eq. (7-6) . Figure 7-1 presents these ratios. The barge-pitch damping ratio is largest in
magnitude and changes sign at the rated wind speed of 11.4 m/s for the ideal closed-loop
method, just like the thrust sensitivity to wind speed. Just above rated, th e damping ratio is less
than −10%. Near the cut-out wind speed of 25 m/s, the positive-valued hydrodynamic-radiation
and viscous damping exceed the magnitude of the negative-valued aerodynamic damping, so the barge-pitch damping ratio becomes slightly positiv e again. In the open-loop method, the barge-
Table 7-1. Pitch-to-Feather Sensitivity of Aerodynamic Thrust to Wind Speed
Wind Speed Rotor Speed Pitch Angle Open-Loop ∂T/∂VIdeal Closed-Loop ∂ T/∂V
(m/s) (rpm) (ș) (N/(m/s)) (N/(m/s))
3.0 – Cut-In 6.97 0.00 29.43E+3
4.0 7.18 0.00 32.81E+3 48.61E+3
5.0 7.51 0.00 36.17E+3 57.17E+3
6.0 7.94 0.00 39.86E+3 64.83E+3
7.0 8.47 0.00 43.63E+3 73.89E+3
8.0 9.16 0.00 46.49E+3 90.33E+3
9.0 10.30 0.00 52.26E+3 106.74E+3
10.0 11.43 0.00 57.97E+3 105.69E+3
11.0 11.89 0.00 57.64E+3 -0.769E+3
12.0 12.10 3.82 74.80E+3 -91.09E+3
13.0 12.10 6.60 79.98E+3 -66.00E+3
14.0 12.10 8.67 82.50E+3 -43.99E+3
15.0 12.10 10.45 83.82E+3 -33.37E+3
16.0 12.10 12.05 84.49E+3 -26.39E+3
17.0 12.10 13.54 84.90E+3 -21.42E+3
18.0 12.10 14.92 85.85E+3 -17.68E+3
19.0 12.10 16.23 86.43E+3 -14.79E+3
20.0 12.10 17.47 85.41E+3 -12.79E+3
21.0 12.10 18.70 84.33E+3 -11.77E+3
22.0 12.10 19.94 84.29E+3 -10.79E+3
23.0 12.10 21.18 85.34E+3 -9.26E+3
24.0 12.10 22.35 85.22E+3 -7.92E+3
25.0 – Cut-Out 12.10 23.47 84.39E+3
126

-0.15-0.10-0.050.000.050.100.150.200.250.30
3 5 7 9 11 13 15 17 19 21 23 25
Wind Speed, m/sBarge-Pitch Damping Ratio, -Open-Loop
Ideal Closed-Loop

Figure 7-1. Pitch-to-feather barge-pitch damping ratios
pitch damping ratio remains positive across all wind speeds. The ratio increases with wind speed
below rated and remains flat above rated. With real blade-pitc h-control speed regulation above
rated, the actual damping ratio is difficult to quantify with this simple model, but will fall
somewhere between the bounds imposed by the open- and ideal closed-loop results.
7.2 Influence of Conventional Wind Turbine Control Methodologies
To improve the barge-pitch damping, I modified the baseline control system with a number of
conventional wind turbine control methodologies. These included (1) adding a second blade-
pitch control loop through feedback of tower-top acceleration, (2) changing from variable blade-
pitch-to-feather to variable blade-pitch-to-stall speed-control regulation, and (3) detuning the
gains in the variable blade-pitch-to-feather ro tor-speed controller. I developed and tested
(through simulation) each approach independently. The rationale behind each approach and the main findings are presented in Sections 7.2.1, 7.2.2, and 7.2.3, respectively.
7.2.1 Feedback of Tower-Top Acceleration
The conventional approach to improving the tower fore-aft damping in land-based wind turbines
is to append the conventional blade-pitch controller for rotor-speed regulation with an additional blade-pitch control loop, which uses a tower-top acceleration measurement [ 3]. Naturally, the
same technique could be applied to modify the platform-pitch damping of an offshore floating
wind turbine. The intent of the new control loop would be to augment the aerodynamic rotor thrust with adjustments to the blade-pitch angle based on the tower-top acceleration measurement. To see the effect of blade-pitc h angle on the platform-pitch damping, consider
127

variations in the aerodynamic thrust with full-span rotor-collective blade-pitch angles, θ, in
addition to hub speed, as was accounted for in Eq. (7-3) :
0TTTT xVθθ∂∂=−+ Δ∂∂& . (7-7)
In Eq. (7-7), Δθ is a small perturbation of the blade-pitc h angles about their operating point. If
the blade-pitch rate in the tower-feedback (T FB) control loop is proportional to a tower-top
acceleration measurement through a gain KPx, then:
PxKxΔθ=&&& (7-8a)
or
t
Px Px
0K xdt K x Δθ==∫&& & . ( 7-8b)
By combining Eqs. (7-8b) and (7-7) with the equations presented in Section 7.1 and simplifying,
the addition of a TFB control loop modifies the effective damping coefficient from Eq. (7-4) and
becomes
Radiation Viscous
x 2
HH
NewTermBB TCLVPxTKθ+ ∂∂=+ −∂∂14243. (7-9)
The effective mass and stiffness coefficients from Eq. (7-4) are left unchanged by the addition of
the TFB control loop.
In an active blade-pitch-to-feather wind turbine, the thrust sensitivity to rotor-collective blade
pitch, Tθ∂∂ , is negative-valued from cut-in to cut-out so damping is increased with a positive
control gain. Once the thrust sensitivity to rotor-collective blade pitch is known and a control
gain is chosen, the effective increase in platform-pitch damping ratio, Δζx, according to the given
model is
Px
x
xxK T
2K Mζθ∂⎛Δ= − ⎜⎞
⎟∂⎝⎠. (7-10)
Alternatively, a proper control gain can be chosen specifically from any desired increase in
platform-pitch damping according to the given model. Just like the thrust sensitivity to wind speed, though, the thrust sensitivity to rotor-collective blade-pitch angle depends on the wind speed, rotor speed, and blade-pitch angle. Cons equently, one cannot obtai n a constant increase
in damping ratio across control regions without gain-scheduling. The gain-scheduling law for
the TFB control system will not, however, be as simple as the law used in the blade-pitch rotor-
speed-regulation controller because the thrust senstitivy to blade pitch is not linearly related to
128

the blade-pitch angle. I calculated the thrust sensitivity to blade pitch from a linearization
analysis in FAST with AeroDyn, and show the results in Table 7-2 .
In the middle of Region 3 (18 m/s), a modest 0.05 increase in effective damping ratio requires a
control gain of KPx = 0.007556 rad/(m/s) and a large 0.5 increase in effective damping ratio
requires a control gain of KPx = 0.07556 rad/(m/s). Naturally, the larger the control gain, the
larger the blade-pitch-rate requi rement. Conversely, to limit th e blade-pitch rate, one has to
minimize the effective increase in damping ratio. From footnote 1 on page 125, barge-pitch
amplitudes in the range of Aξ = 5 to 10ș can result in hub-acceleration amplitudes ranging from
2.31 to 4.61 m/s2. In the middle of Region 3 according to the given model, damping these
motions using the TFB control loop developed previously will require blade-pitch-rate
amplitudes in the range of = 1.0 to 2.0ș/s for the modest 0.05 increase in effective damping
ratio and = 10.0 to 20.0ș/s for the large 0.5 increase in effective damping ratio.
Consequently, only moderately larg e increases in effective damping ratio are achievable with the
given blade-pitch-rate limit of 8ș/s (from Section Δθ&
Δθ&
3.1.6.4).
I incorporated the TFB control loop into my FAST with AeroDyn and HydroDyn simulations
using an extension of the baseline control system DLL. As implemented, the TFB blade-pitch
angle commands were found by measuring the tower-t op fore-aft acceleration, integrating to find
the tower-top fore-aft velocity, and then multiplying by the control gain. This blade-pitch-angle command was then added to the blade-pitch-angle command from the rotor-speed controller,
Table 7-2. Pitch-to-Feather Sensitivity of Aerodynamic
Thrust to Blade Pitch
Wind Speed Rotor Speed Pitch Angle ∂T/∂θ
(m/s) (rpm) (ș) (N/rad)
3.0 – Cut-In 6.97 0.00 -1.556E+6
4.0 7.18 0.00 -1.646E+6
5.0 7.51 0.00 -1.783E+6
6.0 7.94 0.00 -1.982E+6
7.0 8.47 0.00 -2.238E+6
8.0 9.16 0.00 -2.533E+6
9.0 10.30 0.00 -3.201E+6
10.0 11.43 0.00 -3.939E+6
11.0 11.89 0.00 -3.988E+6
12.0 12.10 3.82 -4.603E+6
13.0 12.10 6.60 -4.664E+6
14.0 12.10 8.67 -4.702E+6
15.0 12.10 10.45 -4.733E+6
16.0 12.10 12.05 -4.765E+6
17.0 12.10 13.54 -4.806E+6
18.0 12.10 14.92 -4.905E+6
19.0 12.10 16.23 -4.983E+6
20.0 12.10 17.47 -4.944E+6
21.0 12.10 18.70 -4.906E+6
22.0 12.10 19.94 -4.979E+6
23.0 12.10 21.18 -5.125E+6
24.0 12.10 22.35 -5.182E+6
25.0 – Cut-Out 12.10 23.47 -5.200E+6
129

which had already been saturated for the angle and rate limits. Said another way, I did not
saturate the TFB control system commands.
For the NREL 5-MW wind turbine mounted atop th e ITI Energy barge, I tested the system
response at a variety of wind and wave conditions with both the modest and high TFB gains.
Figure 7-2 shows a response with the high KPx = 0.07556 rad/(m/s) TFB gain for a simulation
with stochastic winds with a mean hub-height wind speed of 18 m/s and irregular waves with a
significant wave height of 3.673 m and a peak spectral period of 13.376 s. (These waves have
the expected value of the significant wave height and the median value of the peak spectral period conditioned on the mean hub-height wind speed at the chosen reference site; see Figure
3-15). The system response with the unmodified (baseline) control system is shown for
comparison in Figure 7-2 . I ran the simulations with all appropriate and available DOFs enabled,
as applied in the loads analysis and described in Section 5.1, but without considering the rotor-
mass imbalance or the increased blade structural-damping ratio. In Figure 7-2 , the ordinates
“GenPwr,” “GenSpeed,” “BlPitch1,” and “PtfmPitch” correspond to the instantaneous electrical
output of the generator, generator (high-speed shaf t) rotational speed, pitch angle of Blade 1, and
platform-pitch angle, respectively.
It may seem surprising at first that the results do not show a large improvement in the damping
of the barge-pitch motion (“PtfmPitch”). The exacerbated excursions in generator speed and
electrical output are more promin ent. These results can be ex plained by thinking about the
problem in more detail than is provided in the simple model. The relative wind speed is highest when the system is pitching into the wind (i.e., from maximum to minimum barge-pitch angles).
02,0004,0006,0008,000
Time (sec)GenPwr, kWBaseline Baseline+TFB
05001,0001,5002,000
Time (sec)GenSpeed, rpm
-40-2002040
Time (sec)BlPitch1, ș
-10-50510
0 50 100 150 200 250 300
Simulation Time, sPtfmPitch, ș

Figure 7-2. System responses with and without a tower-feedback control loop
130

This causes the rotor-speed control system to pitch the blades to feather (more positive) to shed
power and regulate speed while the TFB damping control system pitches the blades to stall
(more negative) to increase thrust and introduce damp ing. The reverse is true when the turbine is
pitching with the wind. In this case, the relative wind speed is lowest when the system pitches downwind, causing the rotor-speed control system to pitch the blades to stall while the TFB damping control system commands pitching to feat her. Said another way, the two blade-pitch
control systems are at odds and fight with each other in this situation. This can be seen by the blade-pitch angle responses of Figure 7-2 , where in many instances, the pitch-angle commands
in the baseline control system move in the opposite direction to the pitch-angle commands in the
combined baseline and TFB control system.
Similar results (not shown) are obtained with the more modest
KPx = 0.007556 rad/(m/s) TFB
gain. Here, the generator speed and power excursions are not as badly exacerbated, but there is
also less improvement in the damp ing of the barge-pitch motion.
The simple model I describe in this section is routinely applied in the design of TFB damping control algorithms for land-based wind turbines. But, because the amplitude of the overall tower
motion is less in land-based turbines, the problem with generator speed and power excursions is
less of an issue. Instead, the control system designer for land-based wind turbines must make a
basic trade-off between improve d tower damping and increased generator speed and power
excursions. For the floating system considered in this work, however, the severity of the tower-
top motions induced by the barge’s movement w ith surface waves renders the conventional TFB
damping control system ineffective.
7.2.2 Active Pitch-to-Stall Speed-Control Regulation
As described in the introduction to this chapter, th e problem to be addressed is that the reduction
in steady-state rotor thrust with increasing wind speed in Region 3, which occurs as a result of variable blade-pitch-to-feather speed-control re gulation, may introduce negative damping in the
platform-pitch mode. This implies that variable blade-pitch-to-stall speed-control regulation may be more effective at damping the barge-pitch motions because drag (and hence thrust) increase as power is shed (to regulate speed) in increasing relative winds in wind turbines controlled by an active pitch-to -stall system. Although variable blade-pitch-to-stall speed-
control regulation has been shown to work effec tively in simulation, it has not been widely
pursued in the wind industry because of the “uncertainty that remains in the theoretical understanding of stalled rotor aerodynamics” [ 3, p. 234]. In spite of this uncertainty, I tested the
effects of active pitch-to-stall speed-control regulation for the floating wind barge concept.
Before pursuing the design of the pitch-to-stall controller, I decided to smooth the airfoil-data
coefficients (as presented in Figure 3-1 through Figure 3-6 ) near stall to eliminate the existing
fluctuations that could have led to numerical problems in the BEM aerodynamic-induction solution algorithm. I modified the airfoils by manually manipulating the lift coefficients.
131

Once the airfoil data were corrected, I redevel oped the full-span rotor-collective blade-pitch
controller according to the same procedure I used to arrive at the blade-pitch-to-feather speed-
control gains (see Section 3.1.6.3). Like I did for the pitch-to-feather controller design, I
calculated the sensitivity of aerodynamic power to blade pitch, Pθ∂∂, by performing a
linearization analysis in FAST with AeroDyn. Table 7-3 shows the results for operation in
Region 3.
The blade-pitch angles that produce the rated mechanical power (5.296610 MW) are negative-
and double-valued over the wind-speed range of Region 3, first decreasing, then increasing, with
increasing wind speed. By being double-valued, it is impossible to use the same gain-scheduling
law I implemented in the active pitch-to-feather controller. But because, the variation in blade-pitch sensitivity across Region 3 is less pronounced, gain scheduling is le ss of a requirement.
Instead, I chose constant gains using the value of
Pθ∂∂ in the middle of Region 3 (18 m/s) to
develop the PID gains. Using the recommended response characteristics of ωφn = 0.6 rad/s and
ζφ = 0.7 [ 29] resulted in gains of KP = −0.00731238 s, KI = −0.00313388, and KD = 0.0 s2. The
gains are negative-valued because Pθ∂∂ is positive-valued. The gains are also smaller in
magnitude than the pitch-to-feather gains at rated because the blade-pitch sensitivity—or control authority—is higher in pitch-to-stall operation.
I incorporated the blade-pitch-to-stall speed-regulation controller into my FAST with AeroDyn
and HydroDyn simulations by a simple modifica tion of the baseline control system DLL. I
modified the gains to the values derived in th is section and I fixed the maximum and minimum
pitch settings at 0ș and − 90ș, respectively. To eliminate the influence of the gain-scheduling law,
I set
θK to an arbitrarily large value. Like I did for the baseline system in Figure 3-12, I obtained
the steady-state response of the land-based NREL 5-MW wind turbine by running a series of
FAST with AeroDyn simulations at a number of given, steady, and uniform wind speeds. The
results for the same output parameters plotted in Figure 3-12 are shown in Figure 7-3 .
Table 7-3. Sensitivity of Aerodynamic Power to Blade
Pitch (to Stall)
Wind Speed Rotor Speed Pitch Angle ∂P/∂θ
(m/s) (rpm) (ș) (watt/rad)
11.4 – Rated 12.1 0.00 -28.24E+6
12.0 12.1 -6.76 27.72E+6
13.0 12.1 -7.50 46.94E+6
14.0 12.1 -7.79 47.14E+6
15.0 12.1 -8.05 49.82E+6
16.0 12.1 -8.22 54.43E+6
17.0 12.1 -8.26 59.92E+6
18.0 12.1 -8.20 65.70E+6
19.0 12.1 -8.05 71.22E+6
20.0 12.1 -7.84 75.64E+6
21.0 12.1 -7.60 81.00E+6
22.0 12.1 -7.32 84.96E+6
23.0 12.1 -7.03 88.59E+6
24.0 12.1 -6.74 89.94E+6
25.0 12.1 -6.46 91.10E+6
132

01,0002,0003,0004,0005,0006,000
3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
Wind Speed, m/sGenSpeed, rpm
RotPwr, kW
GenPwr, kW
RotThrust, kN
RotTorq, kN·mRegion 1½ 2 2½ 3

-10-505101520253035404550
3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
Wind Speed, m/sRotSpeed, rpm
BlPitch1, ș
GenTq, kN·m
TSR, -Region 1½ 2 2½ 3

-2-1012345678910
3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
Wind Speed, m/sOoPDefl1, m
IPDefl1, m
TTDspFA, m
TTDspSS, mRegion 1½ 2 2½ 3

Figure 7-3. Steady-state pitch-to-stall responses as a function of wind speed
133

As shown in Figure 7-3 , the intended increase in rotor thrust (“RotThrust”) with wind speed
across all control regions is noticeable, although the increase is small from just above rated to
cut-out. As a result of the thrust increase, and in contrast to the pitch-to-feather response, the
out-of-plane blade-tip deflection (“OoPDefl1”) and the tower-top fore-aft displacement
(“TTDspFA”) both increase dramatically upon entering Region 3. I left the baseline generator-torque controller unchanged so the steady-state sy stem response is identical to the response of
the pitch-to-feather system below rated wind speed.
As in Section 7.2.1, I tested the system response of the NREL 5-MW wind turbine mounted atop
the ITI Energy barge with this new control syst em at a variety of wind and wave conditions.
Figure 7-4 compares the active pitch-to-feather and ac tive pitch-to-stall system responses for the
simulation with the same wind a nd wave conditions applied to the simulations presented in
Figure 7-2 (i.e., an 18-m/s stochastic wind, a 3.673-m significant wave height, and a 13.376-s
peak spectral period). Again, I ran the simula tions with all appropria te and available DOFs
enabled, but without considering the rotor-mass imbalance or the incr eased blade structural-
damping ratio. As shown in Figure 7-4 , active blade-pitch-to-stall control regulates generator speed—and hence
electrical power—very well. It performs even better than the baseline active blade-pitch-to-
feather controller. What it does not do, however, is dampen the barge-pitch motions as intended.
In fact, the barge-pitch motions are exaggerated in comparison to the response using the baseline active pitch-to-feather controller. This seem ingly contradictory result can be understood by
examining the barge-pitch damping ratios resulting from the active pitch-to-stall control. As for
02,0004,0006,0008,000
Time (sec)GenPwr, kWBaseline (Pitch-to-Feather) Pitch-to-Stall
05001,0001,5002,000
Time (sec)GenSpeed, rpm
-30-1501530
Time (sec)BlPitch1, ș
-20-1001020
0 50 100 150 200 250 300
Simulation Time, sPtfmPitch, ș

Figure 7- 4. Comparison of pitch-to-feather and pitch-to-stall system responses
134

the pitch-to-feather system, the thrust sensitivity to wind speed ( TV∂∂) can be found using the
open-loop and ideal closed-loop methods, and both methods can be used to estimate the barge-
pitch damping ratios. The results of these calculations are presented in Table 7-4 and Figure 7-5 .
In Figure 7-5 , the barge-pitch damping ratios associated with the pitch-to-stall system are plotted
along with the original values presented in Figure 7-1 for the pitch-to-feather system. Because
the two systems are identical below rated wind speed, so are the barge-pitch damping ratios.
Above rated wind speed, however, the pitch-to -stall ratios diverge from the pitch-to-feather
ratios. Unlike the pitch-to-feather values, the barge-pitch damping ratio remains positive-valued
across control regions for the ideal closed-l oop pitch-to-stall method because the thrust
sensitivity to wind speed remains positive-valued (see the last column of Table 7-4). In the
pitch-to-stall system slightly above rated, the open- and ideal closed-loop bounds imposed by the barge-pitch damping ratios converg e toward each other and remain at or near 2.5% across the
remainder of Region 3.
As I mentioned at the end of Section 7.1, with real blade-pitch-control speed regulation above
rated wind speed, the actual damping ratio w ill lie somewhere between the bounds imposed by
the open- and ideal closed-loop results. This implie s that the real blade-pitch-to-stall controller,
regardless of its gains, will give the system a sli ghtly stable barge-pitch damping ratio near 2.5%
across Region 3, starting just above rated. Mo reover, because the barge-pitch motions for the
pitch-to-stall system are larger than those for the pitch-to-feather system in the time histories
presented in Figure 7-4 , I can conclude that the real blade-pitch-to-feather speed controller
Table 7-4. Pitch-to-Stall Sensitivit y of Aerodynamic Thrust to Wind Speed
Wind Speed Rotor Speed Pitch Angle Open-Loop ∂T/∂VIdeal Closed-Loop ∂ T/∂V
(m/s) (rpm) (ș) (N/(m/s)) (N/(m/s))
3.0 – Cut-In 6.97 0.00 29.43E+3
4.0 7.18 0.00 32.81E+3 48.61E+3
5.0 7.51 0.00 36.17E+3 57.17E+3
6.0 7.94 0.00 39.86E+3 64.83E+3
7.0 8.47 0.00 43.63E+3 73.89E+3
8.0 9.16 0.00 46.49E+3 90.33E+3
9.0 10.30 0.00 52.26E+3 106.74E+3
10.0 11.43 0.00 57.97E+3 105.69E+3
11.0 11.89 0.00 57.64E+3 207.25E+3
12.0 12.10 -6.76 15.69E+3 179.29E+3
13.0 12.10 -7.50 9.09E+3 31.74E+3
14.0 12.10 -7.79 9.79E+3 18.75E+3
15.0 12.10 -8.05 9.96E+3 16.07E+3
16.0 12.10 -8.22 8.82E+3 13.58E+3
17.0 12.10 -8.26 7.39E+3 10.97E+3
18.0 12.10 -8.20 5.81E+3 9.11E+3
19.0 12.10 -8.05 4.49E+3 8.26E+3
20.0 12.10 -7.84 3.77E+3 8.08E+3
21.0 12.10 -7.60 2.78E+3 7.87E+3
22.0 12.10 -7.32 2.89E+3 11.15E+3
23.0 12.10 -7.03 3.42E+3 12.79E+3
24.0 12.10 -6.74 4.89E+3 14.10E+3
25.0 – Cut-Out 12.10 -6.46 6.81E+3
135

-0.15-0.10-0.050.000.050.100.150.200.250.30
3 5 7 9 11 13 15 17 19 21 23 25
Wind Speed, m/sBarge-Pitch Damping Ratio, -Pitch-to-Feather – Open-Loop
Pitch-to-Feather – Ideal Closed-Loop
Pitch-to-Stall – Open-Loop
Pitch-to-Stall – Ideal Closed-Loop

Figure 7-5. Pitch-to-feather and -stall barge-pitch damping ratios
actually has an effective damping ratio higher than 2.5% (at least for the conditions considered).
In other words, the real pitch-to-feather barge-pitch damping ratio is actually much greater than what is predicted by the ideal closed-loop results. It is still, however, beneficial to increase the
damping as much as possible.
One possibility for increasing the barge-pitch damp ing through active pitch-to-stall control is to
tailor the airfoil-data coefficients so that rotor thrust increases more with wind speed in Region 3
than what resulted with the existing airfoils. Experimental data from NREL’s Phase VI
Unsteady Aerodynamics Experiment (UAE) [ 27], which tested a passive stall-regulated wind
turbine in the National Full-Scale Aerodynamics Complex at the National Aeronautics and Space
Administration (NASA) Ames Research Center, showed a nearly steady increase in rotor thrust with wind speed from cut-in to cut-out. This would translate into a nearly constant steady-state
thrust sensitivity to wind speed,
TV∂∂ , across all wind speeds for the UAE wind turbine. If the
NREL 5-MW wind turbine were modified to be have comparably (e.g., to make its thrust
sensitivity to wind speed in Region 3 similar to that seen in Region 2), the ideal closed-loop
barge-pitch damping ratio would increase to about 15% in Region 3. This is slightly higher damping than the open-loop damping ratio obtained with active pitch-to-feather control. To get
the necessary augmentation in rotor thrust, however, the existing airfoils will need to be modified
and the rotor will need to be redesigned. Both tasks are beyond the scope of this work. I also
suspect that it would be quite difficult to obtain damping ratios much above 15% through rotor-thrust augmentation and active pitch-to-stall speed regulation, even though a higher amount of
damping is desirable.
136

One might also think that combining the controller developed in this section with the TFB
control loop developed in Section 7.2.1 would be another possibility for improving the barge-
pitch damping through active pitch-to-stall speed-regulation control. But unfortunately, a pitch-to-stall control system cannot be combined with a classic TFB control loop for two reasons.
First, the thrust sensitivity to rotor-collective blade pitch changes sign midway through Region 3, implying that the TFB control gain would also have to change sign midway through Region 3. Otherwise, the TFB control l oop would actually act to reduce the effective platform-pitch
damping in certain operating regions. Second, th e magnitude of the thrust sensitivity to blade
pitch is much smaller with pitch-to-stall control th an with pitch-to-feather control. This implies
that one could not achieve any significant increas e in platform-pitch damping without very large
control gains and resulting blade-pitch-rate requirements. Both inadequacies are observable
from the pitch-to-stall thrust sensitivity, which I calculated from a FAST with AeroDyn
linearization analysis and present in Table 7-5 .
Table 7-5. Pitch-to-Stall Sens itivity of Aerodynamic Thrust
to Blade Pitch
Wind Speed Rotor Speed Pitch Angle ∂T/∂θ
(m/s) (rpm) (ș) (N/rad)
3.0 – Cut-In 6.97 0.00 -1.556E+6
4.0 7.18 0.00 -1.646E+6
5.0 7.51 0.00 -1.783E+6
6.0 7.94 0.00 -1.982E+6
7.0 8.47 0.00 -2.238E+6
8.0 9.16 0.00 -2.533E+6
9.0 10.30 0.00 -3.201E+6
10.0 11.43 0.00 -3.939E+6
11.0 11.89 0.00 -3.988E+6
12.0 12.10 -6.76 -1.216E+6
13.0 12.10 -7.50 -0.388E+6
14.0 12.10 -7.79 -0.279E+6
15.0 12.10 -8.05 -0.109E+6
16.0 12.10 -8.22 0.123E+6
17.0 12.10 -8.26 0.331E+6
18.0 12.10 -8.20 0.536E+6
19.0 12.10 -8.05 0.725E+6
20.0 12.10 -7.84 0.887E+6
21.0 12.10 -7.60 1.069E+6
22.0 12.10 -7.32 1.182E+6
23.0 12.10 -7.03 1.254E+6
24.0 12.10 -6.74 1.251E+6
25.0 – Cut-Out 12.10 -6.46 1.214E+6
7.2.3 Detuning the Gains in the Pitch-to-Feather Controller
Neither the addition of the TFB c ontrol loop presented in Section 7.2.1 nor the modification to
pitch-to-stall rotor-speed regulation presented in Section 7.2.2 gave satisfactory improvements in
the barge-pitch response. This section descri bes one more approach I took to improve the
platform-pitch damping of the ITI Energy wind barge concept through conventional wind turbine control methods.
137

This control strategy was the simplest modification I made to the baseline control system
developed in Section 3.1.6.3, involving only a reduction of gains in the active blade-pitch-to-
feather controller. The basic premise behind this control stra tegy is the understanding that
reducing the gains in the rotor-speed controller will cause the floating wind turbine system to behave less like the results for the ideal closed-loop pitch-to-feather method, and more like the results for the open-loop control method. B ecause of knowledge about barge-pitch damping
ratios acquired from Figure 7-1 or Figure 7-5 , this end result is important.
To maintain a reasonable relationship between th e proportional and integral gains in the rotor-
speed control system, I reduced the gains by choosing a smaller controller-response natural
frequency (
ωφn). I preserved the recommended controller damping ratio ( ζφ = 0.6 to 0.7). The
recommended value found in Ref. [ 29], and the value selected for the baseline control system, of
ωφn = 0.6 rad/s is slightly above th e barge-pitch natural frequency of ωxn = 0.5420 rad/s (see
Section 7.1). This relationship between frequencie s has the potential to introduce negative
damping of the barge-pitch mode. Larsen and Hanson [ 57] found that the smallest controller-
response natural frequency must be less than th e smallest critical support-structure natural
frequency to ensure that the support structure moti ons of an offshore floating wind turbine with
active pitch-to-feather control remain positively damped.
Reducing ωφn by one-third will ensure that the c ontroller-response natural frequency is lower
than the the barge-pitch natural frequency and al so lower than wave-exc itation frequency of all
but the most severe sea states. Using the pr operties for the NREL 5-MW wind turbine, along
with ωφn = 0.4 rad/s and ζφ = 0.7, I derived the resulting reduced (detuned) gains of KP(θ = 0ș) =
0.01255121 s, KI(θ = 0ș) = 0.003586059, and KD = 0.0 s2. Figure 7-6 shows the gains at other
blade-pitch angles, along with the gain-correction factor (which is the same as it was in the
0.00.20.40.60.81.0
0 5 10 15 20
Rotor-Collective Blade-Pitch Angle, șGain-Correction Factor
0.0000.0050.0100.0150.0200.025
Proportional and Integral GainsGain-Correction Factor, –
Proportional Gain, s
Integral Gain, –

Figure 7-6. Detuned blade-pitch control system gain-scheduling law
138

baseline control system). As in Section 3.1.6.3 , I used the upper limit of the recommended
damping ratio range ( ζφ = 0.7) to compensate for neglecting negative damping from the
generator-torque controller in the determination of KP.
As in Sections 7.2.1 and 7.2.2, I tested the system response of the NREL 5-MW wind turbine
mounted atop the ITI Energy barge with this new control system. Figure 7-7 compares the
system responses with the detuned and original (baseline) blade-pitch-to-feather gains for a
simulation with the same wind and wave conditions used in the simulations presented in Figure
7-2 and Figure 7-4 (i.e., an 18-m/s stochastic wind, a 3.673-m significant wave height, and a
13.376-s peak spectral period). As before, I ra n the simulations with all appropriate and
available DOFs enabled, but without considering the rotor-mass imbalance or the increased blade
structural-damping ratio.
As shown in Figure 7-7 , the detuned blade-pitch control system is marginally effective at
reducing the barge-pitch motions. Furthermor e, it attains this positive performance without
negatively affecting the generator speed and power excursions. As a matter of fact, the generator
speed and power excursions have actually been diminished. And all of this has been
accomplished with a reduction in blade-pitch duty cycle!
There is an upper bound, though, to the amount of improvement in the barge-pitch damping that
02,0004,0006,0008,000
Time (sec)GenPwr, kWBaseline Detuned Gains
05001,0001,5002,000
Time (sec)GenSpeed, rpm
06121824
Time (sec)BlPitch1, ș
-10-50510
0 50 100 150 200 250 300
Simulation Time, sPtfmPitch, ș

Figure 7-7. System responses with and without detuned blade-pitch control gains
139

is attainable with a basic detuning of the blad e-pitch control system gains. That upper bound is
simply the amount of damping shown in Figure 7-1 or Figure 7-5 for the open-loop pitch-to-
feather control system, or roughly 13% in Region 3.
In addition, one cannot expect that further and further reductions in the blade-pitch controller
gains will continue to produce improved damping of the barge-pitch motions without eventually
bringing about exacerbated excursions in the syst em response. This is because the rotor-speed
error is unstable in the open-loop (uncontrolled) s cenario in Region 3. [The rotor-speed error
response is negatively damped in Eq. (3-11) if all blade-pitch control gains are zero]. To confirm
this behavior, I reran simulati ons with detuned blade-pitch c ontrol gains derived from varying
values of ωφn, from 0.1 to 0.5 rad/s in steps of 0.1 rad/s. As expected, with ωφn = 0.1 or 0.2 rad/s
the system responses (not shown) exhibited much higher excursions in barge-pitch, generator
speed, and electrical power output. With ωφn = 0.5 rad/s and ωφn = 0.3 rad/s, I obtained
responses (not shown) very similar to the sy stem responses obtained for gains derived with ωφn =
0.4 rad/s. (The barge-pitch da mping from the simulation with ωφn = 0.4 rad/s was slightly better
than the damping with ωφn = 0.3 or 0.5 rad/s.)
To determine the overall effect of the detuned blade-pitch control system, I reran the sea-based
loads analysis with the control system gains derived from ωφn = 0.4 rad/s. Figure 7-8 presents
the sea-to-land ratios for the absolute extremes fr om the rerun loads analysis of DLCs 1.1, 1.3,
1.4, and 1.5. I ran this loads analysis w ith the same model parameters and load-case
prescriptions as in Section 6.1, with the only difference being the blade-pitch control system
gains.2
The parameter names in Figure 7-8 refer to the same simulation outputs plotted in Figure 6-4 and
Figure 6-5 . Moreover, the ratios of each parameter pl otted on the left and labeled as “Baseline”
in Figure 7-8 are the same ratios presented in Figure 6-4; they also correspond to the leftmost
ratios presented in Figure 6-5 (labeled as “100% – Original”). The ratios of each parameter
plotted on the right and labe led as “Detuned Gains” in Figure 7-8 were computed using the land-
based loads derived with the base line control system. In other wo rds, the land-based loads were
not recomputed using the detuned control system.
For most parameters shown in Figure 7-8 , the sea-to-land ratios in the sea-based system with the
detuned gains are less than the sea-to-land ratios with the baseline gains.3 This demonstrates that
detuning the gains in the blade-pitch controller of the sea-based system had a beneficial effect on
the system response. For exam ple, the sea-to-land ratios for the generator- and rotor-speed
excursions of the system with the detuned gains (the upper-right chart in Figure 7-8 ) have
dropped by more than 10% relative to the system with the baseline gains. The speed excursions
in the system with the detuned gains are now only 40% higher than those seen in the turbine

2 Note that the design problems identified in DLCs 2.1a, 6.x, and 7.1a (see Section 6.2) did not depend on the
actions of the control system. They would, then, be unaffected by the reductions in the active blade-pitch-to-feather
controller gains. These design problems will have to be resolved independently of control system improvements.
3 For the parameters where this is not the case, the extrem e loads are not dictated by barge-pitching motion. For
example, the axial forces at the yaw bearing (“YawBrFzp”) and the tower base (“TwrBsFzt”) are dictated by heave
motion, which has not been effected by the detuned gains.
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Baseline Detuned Gains
012345
GenPwr GenTq GenSpeed RotSpeedRatio of Sea to Land
012345
OoPDefl1 IPDefl1 TTDspFA TTDspSSRatio of Sea to Land
5.6

012345
RootFMxy1 RootFzc1 RootMMxy1 RootMzc1Ratio of Sea to Land
012345
RotThrust LSSGagFMyz RotTorq LSSGagMMyzRatio of Sea to Land

012345
YawBrFMxy YawBrFzp YawBrMMxy YawBrMzpRatio of Sea to Land
5.2
012345
TwrBsFMxy TwrBsFzt TwrBsMMxy TwrBsMztRatio of Sea to Land
6.06.4

Figure 7-8. Sea-to-land ratios with and without detuned blade-pitch control gains
installed on land. (In the system with the base line gains, the sea-based excursions were 60%
higher).
In general, the detuned gains have more effect on the sea-to-land ratios of the deflections and
loads as one follows the load path from the blade tip, through the drivetrain and nacelle, to the
tower base. At the root of Bl ade 1 (the middle-left chart in Figure 7-8 ), for example, the sea-to-
land ratios of the internal shear force (“RootFMxy1”) and bending moment (“RootMMxy1”) magnitudes have dropped by more than 10%. But at the base of the tower (the lower-right chart
in Figure 7-8 ), the sea-to-land ratios have dropped by mo re than 25%. This further demonstrates
the effect of the inverted pendulum discussed in Section 6.1. Detuning the gains in the blade-
141

pitch controller reduced the barg e-pitch motions, which have more effect on loading from inertia
farther down the load path.
The excursions in the internal shear force (“TwrBsFMxy”) and bending moment
(“TwrBsMMxy”) magnitudes at the tower base, however, are still more than 400% higher than the excursions seen in the turbine installed on land. This demonstrates that detuning the gains in the baseline blade-pitch controller still did not entirely resolve the barge-pitch-motion problem. To arrive at a technically feasible concept, modifications to the system design will still be
required (except possibly at the most shelte red of sites, as di scussed in Section 6.1).
7.3 Other Ways to Improve the Pitch Damping with Turbine Control
As demonstrated in Section 7.2, conventional wind turbine cont rol methodologies are limited in
what they can do to improve the platform-pitch motions while limiting rotor-speed excursions of
the ITI Energy wind barge concept. A number of other unconventional methods are also worth
considering. Because a quantita tive consideration of each method is beyond the scope of this
work, I leave these considerations for future work. But this section highlights some of the possibilities.
I. Edwards of ITI Energy proposed one idea for an unconventional wind turbine control system.
Edwards suggested that part of the problem with the barge-pitch damping in Region 3 might be
that the generator is already operating at full (rated) power, so that there is no “head room” for
absorbing more power as the barge pitches into the wind as a result of wave excitation. This implies that it might be better to regulate to some “below-rated” power level across all (even high) wind speeds to leave room for absorbing mo re power. This would, perhaps, permit the
wind turbine rotor to capture not only wind powe r, but some of the wave power as well.
Assessing this control strategy would require a study that examines the trade-off between
improving the damping of the barge and reducing the capacity factor of the wind turbine.
Another unconventional wind turbine control strate gy, proposed by Dr. R. Thresher of NREL /
NWTC, would be to regulate the rotor speed of the turbine using nacelle-yaw actuation, instead
of blade-pitch actuation. This strategy could eliminate the problems from the drop in steady-
state rotor thrust with increasing wind speed above rated resulting from blade-pitch-to-feather control. One would, however, have to dete rmine whether the gyroscopic moments induced by
the required yaw rates would ha ve undesirable consequences.
A simple, but unconventionial, modification to the control strategy would be to change Region 3
from a constant generator power to a constant generator-torque control region. With this change,
the generator-torque controller would not introduce negative damping in the rotor-speed response (which must be compensated by the bl ade-pitch controller), and so, might reduce the
rotor-speed excursions. Larson and Hanson [ 57] demonstrated the effectiveness of this
modification for one offshore floating wind turbin e concept. This change, however, would not
improve the barge-pitch damping.
Conventional wind turbine control methodologie s rely on the independent development and
concatenation of multiple single-input, single-out put (SISO) PID-based control loops using the
conventional turbine actuators of blade pitch, generator torque, and nacelle yaw (and, as
142

required, shaft brakes and other actuators). Naturally, modern control theories, such as
disturbance-accommodating control (DAC) [ 35], offer the potential to bring about improved
performance. Previous cont rols studies by Stol [ 90], Hand [ 26], and Wright [ 104] have
demonstrated the applicability of combining a state estimator, a wind-disturbance estimator, and
full-state feedback using DAC to develop mu ltiple-input, multiple-output (MIMO) state-space-
based control systems for mitigating dynamic loads and stabilizing flexible modes of land-based wind turbines without compromising energy capture. But these studies have not yet been extended to offshore floating wind turbines.
Through MIMO state-space-based control, it may be possible to enhance rotor-speed regulation
and platform-pitch damping through unified cont rol of the generator torque and blade-pitch
angles. For example, because rotor-speed regulation requires a blade-pitch command that is opposite of the one required to add damping to the barge-pitch motion (see Section 7.2.1), it
might be possible to develop a combined genera tor-torque and blade-pitc h controller to address
both objectives simultaneously. The generator-torque commands may be able to mitigate the rotor-speed excursions while the blade-pitch co mmands attempt to augment aerodynamic rotor
thrust to dampen the platform-pitch motion. When used in conjunction with off-axis flow through nacelle-yaw actuation, it may also be possible to introduce platform-roll damping
through the blade-pitch comma nds (and thrust augmentation).
Rotor-collective blade-pitch control can be used to adapt rotor thrust, which induces a moment
on the floating platform through the hub-height moment arm, but independent blade-pitch
control may also be useful. For example, i ndependent blade-pitch control can be used to
introduce pitching moments within the rotor itself through asymmetric aerodynamic loading of the rotor. If developed properly, it may be pos sible to use such a moment to counteract the
hydrodynamic pitching loads on the platform brought about by surface waves.
Section 6.1.5 discusses other design alterations, bey ond wind turbine control, that may be
applied to improve the response of the floating wind barge system.
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Chapter 8 Conclusions and Recommendations
The vast deepwater wind resource represents a po tential to use offshore floating wind turbines to
power much of the world with renewable energy . Before I began this project, many floating
wind turbine concepts had been proposed, but fe w had or could have been evaluated because
available modeling capabilities were limited.
The limitations of previous time- and frequency-domain studies on offshore floating wind
turbines motivated my development of simulation capability for modeling the fully coupled aero-
hydro-servo-elastic response of such systems. As presented in Chapter 2 , I developed this
capability by combining the computational me thodologies of the onshore wind turbine and
offshore O&G industries. The aero-servo-elas tic onshore wind turbine simulation capability of
FAST with AeroDyn and MSC.ADAMS with A2AD and AeroDyn were interfaced with the
external hydrodynamic wave-bod y interaction programs SWIM and WAMIT. To establish these
interfaces, I developed modules for treating tim e-domain hydrodynamics (HydroDyn) and quasi-
static mooring system responses. I develope d the HydroDyn hydrodynamics module to account
for linear hydrostatic restoring; nonlinear visc ous drag from incident-wave kinematics, sea
currents, and platform motion; the added-ma ss and damping contributions from linear wave
radiation, including free-surface memory effects; and the incident-wave excitation from linear diffraction in regular or irregular seas. I de veloped my quasi-static mooring line module to
account for the elastic stretching of an array of homogenous taut or slack catenary lines with
seabed interaction. The simulation capability was developed with enough sophistication to address the primary limitations of the previous frequency- and time-domain studies. In addition,
the simulation program has the features required to perform integrated loads analyses. To make it useful for examining the technical feasibility of a variety of offshore floating wind turbine concepts, I also made my simulation capability universal enough to analyze a variety of turbine, support platform, and mooring system configurations.
To support this and other concept studies ai med at assessing offshore wind technology, I
developed the specifications of a representa tive utility-scale multimegawatt turbine now known
as the NREL offshore 5-MW baseline wind turbin e. This wind turbine is a conventional three-
bladed upwind variable-speed variable blade-pitch-to-feather-controlled turbine. In Chapter 3 , I
discussed the development of this wind turbine and gave an overview of the properties of two
floating barges—the ITI Energy barge and MIT / NREL barge. Also in Chapter 3 , I presented
the metocean data at a reference site in the northern North Sea. I used the wind turbine, barges,
and metocean data in my model- verification, loads analysis, and controls-development efforts.
Through model-to-model comparisons, I tested my newly developed simulation capability, as presented in Chapter 4 , to ensure its correctness. I verified that the PSD and probability density
of the wave-elevation record computed by HydroDyn matched the prescribed target spectrum and Gaussian distribution, respectively. I demo nstrated that WAMIT produces acceptable input
for HydroDyn, and from this hydrodynamic input, I showed that HydroDyn correctly generates the radiation impulse-response functions. I also showed that my quasi-static mooring system module correctly solves a classi c benchmark problem for the sta tic equilibrium of a suspended
cable structure. In addition, I demonstrated that my mooring system module predicts nonlinear force-displacement relationships consistent with an independent analysis. Finally, the results
144

from my fully coupled time-domain analysis were shown to agree with results generated from a
frequency-domain approach. The results of all the verification exercises were favorable and
gave me confidence to pursue more thorough investigations into the dynamic behavior of
offshore floating wind turbines.
I then used my simulation capability to perform a preliminary, but integrated, loads analysis for
the NREL 5-MW baseline wind turbine mounted both on land and offshore on the floating ITI
Energy barge, which has slack catenary moorings. I introduced the loads analyses in Chapter 5
and discussed the results in Chapter 6 . I based the analyses on the ultimate load cases and
procedures dictated by the on- and offshore IE C wind turbine design standards and the severe
environmental conditions at the c hosen reference site. By comparing the responses of the land-
and sea-based systems, I was able to quantify th e impact brought about by the dynamic couplings
between the turbine and floating barge in the presence of combined wind and wave loading.
I characterized the dynamic responses by showing that the mean values of the loads and
deflections in the floating turbine were very similar to those that existed on land. The excursions of the loads and deflections, however, exceeded those found on land. I showed that the increased load excursions in the floating system were pr oduced by the barge’s pitching motion, and so
were higher in the tower than in the blades because of the increased effect of inertia. I discussed how the barge concept was susceptible to exces sive pitching during extreme wave conditions,
but showed how the load excursions were redu ced with decreasing severity in the waves.
Relative to the fixed land-based support, I found that the added compliance in the barge led to an
instability of the floating system in yaw when the wind turbine was idling with a faulted blade. I discussed how the compliance of the floating barg e did, however, mitigate a tower side-to-side
instability discovered in the land-based turbine.
In Chapter 7 , I presented the influence of conventiona l wind turbine blade-pitch control actions
on the pitch damping of the NREL 5-MW baseli ne wind turbine mounted atop the ITI Energy
barge. I was concerned that the drop in steady- state wind turbine rotor thrust with wind speed
above rated would lead to negativ e damping of the barge-pitch mode and contribute to the large
system-pitch motions. I demonstrated that ne ither the addition of a control loop through
feedback of tower-top acceleration nor the modification to pitch-to-stall rotor-speed regulation
gave satisfactory improvements in the barge-pitc h response. The latter modification helped me
conclude, however, that the actual barge-pitch damping was considerably higher than that implied by the steady-state rotor thrust response, but that it was still beneficial to increase the
damping as much as possible. I also showed in Chapter 7 that detuning the gains in the baseline
blade-pitch-to-feather controller helped, but still did not entirely resolve the barge-pitch-motion problem.
In summary of my accomplishments, I have satisfi ed my project objectives by (1) developing a
comprehensive simulation capability for modelin g the coupled dynamic response of offshore
floating wind turbines, (2) verifying the simulation capability through model-to-model
comparisons, and (3) applying the simulation capability to the integrated loads analysis for one of the promising system concepts. At the end of all this work, I have not produced a floating wind turbine concept free of problems (although doing so was not one of my objectives). To arrive at a technically and econom ically feasible concept, modifications to the system designs I
presented in this work are still required.
145

My recommendations for future research were scattered throughout this work where appropriate.
In summary, though, future opportunities incl ude enhancing and vali dating the simulation
capability, modifying the turbine and barge system designs, performing additional iterations in the design loads analysis, applying advanced c ontrol solutions, and extending the work to other
promising floating platform concepts.
Though not specific to the modeling of offshore wi nd turbines, it would be advantageous to add
a torsion DOF to the modal representation of the tower in FAST. In addition, extending the
modal representation of the blades to include mass and elastic offsets, torsion DOFs, and coupled
mode-shape propertie s would be useful.
Additional enhancements to impr ove the simulation of floating o ffshore wind turbines are also
possible. For example, one could add capabilities that would allow for modeling and testing
various mechanisms for stabilizing the barge-pitch motion, such as TMDs, OWCs, or other active and passive control devices. For the de tailed analysis of some designs (see Section 2.2), it
would be beneficial to introduce second-order effects into my HydroDyn hydrodynamics
module, including the effects of intermittent wetting and mean-drift, slow-drift, and sum-
frequency excitation. It would also be advantageous to add the potential loading from VIV and
from sea ice, and to replace my quasi-static moor ing system module with a fully coupled module
that can handle the line dynamics. Finally, the models should be validated against experimental
data derived from wave-tank te sts and sub- and full-scale prototypes installed offshore.
This work can also be extended to enable th e simulation tools to model the coupled dynamic
response of fixed-bottom offshore wind turbines. For monopile support structures in shallow
water, nonlinear wave-kinematic s models and Morison’s equati on for the wave-induced loading
must be introduced. For tripod and space-frame designs in intermediate depths, more sophisticated structural-dynamic and hydrod ynamic models, including member-to-member
interactions, will be required. Having a single code capable of modeling a large range of support
structures and water depths would allow one to perform conceptual studies that attempt to find
the optimal transition depth between fixed-bo ttom and floating platform support structures.
Independent of code enhancements, the simulation capability as it exists now can also be applied in many important research projects. For instance, the loads-analysis process I used in this work is also applicable to other floating platform concepts, including TLPs and spar buoys. The process could also be applied for varying wind turbine concepts with unconventional features,
such as light-weight rotors, ratings higher than 5 MW, two instead of three blades, or downwind
instead of upwind rotors. (Reference [ 14] discusses how these unconven tional features might be
advantageous in floating systems). Such loads analyses should be performed to determine which
concept—or hybrid thereof—has the best overall technical advantage.
For the particular system concept analyzed in this work, Sections 6.1.5, 6.2, and 7.3 suggested
design modifications and active and passive control features th at could potentially reduce the
barge motions, improve the turbine response, and eliminate the instabilities. These
recommended future projects included
• Incorporating actively controlled OWCs into the barge
• Incorporating passively controlled TMDs or anti-roll stabilizers into the barge or turbine
146

• Introducing unconventional and / or advanced control strategies into the wind turbine
• Decoupling the turbine and barge moti ons by adding new articulations
• Modifying the geometry of the turbine, barge, and / or mooring system.
After improvements to the system design are made , it would be constructi ve to rerun the loads
analysis to reassess the concept’s technical feasibilit y. It would also be beneficial to expand the
set of load cases considered. It would, for example, be useful to add the load cases that would
allow one to quantify the impact of the platfo rm motions on the fatigue life of the supported
wind turbine.
Once suitable design modifications have made the concept more technically feasible, it will be
important to assess the economics of the system, including the influences of manufacturing, installation, and decommissioning. System-w ide optimization will improve the economics.
If the technical challenges can be solved in an economically feasible way, the possibility of using offshore floating wind turbines to power much of the world with an indigenous, nonpolluting, and inexhaustible energy source can become real.
147

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Appendix A FAST Input Files for the 5-MW Wind Turbine
A.1 Primary Input File
‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐ 
‐‐‐‐‐‐‐  FAST INPUT FILE ‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐ 
NREL 5.0 MW Baseline  Wind Turbine  for Use in Offshore  Analysis.  
Properties  from Dutch Offshore  Wind Energy Converter  (DOWEC)  6MW Pre‐Design (10046_009.pdf)  and REpower  5M 5MW (5m_uk.pdf);  C 
‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐  SIMULATION  CONTROL  ‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐ 
False        Echo        ‐  Echo input data to "echo.out"  (flag) 
   3         ADAMSPrep    ‐  ADAMS preprocessor  mode {1: Run FAST, 2: use FAST as a preprocessor  to create an ADAMS model, 3: do  
   1         AnalMode     ‐  Analysis  mode {1:  Run a time‐marching  simulation,  2: create a periodic  linearized  model} (switch)  
   3         NumBl       ‐  Number of blades (‐) 
 630.0       TMax        ‐  Total run time (s) 
   0.0125   DT          ‐  Integration  time step (s) 
‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐  TURBINE  CONTROL  ‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐ 
   0         YCMode      ‐  Yaw control  mode {0: none, 1: user‐defined  from routine  UserYawCont,  2: user‐defined  from Simulink}   
9999.9       TYCOn       ‐  Time to enable active yaw control  (s) [unused  when YCMode=0]  
   1         PCMode      ‐  Pitch control  mode {0: none, 1: user‐defined  from routine  PitchCntrl,  2: user‐defined  from Simulink  
   0.0       TPCOn       ‐  Time to enable active pitch control  (s) [unused  when PCMode=0]  
   2         VSContrl     ‐  Variable ‐speed control  mode {0: none, 1: simple VS, 2: user‐defined  from routine  UserVSCont,  3: use 
9999.9       VS_RtGnSp    ‐  Rated generator  speed for simple variable ‐speed generator  control  (HSS side) (rpm) [used only when  
9999.9       VS_RtTq      ‐  Rated generator  torque/constant  generator  torque in Region 3 for simple variable ‐speed generator  co 
9999.9       VS_Rgn2K     ‐  Generator  torque constant  in Region 2 for simple variable ‐speed generator  control  (HSS side) (N‐m/r 
9999.9       VS_SlPc      ‐  Rated generator  slip percentage  in Region 2 1/2 for simple variable ‐speed generator  control  (%) [us 
   2         GenModel     ‐  Generator  model {1: simple,  2: Thevenin,  3: user‐defined  from routine  UserGen}  (switch)  [used only  
True         GenTiStr     ‐  Method to start the generator  {T: timed using TimGenOn,  F: generator  speed using SpdGenOn}  (flag) 
True         GenTiStp     ‐  Method to stop the generator  {T: timed using TimGenOf,  F: when generator  power = 0} (flag) 
9999.9       SpdGenOn     ‐  Generator  speed to turn on the generator  for a startup  (HSS speed) (rpm) [used only when GenTiStr=F  
   0.0       TimGenOn     ‐  Time to turn on the generator  for a startup  (s) [used only when GenTiStr=True]  
9999.9       TimGenOf     ‐  Time to turn off the generator  (s) [used only when GenTiStp=True]  
   1         HSSBrMode    ‐  HSS brake model {1: simple,  2: user‐defined  from routine  UserHSSBr}  (switch)  
9999.9       THSSBrDp     ‐  Time to initiate  deployment  of the HSS brake (s) 
9999.9       TiDynBrk     ‐  Time to initiate  deployment  of the dynamic  generator  brake [CURRENTLY  IGNORED]  (s) 
9999.9       TTpBrDp(1)   ‐  Time to initiate  deployment  of tip brake 1 (s) 
9999.9       TTpBrDp(2)   ‐  Time to initiate  deployment  of tip brake 2 (s) 
9999.9       TTpBrDp(3)   ‐  Time to initiate  deployment  of tip brake 3 (s) [unused  for 2 blades]  
9999.9       TBDepISp(1)  ‐ Deployment ‐initiation  speed for the tip brake on blade 1 (rpm) 
9999.9       TBDepISp(2)  ‐ Deployment ‐initiation  speed for the tip brake on blade 2 (rpm) 
9999.9       TBDepISp(3)  ‐ Deployment ‐initiation  speed for the tip brake on blade 3 (rpm) [unused  for 2 blades]  
9999.9       TYawManS     ‐  Time to start override  yaw maneuver  and end standard  yaw control  (s) 
   0.3       YawManRat    ‐  Yaw rate (in absolute  value) at which override  yaw maneuver  heads toward final yaw angle (deg/s)  
   0.0       NacYawF      ‐  Final yaw angle for override  yaw maneuvers  (degrees)  
9999.9       TPitManS(1)  ‐ Time to start override  pitch maneuver  for blade 1 and end  standard  pitch control  (s) 
9999.9       TPitManS(2)  ‐ Time to start override  pitch maneuver  for blade 2 and end  standard  pitch control  (s) 
9999.9       TPitManS(3)  ‐ Time to start override  pitch maneuver  for blade 3 and end  standard  pitch control  (s) [unused  for 2  
   8.0       PitManRat(1) ‐ Pitch rate (in absolute  value) at which override  pitch maneuver  for blade 1 heads toward final pitc 
   8.0       PitManRat(2) ‐ Pitch rate (in absolute  value) at which override  pitch maneuver  for blade 2 heads toward final pitc 
   8.0       PitManRat(3) ‐ Pitch rate (in absolute  value) at which override  pitch maneuver  for blade 3 heads toward final pitc 
   0.0       BlPitch(1)   ‐  Blade 1 initial  pitch (degrees)  
   0.0       BlPitch(2)   ‐  Blade 2 initial  pitch (degrees)  
   0.0       BlPitch(3)   ‐  Blade 3 initial  pitch (degrees)  [unused  for 2 blades]  
   0.0       BlPitchF(1)  ‐ Blade 1 final pitch for override  pitch maneuvers  (degrees)  
   0.0       BlPitchF(2)  ‐ Blade 2 final pitch for override  pitch maneuvers  (degrees)  
   0.0       BlPitchF(3)  ‐ Blade 3 final pitch for override  pitch maneuvers  (degrees)  [unused  for 2 blades]  
‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐  ENVIRONMENTAL  CONDITIONS  ‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐ 
   9.80665   Gravity      ‐  Gravitational  acceleration  (m/s^2)  
‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐  FEATURE  FLAGS ‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐ 
True         FlapDOF1     ‐  First flapwise  blade mode DOF (flag) 
True         FlapDOF2     ‐  Second flapwise  blade mode DOF (flag) 
True         EdgeDOF      ‐  First edgewise  blade mode DOF (flag) 
False        TeetDOF      ‐  Rotor‐teeter DOF (flag) [unused  for 3 blades]  
True         DrTrDOF      ‐  Drivetrain  rotational ‐flexibility  DOF (flag) 
True         GenDOF      ‐  Generator  DOF  (flag) 
True         YawDOF      ‐  Yaw  DOF (flag) 
True         TwFADOF1     ‐  First fore‐aft tower bending ‐mode DOF (flag) 
True         TwFADOF2     ‐  Second fore‐aft tower bending ‐mode DOF (flag) 
True         TwSSDOF1     ‐  First side‐to‐side tower bending ‐mode DOF (flag) 
True         TwSSDOF2     ‐  Second side‐to‐side tower bending ‐mode DOF (flag) 
True         CompAero     ‐  Compute  aerodynamic  forces (flag) 
False        CompNoise    ‐  Compute  aerodynamic  noise (flag) 
‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐  INITIAL  CONDITIONS  ‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐ 
   0.0       OoPDefl      ‐  Initial  out‐of‐plane blade‐tip displacement  (meters)  
   0.0       IPDefl      ‐  Initial  in‐plane blade‐tip deflection  (meters)  
   0.0       TeetDefl     ‐  Initial  or fixed teeter angle (degrees)  [unused  for 3 blades]  
   0.0       Azimuth      ‐  Initial  azimuth  angle for blade 1 (degrees)  
  12.1       RotSpeed     ‐  Initial  or fixed rotor speed (rpm) 
   0.0       NacYaw      ‐  Initial  or fixed nacelle ‐yaw angle (degrees)  
   0.0       TTDspFA      ‐  Initial  fore‐aft tower‐top displacement  (meters)  
   0.0       TTDspSS      ‐  Initial  side‐to‐side tower‐top displacement  (meters)  
159

‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐  TURBINE  CONFIGURATION  ‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐ 
  63.0       TipRad      ‐  The distance  from the rotor apex to the blade tip (meters)  
   1.5       HubRad      ‐  The distance  from the rotor apex to the blade root (meters)  
   1         PSpnElN      ‐  Number of the  innermost  blade element  which is still part of the pitchable  portion  of the blade for  
   0.0       UndSling     ‐  Undersling  length [distance  from teeter pin to the rotor apex] (meters)  [unused  for 3 blades]  
   0.0       HubCM       ‐  Distance  from rotor apex to hub mass [positive  downwind]  (meters)  
  ‐5.01910   OverHang     ‐  Distance  from yaw  axis to rotor apex [3 blades]  or teeter pin [2 blades]  (meters)  
   1.9       NacCMxn      ‐  Downwind  distance  from the tower‐top to the  nacelle  CM (meters)  
   0.0       NacCMyn      ‐  Lateral   distance  from the tower‐top to the  nacelle  CM (meters)  
   1.75      NacCMzn      ‐  Vertical  distance  from the tower‐top to the  nacelle  CM (meters)  
  87.6       TowerHt      ‐  Height of tower above ground level [onshore]  or MSL [offshore]  (meters)  
   1.96256   Twr2Shft     ‐  Vertical  distance  from the tower‐top to the  rotor shaft (meters)  
   0.0       TwrRBHt      ‐  Tower rigid base height (meters)  
  ‐5.0       ShftTilt     ‐  Rotor shaft tilt angle (degrees)  
   0.0       Delta3      ‐  Delta‐3 angle for  teetering  rotors (degrees)  [unused  for 3 blades]  
  ‐2.5       PreCone(1)   ‐  Blade 1 cone angle (degrees)  
  ‐2.5       PreCone(2)   ‐  Blade 2 cone angle (degrees)  
  ‐2.5       PreCone(3)   ‐  Blade 3 cone angle (degrees)  [unused  for 2 blades]  
   0.0       AzimB1Up     ‐  Azimuth  value to use for I/O when blade 1 points up (degrees)  
‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐  MASS AND INERTIA  ‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐ 
   0.0       YawBrMass    ‐  Yaw bearing  mass (kg) 
 240.00E3    NacMass      ‐  Nacelle  mass (kg) 
  56.78E3    HubMass      ‐  Hub  mass (kg) 
   0.0       TipMass(1)   ‐  Tip‐brake mass, blade 1 (kg) 
   0.0       TipMass(2)   ‐  Tip‐brake mass, blade 2 (kg) 
   0.0       TipMass(3)   ‐  Tip‐brake mass, blade 3 (kg) [unused  for 2 blades]  
2607.89E3    NacYIner     ‐  Nacelle  inertia  about yaw axis (kg m^2) 
 534.116      GenIner      ‐  Generator  inertia  about HSS (kg m^2) 
 115.926E3   HubIner      ‐  Hub inertia  about rotor axis [3 blades]  or teeter axis [2 blades]  (kg m^2) 
‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐  DRIVETRAIN  ‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐ 
 100.0       GBoxEff      ‐  Gearbox  efficiency  (%) 
  94.4       GenEff      ‐  Generator  efficiency  [ignored  by the Thevenin  and user‐defined  generator  models]  (%) 
  97.0       GBRatio      ‐  Gearbox  ratio (‐) 
False        GBRevers     ‐  Gearbox  reversal  {T: if rotor and generator  rotate in opposite  directions}  (flag) 
  28.1162E3  HSSBrTqF     ‐  Fully deployed  HSS‐brake torque (N‐m) 
   0.6       HSSBrDT      ‐  Time for HSS‐brake to reach full deployment  once initiated  (sec) [used only when HSSBrMode=1]  
             DynBrkFi     ‐  File containing  a mech‐gen‐torque vs HSS‐speed curve for a dynamic  brake [CURRENTLY  IGNORED]  (quote 
 867.637E6   DTTorSpr     ‐  Drivetrain  torsional  spring (N‐m/rad) 
   6.215E6   DTTorDmp     ‐  Drivetrain  torsional  damper (N‐m/(rad/s))  
‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐  SIMPLE INDUCTION  GENERATOR  ‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐ 
9999.9       SIG_SlPc     ‐  Rated generator  slip percentage  (%) [used only when VSContrl=0  and GenModel=1]  
9999.9       SIG_SySp     ‐  Synchronous  (zero‐torque)  generator  speed (rpm) [used only when VSContrl=0  and GenModel=1]  
9999.9       SIG_RtTq     ‐  Rated torque (N‐m) [used only when VSContrl=0  and GenModel=1]  
9999.9       SIG_PORt     ‐  Pull‐out ratio (Tpullout/Trated)  (‐) [used only when VSContrl=0  and GenModel=1]  
‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐  THEVENIN ‐EQUIVALENT  INDUCTION  GENERATOR  ‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐ 
9999.9       TEC_Freq     ‐  Line frequency  [50 or 60] (Hz) [used only when VSContrl=0  and GenModel=2]  
9998         TEC_NPol     ‐  Number of poles [even integer  > 0] (‐) [used only when VSContrl=0  and GenModel=2]  
9999.9       TEC_SRes     ‐  Stator resistance  (ohms) [used only when VSContrl=0  and GenModel=2]  
9999.9       TEC_RRes     ‐  Rotor resistance  (ohms) [used only when VSContrl=0  and GenModel=2]  
9999.9       TEC_VLL      ‐  Line‐to‐line RMS voltage  (volts)  [used only when VSContrl=0  and  GenModel=2]  
9999.9       TEC_SLR      ‐  Stator leakage  reactance  (ohms) [used only when VSContrl=0  and GenModel=2]  
9999.9       TEC_RLR      ‐  Rotor leakage  reactance  (ohms) [used only when VSContrl=0  and GenModel=2]  
9999.9       TEC_MR      ‐  Magnetizing  reactance  (ohms) [used only when VSContrl=0  and GenModel=2]  
‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐  PLATFORM  ‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐ 
   3         PtfmModel    ‐  Platform  model {0: none, 1: onshore,  2: fixed bottom offshore,  3: floating  offshore}  (switch)  
"NRELOffshrBsline5MW_Platform_ITIBarge4.dat"       PtfmFile     ‐  Name of file containing  platform  properties  (quoted  string)  [u 
‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐  TOWER ‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐ 
  20         TwrNodes     ‐  Number of tower nodes used for analysis  (‐) 
"NRELOffshrBsline5MW_Tower_ITIBarge4.dat"          TwrFile      ‐  Name of file containing  tower properties  (quoted  string)  
‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐  NACELLE ‐YAW ‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐ 
9028.32E6    YawSpr      ‐  Nacelle ‐yaw spring constant  (N‐m/rad) 
  19.16E6    YawDamp      ‐  Nacelle ‐yaw damping  constant  (N‐m/(rad/s))  
   0.0       YawNeut      ‐  Neutral  yaw position ‐‐yaw spring force is zero at this yaw (degrees)  
‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐  FURLING  ‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐ 
False        Furling      ‐  Read in additional  model properties  for furling  turbine  (flag) 
             FurlFile     ‐  Name of file containing  furling  properties  (quoted  string)  [unused  when Furling=False]  
‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐  ROTOR‐TEETER ‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐ 
   0         TeetMod      ‐  Rotor‐teeter spring/damper  model {0: none, 1: standard,  2: user‐defined  from routine  UserTeet}  (swi 
   0.0       TeetDmpP     ‐  Rotor‐teeter damper position  (degrees)  [used only for 2 blades and when TeetMod=1]  
   0.0       TeetDmp      ‐  Rotor‐teeter damping  constant  (N‐m/(rad/s))  [used only for 2 blades and when TeetMod=1]  
   0.0       TeetCDmp     ‐  Rotor‐teeter rate‐independent  Coulomb ‐damping  moment (N‐m) [used only for 2 blades and when TeetMod  
   0.0       TeetSStP     ‐  Rotor‐teeter soft‐stop position  (degrees)  [used only for 2 blades and when TeetMod=1]  
   0.0       TeetHStP     ‐  Rotor‐teeter hard‐stop position  (degrees)  [used only for 2 blades and when TeetMod=1]  
   0.0       TeetSSSp     ‐  Rotor‐teeter soft‐stop linear‐spring constant  (N‐m/rad) [used only for 2 blades and when TeetMod=1]  
   0.0       TeetHSSp     ‐  Rotor‐teeter hard‐stop linear‐spring constant  (N‐m/rad) [used only for 2 blades and when TeetMod=1]  
‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐  TIP‐BRAKE ‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐ 
   0.0       TBDrConN     ‐  Tip‐brake drag constant  during normal operation,  Cd*Area  (m^2) 
   0.0       TBDrConD     ‐  Tip‐brake drag constant  during fully‐deployed  operation,  Cd*Area  (m^2) 
   0.0       TpBrDT      ‐  Time for tip‐brake to reach full deployment  once released  (sec) 
‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐  BLADE ‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐ 
"NRELOffshrBsline5MW_Blade.dat"                    BldFile(1)   ‐  Name of file containing  properties  for blade 1 (quoted  string)  
"NRELOffshrBsline5MW_Blade.dat"                    BldFile(2)   ‐  Name of file containing  properties  for blade 2 (quoted  string)  
"NRELOffshrBsline5MW_Blade.dat"                    BldFile(3)   ‐  Name of file containing  properties  for blade 3 (quoted  string)   
‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐  AERODYN  ‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐ 
160

"NRELOffshrBsline5MW_AeroDyn.ipt"                  ADFile      ‐  Name of file containing  AeroDyn  input parameters  (quoted  strin 
‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐  NOISE ‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐ 
             NoiseFile    ‐  Name of file containing  aerodynamic  noise input parameters  (quoted  string)  [used only when CompNois  
‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐  ADAMS ‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐ 
"NRELOffshrBsline5MW_ADAMSSpecific.dat"            ADAMSFile    ‐  Name of file containing  ADAMS‐specific  input parameters  (quote 
‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐  LINEARIZATION  CONTROL  ‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐ 
"NRELOffshrBsline5MW_Linear.dat"                   LinFile      ‐  Name of file containing  FAST linearization  parameters  (quoted   
‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐  OUTPUT ‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐ 
True         SumPrint     ‐  Print summary  data to "<RootName>.fsm"  (flag) 
True         TabDelim     ‐  Generate  a tab‐delimited  tabular  output file. (flag) 
"ES10.3E2"   OutFmt      ‐  Format used for tabular  output except time.  Resulting  field should be 10 characters.  (quoted  strin 
  30.0       TStart      ‐  Time to begin tabular  output (s) 
   4         DecFact      ‐  Decimation  factor for tabular  output {1: output every time step} (‐) 
   1.0       SttsTime     ‐  Amount of time between  screen status messages  (sec) 
  ‐3.09528   NcIMUxn      ‐  Downwind  distance  from the tower‐top to the  nacelle  IMU (meters)  
   0.0       NcIMUyn      ‐  Lateral   distance  from the tower‐top to the  nacelle  IMU (meters)  
   2.23336   NcIMUzn      ‐  Vertical  distance  from the tower‐top to the  nacelle  IMU (meters)  
   1.912     ShftGagL     ‐  Distance  from rotor apex [3 blades]  or teeter pin [2 blades]  to shaft strain gages [positive  for up 
   1         NTwGages     ‐  Number of tower nodes that have strain gages for output [0 to 9] (‐) 
  10         TwrGagNd     ‐  List of tower nodes that have strain gages [1 to TwrNodes]  (‐) [unused  if NTwGages=0]  
   1         NBlGages     ‐  Number of blade nodes that have strain gages for output [0 to 9] (‐) 
   9         BldGagNd     ‐  List of blade nodes that have strain gages [1 to BldNodes]  (‐) [unused  if NBlGages=0]  
             OutList      ‐  The next line(s)  contains  a list of output parameters.   See OutList.txt  for a listing  of available   
"WindVxi   , WindVyi   , WindVzi"                               ‐  Longitudinal,  lateral,  and vertical  wind speeds 
"WaveElev"                                                    ‐  Wave elevation  at the platform  reference  point 
"Wave1Vxi  , Wave1Vyi  , Wave1Vzi"                              ‐  Longitudinal,  lateral,  and vertical  wave particle  velocities  a 
"Wave1Axi  , Wave1Ayi  , Wave1Azi"                              ‐  Longitudinal,  lateral,  and vertical  wave particle  acceleration  
"GenPwr    , GenTq"                                           ‐  Electrical  generator  power and torque 
"HSSBrTq"                                                     ‐  High‐speed shaft brake torque 
"BldPitch1,  BldPitch2,  BldPitch3"                             ‐  Pitch angles for blades 1, 2, and 3 
"Azimuth"                                                     ‐  Blade 1 azimuth  angle 
"RotSpeed  , GenSpeed"                                         ‐  Low‐speed shaft and high‐speed shaft speeds 
"NacYaw    , NacYawErr"                                        ‐  Nacelle  yaw angle and nacelle  yaw error estimate  
"OoPDefl1  , IPDefl1   , TwstDefl1"                             ‐  Blade 1 out‐of‐plane and in‐plane deflections  and tip twist 
"OoPDefl2  , IPDefl2   , TwstDefl2"                             ‐  Blade 2 out‐of‐plane and in‐plane deflections  and tip twist 
"OoPDefl3  , IPDefl3   , TwstDefl3"                             ‐  Blade 3 out‐of‐plane and in‐plane deflections  and tip twist 
"TwrClrnc1,  TwrClrnc2,  TwrClrnc3"                             ‐  Tip‐to‐tower clearance  estimate  for blades 1, 2, and 3 
"NcIMUTAxs,  NcIMUTAys,  NcIMUTAzs"                             ‐  Nacelle  IMU translational  accelerations  (absolute)  in the nonr 
"TTDspFA   , TTDspSS   , TTDspTwst"                             ‐  Tower fore‐aft and side‐to‐side displacements  and top twist 
"PtfmSurge,  PtfmSway  , PtfmHeave"                             ‐  Platform  translational  surge, sway, and heave displacements  
"PtfmRoll  , PtfmPitch,  PtfmYaw"                               ‐  Platform  rotational  roll, pitch and yaw displacements  
"PtfmTAxt  , PtfmTAyt  , PtfmTAzt"                              ‐  Platform  translation  accelerations  (absolute)  in the tower‐bas 
"RootFxc1  , RootFyc1  , RootFzc1"                              ‐  Out‐of‐plane shear, in‐plane shear, and axial forces at the ro 
"RootMxc1  , RootMyc1  , RootMzc1"                              ‐  In‐plane bending,  out‐of‐plane bending,  and pitching  moments  a 
"RootFxc2  , RootFyc2  , RootFzc2"                              ‐  Out‐of‐plane shear, in‐plane shear, and axial forces at the ro 
"RootMxc2  , RootMyc2  , RootMzc2"                              ‐  In‐plane bending,  out‐of‐plane bending,  and pitching  moments  a 
"RootFxc3  , RootFyc3  , RootFzc3"                              ‐  Out‐of‐plane shear, in‐plane shear, and axial forces at the ro 
"RootMxc3  , RootMyc3  , RootMzc3"                              ‐  In‐plane bending,  out‐of‐plane bending,  and pitching  moments  a 
"Spn1MLxb1,  Spn1MLyb1,  Spn1MLzb1"                             ‐  Blade 1 local edgewise  bending,  flapwise  bending,  and pitching   
"Spn1MLxb2,  Spn1MLyb2,  Spn1MLzb2"                             ‐  Blade 2 local edgewise  bending,  flapwise  bending,  and pitching   
"Spn1MLxb3,  Spn1MLyb3,  Spn1MLzb3"                             ‐  Blade 3 local edgewise  bending,  flapwise  bending,  and pitching   
"RotThrust,  LSSGagFya,  LSSGagFza"                             ‐  Rotor thrust and low‐speed shaft 0‐ and 90‐rotating  shear forc 
"RotTorq   , LSSGagMya,  LSSGagMza"                             ‐  Rotor torque and low‐speed shaft 0‐ and 90‐rotating  bending  mo 
"YawBrFxp  , YawBrFyp  , YawBrFzp"                              ‐  Fore‐aft shear, side‐to‐side shear, and vertical  forces at the  
"YawBrMxp  , YawBrMyp  , YawBrMzp"                              ‐  Side‐to‐side bending,  fore‐aft bending,  and yaw moments  at the  
"TwrBsFxt  , TwrBsFyt  , TwrBsFzt"                              ‐  Fore‐aft shear, side‐to‐side shear, and vertical  forces at the  
"TwrBsMxt  , TwrBsMyt  , TwrBsMzt"                              ‐  Side‐to‐side bending,  fore‐aft bending,  and yaw moments  at the  
"TwHt1MLxt,  TwHt1MLyt,  TwHt1MLzt"                             ‐  Local side‐to‐side bending,  fore‐aft bending,  and yaw moments   
"Fair1Ten  , Fair1Ang  , Anch1Ten  , Anch1Ang"                   ‐  Line 1 fairlead  and anchor effective  tensions  and vertical  ang 
"Fair2Ten  , Fair2Ang  , Anch2Ten  , Anch2Ang"                   ‐  Line 2 fairlead  and anchor effective  tensions  and vertical  ang 
"Fair3Ten  , Fair3Ang  , Anch3Ten  , Anch3Ang"                   ‐  Line 3 fairlead  and anchor effective  tensions  and vertical  ang 
"Fair4Ten  , Fair4Ang  , Anch4Ten  , Anch4Ang"                   ‐  Line 4 fairlead  and anchor effective  tensions  and vertical  ang 
"Fair5Ten  , Fair5Ang  , Anch5Ten  , Anch5Ang"                   ‐  Line 5 fairlead  and anchor effective  tensions  and vertical  ang 
"Fair6Ten  , Fair6Ang  , Anch6Ten  , Anch6Ang"                   ‐  Line 6 fairlead  and anchor effective  tensions  and vertical  ang 
"Fair7Ten  , Fair7Ang  , Anch7Ten  , Anch7Ang"                   ‐  Line 7 fairlead  and anchor effective  tensions  and vertical  ang 
"Fair8Ten  , Fair8Ang  , Anch8Ten  , Anch8Ang"                   ‐  Line 8 fairlead  and anchor effective  tensions  and vertical  ang 
"TipSpdRat,  RotCp     , RotCt     , RotCq"                     ‐  Rotor tip speed ratio and power, thrust,  and torque coefficien  
END of FAST input file (the word "END" must appear in the first 3 columns  of this last line). 
‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐ 
A.2 Blade Input File – NRELOffshrBsline5MW_Blade.dat
‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐ 
‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐  FAST INDIVIDUAL  BLADE FILE ‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐ 
NREL 5.0 MW offshore  baseline  blade input properties.  
‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐  BLADE PARAMETERS  ‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐ 
  49         NBlInpSt     ‐  Number of blade input stations  (‐) 
False        CalcBMode    ‐  Calculate  blade mode shapes internally  {T: ignore mode shapes from below, F: use mode shapes from b 
   0.477465  BldFlDmp(1)  ‐ Blade flap mode #1 structural  damping  in percent  of critical  (%) 
   0.477465  BldFlDmp(2)  ‐ Blade flap mode #2 structural  damping  in percent  of critical  (%) 
   0.477465  BldEdDmp(1)  ‐ Blade edge mode #1 structural  damping  in percent  of critical  (%) 
‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐  BLADE ADJUSTMENT  FACTORS  ‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐ 
   1.0       FlStTunr(1)  ‐ Blade flapwise  modal stiffness  tuner, 1st mode (‐) 
161

1.0       FlStTunr(2)  ‐ Blade flapwise  modal stiffness  tuner, 2nd mode (‐) 
   1.04536   AdjBlMs      ‐  Factor to adjust blade mass density  (‐) 
   1.0       AdjFlSt      ‐  Factor to adjust blade flap stiffness  (‐) 
   1.0       AdjEdSt      ‐  Factor to adjust blade edge stiffness  (‐) 
‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐  DISTRIBUTED  BLADE PROPERTIES  ‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐ ‐‐‐‐‐‐ 
BlFract   AeroCent   StrcTwst   BMassDen   FlpStff       EdgStff       GJStff      EAStff       Alpha  FlpIner   EdgIner   PrecrvRef   Pre 
(‐)       (‐)        (deg)      (kg/m)     (Nm^2)       (Nm^2)       (Nm^2)      (N)          (‐)     (kg m)   (kg m)   (m)         (m) 
0.00000   0.25000    13.308     678.935    18110.00E6   18113.60E6   5564.40E6    9729.48E6   0.0      972.86   973.04  0.0         0.0 
0.00325   0.25000    13.308     678.935    18110.00E6   18113.60E6   5564.40E6    9729.48E6   0.0      972.86   973.04  0.0         0.0 
0.01951   0.24951    13.308     773.363    19424.90E6   19558.60E6   5431.59E6   10789.50E6   0.0     1091.52   1066.38   0.0         0.0 
0.03577   0.24510    13.308     740.550    17455.90E6   19497.80E6   4993.98E6   10067.23E6   0.0      966.09  1047.36   0.0         0.0 
0.05203   0.23284    13.308     740.042    15287.40E6   19788.80E6   4666.59E6    9867.78E6   0.0      873.81  1099.75   0.0         0.0 
0.06829   0.22059    13.308     592.496    10782.40E6   14858.50E6   3474.71E6    7607.86E6   0.0      648.55   873.02  0.0         0.0 
0.08455   0.20833    13.308     450.275      7229.72E6   10220.60E6   2323.54E6    5491.26E6   0.0      456.76   641.49  0.0         0.0 
0.10081   0.19608    13.308     424.054      6309.54E6    9144.70E6   1907.87E6    4971.30E6   0.0      400.53   593.73  0.0         0.0 
0.11707   0.18382    13.308     400.638      5528.36E6    8063.16E6   1570.36E6    4493.95E6   0.0      351.61   547.18  0.0         0.0 
0.13335   0.17156    13.308     382.062      4980.06E6    6884.44E6   1158.26E6    4034.80E6   0.0      316.12   490.84  0.0         0.0 
0.14959   0.15931    13.308     399.655      4936.84E6    7009.18E6   1002.12E6    4037.29E6   0.0      303.60   503.86  0.0         0.0 
0.16585   0.14706    13.308     426.321      4691.66E6    7167.68E6    855.90E6    4169.72E6   0.0      289.24   544.70  0.0         0.0 
0.18211   0.13481    13.181     416.820      3949.46E6    7271.66E6    672.27E6    4082.35E6   0.0      246.57   569.90   0.0         0.0 
0.19837   0.12500    12.848     406.186      3386.52E6    7081.70E6    547.49E6    4085.97E6   0.0      215.91   601.28  0.0         0.0 
0.21465   0.12500    12.192     381.420      2933.74E6    6244.53E6    448.84E6    3668.34E6   0.0      187.11   546.56  0.0         0.0 
0.23089   0.12500    11.561     352.822      2568.96E6    5048.96E6    335.92E6    3147.76E6   0.0      160.84   468.71  0.0         0.0 
0.24715   0.12500    11.072     349.477      2388.65E6    4948.49E6    311.35E6    3011.58E6   0.0      148.56   453.76  0.0         0.0 
0.26341   0.12500    10.792     346.538      2271.99E6    4808.02E6    291.94E6    2882.62E6   0.0      140.30   436.22  0.0         0.0 
0.29595   0.12500    10.232     339.333      2050.05E6    4501.40E6    261.00E6    2613.97E6   0.0      124.61   398.18  0.0         0.0 
0.32846   0.12500      9.672     330.004      1828.25E6    4244.07E6    228.82E6    2357.48E6   0.0      109.42   362.08  0.0         0.0 
0.36098   0.12500      9.110     321.990      1588.71E6    3995.28E6    200.75E6    2146.86E6   0.0       94.36   335.01  0.0         0.0 
0.39350   0.12500      8.534     313.820      1361.93E6    3750.76E6    174.38E6    1944.09E6   0.0       80.24   308.57  0.0         0.0 
0.42602   0.12500      7.932     294.734      1102.38E6    3447.14E6    144.47E6    1632.70E6   0.0       62.67   263.87  0.0         0.0 
0.45855   0.12500      7.321     287.120       875.80E6    3139.07E6    119.98E6    1432.40E6   0.0       49.42   237.06  0.0         0.0 
0.49106   0.12500      6.711     263.343       681.30E6    2734.24E6      81.19E6    1168.76E6   0.0       37.34   196.41  0.0         0.0 
0.52358   0.12500      6.122     253.207       534.72E6    2554.87E6      69.09E6    1047.43E6   0.0       29.14   180.34  0.0         0.0 
0.55610   0.12500      5.546     241.666       408.90E6    2334.03E6      57.45E6      922.95E6   0.0       22.16   162.43   0.0         0.0 
0.58862   0.12500      4.971     220.638       314.54E6    1828.73E6      45.92E6      760.82E6   0.0       17.33   134.83  0.0         0.0 
0.62115   0.12500      4.401     200.293       238.63E6    1584.10E6      35.98E6      648.03E6   0.0       13.30   116.30  0.0         0.0 
0.65366   0.12500      3.834     179.404       175.88E6    1323.36E6      27.44E6      539.70E6   0.0        9.96     97.98  0.0         0.0 
0.68618   0.12500      3.332     165.094       126.01E6    1183.68E6      20.90E6      531.15E6   0.0        7.30     98.93  0.0         0.0 
0.71870   0.12500      2.890     154.411       107.26E6    1020.16E6      18.54E6      460.01E6   0.0        6.22     85.78  0.0         0.0 
0.75122   0.12500      2.503     138.935        90.88E6      797.81E6      16.28E6      375.75E6   0.0        5.19     69.96  0.0         0.0 
0.78376   0.12500      2.116     129.555        76.31E6      709.61E6      14.53E6      328.89E6   0.0        4.36     61.41  0.0         0.0 
0.81626   0.12500      1.730     107.264        61.05E6      518.19E6       9.07E6     244.04E6   0.0        3.36     45.44  0.0         0.0 
0.84878   0.12500      1.342      98.776       49.48E6      454.87E6       8.06E6     211.60E6   0.0        2.75     39.57  0.0         0.0 
0.88130   0.12500      0.954      90.248       39.36E6      395.12E6       7.08E6     181.52E6   0.0        2.21     34.09  0.0         0.0 
0.89756   0.12500      0.760      83.001       34.67E6      353.72E6       6.09E6     160.25E6   0.0        1.93     30.12  0.0         0.0 
0.91382   0.12500      0.574      72.906       30.41E6      304.73E6       5.75E6     109.23E6   0.0        1.69     20.15  0.0         0.0 
0.93008   0.12500      0.404      68.772       26.52E6      281.42E6       5.33E6     100.08E6   0.0        1.49     18.53  0.0         0.0 
0.93821   0.12500      0.319      66.264       23.84E6      261.71E6       4.94E6      92.24E6   0.0        1.34     17.11  0.0         0.0 
0.94636   0.12500      0.253      59.340       19.63E6      158.81E6       4.24E6      63.23E6   0.0        1.10     11.55  0.0         0.0 
0.95447   0.12500      0.216      55.914       16.00E6      137.88E6       3.66E6      53.32E6   0.0        0.89      9.77  0.0         0.0 
0.96260   0.12500      0.178      52.484       12.83E6      118.79E6       3.13E6      44.53E6   0.0        0.71      8.19  0.0         0.0 
0.97073   0.12500      0.140      49.114       10.08E6      101.63E6       2.64E6      36.90E6   0.0        0.56      6.82  0.0         0.0 
0.97886   0.12500      0.101      45.818        7.55E6      85.07E6       2.17E6      29.92E6   0.0        0.42      5.57  0.0         0.0 
0.98699   0.12500      0.062      41.669        4.60E6      64.26E6       1.58E6      21.31E6   0.0        0.25      4.01  0.0         0.0 
0.99512   0.12500      0.023      11.453        0.25E6       6.61E6      0.25E6       4.85E6  0.0        0.04      0.94  0.0         0.0 
1.00000   0.12500      0.000      10.319        0.17E6       5.01E6      0.19E6       3.53E6  0.0        0.02      0.68  0.0         0.0 
‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐  BLADE MODE SHAPES ‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐ 
   0.0622   BldFl1Sh(2)  ‐ Flap mode 1, coeff of x^2 
   1.7254   BldFl1Sh(3)  ‐             , coeff of x^3 
  ‐3.2452   BldFl1Sh(4)  ‐             , coeff of x^4 
   4.7131   BldFl1Sh(5)  ‐             , coeff of x^5 
  ‐2.2555   BldFl1Sh(6)  ‐             , coeff of x^6 
  ‐0.5809   BldFl2Sh(2)  ‐ Flap mode 2, coeff of x^2 
   1.2067   BldFl2Sh(3)  ‐             , coeff of x^3 
 ‐15.5349    BldFl2Sh(4)  ‐             , coeff of x^4 
  29.7347    BldFl2Sh(5)  ‐             , coeff of x^5 
 ‐13.8255    BldFl2Sh(6)  ‐             , coeff of x^6 
   0.3627   BldEdgSh(2)  ‐ Edge mode 1, coeff of x^2 
   2.5337   BldEdgSh(3)  ‐             , coeff of x^3 
  ‐3.5772   BldEdgSh(4)  ‐             , coeff of x^4 
   2.3760   BldEdgSh(5)  ‐             , coeff of x^5 
  ‐0.6952   BldEdgSh(6)  ‐             , coeff of x^6 
A.3 Tower Input File – NRELOffshrBsline5MW_Tower_ITIBarge4.dat
‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐ 
‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐  FAST TOWER FILE ‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐ 
NREL 5.0 MW offshore  baseline  tower input properties  for the  ITI Energy barge with 4m draft. 
‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐  TOWER PARAMETERS  ‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐ 
  11         NTwInpSt     ‐  Number of input stations  to specify  tower geometry  
False        CalcTMode    ‐  Calculate  tower mode shapes internally  {T: ignore mode shapes from below, F: use mode shapes from b 
   1.0       TwrFADmp(1)  ‐ Tower 1st fore‐aft mode structural  damping  ratio (%) 
   1.0       TwrFADmp(2)  ‐ Tower 2nd fore‐aft mode structural  damping  ratio (%) 
162

1.0       TwrSSDmp(1)  ‐ Tower 1st side‐to‐side mode structural  damping  ratio (%) 
   1.0       TwrSSDmp(2)  ‐ Tower 2nd side‐to‐side mode structural  damping  ratio (%) 
‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐  TOWER ADJUSTMUNT  FACTORS  ‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐ 
   1.0       FAStTunr(1)  ‐ Tower fore‐aft modal stiffness  tuner, 1st mode (‐) 
   1.0       FAStTunr(2)  ‐ Tower fore‐aft modal stiffness  tuner, 2nd mode (‐) 
   1.0       SSStTunr(1)  ‐ Tower side‐to‐side stiffness  tuner, 1st mode (‐) 
   1.0       SSStTunr(2)  ‐ Tower side‐to‐side stiffness  tuner, 2nd mode (‐) 
   1.0       AdjTwMa      ‐  Factor to adjust tower mass density  (‐) 
   1.0       AdjFASt      ‐  Factor to adjust tower fore‐aft stiffness  (‐) 
   1.0       AdjSSSt      ‐  Factor to adjust tower side‐to‐side stiffness  (‐) 
‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐  DISTRIBUTED  TOWER PROPERTIES  ‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐ 
HtFract   TMassDen   TwFAStif    TwSSStif    TwGJStif    TwEAStif    TwFAIner   TwSSIner   TwFAcgOf   TwSScgOf  
(‐)       (kg/m)     (Nm^2)      (Nm^2)      (Nm^2)      (N)         (kg m)     (kg m)     (m)        (m) 
0.0       5590.87    614.343E9   614.343E9   472.751E9   138.127E9   24866.3    24866.3    0.0        0.0 
0.1       5232.43    534.821E9   534.821E9   411.558E9   129.272E9   21647.5    21647.5    0.0        0.0 
0.2       4885.76    463.267E9   463.267E9   356.495E9   120.707E9   18751.3    18751.3    0.0        0.0 
0.3       4550.87    399.131E9   399.131E9   307.141E9   112.433E9   16155.3    16155.3    0.0        0.0 
0.4       4227.75    341.883E9   341.883E9   263.087E9   104.450E9   13838.1    13838.1    0.0        0.0 
0.5       3916.41    291.011E9   291.011E9   223.940E9    96.758E9   11779.0    11779.0    0.0        0.0 
0.6       3616.83    246.027E9   246.027E9   189.323E9    89.357E9    9958.2     9958.2   0.0        0.0 
0.7       3329.03    206.457E9   206.457E9   158.874E9    82.247E9    8356.6     8356.6   0.0        0.0 
0.8       3053.01    171.851E9   171.851E9   132.244E9    75.427E9    6955.9     6955.9   0.0        0.0 
0.9       2788.75    141.776E9   141.776E9   109.100E9    68.899E9    5738.6     5738.6   0.0        0.0 
1.0       2536.27    115.820E9   115.820E9    89.126E9    62.661E9    4688.0     4688.0   0.0        0.0 
‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐  TOWER FORE‐AFT MODE SHAPES ‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐ 
   0.7585   TwFAM1Sh(2)  ‐ Mode 1, coefficient  of x^2 term 
   0.6185   TwFAM1Sh(3)  ‐        , coefficient  of x^3 term 
  ‐0.1085   TwFAM1Sh(4)  ‐        , coefficient  of x^4 term 
  ‐0.5510   TwFAM1Sh(5)  ‐        , coefficient  of x^5 term 
   0.2825   TwFAM1Sh(6)  ‐        , coefficient  of x^6 term 
  98.8570    TwFAM2Sh(2)  ‐ Mode 2, coefficient  of x^2 term 
‐146.7007    TwFAM2Sh(3)  ‐        , coefficient  of x^3 term 
 135.7499    TwFAM2Sh(4)  ‐        , coefficient  of x^4 term 
‐166.3440    TwFAM2Sh(5)  ‐        , coefficient  of x^5 term 
  79.4379    TwFAM2Sh(6)  ‐        , coefficient  of x^6 term 
‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐  TOWER SIDE‐TO‐SIDE MODE SHAPES ‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐ 
   2.7352   TwSSM1Sh(2)  ‐ Mode 1, coefficient  of x^2 term 
  ‐7.6228   TwSSM1Sh(3)  ‐        , coefficient  of x^3 term 
  13.1976    TwSSM1Sh(4)  ‐        , coefficient  of x^4 term 
 ‐10.2992    TwSSM1Sh(5)  ‐        , coefficient  of x^5 term 
   2.9892   TwSSM1Sh(6)  ‐        , coefficient  of x^6 term 
  90.7938    TwSSM2Sh(2)  ‐ Mode 2, coefficient  of x^2 term 
‐174.3108    TwSSM2Sh(3)  ‐        , coefficient  of x^3 term 
 190.5109    TwSSM2Sh(4)  ‐        , coefficient  of x^4 term 
‐165.1911    TwSSM2Sh(5)  ‐        , coefficient  of x^5 term 
  59.1972    TwSSM2Sh(6)  ‐        , coefficient  of x^6 term 
A W_ADAMSSpecific.dat .4 ADAMS Input File – NRELOffshrBsline5M
‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐ 
‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐  FAST 2 ADAMS PREPROCESSOR,  ADAMS‐SPECIFIC  DATA FILE ‐‐‐‐‐ 
NREL 5.0 MW offshore  baseline  ADAMS‐specific  input properties.  
‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐  FEATURE  FLAGS ‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐ 
True         SaveGrphcs   ‐  Save GRAPHICS  output (flag) 
False        MakeLINacf   ‐  Make an ADAMS/LINEAR  control  / command  file (flag) 
‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐  DAMPING  PARAMETERS  ‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐ ‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐ 
   0.01      CRatioTGJ    ‐  Ratio of damping  to stiffness  for the tower torsion      deflection   (‐) 
   0.01      CRatioTEA    ‐  Ratio of damping  to stiffness  for the tower extensional  deflection   (‐) 
   0.01      CRatioBGJ    ‐  Ratio of damping  to stiffness  for the blade torsion       deflections  (‐) 
   0.01      CRatioBEA    ‐  Ratio of damping  to stiffness  for the blade extensional  deflections  (‐) 
‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐  BLADE PITCH ACTUATOR  PARAMETERS  ‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐ 
 971.350E6   BPActrSpr    ‐  Blade pitch actuator  spring stiffness  constant  (N‐m/rad) 
   0.206E6   BPActrDmp    ‐  Blade pitch actuator  damping            constant  (N‐m/(rad/s))  
‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐  GRAPHICS  PARAMETERS  ‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐ 
  20         NSides      ‐  Number of sides used in GRAPHICS  CYLINDER  and FRUSTUM  statement s (‐) 
   3.000     TwrBaseRad   ‐  Tower base radius used for linearly  tapered  tower GRAPHICS  CYLINDERs (m) 
   1.935     TwrTopRad    ‐  Tower top  radius used for linearly  tapered  tower GRAPHICS  CYLINDERs  (m) 
   7.0       NacLength    ‐  Length of nacelle  used for the nacelle  GRAPHICS  (m) 
   1.75      NacRadBot    ‐  Bottom (opposite  rotor) radius of nacelle  FRUSTUM  used for the nacelle  GRAPHICS  (m) 
   1.75      NacRadTop    ‐  Top     (rotor end)       radius of nacelle  FRUSTUM  used for the nacelle  GRAPHICS (m) 
   1.0       GBoxLength   ‐  Length,  width, and height of the gearbox  BOX for gearbox  GRAPHICS  (m) 
   2.39      GenLength    ‐  Length of the  generator  CYLINDER  used for generator  GRAPHICS  (m) 
   1.195     HSSLength    ‐  Length of the  high‐speed shaft CYLINDER  used for HSS GRAPHICS  (m) 
   4.78      LSSLength    ‐  Length of the  low‐ speed shaft CYLINDER  used for LSS GRAPHICS  (m) 
   0.75      GenRad      ‐  Radius of the  generator  CYLINDER  used for generator  GRAPHICS  (m) 
   0.2       HSSRad      ‐  Radius of the  high‐speed shaft CYLINDER  used for HSS GRAPHICS  (m) 
   0.4       LSSRad      ‐  Radius of the  low ‐ speed shaft CYLINDER  used for LSS GRAPHICS  (m) 
   0.875     HubCylRad    ‐  Radius of hub  CYLINDER  used for hub GRAPHICS  (m) 
   0.18      ThkOvrChrd   ‐  Ratio of blade thickness  to blade chord used for blade element  BOX GRAPHICS  (‐) 
   0.0       BoomRad      ‐  Radius of the  tail boom CYLINDER  used for tail boom GRAPHICS  (m) 
163

A.5 Linearization Input File – NRELOffshrBsline5MW_Linear.dat
‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐ 
‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐  FAST LINEARIZATION  CONTROL  FILE ‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐ 
NREL 5.0 MW offshore  baseline  linearization  input properties.  
‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐  PERIODIC  STEADY STATE SOLUTION  ‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐ 
True         CalcStdy     ‐  Calculate  periodic  steady state condition  {False:  linearize  about initial  conditions}  (flag) 
   3         TrimCase     ‐  Trim case {1:  find nacelle  yaw, 2: find generator  torque,  3: find collective  blade pitch} (switch)   
   0.0001   DispTol      ‐  Convergence  tolerance  for the 2‐norm of displacements  in the periodic  steady state calculation  (rad  
   0.0010    VelTol      ‐  Convergence  tolerance  for the 2‐norm of velocities      in the periodic  steady state calculation  (rad 
‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐  MODEL LINEARIZATION  ‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐ 
  36         NAzimStep    ‐  Number of equally ‐spaced azimuth  steps in periodic  linearized  model (‐) 
   1         MdlOrder     ‐  Order of output linearized  model {1: 1st order A, B, Bd, C, D, Dd; 2: 2nd order M, C, K, F, Fd, Vel 
‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐  INPUTS AND DISTURBANCES  ‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐ 
   0         NInputs      ‐  Number of control  inputs [0 (none) or 1 to 4+NumBl]  (‐) 
             CntrlInpt    ‐  List   of control  inputs [1 to NInputs]  {1: nacelle  yaw angle, 2: nacelle  yaw rate, 3: generator  to 
   0         NDisturbs    ‐  Number of wind disturbances  [0 (none) or 1 to 7] (‐) 
             Disturbnc    ‐  List   of input wind disturbances  [1 to NDisturbs]  {1: horizontal  hub‐height wind speed, 2: horizon  
164

Appendix B AeroDyn Input Files for the 5-MW Wind Turbine
B.1 Primary Input File – NRELOffshrBsline5MW_AeroDyn.ipt
NREL 5.0 MW offshore  baseline  aerodynamic  input properties;  Compatible  with AeroDyn  v12.60i.  
SI           SysUnits     ‐  System of units used for input and output [must be SI for  FAST] (unquoted  string)  
BEDDOES       StallMod     ‐  Dynamic  stall included  [BEDDOES  or STEADY]  (unquoted  string)  
USE_CM       UseCm       ‐  Use aerodynamic  pitching  moment model? [USE_CM  or NO_CM] (unquoted  string)  
EQUIL        InfModel     ‐  Inflow model [DYNIN or EQUIL] (unquoted  string)  
   3         max_r_power  ‐ Max polynomial  power in radial direction  (‐) [max 22] 
   3         m_modes      ‐  Number of modes in azimuthal  direction  (‐) [max 22] 
False        Use_GDW_Vel_Filter   ‐  Use the incoming  velocity  filter in GDW (flag) 
False        Use_Vortex_Ring_GDW  ‐ Use the vortex ring correction  in GDW (flag) 
   0.679061  tau_GDW      ‐  Time constant  for  GDW (‐) {0.0: no wake delay, 0.679061  = 32/(15*pi)  recommended}  
WAKE         IndModel     ‐  Induction ‐factor model [NONE or WAKE or SWIRL] (unquoted  string)  
   0.005     AToler      ‐  Induction ‐factor tolerance  (convergence  criteria)  (‐) 
PRANDtl       TLModel      ‐  Tip‐loss model (EQUIL only) [PRANDtl,  GTECH, or NONE] (unquoted  string)  
PRANDtl       HLModel      ‐  Hub‐loss model (EQUIL only) [PRANdtl  or NONE] (unquoted  string)  
"WindData\90m_12mps"                               WindFile     ‐  Name of file containing  wind data (quoted  string)  
  90.0       HH          ‐  Wind reference  (hub) height [TowerHt+Twr2Shft+OverHang*SIN(ShftTilt)]  (m) 
True         TwrPotent    ‐  Calculate  tower potential  flow (flag) 
False        TwrShadow    ‐  Calculate  tower shadow (flag) 
True         TwrRead      ‐  Read in filename  below even if above is False (used for tower drag in some Dyn progs) (flag) 
"NRELOffshrBsline5MW_AeroDyn_Tower.dat"            TwrFile      ‐  Tower drag file name (quoted  string)  
   1.225     AirDens      ‐  Air density  (kg/m^3)  
   1.464E‐5 KinVisc      ‐  Kinematic  air  viscosity  [CURRENTLY  IGNORED]  (m^2/sec)  
   0.02479   DTAero      ‐  Time interval  for  aerodynamic  calculations  (sec) 
   8         NumFoil      ‐  Number of airfoil  files (‐) 
"AeroData\Cylinder1.dat"                           FoilNm      ‐  Names of the airfoil  files [NumFoil  lines] (quoted  strings)  
"AeroData\Cylinder2.dat"  
"AeroData\DU40_A17.dat"  
"AeroData\DU35_A17.dat"  
"AeroData\DU30_A17.dat"  
"AeroData\DU25_A17.dat"  
"AeroData\DU21_A17.dat"  
"AeroData\NACA64_A17.dat"  
  17         BldNodes     ‐  Number of blade nodes used for analysis  (‐) 
RNodes   AeroTwst   DRNodes   Chord  NFoil  PrnElm 
 2.8667  13.308     2.7333   3.542  1       NOPRINT  
 5.6000  13.308     2.7333   3.854  1       NOPRINT  
 8.3333  13.308     2.7333   4.167  2       NOPRINT  
11.7500   13.308     4.1000   4.557  3       NOPRINT  
15.8500   11.480     4.1000   4.652  4       NOPRINT  
19.9500   10.162     4.1000   4.458  4       NOPRINT  
24.0500    9.011     4.1000   4.249  5       NOPRINT  
28.1500    7.795     4.1000   4.007  6       NOPRINT  
32.2500    6.544     4.1000   3.748  6       NOPRINT  
36.3500    5.361     4.1000   3.502  7       NOPRINT  
40.4500    4.188     4.1000   3.256  7       NOPRINT  
44.5500    3.125     4.1000   3.010  8       NOPRINT  
48.6500    2.319     4.1000   2.764  8       NOPRINT  
52.7500    1.526     4.1000   2.518  8       NOPRINT  
56.1667    0.863     2.7333   2.313  8       NOPRINT  
58.9000    0.370     2.7333   2.086  8       NOPRINT  
61.6333    0.106     2.7333   1.419  8       NOPRINT  
B.2 Tower Input File – NRELO ffshrBsline5MW_AeroDyn_Tower.dat
NREL 5.0 MW offshore  baseline  aerodynamic  tower CD input properties.  
Compatible  with AeroDyn  v12.60i.  
  12         NTwrHt      ‐  Number of tower input height stations  listed (‐) 
   1         NTwrRe      ‐  Number of tower Re values (‐) 
   1         NTwrCD      ‐  Number of tower CD columns  (‐) 
   0.0       Tower_Wake_Constant  ‐ Tower wake constant  (‐) {0.0: full potential  flow, 0.1: Bak model} 
‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐  DISTRIBUTED  TOWER PROPERTIES  ‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐ 
TwrHtFr   TwrWid  NTwrCDCol  
0.00000   6.000   1 
0.09733   5.787   1 
0.19467   5.574   1 
0.29200   5.361   1 
0.38933   5.148   1 
0.48667   4.935   1 
0.58400   4.722   1 
0.68133   4.509   1 
0.77867   4.296   1 
0.87600   4.083   1 
0.97333   3.870   1 
165

1.00000   3.870   1 
‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐  Re v CD PROPERTIES  ‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐ 
TwrRe  TwrCD1  TwrCD2  TwrCD2  … 
1.0     0.0 
B.3 Airfoil-Data Input File – Cylinder1.dat
Round root section  with a Cd of 0.50 
Made by Jason Jonkman  
   1         Number of airfoil  tables in this file 
   0.0       Table ID parameter  
   0.0       Stall angle (deg) 
   0.0       No longer used, enter zero 
   0.0       No longer used, enter zero 
   0.0       No longer used, enter zero 
   0.0       Zero Cn angle of attack (deg) 
   0.0       Cn slope for zero lift (dimensionless)  
   0.0       Cn extrapolated  to value at positive  stall angle of attack 
   0.0       Cn at stall value for negative  angle of attack 
   0.0       Angle of attack for minimum  CD (deg) 
   0.50      Minimum  CD value 
‐180.00     0.000   0.5000   0.000 
   0.00     0.000   0.5000   0.000 
 180.00     0.000   0.5000   0.000 
B.4 Airfoil-Data Input File – Cylinder2.dat
Round root section  with a Cd of 0.35 
Made by Jason Jonkman  
   1         Number of airfoil  tables in this file 
   0.0       Table ID parameter  
   0.0       Stall angle (deg) 
   0.0       No longer used, enter zero 
   0.0       No longer used, enter zero 
   0.0       No longer used, enter zero 
   0.0       Zero Cn angle of attack (deg) 
   0.0       Cn slope for zero lift (dimensionless)  
   0.0       Cn extrapolated  to value at positive  stall angle of attack 
   0.0       Cn at stall value for negative  angle of attack 
   0.0       Angle of attack for minimum  CD (deg) 
   0.35      Minimum  CD value 
‐180.00     0.000   0.3500   0.000 
   0.00     0.000   0.3500   0.000 
 180.00     0.000   0.3500   0.000 
B.5 Airfoil-Data Input File – DU40_A17.dat
DU40 airfoil  with an aspect ratio of 17.  Original  ‐180 to 180deg Cl,  Cd, and Cm versus AOA data taken from Appendix  A of DOW 
Cl and Cd values corrected  for rotational  stall delay and Cd values corrected  using the Viterna  method for 0 to 90deg AOA by  
   1         Number of airfoil  tables in this file 
   0.0       Table ID parameter  
   9.00      Stall angle (deg) 
   0.0       No longer used, enter zero 
   0.0       No longer used, enter zero 
   0.0       No longer used, enter zero 
  ‐1.3430   Zero Cn angle of attack (deg) 
   7.4888   Cn slope for zero lift (dimensionless)  
   1.3519   Cn extrapolated  to value at positive  stall angle of attack 
  ‐0.3226   Cn at stall value for negative  angle of attack 
   0.00      Angle of attack for minimum  CD (deg) 
   0.0113   Minimum  CD value 
‐180.00     0.000   0.0602   0.0000 
‐175.00     0.218   0.0699   0.0934 
‐170.00     0.397   0.1107   0.1697 
‐160.00     0.642   0.3045   0.2813 
‐155.00     0.715   0.4179   0.3208 
‐150.00     0.757   0.5355   0.3516 
‐145.00     0.772   0.6535   0.3752 
‐140.00     0.762   0.7685   0.3926 
‐135.00     0.731   0.8777   0.4048 
‐130.00     0.680   0.9788   0.4126 
‐125.00     0.613   1.0700   0.4166 
‐120.00     0.532   1.1499   0.4176 
‐115.00     0.439   1.2174   0.4158 
‐110.00     0.337   1.2716   0.4117 
‐105.00     0.228   1.3118   0.4057 
‐100.00     0.114   1.3378   0.3979 
166

‐95.00    ‐ 0.002   1.3492    0.3887  
 ‐90.00    ‐ 0.120   1.3460    0.3781  
 ‐85.00    ‐ 0.236   1.3283    0.3663  
 ‐80.00    ‐ 0.349   1.2964    0.3534  
 ‐75.00    ‐ 0.456   1.2507    0.3394  
 ‐70.00    ‐ 0.557   1.1918    0.3244  
 ‐65.00    ‐ 0.647   1.1204    0.3084  
 ‐60.00    ‐ 0.727   1.0376    0.2914  
 ‐55.00    ‐ 0.792   0.9446    0.2733  
 ‐50.00    ‐ 0.842   0.8429    0.2543  
 ‐45.00    ‐ 0.874   0.7345    0.2342  
 ‐40.00    ‐ 0.886   0.6215    0.2129  
 ‐35.00    ‐ 0.875   0.5067    0.1906  
 ‐30.00    ‐ 0.839   0.3932    0.1670  
 ‐25.00    ‐ 0.777   0.2849    0.1422  
 ‐24.00    ‐ 0.761   0.2642    0.1371  
 ‐23.00    ‐ 0.744   0.2440    0.1320  
 ‐22.00    ‐ 0.725   0.2242    0.1268  
 ‐21.00    ‐ 0.706   0.2049    0.1215  
 ‐20.00    ‐ 0.685   0.1861    0.1162  
 ‐19.00    ‐ 0.662   0.1687    0.1097  
 ‐18.00    ‐ 0.635   0.1533    0.1012  
 ‐17.00    ‐ 0.605   0.1398    0.0907  
 ‐16.00    ‐ 0.571   0.1281    0.0784  
 ‐15.00    ‐ 0.534   0.1183    0.0646  
 ‐14.00    ‐ 0.494   0.1101    0.0494  
 ‐13.00    ‐ 0.452   0.1036    0.0330  
 ‐12.00    ‐ 0.407   0.0986    0.0156  
 ‐11.00    ‐ 0.360   0.0951   ‐0.0026  
 ‐10.00    ‐ 0.311   0.0931   ‐0.0213  
  ‐8.00   ‐ 0.208   0.0930  ‐0.0600 
  ‐6.00   ‐ 0.111   0.0689  ‐0.0500 
  ‐5.50   ‐ 0.090   0.0614  ‐0.0516 
  ‐5.00   ‐ 0.072   0.0547  ‐0.0532 
  ‐4.50   ‐ 0.065   0.0480  ‐0.0538 
  ‐4.00   ‐ 0.054   0.0411  ‐0.0544 
  ‐3.50   ‐ 0.017   0.0349  ‐0.0554 
  ‐3.00     0.003   0.0299  ‐0.0558 
  ‐2.50     0.014   0.0255  ‐0.0555 
  ‐2.00     0.009   0.0198  ‐0.0534 
  ‐1.50     0.004   0.0164  ‐0.0442 
  ‐1.00     0.036   0.0147  ‐0.0469 
  ‐0.50     0.073   0.0137  ‐0.0522 
   0.00     0.137   0.0113  ‐0.0573 
   0.50     0.213   0.0114  ‐0.0644 
   1.00     0.292   0.0118  ‐0.0718 
   1.50     0.369   0.0122  ‐0.0783 
   2.00     0.444   0.0124  ‐0.0835 
   2.50     0.514   0.0124  ‐0.0866 
   3.00     0.580   0.0123  ‐0.0887 
   3.50     0.645   0.0120  ‐0.0900 
   4.00     0.710   0.0119  ‐0.0914 
   4.50     0.776   0.0122  ‐0.0933 
   5.00     0.841   0.0125  ‐0.0947 
   5.50     0.904   0.0129  ‐0.0957 
   6.00     0.967   0.0135  ‐0.0967 
   6.50     1.027   0.0144  ‐0.0973 
   7.00     1.084   0.0158  ‐0.0972 
   7.50     1.140   0.0174  ‐0.0972 
   8.00     1.193   0.0198  ‐0.0968 
   8.50     1.242   0.0231  ‐0.0958 
   9.00     1.287   0.0275  ‐0.0948 
   9.50     1.333   0.0323  ‐0.0942 
  10.00      1.368   0.0393   ‐0.0926  
  10.50      1.400   0.0475   ‐0.0908  
  11.00      1.425   0.0580   ‐0.0890  
  11.50      1.449   0.0691   ‐0.0877  
  12.00      1.473   0.0816   ‐0.0870  
  12.50      1.494   0.0973   ‐0.0870  
  13.00      1.513   0.1129   ‐0.0876  
  13.50      1.538   0.1288   ‐0.0886  
  14.50      1.587   0.1650   ‐0.0917  
  15.00      1.614   0.1845   ‐0.0939  
  15.50      1.631   0.2052   ‐0.0966  
  16.00      1.649   0.2250   ‐0.0996  
  16.50      1.666   0.2467   ‐0.1031  
  17.00      1.681   0.2684   ‐0.1069  
  17.50      1.699   0.2900   ‐0.1110  
  18.00      1.719   0.3121   ‐0.1157  
  19.00      1.751   0.3554   ‐0.1242  
  19.50      1.767   0.3783   ‐0.1291  
  20.50      1.798   0.4212   ‐0.1384  
  21.00      1.810   0.4415   ‐0.1416  
  22.00      1.830   0.4830   ‐0.1479  
167

23.00      1.847   0.5257   ‐0.1542  
  24.00      1.861   0.5694   ‐0.1603  
  25.00      1.872   0.6141   ‐0.1664  
  26.00      1.881   0.6593   ‐0.1724  
  28.00      1.894   0.7513   ‐0.1841  
  30.00      1.904   0.8441   ‐0.1954  
  32.00      1.915   0.9364   ‐0.2063  
  35.00      1.929   1.0722   ‐0.2220  
  40.00      1.903   1.2873   ‐0.2468  
  45.00      1.820   1.4796   ‐0.2701  
  50.00      1.690   1.6401   ‐0.2921  
  55.00      1.522   1.7609   ‐0.3127  
  60.00      1.323   1.8360   ‐0.3321  
  65.00      1.106   1.8614   ‐0.3502  
  70.00      0.880   1.8347   ‐0.3672  
  75.00      0.658   1.7567   ‐0.3830  
  80.00      0.449   1.6334   ‐0.3977  
  85.00      0.267   1.4847   ‐0.4112  
  90.00      0.124   1.3879   ‐0.4234  
  95.00      0.002   1.3912   ‐0.4343  
 100.00   ‐ 0.118   1.3795  ‐0.4437 
 105.00   ‐ 0.235   1.3528  ‐0.4514 
 110.00   ‐ 0.348   1.3114  ‐0.4573 
 115.00   ‐ 0.453   1.2557  ‐0.4610 
 120.00   ‐ 0.549   1.1864  ‐0.4623 
 125.00   ‐ 0.633   1.1041  ‐0.4606 
 130.00   ‐ 0.702   1.0102  ‐0.4554 
 135.00   ‐ 0.754   0.9060  ‐0.4462 
 140.00   ‐ 0.787   0.7935  ‐0.4323 
 145.00   ‐ 0.797   0.6750  ‐0.4127 
 150.00   ‐ 0.782   0.5532  ‐0.3863 
 155.00   ‐ 0.739   0.4318  ‐0.3521 
 160.00   ‐ 0.664   0.3147  ‐0.3085 
 170.00   ‐ 0.410   0.1144  ‐0.1858 
 175.00   ‐ 0.226   0.0702  ‐0.1022 
 180.00     0.000   0.0602   0.0000 
B.6 Airfoil-Data Input File – DU35_A17.dat
DU35 airfoil  with an aspect ratio of 17.  Original  ‐180 to 180deg Cl,  Cd, and Cm versus AOA data taken from Appendix  A of DOW 
Cl and Cd values corrected  for rotational  stall delay and Cd values corrected  using the Viterna  method for 0 to 90deg AOA by  
   1         Number of airfoil  tables in this file 
   0.0       Table ID parameter  
  11.50       Stall angle (deg) 
   0.0       No longer used, enter zero 
   0.0       No longer used, enter zero 
   0.0       No longer used, enter zero 
  ‐1.8330   Zero Cn angle of attack (deg) 
   7.1838   Cn slope for zero lift (dimensionless)  
   1.6717   Cn extrapolated  to value at positive  stall angle of attack 
  ‐0.3075   Cn at stall value for negative  angle of attack 
   0.00      Angle of attack for minimum  CD (deg) 
   0.0094   Minimum  CD value 
‐180.00     0.000   0.0407   0.0000 
‐175.00     0.223   0.0507   0.0937 
‐170.00     0.405   0.1055   0.1702 
‐160.00     0.658   0.2982   0.2819 
‐155.00     0.733   0.4121   0.3213 
‐150.00     0.778   0.5308   0.3520 
‐145.00     0.795   0.6503   0.3754 
‐140.00     0.787   0.7672   0.3926 
‐135.00     0.757   0.8785   0.4046 
‐130.00     0.708   0.9819   0.4121 
‐125.00     0.641   1.0756   0.4160 
‐120.00     0.560   1.1580   0.4167 
‐115.00     0.467   1.2280   0.4146 
‐110.00     0.365   1.2847   0.4104 
‐105.00     0.255   1.3274   0.4041 
‐100.00     0.139   1.3557   0.3961 
 ‐95.00      0.021   1.3692    0.3867  
 ‐90.00    ‐ 0.098   1.3680    0.3759  
 ‐85.00    ‐ 0.216   1.3521    0.3639  
 ‐80.00    ‐ 0.331   1.3218    0.3508  
 ‐75.00    ‐ 0.441   1.2773    0.3367  
 ‐70.00    ‐ 0.544   1.2193    0.3216  
 ‐65.00    ‐ 0.638   1.1486    0.3054  
 ‐60.00    ‐ 0.720   1.0660    0.2884  
 ‐55.00    ‐ 0.788   0.9728    0.2703  
 ‐50.00    ‐ 0.840   0.8705    0.2512  
 ‐45.00    ‐ 0.875   0.7611    0.2311  
 ‐40.00    ‐ 0.889   0.6466    0.2099  
 ‐35.00    ‐ 0.880   0.5299    0.1876  
168

‐30.00    ‐ 0.846   0.4141    0.1641  
 ‐25.00    ‐ 0.784   0.3030    0.1396  
 ‐24.00    ‐ 0.768   0.2817    0.1345  
 ‐23.00    ‐ 0.751   0.2608    0.1294  
 ‐22.00    ‐ 0.733   0.2404    0.1243  
 ‐21.00    ‐ 0.714   0.2205    0.1191  
 ‐20.00    ‐ 0.693   0.2011    0.1139  
 ‐19.00    ‐ 0.671   0.1822    0.1086  
 ‐18.00    ‐ 0.648   0.1640    0.1032  
 ‐17.00    ‐ 0.624   0.1465    0.0975  
 ‐16.00    ‐ 0.601   0.1300    0.0898  
 ‐15.00    ‐ 0.579   0.1145    0.0799  
 ‐14.00    ‐ 0.559   0.1000    0.0682  
 ‐13.00    ‐ 0.539   0.0867    0.0547  
 ‐12.00    ‐ 0.519   0.0744    0.0397  
 ‐11.00    ‐ 0.499   0.0633    0.0234  
 ‐10.00    ‐ 0.480   0.0534    0.0060  
  ‐5.54   ‐ 0.385   0.0245  ‐0.0800 
  ‐5.04   ‐ 0.359   0.0225  ‐0.0800 
  ‐4.54   ‐ 0.360   0.0196  ‐0.0800 
  ‐4.04   ‐ 0.355   0.0174  ‐0.0800 
  ‐3.54   ‐ 0.307   0.0162  ‐0.0800 
  ‐3.04   ‐ 0.246   0.0144  ‐0.0800 
  ‐3.00   ‐ 0.240   0.0240  ‐0.0623 
  ‐2.50   ‐ 0.163   0.0188  ‐0.0674 
  ‐2.00   ‐ 0.091   0.0160  ‐0.0712 
  ‐1.50   ‐ 0.019   0.0137  ‐0.0746 
  ‐1.00     0.052   0.0118  ‐0.0778 
  ‐0.50     0.121   0.0104  ‐0.0806 
   0.00     0.196   0.0094  ‐0.0831 
   0.50     0.265   0.0096  ‐0.0863 
   1.00     0.335   0.0098  ‐0.0895 
   1.50     0.404   0.0099  ‐0.0924 
   2.00     0.472   0.0100  ‐0.0949 
   2.50     0.540   0.0102  ‐0.0973 
   3.00     0.608   0.0103  ‐0.0996 
   3.50     0.674   0.0104  ‐0.1016 
   4.00     0.742   0.0105  ‐0.1037 
   4.50     0.809   0.0107  ‐0.1057 
   5.00     0.875   0.0108  ‐0.1076 
   5.50     0.941   0.0109  ‐0.1094 
   6.00     1.007   0.0110  ‐0.1109 
   6.50     1.071   0.0113  ‐0.1118 
   7.00     1.134   0.0115  ‐0.1127 
   7.50     1.198   0.0117  ‐0.1138 
   8.00     1.260   0.0120  ‐0.1144 
   8.50     1.318   0.0126  ‐0.1137 
   9.00     1.368   0.0133  ‐0.1112 
   9.50     1.422   0.0143  ‐0.1100 
  10.00      1.475   0.0156   ‐0.1086  
  10.50      1.523   0.0174   ‐0.1064  
  11.00      1.570   0.0194   ‐0.1044  
  11.50      1.609   0.0227   ‐0.1013  
  12.00      1.642   0.0269   ‐0.0980  
  12.50      1.675   0.0319   ‐0.0953  
  13.00      1.700   0.0398   ‐0.0925  
  13.50      1.717   0.0488   ‐0.0896  
  14.00      1.712   0.0614   ‐0.0864  
  14.50      1.703   0.0786   ‐0.0840  
  15.50      1.671   0.1173   ‐0.0830  
  16.00      1.649   0.1377   ‐0.0848  
  16.50      1.621   0.1600   ‐0.0880  
  17.00      1.598   0.1814   ‐0.0926  
  17.50      1.571   0.2042   ‐0.0984  
  18.00      1.549   0.2316   ‐0.1052  
  19.00      1.544   0.2719   ‐0.1158  
  19.50      1.549   0.2906   ‐0.1213  
  20.00      1.565   0.3085   ‐0.1248  
  21.00      1.565   0.3447   ‐0.1317  
  22.00      1.563   0.3820   ‐0.1385  
  23.00      1.558   0.4203   ‐0.1452  
  24.00      1.552   0.4593   ‐0.1518  
  25.00      1.546   0.4988   ‐0.1583  
  26.00      1.539   0.5387   ‐0.1647  
  28.00      1.527   0.6187   ‐0.1770  
  30.00      1.522   0.6978   ‐0.1886  
  32.00      1.529   0.7747   ‐0.1994  
  35.00      1.544   0.8869   ‐0.2148  
  40.00      1.529   1.0671   ‐0.2392  
  45.00      1.471   1.2319   ‐0.2622  
  50.00      1.376   1.3747   ‐0.2839  
  55.00      1.249   1.4899   ‐0.3043  
  60.00      1.097   1.5728   ‐0.3236  
  65.00      0.928   1.6202   ‐0.3417  
169

70.00      0.750   1.6302   ‐0.3586  
  75.00      0.570   1.6031   ‐0.3745  
  80.00      0.396   1.5423   ‐0.3892  
  85.00      0.237   1.4598   ‐0.4028  
  90.00      0.101   1.4041   ‐0.4151  
  95.00    ‐ 0.022   1.4053   ‐0.4261  
 100.00   ‐ 0.143   1.3914  ‐0.4357 
 105.00   ‐ 0.261   1.3625  ‐0.4437 
 110.00   ‐ 0.374   1.3188  ‐0.4498 
 115.00   ‐ 0.480   1.2608  ‐0.4538 
 120.00   ‐ 0.575   1.1891  ‐0.4553 
 125.00   ‐ 0.659   1.1046  ‐0.4540 
 130.00   ‐ 0.727   1.0086  ‐0.4492 
 135.00   ‐ 0.778   0.9025  ‐0.4405 
 140.00   ‐ 0.809   0.7883  ‐0.4270 
 145.00   ‐ 0.818   0.6684  ‐0.4078 
 150.00   ‐ 0.800   0.5457  ‐0.3821 
 155.00   ‐ 0.754   0.4236  ‐0.3484 
 160.00   ‐ 0.677   0.3066  ‐0.3054 
 170.00   ‐ 0.417   0.1085  ‐0.1842 
 175.00   ‐ 0.229   0.0510  ‐0.1013 
 180.00     0.000   0.0407   0.0000 
B.7 Airfoil-Data Input File – DU30_A17.dat
DU30 airfoil  with an aspect ratio of 17.  Original  ‐180 to 180deg Cl,  Cd, and Cm versus AOA data taken from Appendix  A of DOW 
Cl and Cd values corrected  for rotational  stall delay and Cd values corrected  using the Viterna  method for 0 to 90deg AOA by  
   1         Number of airfoil  tables in this file 
   0.0       Table ID parameter  
   9.00      Stall angle (deg) 
   0.0       No longer used, enter zero 
   0.0       No longer used, enter zero 
   0.0       No longer used, enter zero 
  ‐2.3220   Zero Cn angle of attack (deg) 
   7.3326   Cn slope for zero lift (dimensionless)  
   1.4490   Cn extrapolated  to value at positive  stall angle of attack 
  ‐0.6138   Cn at stall value for negative  angle of attack 
   0.00      Angle of attack for minimum  CD (deg) 
   0.0087   Minimum  CD value 
‐180.00     0.000   0.0267   0.0000 
‐175.00     0.274   0.0370   0.1379 
‐170.00     0.547   0.0968   0.2778 
‐160.00     0.685   0.2876   0.2740 
‐155.00     0.766   0.4025   0.3118 
‐150.00     0.816   0.5232   0.3411 
‐145.00     0.836   0.6454   0.3631 
‐140.00     0.832   0.7656   0.3791 
‐135.00     0.804   0.8807   0.3899 
‐130.00     0.756   0.9882   0.3965 
‐125.00     0.690   1.0861   0.3994 
‐120.00     0.609   1.1730   0.3992 
‐115.00     0.515   1.2474   0.3964 
‐110.00     0.411   1.3084   0.3915 
‐105.00     0.300   1.3552   0.3846 
‐100.00     0.182   1.3875   0.3761 
 ‐95.00      0.061   1.4048    0.3663  
 ‐90.00    ‐ 0.061   1.4070    0.3551  
 ‐85.00    ‐ 0.183   1.3941    0.3428  
 ‐80.00    ‐ 0.302   1.3664    0.3295  
 ‐75.00    ‐ 0.416   1.3240    0.3153  
 ‐70.00    ‐ 0.523   1.2676    0.3001  
 ‐65.00    ‐ 0.622   1.1978    0.2841  
 ‐60.00    ‐ 0.708   1.1156    0.2672  
 ‐55.00    ‐ 0.781   1.0220    0.2494  
 ‐50.00    ‐ 0.838   0.9187    0.2308  
 ‐45.00    ‐ 0.877   0.8074    0.2113  
 ‐40.00    ‐ 0.895   0.6904    0.1909  
 ‐35.00    ‐ 0.889   0.5703    0.1696  
 ‐30.00    ‐ 0.858   0.4503    0.1475  
 ‐25.00    ‐ 0.832   0.3357    0.1224  
 ‐24.00    ‐ 0.852   0.3147    0.1156  
 ‐23.00    ‐ 0.882   0.2946    0.1081  
 ‐22.00    ‐ 0.919   0.2752    0.1000  
 ‐21.00    ‐ 0.963   0.2566    0.0914  
 ‐20.00    ‐ 1.013   0.2388    0.0823  
 ‐19.00    ‐ 1.067   0.2218    0.0728  
 ‐18.00    ‐ 1.125   0.2056    0.0631  
 ‐17.00    ‐ 1.185   0.1901    0.0531  
 ‐16.00    ‐ 1.245   0.1754    0.0430  
 ‐15.25    ‐ 1.290   0.1649    0.0353  
 ‐14.24    ‐ 1.229   0.1461    0.0240  
 ‐13.24    ‐ 1.148   0.1263    0.0100  
170

‐12.22    ‐ 1.052   0.1051   ‐0.0090  
 ‐11.22    ‐ 0.965   0.0886   ‐0.0230  
 ‐10.19    ‐ 0.867   0.0740   ‐0.0336  
  ‐9.70   ‐ 0.822   0.0684  ‐0.0375 
  ‐9.18   ‐ 0.769   0.0605  ‐0.0440 
  ‐8.18   ‐ 0.756   0.0270  ‐0.0578 
  ‐7.19   ‐ 0.690   0.0180  ‐0.0590 
  ‐6.65   ‐ 0.616   0.0166  ‐0.0633 
  ‐6.13   ‐ 0.542   0.0152  ‐0.0674 
  ‐6.00   ‐ 0.525   0.0117  ‐0.0732 
  ‐5.50   ‐ 0.451   0.0105  ‐0.0766 
  ‐5.00   ‐ 0.382   0.0097  ‐0.0797 
  ‐4.50   ‐ 0.314   0.0092  ‐0.0825 
  ‐4.00   ‐ 0.251   0.0091  ‐0.0853 
  ‐3.50   ‐ 0.189   0.0089  ‐0.0884 
  ‐3.00   ‐ 0.120   0.0089  ‐0.0914 
  ‐2.50   ‐ 0.051   0.0088  ‐0.0942 
  ‐2.00     0.017   0.0088  ‐0.0969 
  ‐1.50     0.085   0.0088  ‐0.0994 
  ‐1.00     0.152   0.0088  ‐0.1018 
  ‐0.50     0.219   0.0088  ‐0.1041 
   0.00     0.288   0.0087  ‐0.1062 
   0.50     0.354   0.0087  ‐0.1086 
   1.00     0.421   0.0088  ‐0.1107 
   1.50     0.487   0.0089  ‐0.1129 
   2.00     0.554   0.0090  ‐0.1149 
   2.50     0.619   0.0091  ‐0.1168 
   3.00     0.685   0.0092  ‐0.1185 
   3.50     0.749   0.0093  ‐0.1201 
   4.00     0.815   0.0095  ‐0.1218 
   4.50     0.879   0.0096  ‐0.1233 
   5.00     0.944   0.0097  ‐0.1248 
   5.50     1.008   0.0099  ‐0.1260 
   6.00     1.072   0.0101  ‐0.1270 
   6.50     1.135   0.0103  ‐0.1280 
   7.00     1.197   0.0107  ‐0.1287 
   7.50     1.256   0.0112  ‐0.1289 
   8.00     1.305   0.0125  ‐0.1270 
   9.00     1.390   0.0155  ‐0.1207 
   9.50     1.424   0.0171  ‐0.1158 
  10.00      1.458   0.0192   ‐0.1116  
  10.50      1.488   0.0219   ‐0.1073  
  11.00      1.512   0.0255   ‐0.1029  
  11.50      1.533   0.0307   ‐0.0983  
  12.00      1.549   0.0370   ‐0.0949  
  12.50      1.558   0.0452   ‐0.0921  
  13.00      1.470   0.0630   ‐0.0899  
  13.50      1.398   0.0784   ‐0.0885  
  14.00      1.354   0.0931   ‐0.0885  
  14.50      1.336   0.1081   ‐0.0902  
  15.00      1.333   0.1239   ‐0.0928  
  15.50      1.326   0.1415   ‐0.0963  
  16.00      1.329   0.1592   ‐0.1006  
  16.50      1.326   0.1743   ‐0.1042  
  17.00      1.321   0.1903   ‐0.1084  
  17.50      1.331   0.2044   ‐0.1125  
  18.00      1.333   0.2186   ‐0.1169  
  18.50      1.340   0.2324   ‐0.1215  
  19.00      1.362   0.2455   ‐0.1263  
  19.50      1.382   0.2584   ‐0.1313  
  20.00      1.398   0.2689   ‐0.1352  
  20.50      1.426   0.2814   ‐0.1406  
  21.00      1.437   0.2943   ‐0.1462  
  22.00      1.418   0.3246   ‐0.1516  
  23.00      1.397   0.3557   ‐0.1570  
  24.00      1.376   0.3875   ‐0.1623  
  25.00      1.354   0.4198   ‐0.1676  
  26.00      1.332   0.4524   ‐0.1728  
  28.00      1.293   0.5183   ‐0.1832  
  30.00      1.265   0.5843   ‐0.1935  
  32.00      1.253   0.6492   ‐0.2039  
  35.00      1.264   0.7438   ‐0.2193  
  40.00      1.258   0.8970   ‐0.2440  
  45.00      1.217   1.0402   ‐0.2672  
  50.00      1.146   1.1686   ‐0.2891  
  55.00      1.049   1.2779   ‐0.3097  
  60.00      0.932   1.3647   ‐0.3290  
  65.00      0.799   1.4267   ‐0.3471  
  70.00      0.657   1.4621   ‐0.3641  
  75.00      0.509   1.4708   ‐0.3799  
  80.00      0.362   1.4544   ‐0.3946  
  85.00      0.221   1.4196   ‐0.4081  
  90.00      0.092   1.3938   ‐0.4204  
  95.00    ‐ 0.030   1.3943   ‐0.4313  
171

100.00   ‐ 0.150   1.3798  ‐0.4408 
 105.00   ‐ 0.267   1.3504  ‐0.4486 
 110.00   ‐ 0.379   1.3063  ‐0.4546 
 115.00   ‐ 0.483   1.2481  ‐0.4584 
 120.00   ‐ 0.578   1.1763  ‐0.4597 
 125.00   ‐ 0.660   1.0919  ‐0.4582 
 130.00   ‐ 0.727   0.9962  ‐0.4532 
 135.00   ‐ 0.777   0.8906  ‐0.4441 
 140.00   ‐ 0.807   0.7771  ‐0.4303 
 145.00   ‐ 0.815   0.6581  ‐0.4109 
 150.00   ‐ 0.797   0.5364  ‐0.3848 
 155.00   ‐ 0.750   0.4157  ‐0.3508 
 160.00   ‐ 0.673   0.3000  ‐0.3074 
 170.00   ‐ 0.547   0.1051  ‐0.2786 
 175.00   ‐ 0.274   0.0388  ‐0.1380 
 180.00     0.000   0.0267   0.0000 
B.8 Airfoil-Data Input File – DU25_A17.dat
DU25 airfoil  with an aspect ratio of 17.  Original  ‐180 to 180deg Cl,  Cd, and Cm versus AOA data taken from Appendix  A of DOW 
Cl and Cd values corrected  for rotational  stall delay and Cd values corrected  using the Viterna  method for 0 to 90deg AOA by  
   1         Number of airfoil  tables in this file 
   0.0       Table ID parameter  
   8.50      Stall angle (deg) 
   0.0       No longer used, enter zero 
   0.0       No longer used, enter zero 
   0.0       No longer used, enter zero 
  ‐4.2422   Zero Cn angle of attack (deg) 
   6.4462   Cn slope for zero lift (dimensionless)  
   1.4336   Cn extrapolated  to value at positive  stall angle of attack 
  ‐0.6873   Cn at stall value for negative  angle of attack 
   0.00      Angle of attack for minimum  CD (deg) 
   0.0065   Minimum  CD value 
‐180.00     0.000   0.0202   0.0000 
‐175.00     0.368   0.0324   0.1845 
‐170.00     0.735   0.0943   0.3701 
‐160.00     0.695   0.2848   0.2679 
‐155.00     0.777   0.4001   0.3046 
‐150.00     0.828   0.5215   0.3329 
‐145.00     0.850   0.6447   0.3540 
‐140.00     0.846   0.7660   0.3693 
‐135.00     0.818   0.8823   0.3794 
‐130.00     0.771   0.9911   0.3854 
‐125.00     0.705   1.0905   0.3878 
‐120.00     0.624   1.1787   0.3872 
‐115.00     0.530   1.2545   0.3841 
‐110.00     0.426   1.3168   0.3788 
‐105.00     0.314   1.3650   0.3716 
‐100.00     0.195   1.3984   0.3629 
 ‐95.00      0.073   1.4169    0.3529  
 ‐90.00    ‐ 0.050   1.4201    0.3416  
 ‐85.00    ‐ 0.173   1.4081    0.3292  
 ‐80.00    ‐ 0.294   1.3811    0.3159  
 ‐75.00    ‐ 0.409   1.3394    0.3017  
 ‐70.00    ‐ 0.518   1.2833    0.2866  
 ‐65.00    ‐ 0.617   1.2138    0.2707  
 ‐60.00    ‐ 0.706   1.1315    0.2539  
 ‐55.00    ‐ 0.780   1.0378    0.2364  
 ‐50.00    ‐ 0.839   0.9341    0.2181  
 ‐45.00    ‐ 0.879   0.8221    0.1991  
 ‐40.00    ‐ 0.898   0.7042    0.1792  
 ‐35.00    ‐ 0.893   0.5829    0.1587  
 ‐30.00    ‐ 0.862   0.4616    0.1374  
 ‐25.00    ‐ 0.803   0.3441    0.1154  
 ‐24.00    ‐ 0.792   0.3209    0.1101  
 ‐23.00    ‐ 0.789   0.2972    0.1031  
 ‐22.00    ‐ 0.792   0.2730    0.0947  
 ‐21.00    ‐ 0.801   0.2485    0.0849  
 ‐20.00    ‐ 0.815   0.2237    0.0739  
 ‐19.00    ‐ 0.833   0.1990    0.0618  
 ‐18.00    ‐ 0.854   0.1743    0.0488  
 ‐17.00    ‐ 0.879   0.1498    0.0351  
 ‐16.00    ‐ 0.905   0.1256    0.0208  
 ‐15.00    ‐ 0.932   0.1020    0.0060  
 ‐14.00    ‐ 0.959   0.0789   ‐0.0091  
 ‐13.00    ‐ 0.985   0.0567   ‐0.0243  
 ‐13.00    ‐ 0.985   0.0567   ‐0.0243  
 ‐12.01    ‐ 0.953   0.0271   ‐0.0349  
 ‐11.00    ‐ 0.900   0.0303   ‐0.0361  
  ‐9.98   ‐ 0.827   0.0287  ‐0.0464 
  ‐8.98   ‐ 0.753   0.0271  ‐0.0534 
  ‐8.47   ‐ 0.691   0.0264  ‐0.0650 
172

‐7.45   ‐ 0.555   0.0114  ‐0.0782 
  ‐6.42   ‐ 0.413   0.0094  ‐0.0904 
  ‐5.40   ‐ 0.271   0.0086  ‐0.1006 
  ‐5.00   ‐ 0.220   0.0073  ‐0.1107 
  ‐4.50   ‐ 0.152   0.0071  ‐0.1135 
  ‐4.00   ‐ 0.084   0.0070  ‐0.1162 
  ‐3.50   ‐ 0.018   0.0069  ‐0.1186 
  ‐3.00     0.049   0.0068  ‐0.1209 
  ‐2.50     0.115   0.0068  ‐0.1231 
  ‐2.00     0.181   0.0068  ‐0.1252 
  ‐1.50     0.247   0.0067  ‐0.1272 
  ‐1.00     0.312   0.0067  ‐0.1293 
  ‐0.50     0.377   0.0067  ‐0.1311 
   0.00     0.444   0.0065  ‐0.1330 
   0.50     0.508   0.0065  ‐0.1347 
   1.00     0.573   0.0066  ‐0.1364 
   1.50     0.636   0.0067  ‐0.1380 
   2.00     0.701   0.0068  ‐0.1396 
   2.50     0.765   0.0069  ‐0.1411 
   3.00     0.827   0.0070  ‐0.1424 
   3.50     0.890   0.0071  ‐0.1437 
   4.00     0.952   0.0073  ‐0.1448 
   4.50     1.013   0.0076  ‐0.1456 
   5.00     1.062   0.0079  ‐0.1445 
   6.00     1.161   0.0099  ‐0.1419 
   6.50     1.208   0.0117  ‐0.1403 
   7.00     1.254   0.0132  ‐0.1382 
   7.50     1.301   0.0143  ‐0.1362 
   8.00     1.336   0.0153  ‐0.1320 
   8.50     1.369   0.0165  ‐0.1276 
   9.00     1.400   0.0181  ‐0.1234 
   9.50     1.428   0.0211  ‐0.1193 
  10.00      1.442   0.0262   ‐0.1152  
  10.50      1.427   0.0336   ‐0.1115  
  11.00      1.374   0.0420   ‐0.1081  
  11.50      1.316   0.0515   ‐0.1052  
  12.00      1.277   0.0601   ‐0.1026  
  12.50      1.250   0.0693   ‐0.1000  
  13.00      1.246   0.0785   ‐0.0980  
  13.50      1.247   0.0888   ‐0.0969  
  14.00      1.256   0.1000   ‐0.0968  
  14.50      1.260   0.1108   ‐0.0973  
  15.00      1.271   0.1219   ‐0.0981  
  15.50      1.281   0.1325   ‐0.0992  
  16.00      1.289   0.1433   ‐0.1006  
  16.50      1.294   0.1541   ‐0.1023  
  17.00      1.304   0.1649   ‐0.1042  
  17.50      1.309   0.1754   ‐0.1064  
  18.00      1.315   0.1845   ‐0.1082  
  18.50      1.320   0.1953   ‐0.1110  
  19.00      1.330   0.2061   ‐0.1143  
  19.50      1.343   0.2170   ‐0.1179  
  20.00      1.354   0.2280   ‐0.1219  
  20.50      1.359   0.2390   ‐0.1261  
  21.00      1.360   0.2536   ‐0.1303  
  22.00      1.325   0.2814   ‐0.1375  
  23.00      1.288   0.3098   ‐0.1446  
  24.00      1.251   0.3386   ‐0.1515  
  25.00      1.215   0.3678   ‐0.1584  
  26.00      1.181   0.3972   ‐0.1651  
  28.00      1.120   0.4563   ‐0.1781  
  30.00      1.076   0.5149   ‐0.1904  
  32.00      1.056   0.5720   ‐0.2017  
  35.00      1.066   0.6548   ‐0.2173  
  40.00      1.064   0.7901   ‐0.2418  
  45.00      1.035   0.9190   ‐0.2650  
  50.00      0.980   1.0378   ‐0.2867  
  55.00      0.904   1.1434   ‐0.3072  
  60.00      0.810   1.2333   ‐0.3265  
  65.00      0.702   1.3055   ‐0.3446  
  70.00      0.582   1.3587   ‐0.3616  
  75.00      0.456   1.3922   ‐0.3775  
  80.00      0.326   1.4063   ‐0.3921  
  85.00      0.197   1.4042   ‐0.4057  
  90.00      0.072   1.3985   ‐0.4180  
  95.00    ‐ 0.050   1.3973   ‐0.4289  
 100.00   ‐ 0.170   1.3810  ‐0.4385 
 105.00   ‐ 0.287   1.3498  ‐0.4464 
 110.00   ‐ 0.399   1.3041  ‐0.4524 
 115.00   ‐ 0.502   1.2442  ‐0.4563 
 120.00   ‐ 0.596   1.1709  ‐0.4577 
 125.00   ‐ 0.677   1.0852  ‐0.4563 
 130.00   ‐ 0.743   0.9883  ‐0.4514 
 135.00   ‐ 0.792   0.8818  ‐0.4425 
173

140.00   ‐ 0.821   0.7676  ‐0.4288 
 145.00   ‐ 0.826   0.6481  ‐0.4095 
 150.00   ‐ 0.806   0.5264  ‐0.3836 
 155.00   ‐ 0.758   0.4060  ‐0.3497 
 160.00   ‐ 0.679   0.2912  ‐0.3065 
 170.00   ‐ 0.735   0.0995  ‐0.3706 
 175.00   ‐ 0.368   0.0356  ‐0.1846 
 180.00     0.000   0.0202   0.0000 
B.9 Airfoil-Data Input File – DU21_A17.dat
DU21 airfoil  with an aspect ratio of 17.  Original  ‐180 to 180deg Cl,  Cd, and Cm versus AOA data taken from Appendix  A of DOW 
Cl and Cd values corrected  for rotational  stall delay and Cd values corrected  using the Viterna  method for 0 to 90deg AOA by  
   1         Number of airfoil  tables in this file 
   0.0       Table ID parameter  
   8.00      Stall angle (deg) 
   0.0       No longer used, enter zero 
   0.0       No longer used, enter zero 
   0.0       No longer used, enter zero 
  ‐5.0609   Zero Cn angle of attack (deg) 
   6.2047   Cn slope for zero lift (dimensionless)  
   1.4144   Cn extrapolated  to value at positive  stall angle of attack 
  ‐0.5324   Cn at stall value for negative  angle of attack 
  ‐1.50      Angle of attack for minimum  CD (deg) 
   0.0057   Minimum  CD value 
‐180.00     0.000   0.0185   0.0000 
‐175.00     0.394   0.0332   0.1978 
‐170.00     0.788   0.0945   0.3963 
‐160.00     0.670   0.2809   0.2738 
‐155.00     0.749   0.3932   0.3118 
‐150.00     0.797   0.5112   0.3413 
‐145.00     0.818   0.6309   0.3636 
‐140.00     0.813   0.7485   0.3799 
‐135.00     0.786   0.8612   0.3911 
‐130.00     0.739   0.9665   0.3980 
‐125.00     0.675   1.0625   0.4012 
‐120.00     0.596   1.1476   0.4014 
‐115.00     0.505   1.2206   0.3990 
‐110.00     0.403   1.2805   0.3943 
‐105.00     0.294   1.3265   0.3878 
‐100.00     0.179   1.3582   0.3796 
 ‐95.00      0.060   1.3752    0.3700  
 ‐90.00    ‐ 0.060   1.3774    0.3591  
 ‐85.00    ‐ 0.179   1.3648    0.3471  
 ‐80.00    ‐ 0.295   1.3376    0.3340  
 ‐75.00    ‐ 0.407   1.2962    0.3199  
 ‐70.00    ‐ 0.512   1.2409    0.3049  
 ‐65.00    ‐ 0.608   1.1725    0.2890  
 ‐60.00    ‐ 0.693   1.0919    0.2722  
 ‐55.00    ‐ 0.764   1.0002    0.2545  
 ‐50.00    ‐ 0.820   0.8990    0.2359  
 ‐45.00    ‐ 0.857   0.7900    0.2163  
 ‐40.00    ‐ 0.875   0.6754    0.1958  
 ‐35.00    ‐ 0.869   0.5579    0.1744  
 ‐30.00    ‐ 0.838   0.4405    0.1520  
 ‐25.00    ‐ 0.791   0.3256    0.1262  
 ‐24.00    ‐ 0.794   0.3013    0.1170  
 ‐23.00    ‐ 0.805   0.2762    0.1059  
 ‐22.00    ‐ 0.821   0.2506    0.0931  
 ‐21.00    ‐ 0.843   0.2246    0.0788  
 ‐20.00    ‐ 0.869   0.1983    0.0631  
 ‐19.00    ‐ 0.899   0.1720    0.0464  
 ‐18.00    ‐ 0.931   0.1457    0.0286  
 ‐17.00    ‐ 0.964   0.1197    0.0102  
 ‐16.00    ‐ 0.999   0.0940   ‐0.0088  
 ‐15.00    ‐ 1.033   0.0689   ‐0.0281  
 ‐14.50    ‐ 1.050   0.0567   ‐0.0378  
 ‐12.01    ‐ 0.953   0.0271   ‐0.0349  
 ‐11.00    ‐ 0.900   0.0303   ‐0.0361  
  ‐9.98   ‐ 0.827   0.0287  ‐0.0464 
  ‐8.12   ‐ 0.536   0.0124  ‐0.0821 
  ‐7.62   ‐ 0.467   0.0109  ‐0.0924 
  ‐7.11   ‐ 0.393   0.0092  ‐0.1015 
  ‐6.60   ‐ 0.323   0.0083  ‐0.1073 
  ‐6.50   ‐ 0.311   0.0089  ‐0.1083 
  ‐6.00   ‐ 0.245   0.0082  ‐0.1112 
  ‐5.50   ‐ 0.178   0.0074  ‐0.1146 
  ‐5.00   ‐ 0.113   0.0069  ‐0.1172 
  ‐4.50   ‐ 0.048   0.0065  ‐0.1194 
  ‐4.00     0.016   0.0063  ‐0.1213 
  ‐3.50     0.080   0.0061  ‐0.1232 
  ‐3.00     0.145   0.0058  ‐0.1252 
  ‐2.50     0.208   0.0057  ‐0.1268 
174

‐2.00     0.270   0.0057  ‐0.1282 
  ‐1.50     0.333   0.0057  ‐0.1297 
  ‐1.00     0.396   0.0057  ‐0.1310 
  ‐0.50     0.458   0.0057  ‐0.1324 
   0.00     0.521   0.0057  ‐0.1337 
   0.50     0.583   0.0057  ‐0.1350 
   1.00     0.645   0.0058  ‐0.1363 
   1.50     0.706   0.0058  ‐0.1374 
   2.00     0.768   0.0059  ‐0.1385 
   2.50     0.828   0.0061  ‐0.1395 
   3.00     0.888   0.0063  ‐0.1403 
   3.50     0.948   0.0066  ‐0.1406 
   4.00     0.996   0.0071  ‐0.1398 
   4.50     1.046   0.0079  ‐0.1390 
   5.00     1.095   0.0090  ‐0.1378 
   5.50     1.145   0.0103  ‐0.1369 
   6.00     1.192   0.0113  ‐0.1353 
   6.50     1.239   0.0122  ‐0.1338 
   7.00     1.283   0.0131  ‐0.1317 
   7.50     1.324   0.0139  ‐0.1291 
   8.00     1.358   0.0147  ‐0.1249 
   8.50     1.385   0.0158  ‐0.1213 
   9.00     1.403   0.0181  ‐0.1177 
   9.50     1.401   0.0211  ‐0.1142 
  10.00      1.358   0.0255   ‐0.1103  
  10.50      1.313   0.0301   ‐0.1066  
  11.00      1.287   0.0347   ‐0.1032  
  11.50      1.274   0.0401   ‐0.1002  
  12.00      1.272   0.0468   ‐0.0971  
  12.50      1.273   0.0545   ‐0.0940  
  13.00      1.273   0.0633   ‐0.0909  
  13.50      1.273   0.0722   ‐0.0883  
  14.00      1.272   0.0806   ‐0.0865  
  14.50      1.273   0.0900   ‐0.0854  
  15.00      1.275   0.0987   ‐0.0849  
  15.50      1.281   0.1075   ‐0.0847  
  16.00      1.284   0.1170   ‐0.0850  
  16.50      1.296   0.1270   ‐0.0858  
  17.00      1.306   0.1368   ‐0.0869  
  17.50      1.308   0.1464   ‐0.0883  
  18.00      1.308   0.1562   ‐0.0901  
  18.50      1.308   0.1664   ‐0.0922  
  19.00      1.308   0.1770   ‐0.0949  
  19.50      1.307   0.1878   ‐0.0980  
  20.00      1.311   0.1987   ‐0.1017  
  20.50      1.325   0.2100   ‐0.1059  
  21.00      1.324   0.2214   ‐0.1105  
  22.00      1.277   0.2499   ‐0.1172  
  23.00      1.229   0.2786   ‐0.1239  
  24.00      1.182   0.3077   ‐0.1305  
  25.00      1.136   0.3371   ‐0.1370  
  26.00      1.093   0.3664   ‐0.1433  
  28.00      1.017   0.4246   ‐0.1556  
  30.00      0.962   0.4813   ‐0.1671  
  32.00      0.937   0.5356   ‐0.1778  
  35.00      0.947   0.6127   ‐0.1923  
  40.00      0.950   0.7396   ‐0.2154  
  45.00      0.928   0.8623   ‐0.2374  
  50.00      0.884   0.9781   ‐0.2583  
  55.00      0.821   1.0846   ‐0.2782  
  60.00      0.740   1.1796   ‐0.2971  
  65.00      0.646   1.2617   ‐0.3149  
  70.00      0.540   1.3297   ‐0.3318  
  75.00      0.425   1.3827   ‐0.3476  
  80.00      0.304   1.4202   ‐0.3625  
  85.00      0.179   1.4423   ‐0.3763  
  90.00      0.053   1.4512   ‐0.3890  
  95.00    ‐ 0.073   1.4480   ‐0.4004  
 100.00   ‐ 0.198   1.4294  ‐0.4105 
 105.00   ‐ 0.319   1.3954  ‐0.4191 
 110.00   ‐ 0.434   1.3464  ‐0.4260 
 115.00   ‐ 0.541   1.2829  ‐0.4308 
 120.00   ‐ 0.637   1.2057  ‐0.4333 
 125.00   ‐ 0.720   1.1157  ‐0.4330 
 130.00   ‐ 0.787   1.0144  ‐0.4294 
 135.00   ‐ 0.836   0.9033  ‐0.4219 
 140.00   ‐ 0.864   0.7845  ‐0.4098 
 145.00   ‐ 0.869   0.6605  ‐0.3922 
 150.00   ‐ 0.847   0.5346  ‐0.3682 
 155.00   ‐ 0.795   0.4103  ‐0.3364 
 160.00   ‐ 0.711   0.2922  ‐0.2954 
 170.00   ‐ 0.788   0.0969  ‐0.3966 
 175.00   ‐ 0.394   0.0334  ‐0.1978 
 180.00     0.000   0.0185   0.0000 
175

B ile – NACA64_A17.dat
, and Cm versus AOA data taken from Appendix  A of D .10 Airfoil-Data Input F
NACA64 airfoil  with an aspect ratio of 17.  Original  ‐180 to 180deg Cl, Cd
Cl and Cd values corrected  for rotational  stall delay and Cd values correc ted using the Viterna  method for 0 to 90deg AOA by  
   1         Number of airfoil  tables in this file 
   0.0       Table ID parameter  
   9.00      Stall angle (deg) 
   0.0       No longer used, enter zero 
   0.0       No longer used, enter zero 
   0.0       No longer used, enter zero 
  ‐4.4320   Zero Cn angle of attack (deg ) 
   6.0031   Cn slope for zero lift (dime nsionless)  
   1.4073   Cn extrapolated  to value at positive  stall angle of attack 
  ‐0.7945   Cn at stall value for negative  angle of attack 
  ‐1.00      Angle of attack for minimum  CD (deg) 
   0.0052   Minimum  CD value 
‐180.00     0.000   0.0198   0.0000 
‐175.00     0.374   0.0341   0.1880 
‐170.00     0.749   0.0955   0.3770 
‐160.00     0.659   0.2807   0.2747 
‐155.00     0.736   0.3919   0.3130 
‐150.00     0.783   0.5086   0.3428 
‐145.00     0.803   0.6267   0.3654 
‐140.00     0.798   0.7427   0.3820 
‐135.00     0.771   0.8537   0.3935 
‐130.00     0.724   0.9574   0.4007 
‐125.00     0.660   1.0519   0.4042 
‐120.00     0.581   1.1355   0.4047 
‐115.00     0.491   1.2070   0.4025 
‐110.00     0.390   1.2656   0.3981 
‐105.00     0.282   1.3104   0.3918 
‐100.00     0.169   1.3410   0.3838 
 ‐95.00      0.052   1.3572    0.3743  
 ‐90.00    ‐ 0.067   1.3587    0.3636  
 ‐85.00    ‐ 0.184   1.3456    0.3517  
 ‐80.00    ‐ 0.299   1.3181    0.3388  
 ‐75.00    ‐ 0.409   1.2765    0.3248  
 ‐70.00    ‐ 0.512   1.2212    0.3099  
 ‐65.00    ‐ 0.606   1.1532    0.2940  
 ‐60.00    ‐ 0.689   1.0731    0.2772  
 ‐55.00    ‐ 0.759   0.9822    0.2595  
 ‐50.00    ‐ 0.814   0.8820    0.2409  
 ‐45.00    ‐ 0.850   0.7742    0.2212  
 ‐40.00    ‐ 0.866   0.6610    0.2006  
 ‐35.00    ‐ 0.860   0.5451    0.1789  
 ‐30.00    ‐ 0.829   0.4295    0.1563  
 ‐25.00    ‐ 0.853   0.3071    0.1156  
 ‐24.00    ‐ 0.870   0.2814    0.1040  
 ‐23.00    ‐ 0.890   0.2556    0.0916  
 ‐22.00    ‐ 0.911   0.2297    0.0785  
 ‐21.00    ‐ 0.934   0.2040    0.0649  
 ‐20.00    ‐ 0.958   0.1785    0.0508  
 ‐19.00    ‐ 0.982   0.1534    0.0364  
 ‐18.00    ‐ 1.005   0.1288    0.0218  
 ‐17.00    ‐ 1.082   0.1037    0.0129  
 ‐16.00    ‐ 1.113   0.0786   ‐0.0028  
 ‐15.00    ‐ 1.105   0.0535   ‐0.0251  
 ‐14.00    ‐ 1.078   0.0283   ‐0.0419  
 ‐13.50    ‐ 1.053   0.0158   ‐0.0521  
 ‐13.00    ‐ 1.015   0.0151   ‐0.0610  
 ‐12.00    ‐ 0.904   0.0134   ‐0.0707  
 ‐11.00    ‐ 0.807   0.0121   ‐0.0722  
 ‐10.00    ‐ 0.711   0.0111   ‐0.0734  
  ‐9.00   ‐ 0.595   0.0099  ‐0.0772 
  ‐8.00   ‐ 0.478   0.0091  ‐0.0807 
  ‐7.00   ‐ 0.375   0.0086  ‐0.0825 
  ‐6.00   ‐ 0.264   0.0082  ‐0.0832 
  ‐5.00   ‐ 0.151   0.0079  ‐0.0841 
  ‐4.00   ‐ 0.017   0.0072  ‐0.0869 
  ‐3.00     0.088   0.0064  ‐0.0912 
  ‐2.00     0.213   0.0054  ‐0.0946 
  ‐1.00     0.328   0.0052  ‐0.0971 
   0.00     0.442   0.0052  ‐0.1014 
   1.00     0.556   0.0052  ‐0.1076 
   2.00     0.670   0.0053  ‐0.1126 
   3.00     0.784   0.0053  ‐0.1157 
   4.00     0.898   0.0054  ‐0.1199 
   5.00     1.011   0.0058  ‐0.1240 
   6.00     1.103   0.0091  ‐0.1234 
   7.00     1.181   0.0113  ‐0.1184 
   8.00     1.257   0.0124  ‐0.1163 
   8.50     1.293   0.0130  ‐0.1163 
   9.00     1.326   0.0136  ‐0.1160 
176

9.50     1.356   0.0143  ‐0.1154 
  10.00      1.382   0.0150   ‐0.1149  
  10.50      1.400   0.0267   ‐0.1145  
  11.00      1.415   0.0383   ‐0.1143  
  11.50      1.425   0.0498   ‐0.1147  
  12.00      1.434   0.0613   ‐0.1158  
  12.50      1.443   0.0727   ‐0.1165  
  13.00      1.451   0.0841   ‐0.1153  
  13.50      1.453   0.0954   ‐0.1131  
  14.00      1.448   0.1065   ‐0.1112  
  14.50      1.444   0.1176   ‐0.1101  
  15.00      1.445   0.1287   ‐0.1103  
  15.50      1.447   0.1398   ‐0.1109  
  16.00      1.448   0.1509   ‐0.1114  
  16.50      1.444   0.1619   ‐0.1111  
  17.00      1.438   0.1728   ‐0.1097  
  17.50      1.439   0.1837   ‐0.1079  
  18.00      1.448   0.1947   ‐0.1080  
  18.50      1.452   0.2057   ‐0.1090  
  19.00      1.448   0.2165   ‐0.1086  
  19.50      1.438   0.2272   ‐0.1077  
  20.00      1.428   0.2379   ‐0.1099  
  21.00      1.401   0.2590   ‐0.1169  
  22.00      1.359   0.2799   ‐0.1190  
  23.00      1.300   0.3004   ‐0.1235  
  24.00      1.220   0.3204   ‐0.1393  
  25.00      1.168   0.3377   ‐0.1440  
  26.00      1.116   0.3554   ‐0.1486  
  28.00      1.015   0.3916   ‐0.1577  
  30.00      0.926   0.4294   ‐0.1668  
  32.00      0.855   0.4690   ‐0.1759  
  35.00      0.800   0.5324   ‐0.1897  
  40.00      0.804   0.6452   ‐0.2126  
  45.00      0.793   0.7573   ‐0.2344  
  50.00      0.763   0.8664   ‐0.2553  
  55.00      0.717   0.9708   ‐0.2751  
  60.00      0.656   1.0693   ‐0.2939  
  65.00      0.582   1.1606   ‐0.3117  
  70.00      0.495   1.2438   ‐0.3285  
  75.00      0.398   1.3178   ‐0.3444  
  80.00      0.291   1.3809   ‐0.3593  
  85.00      0.176   1.4304   ‐0.3731  
  90.00      0.053   1.4565   ‐0.3858  
  95.00    ‐ 0.074   1.4533   ‐0.3973  
 100.00   ‐ 0.199   1.4345  ‐0.4075 
 105.00   ‐ 0.321   1.4004  ‐0.4162 
 110.00   ‐ 0.436   1.3512  ‐0.4231 
 115.00   ‐ 0.543   1.2874  ‐0.4280 
 120.00   ‐ 0.640   1.2099  ‐0.4306 
 125.00   ‐ 0.723   1.1196  ‐0.4304 
 130.00   ‐ 0.790   1.0179  ‐0.4270 
 135.00   ‐ 0.840   0.9064  ‐0.4196 
 140.00   ‐ 0.868   0.7871  ‐0.4077 
 145.00   ‐ 0.872   0.6627  ‐0.3903 
 150.00   ‐ 0.850   0.5363  ‐0.3665 
 155.00   ‐ 0.798   0.4116  ‐0.3349 
 160.00   ‐ 0.714   0.2931  ‐0.2942 
 170.00   ‐ 0.749   0.0971  ‐0.3771 
 175.00   ‐ 0.374   0.0334  ‐0.1879 
 180.00     0.000   0.0198   0.0000 
177

Appendix C Source Code for the Baseline Turbine Control
System DLL
!=======================================================================  
SUBROUTINE  DISCON ( avrSWAP,  aviFAIL,  accINFILE,  avcOUTNAME,  avcMSG ) 
!DEC$ ATTRIBUTES  DLLEXPORT,  ALIAS:'DISCON'  :: DISCON 
 
 
   ! This Bladed‐style DLL controller  is used to implement  a variable ‐speed 
   ! generator ‐torque controller  and PI collective  blade pitch controller  for 
   ! the NREL Offshore  5MW baseline  wind turbine.   This routine  was written  by 
   ! J. Jonkman  of NREL/NWTC  for use in the IEA Annex XXIII OC3 studies.  
 
 
IMPLICIT                          NONE 
 
    ! Passed Variables:  
 REAL(4),      INTENT(INOUT)      :: avrSWAP    (*)                                    ! The swap array, used to pass data to, and r 
 INTEGER(4),  INTENT(   OUT)     :: aviFAIL                                           ! A flag used to indicate  the success  of this  
 INTEGER(1),  INTENT(IN    )     :: accINFILE  (*)                                    ! The address  of the first record of an array  
INTEGER(1),  INTENT(   OUT)     :: avcMSG     (*)                                    ! The address  of the first record of an array  
INTEGER(1),  INTENT(IN    )     :: avcOUTNAME(*)                                     ! The address  of the first record of an array  
 
 
   ! Local Variables:  
 
REAL(4)                        :: Alpha                                            ! Current  coefficient  in the recursive,  singl 
REAL(4)                        :: BlPitch    (3)                                    ! Current  values of the blade pitch angles,  r 
REAL(4)                        :: ElapTime                                          ! Elapsed  time since the last call to the con 
REAL(4),  PARAMETER             :: CornerFreq      =        1.570796                    ! Corner frequency  (‐3dB point) in the recurs 
REAL(4)                        :: GenSpeed                                          ! Current   HSS (generator)  speed, rad/s. 
REAL(4),  SAVE                 :: GenSpeedF                                         ! Filtered  HSS (generator)  speed, rad/s. 
REAL(4)                        :: GenTrq                                           ! Electrical  generator  torque,  N‐m. 
REAL(4)                        :: GK                                               ! Current  value of the gain correction  factor 
REAL(4)                        :: HorWindV                                          ! Horizontal  hub‐heigh wind speed, m/s. 
REAL(4),  SAVE                 :: IntSpdErr                                         ! Current  integral  of speed error w.r.t. time 
REAL(4),  SAVE                 :: LastGenTrq                                        ! Commanded  electrical  generator  torque the l 
REAL(4),  SAVE                 :: LastTime                                          ! Last time this DLL was called,  sec. 
REAL(4),  SAVE                 :: LastTimePC                                        ! Last time the pitch  controller  was called,   
REAL(4),  SAVE                 :: LastTimeVS                                        ! Last time the torque controller  was called,   
REAL(4),  PARAMETER             :: OnePlusEps      = 1.0 + EPSILON(OnePlusEps)         ! The number slighty  greater  than unity in si 
REAL(4),  PARAMETER             :: PC_DT          =        0.00125                     ! Communication  interval  for pitch  controlle  
REAL(4),  PARAMETER             :: PC_KI          =        0.008068634                 ! Integral  gain for pitch controller  at rated  
REAL(4),  PARAMETER             :: PC_KK          =        0.1099965                   ! Pitch angle were the the derivative  of the  
REAL(4),  PARAMETER             :: PC_KP          =        0.01882681                  ! Proportional  gain for pitch controller  at r 
REAL(4),  PARAMETER             :: PC_MaxPit       =        1.570796                    ! Maximum  pitch setting  in pitch controller,   
REAL(4),  PARAMETER             :: PC_MaxRat       =        0.1396263                   ! Maximum  pitch  rate (in absolute  value) in  
REAL(4),  PARAMETER             :: PC_MinPit       =        0.0                        ! Minimum  pitch setting  in pitch controller,   
REAL(4),  PARAMETER             :: PC_RefSpd       =      122.9096                      ! Desired  (reference)  HSS speed for pitch con 
REAL(4),  SAVE                 :: PitCom     (3)                                    ! Commanded  pitch of each blade the last time  
REAL(4)                        :: PitComI                                           ! Integral  term of command  pitch, rad. 
REAL(4)                        :: PitComP                                           ! Proportional  term of command  pitch, rad. 
REAL(4)                        :: PitComT                                           ! Total command  pitch based on the sum of the  
REAL(4)                        :: PitRate    (3)                                    ! Pitch rates of each blade based on the curr 
REAL(4),  PARAMETER             :: R2D            =       57.295780                    ! Factor to convert  radians  to degrees.  
REAL(4),  PARAMETER             :: RPS2RPM         =        9.5492966                   ! Factor to convert  radians  per second to rev 
REAL(4)                        :: SpdErr                                           ! Current  speed error, rad/s. 
REAL(4)                        :: Time                                             ! Current  simulation  time, sec. 
REAL(4)                        :: TrqRate                                           ! Torque rate based on the current  and last t 
REAL(4),  PARAMETER             :: VS_CtInSp       =       70.16224                     ! Transitional  generator  speed (HSS side) bet 
REAL(4),  PARAMETER             :: VS_DT          =        0.00125                     ! Communication  interval  for torque controlle  
REAL(4),  PARAMETER             :: VS_MaxRat       =   15000.0                         ! Maximum  torque rate (in absolute  value) in  
REAL(4),  PARAMETER             :: VS_MaxTq        =   47402.91                        ! Maximum  generator  torque in Region 3 (HSS s 
REAL(4),  PARAMETER             :: VS_Rgn2K        =        2.332287                    ! Generator  torque constant  in Region 2 (HSS  
REAL(4),  PARAMETER             :: VS_Rgn2Sp       =       91.21091                     ! Transitional  generator  speed (HSS side) bet 
REAL(4),  PARAMETER             :: VS_Rgn3MP       =        0.01745329                  ! Minimum  pitch angle at which the torque is  
REAL(4),  PARAMETER             :: VS_RtGnSp       =      121.6805                      ! Rated generator  speed (HSS side), rad/s. ‐‐  
REAL(4),  PARAMETER             :: VS_RtPwr        = 5296610.0                         ! Rated generator  generator  power in Region 3 
REAL(4),  SAVE                 :: VS_Slope15                                        ! Torque/speed  slope of region 1 1/2 cut‐in t 
REAL(4),  SAVE                 :: VS_Slope25                                        ! Torque/speed  slope of region 2 1/2 inductio  
REAL(4),  PARAMETER             :: VS_SlPc         =       10.0                        ! Rated generator  slip percentage  in Region 2  
REAL(4),  SAVE                 :: VS_SySp                                           ! Synchronous  speed of region 2 1/2 induction   
REAL(4),  SAVE                 :: VS_TrGnSp                                         ! Transitional  generator  speed (HSS side) bet 
 
INTEGER(4)                     :: I                                                ! Generic  index. 
INTEGER(4)                     :: iStatus                                           ! A status flag set by the simulation  as foll 
178

INTEGER(4)                     :: K                                                ! Loops through  blades.  
INTEGER(4)                     :: NumBl                                            ! Number of blades,  (‐). 
INTEGER(4),  PARAMETER          :: UnDb           = 85                               ! I/O unit for the debugging  information  
 
INTEGER(1)                     :: iInFile    ( 256)                                 ! CHARACTER  string cInFile   stored as a 1‐byt 
INTEGER(1)                     :: iMessage   ( 256)                                 ! CHARACTER  string cMessage  stored as a 1‐byt 
INTEGER(1),  SAVE              :: iOutName   (1024)                                 ! CHARACTER  string cOutName  stored as a 1‐byt 
 
LOGICAL(1),  PARAMETER          :: PC_DbgOut       = .FALSE.                           ! Flag to indicate  whether  to output debuggin  
 
CHARACTER(  256)               :: cInFile                                           ! CHARACTER  string giving the name of the par 
CHARACTER(  256)               :: cMessage                                          ! CHARACTER  string giving a message  that will  
CHARACTER(1024),  SAVE         :: cOutName                                          ! CHARACTER  string giving the simulation  run  
CHARACTER(    1), PARAMETER    :: Tab            = CHAR( 9 )                        ! The tab character.  
CHARACTER(   25), PARAMETER    :: FmtDat     = "(F8.3,99('"//Tab//"',ES10.3E2,:))"  ! The format of the debugging  data 
 
 
   ! Set EQUIVALENCE  relationships  between  INTEGER(1)  byte arrays and CHARACTER  strings:  
 EQUIVALENCE  (iInFile  , cInFile  ) 
EQUIVALENCE  (iMessage,  cMessage)  
EQUIVALENCE  (iOutName,  cOutName)  
 
 
 
 
   ! Load variables  from calling  program  (See Appendix  A of Bladed User's Guide):  
 
iStatus        = NINT( avrSWAP(  1) ) 
NumBl         = NINT( avrSWAP(61)  ) 
 
BlPitch   (1) =        avrSWAP(  4)    
BlPitch   (2) =        avrSWAP(33)  
BlPitch   (3) =        avrSWAP(34)     
GenSpeed       =        avrSWAP(20)  
HorWindV       =        avrSWAP(27)  
Time          =        avrSWAP(  2) 
    
 
 
   ! Initialize  aviFAIL  to 0: 
 
aviFAIL        = 0 
  
    ! Read any External  Controller  Parameters  specified  in the User Interface  
   !   and initialize  variables:  
 
IF ( iStatus  == 0 )  THEN  ! .TRUE. if were on the first call to the DLL 
  
   ! Convert  byte arrays to CHARACTER  strings,  for convenience:  
 
   DO I = 1,MIN(  256, NINT( avrSWAP(50)  ) ) 
       iInFile  (I) = accINFILE  (I)   ! Sets cInfile   by EQUIVALENCE  
   ENDDO 
   DO I = 1,MIN( 1024, NINT( avrSWAP(51)  ) ) 
       iOutName(I)  = avcOUTNAME(I)    ! Sets cOutName  by EQUIVALENCE  
   ENDDO 
 
 
   ! Inform users that we are using this user‐defined  routine:  
    aviFAIL   = 1 
   cMessage  = 'Running  with torque and pitch control  of the NREL offshore  '// & 
               '5MW baseline  wind turbine  from DISCON.dll  as written  by J. '// & 
               'Jonkman  of NREL/NWTC  for  use  in the IEA Annex XXIII OC3 '   // & 
               'studies.'  
 
 
   ! Determine  some torque control  parameters  not specified  directly:  
    VS_SySp      = VS_RtGnSp/(  1.0 +  0.01*VS_SlPc  ) 
   VS_Slope15  = ( VS_Rgn2K*VS_Rgn2Sp*VS_Rgn2Sp  )/( VS_Rgn2Sp  ‐ VS_CtInSp  ) 
   VS_Slope25  = ( VS_RtPwr/VS_RtGnSp             )/( VS_RtGnSp  ‐ VS_SySp    ) 
   IF ( VS_Rgn2K  == 0.0 )  THEN  ! .TRUE. if the Region 2 torque is flat, and thus, the denominator  in the ELSE condition  is  
       VS_TrGnSp  = VS_SySp  
   ELSE                           ! .TRUE. if the Region 2 torque is quadratic  with speed 
       VS_TrGnSp  = ( VS_Slope25  ‐ SQRT( VS_Slope25*(  VS_Slope25  ‐ 4.0*VS_Rgn2K*VS_SySp  ) ) )/( 2.0*VS_Rgn2K  ) 
   ENDIF 
 
 
   ! Check validity  of input parameters:  
 
179

IF ( CornerFreq  <= 0.0 )  THEN 
       aviFAIL   = ‐1 
       cMessage  = 'CornerFreq  must be greater  than zero.' 
   ENDIF 
 
   IF ( VS_DT      <= 0.0 )  THEN 
       aviFAIL   = ‐1 
       cMessage  = 'VS_DT must be greater  than zero.' 
   ENDIF 
    IF ( VS_CtInSp  <  0.0 )  THEN 
       aviFAIL   = ‐1 
       cMessage  = 'VS_CtInSp  must not be negative.'  
   ENDIF 
 
   IF ( VS_Rgn2Sp  <= VS_CtInSp  )  THEN 
       aviFAIL   = ‐1 
       cMessage  = 'VS_Rgn2Sp  must be greater  than VS_CtInSp.'  
   ENDIF 
 
   IF ( VS_TrGnSp  <  VS_Rgn2Sp  )  THEN 
       aviFAIL   = ‐1 
       cMessage  = 'VS_TrGnSp  must not be less than VS_Rgn2Sp.'  
   ENDIF 
 
   IF ( VS_SlPc    <= 0.0 )  THEN 
       aviFAIL   = ‐1 
       cMessage  = 'VS_SlPc  must be greater  than zero.' 
   ENDIF 
 
   IF ( VS_MaxRat  <= 0.0 )  THEN 
       aviFAIL   =  ‐1 
       cMessage  = 'VS_MaxRat  must be greater  than zero.' 
   ENDIF 
 
   IF ( VS_RtPwr   <  0.0 )  THEN 
       aviFAIL   = ‐1 
       cMessage  = 'VS_RtPwr  must not be negative.'  
   ENDIF 
 
   IF ( VS_Rgn2K   <  0.0 )  THEN 
       aviFAIL   = ‐1 
       cMessage  = 'VS_Rgn2K  must not be negative.'  
   ENDIF 
    IF ( VS_Rgn2K*VS_RtGnSp*VS_RtGnSp  > VS_RtPwr/VS_RtGnSp  )  THEN 
       aviFAIL   = ‐1 
       cMessage  = 'VS_Rgn2K*VS_RtGnSp^2  must not be greater  than VS_RtPwr/VS_RtGnSp.'  
   ENDIF 
    IF ( VS_MaxTq                       < VS_RtPwr/VS_RtGnSp  )  THEN 
       aviFAIL   = ‐1 
       cMessage  = 'VS_RtPwr/VS_RtGnSp  must not be greater  than VS_MaxTq.'  
   ENDIF 
    IF ( PC_DT      <= 0.0 )  THEN 
       aviFAIL   = ‐1 
       cMessage  = 'PC_DT must be greater  than zero.' 
   ENDIF 
    IF ( PC_KI      <= 0.0 )  THEN 
       aviFAIL   = ‐1 
       cMessage  = 'PC_KI must be greater  than zero.' 
   ENDIF 
 
   IF ( PC_KK      <= 0.0 )  THEN 
       aviFAIL   = ‐1 
       cMessage  = 'PC_KK must be greater  than zero.' 
   ENDIF 
    IF ( PC_RefSpd  <= 0.0 )  THEN 
       aviFAIL   = ‐1 
       cMessage  = 'PC_RefSpd  must be greater  than zero.' 
   ENDIF 
       IF  ( PC_MaxRat  <= 0.0 )  THEN 
       aviFAIL   = ‐1 
       cMessage  = 'PC_MaxRat  must be greater  than zero.' 
   ENDIF 
    IF ( PC_MinPit  >= PC_MaxPit  )  THEN 
       aviFAIL   = ‐1 
       cMessage  = 'PC_MinPit  must be less than PC_MaxPit.'  
   ENDIF 
 
180

! If we're debugging  the pitch controller,  open the debug file and write the 
   !   header:  
 
   IF ( PC_DbgOut  )  THEN 
        OPEN ( UnDb, FILE=TRIM(  cOutName  )//'.dbg',  STATUS='REPLACE'  ) 
 
       WRITE (UnDb,'(/////)')  
       WRITE (UnDb,'(A)')   'Time '//Tab//'ElapTime'//Tab//'HorWindV'//Tab//'GenSpeed'//Tab//'GenSpeedF'//Tab//'RelSpdErr'//Tab  
                           'SpdErr  '//Tab//'IntSpdErr'//Tab//'GK  '//Tab//'PitComP'//Tab//'PitComI'//Tab//'PitComT'//Tab//          
                           'PitRate1'//Tab//'PitCom1'  
       WRITE (UnDb,'(A)')   '(sec)'//Tab//'(sec)    '//Tab//'(m/sec)  '//Tab//'(rpm)    '//Tab//'(rpm)      '//Tab//'(%)        '//Tab 
                           '(rad/s)'//Tab//'(rad)      '//Tab//'( ‐)'//Tab//'(deg)   '//Tab//'(deg)   '//Tab//'(deg)   '//Tab//          
                           '(deg/s)  '//Tab//'(deg)   ' 
 
   ENDIF 
 
 
   ! Initialize  the SAVEd variables:  
   ! NOTE: LastGenTrq,  though SAVEd, is initialized  in the torque controller  
   !        below for simplicity,  not here. 
 
   GenSpeedF   = GenSpeed                          ! This will ensure that generator  speed filter will use the initial  value of  
   PitCom       = BlPitch                           ! This will ensure that the variable  speed controller  picks the correct  contr 
   GK          = 1.0/( 1.0 + PitCom(1)/PC_KK  )   ! This will ensure that the pitch angle is unchanged  if the initial  SpdErr is  
   IntSpdErr   = PitCom(1)/(  GK*PC_KI  )           ! This will ensure that the pitch angle is unchanged  if the initial  SpdErr is  
    LastTime    = Time                             ! This will ensure that generator  speed filter will use the initial  value of  
   LastTimePC  = Time ‐ PC_DT                     ! This will ensure that the pitch  controller  is called on the first pass  
   LastTimeVS  = Time ‐ VS_DT                     ! This will ensure that the torque controller  is called on the first pass  
  
ENDIF 
 
 
 
   ! Main control  calculations:  
 
IF ( ( iStatus  >= 0 ) .AND. ( aviFAIL  >= 0 ) )  THEN  ! Only compute  control  calculations  if no error has occured  and we are  
 
 
 
   ! Abort if the user has not requested  a pitch angle actuator  (See Appendix  A 
   !   of Bladed User's Guide):  
    IF ( NINT(avrSWAP(10))  /= 0 )  THEN ! .TRUE. if a pitch angle actuator  hasn't been requested  
       aviFAIL   = ‐1 
       cMessage  = 'Pitch angle actuator  not requested.'  
   ENDIF  
 
 
   ! Set unused outputs  to zero (See Appendix  A of Bladed User's Guide):  
 
   avrSWAP(36)  = 0.0 ! Shaft brake status:  0=off 
   avrSWAP(41)  = 0.0 ! Demanded  yaw actuator  torque 
   avrSWAP(46)  = 0.0 ! Demanded  pitch rate (Collective  pitch) 
   avrSWAP(48)  = 0.0 ! Demanded  nacelle  yaw rate 
   avrSWAP(65)  = 0.0 ! Number of variables  returned  for logging  
   avrSWAP(72)  = 0.0 ! Generator  startup  resistance  
   avrSWAP(79)  = 0.0 ! Request  for loads: 0=none 
   avrSWAP(80)  = 0.0 ! Variable  slip current  status 
   avrSWAP(81)  = 0.0 ! Variable  slip current  demand 
 
 
!=======================================================================  
 
 
   ! Filter the HSS (generator)  speed measurement:  
   ! NOTE: This is a very simple recursive,  single‐pole, low‐pass filter with 
   !        exponential  smoothing.  
    ! Update the coefficient  in the recursive  formula  based on the elapsed  time 
   !   since the last call to the controller:  
    Alpha      = EXP( ( LastTime  ‐ Time )*CornerFreq  ) 
  
   ! Apply the filter:  
 
   GenSpeedF  = ( 1.0 ‐ Alpha )*GenSpeed  + Alpha*GenSpeedF  
  
!=======================================================================  
 
181

! Variable ‐speed torque control:  
    ! Compute  the elapsed  time since the last call to the controller:  
    ElapTime  = Time ‐ LastTimeVS  
  
   ! Only perform  the control  calculations  if the elapsed  time is greater  than 
   !   or equal to the communication  interval  of the torque controller:  
   ! NOTE: Time is scaled by OnePlusEps  to ensure that the contoller  is called 
   !        at every time step when VS_DT = DT, even in the presence  of 
   !        numerical  precision  errors.  
 
   IF ( ( Time*OnePlusEps  ‐ LastTimeVS  ) >= VS_DT )  THEN 
 
 
   ! Compute  the generator  torque,  which depends  on which region we are in: 
        IF ( (   GenSpeedF  >= VS_RtGnSp  ) .OR. (  PitCom(1)  >= VS_Rgn3MP  ) )  THEN ! We are in region 3 ‐ power is constant  
          GenTrq = VS_RtPwr/GenSpeedF  
       ELSEIF ( GenSpeedF  <= VS_CtInSp  )  THEN                                     ! We are in region 1 ‐ torque is zero 
          GenTrq = 0.0 
       ELSEIF ( GenSpeedF  <  VS_Rgn2Sp  )  THEN                                     ! We are in region 1 1/2 ‐ linear ramp in to 
          GenTrq = VS_Slope15*(  GenSpeedF  ‐ VS_CtInSp  ) 
       ELSEIF ( GenSpeedF  <  VS_TrGnSp  )  THEN                                     ! We are in region 2 ‐ optimal  torque is pro 
          GenTrq = VS_Rgn2K*GenSpeedF*GenSpeedF  
       ELSE                                                                        ! We are in region 2 1/2 ‐ simple induction   
          GenTrq = VS_Slope25*(  GenSpeedF  ‐ VS_SySp    ) 
       ENDIF 
  
   ! Saturate  the commanded  torque using the maximum  torque limit: 
 
       GenTrq  = MIN( GenTrq                     , VS_MaxTq   )   ! Saturate  the command  using the maximum  torque limit 
  
   ! Saturate  the commanded  torque using the torque rate limit: 
        IF ( iStatus  == 0 )  LastGenTrq  = GenTrq                  ! Initialize  the value of LastGenTrq  on the first pass only 
       TrqRate  = ( GenTrq ‐ LastGenTrq  )/ElapTime                 ! Torque rate (unsaturated)  
       TrqRate  = MIN( MAX( TrqRate,  ‐VS_MaxRat  ), VS_MaxRat  )   ! Saturate  the torque rate using its maximum  absolute  value 
       GenTrq  = LastGenTrq  + TrqRate*ElapTime                    ! Saturate  the command  using the torque rate limit 
  
   ! Reset the values of LastTimeVS  and LastGenTrq  to the current  values:  
 
       LastTimeVS  = Time 
       LastGenTrq  = GenTrq 
 
 
   ENDIF 
 
 
   ! Set the generator  contactor  status,  avrSWAP(35),  to main (high speed)  
   !   variable ‐speed generator,  the torque override  to yes, and command  the 
   !   generator  torque (See Appendix  A of Bladed User's Guide):  
    avrSWAP(35)  = 1.0           ! Generator  contactor  status:  1=main (high speed) variable ‐speed generator  
   avrSWAP(56)  = 0.0           ! Torque override:  0=yes 
   avrSWAP(47)  = LastGenTrq    ! Demanded  generator  torque 
 
 
!=======================================================================  
 
 
   ! Pitch control:  
 
   ! Compute  the elapsed  time since the last call to the controller:  
    ElapTime  = Time ‐ LastTimePC  
  
   ! Only perform  the control  calculations  if the elapsed  time is greater  than 
   !   or equal to the communication  interval  of the pitch controller:  
   ! NOTE: Time is scaled by OnePlusEps  to ensure that the contoller  is called 
   !        at every time step when PC_DT = DT, even in the presence  of 
   !        numerical  precision  errors.  
    IF ( ( Time*OnePlusEps  ‐ LastTimePC  ) >= PC_DT )  THEN 
  
   ! Compute  the gain scheduling  correction  factor based on the previously  
   !   commanded  pitch angle for blade 1: 
 
182

GK = 1.0/( 1.0 + PitCom(1)/PC_KK  ) 
 
 
   ! Compute  the current  speed error and its integral  w.r.t. time; saturate  the 
   !   integral  term using the pitch angle limits:  
 
       SpdErr     = GenSpeedF  ‐ PC_RefSpd                                   ! Current  speed error 
       IntSpdErr  = IntSpdErr  + SpdErr*ElapTime                             ! Current  integral  of speed error w.r.t. time 
       IntSpdErr  = MIN( MAX( IntSpdErr,  PC_MinPit/(  GK*PC_KI  ) ), & 
                                        PC_MaxPit/(  GK*PC_KI  )       )     ! Saturate  the integral  term using the pitch angle li 
  
   ! Compute  the pitch commands  associated  with the proportional  and integral  
   !   gains: 
        PitComP    = GK*PC_KP*    SpdErr                                     ! Proportional  term 
       PitComI    = GK*PC_KI*IntSpdErr                                      ! Integral  term (saturated)  
 
 
   ! Superimpose  the individual  commands  to get the total pitch command;  
   !   saturate  the overall  command  using the pitch angle limits:  
        PitComT    = PitComP  + PitComI                                       ! Overall  command  (unsaturated)  
       PitComT    = MIN( MAX( PitComT,  PC_MinPit  ), PC_MaxPit  )            ! Saturate  the overall  command  using the pitch angle  
 
 
   ! Saturate  the overall  commanded  pitch using the pitch rate limit: 
   ! NOTE: Since the current  pitch angle may be different  for each blade 
   !        (depending  on the type of actuator  implemented  in the structural  
   !        dynamics  model),  this pitch rate limit calculation  and the 
   !        resulting  overall  pitch angle command  may be different  for each 
   !        blade. 
        DO K = 1,NumBl  ! Loop through  all blades 
 
          PitRate(K)  = ( PitComT  ‐ BlPitch(K)  )/ElapTime                   ! Pitch rate of blade K (unsaturated)  
          PitRate(K)  = MIN( MAX( PitRate(K),  ‐PC_MaxRat  ), PC_MaxRat  )   ! Saturate  the pitch rate of blade K using its maximu 
          PitCom (K) = BlPitch(K)  + PitRate(K)*ElapTime                    ! Saturate  the overall  command  of blade K using the p 
        ENDDO           ! K ‐ all blades 
 
 
   ! Reset the value of LastTimePC  to the current  value: 
        LastTimePC  = Time 
 
 
   ! Output debugging  information  if requested:  
        IF ( PC_DbgOut  )  WRITE  (UnDb,FmtDat)   Time, ElapTime,  HorWindV,  GenSpeed*RPS2RPM,  GenSpeedF*RPS2RPM,             & 
                                              100.0*SpdErr/PC_RefSpd,  SpdErr,  IntSpdErr,  GK, PitComP*R2D,  PitComI*R2D,  & 
                                              PitComT*R2D,  PitRate(1)*R2D,  PitCom(1)*R2D  
 
 
   ENDIF 
  
   ! Set the pitch override  to yes and command  the pitch demanded  from the last 
   !   call to the controller  (See Appendix  A of Bladed User's Guide):  
    avrSWAP(55)  = 0.0        ! Pitch override:  0=yes 
    avrSWAP(42)  = PitCom(1)  ! Use the command  angles of all blades if using individual  pitch 
   avrSWAP(43)  = PitCom(2)  ! " 
   avrSWAP(44)  = PitCom(3)  ! " 
    avrSWAP(45)  = PitCom(1)  ! Use the command  angle of blade 1 if using collective  pitch 
 
 
!=======================================================================  
  
   ! Reset the value of LastTime  to the current  value: 
 
   LastTime  = Time 
  
ENDIF 
 
 
   ! Convert  CHARACTER  string to byte array for the return message:  
 DO I = 1,MIN(  256, NINT( avrSWAP(49)  ) ) 
   avcMSG(I)  = iMessage(I)  ! Same as cMessage  by EQUIVALENCE  
ENDDO 
183

RETURN 
END SUBROUTINE  DISCON 
!=======================================================================  
184

Appendix D Input Files for the ITI Energy Barge
D.1 FAST Platform / HydroDyn Input File
‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐ 
‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐  FAST PLATFORM  FILE ‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐ 
NREL 5.0 MW offshore  baseline  floating  platform  input properties  for the ITI Energy barge with 4m draft. 
‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐  FEATURE  FLAGS (CONT) ‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐ 
True         PtfmSgDOF    ‐  Platform  horizontal  surge translation  DOF (flag) 
True         PtfmSwDOF    ‐  Platform  horizontal  sway translation  DOF (flag) 
True         PtfmHvDOF    ‐  Platform  vertical  heave translation  DOF (flag) 
True         PtfmRDOF     ‐  Platform  roll tilt rotation  DOF (flag) 
True         PtfmPDOF     ‐  Platform  pitch tilt rotation  DOF (flag) 
True         PtfmYDOF     ‐  Platform  yaw rotation  DOF (flag) 
‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐  INITIAL  CONDITIONS  (CONT) ‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐ 
   0.0       PtfmSurge    ‐  Initial  or fixed horizontal  surge translational  displacement  of platform  (meters)  
   0.0       PtfmSway     ‐  Initial  or fixed horizontal  sway translational  displacement  of platform  (meters)  
   0.0       PtfmHeave    ‐  Initial  or fixed vertical  heave translational  displacement  of platform  (meters)  
   0.0       PtfmRoll     ‐  Initial  or fixed roll tilt rotational  displacement  of platform  (degrees)  
   0.0       PtfmPitch    ‐  Initial  or fixed pitch tilt rotational  displacement  of platform  (degrees)  
   0.0       PtfmYaw      ‐  Initial  or fixed yaw rotational  displacement  of platform  (degrees)  
‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐  TURBINE  CONFIGURATION  (CONT) ‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐ 
   0.0       TwrDraft     ‐  Downward  distance  from the ground level [onshore]  or MSL [offshore]  to the tower base platform  conn 
   0.281768  PtfmCM      ‐  Downward  distance  from the ground level [onshore]  or MSL [offshore]  to the platform  CM (meters)  
   0.0       PtfmRef      ‐  Downward  distance  from the ground level [onshore]  or MSL [offshore]  to the platform  reference  point  
‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐  MASS AND INERTIA  (CONT) ‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐ 
5452.0E3      PtfmMass     ‐  Platform  mass (kg) 
 726.9E6      PtfmRIner    ‐  Platform  inertia  for roll tilt rotation  about the platform  CM (kg m^2) 
 726.9E6      PtfmPIner    ‐  Platform  inertia  for pitch tilt rotation  about the platform  CM (kg m^2) 
1453.9E6      PtfmYIner    ‐  Platfrom  inertia  for yaw rotation  about the platform  CM (kg m^2) 
‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐  PLATFORM  (CONT) ‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐ 
FltngPtfmLd  PtfmLdMod    ‐  Platform  loading  model {0: none, 1: user‐defined  from routine  UserPtfmLd}  (switch)  
"PlatformDesigns\WAMIT\ITIBarge4\Barge"            WAMITFile    ‐  Root name of WAMIT output files containing  the linear,  nondime  
6000.0       PtfmVol0     ‐  Displaced  volume of water when the platform  is in its undisplaced  position  (m^3) [USE THE SAME VALU 
   8         PtfmNodes    ‐  Number of platform  nodes used in calculation  of viscous  drag term from Morison's  equation  (‐) 
   4.0       PtfmDraft    ‐  Effective  platform  draft     in calculation  of viscous  drag term from Morison's  equation  (meters)  
  45.1352    PtfmDiam     ‐  Effective  platform  diameter  in calculation  of viscous  drag term from Morison's  equation  (meters)  NO 
   1.0       PtfmCD      ‐  Effective  platform  normalized  hydrodynamic  viscous  drag coefficient  in calculation  of viscous  drag  
  60.0       RdtnTMax     ‐  Analysis  time for  wave radiation  kernel calculations  (sec) [determines  RdtnDOmega=Pi/RdtnTMax  in th 
   0.025     RdtnDT      ‐  Time step for  wave radiation  kernel calculations  (sec) [DT<=RdtnDT<=0.1  recommended]  [determines  Rd 
‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐  MOORING  LINES ‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐ 
   8         NumLines     ‐  Number of mooring  lines (‐) 
   1         LineMod      ‐  Mooring  line model {1: standard  quasi‐static,  2: user‐defined  from routine  UserLine}  (switch)  [used  
LRadAnch   LAngAnch   LDpthAnch   LRadFair   LAngFair    LDrftFair   LUnstrLen   LDiam   LMassDen   LEAStff   LSeabedCD   LTenTol  [used  
(m)        (deg)      (m)         (m)        (deg)       (m)         (m)         (m)      (kg/m)     (N)       (‐)         (‐)      [used  
 423.422    23.965   150.0       28.2843      45.0       4.0         473.312      0.0809  130.403    589.0E6   1.0         0.0001 
 423.422    66.035   150.0       28.2843      45.0       4.0         473.312      0.0809  130.403    589.0E6   1.0         0.0001 
 423.422   113.965    150.0       28.2843    135.0       4.0         473.312      0.0809  130.403    589.0E6   1.0         0.0001 
 423.422   156.035    150.0       28.2843    135.0       4.0         473.312      0.0809  130.403    589.0E6   1.0         0.0001 
 423.422   203.965    150.0       28.2843    225.0       4.0         473.312      0.0809  130.403    589.0E6   1.0         0.0001 
 423.422   246.035    150.0       28.2843    225.0       4.0         473.312      0.0809  130.403    589.0E6   1.0         0.0001 
 423.422   293.965    150.0       28.2843    315.0       4.0         473.312      0.0809  130.403    589.0E6   1.0         0.0001 
 423.422   336.035    150.0       28.2843    315.0       4.0         473.312      0.0809  130.403    589.0E6   1.0         0.0001 
‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐  WAVES ‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐ 
1025.0       WtrDens      ‐  Water density  (kg/m^3)  
 150.0       WtrDpth      ‐  Water depth (meters)  [USE THE SAME VALUE SPECIFIED  IN THE  WAMIT .POT FILE!] 
   2         WaveMod      ‐  Incident  wave kinematics  model {0: none=still  water, 1: plane progressive  (regular),  2: JONSWAP/Pie  
3630.0       WaveTMax     ‐  Analysis  time for  incident  wave calculations  (sec) [unused  when WaveMod=0]  [determines  WaveDOmega=2  
   0.25      WaveDT      ‐  Time step for  incident  wave calculations  (sec) [unused  when WaveMod=0]  [0.1<=WaveDT<=1.0  recommende  
   5.0       WaveHs      ‐  Significant  wave height of incident  waves (meters)  [used only when WaveMod=1  or 2] 
  12.4       WaveTp      ‐  Peak spectral  period of incident  waves (sec) [used only when WaveMod=1  or 2] 
DEFAULT       WavePkShp    ‐  Peak shape parameter  of incident  wave spectrum  (‐) or DEFAULT  (unquoted  string)  [used only when Wav 
   0.0       WaveDir      ‐  Incident  wave propagation  heading  direction  (degrees)  [unused  when WaveMod=0]  
123456789    WaveSeed(1)  ‐ First  random seed of incident  waves [‐2147483648  to 2147483647]  (‐) [unused  when WaveMod=0]  
1011121314   WaveSeed(2)  ‐ Second random seed of incident  waves [‐2147483648  to 2147483647]  (‐) [unused  when WaveMod=0]  
‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐  CURRENT  ‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐ 
   0         CurrMod      ‐  Current  profile  model {0: none=no  current,  1: standard,  2: user‐defined  from routine  UserCurrent}  ( 
   0.0       CurrSSV0     ‐  Sub‐surface  current  velocity  at still water level (m/s) [used only when CurrMod=1]  
DEFAULT       CurrSSDir    ‐  Sub‐surface  current  heading  direction  (degrees)  or DEFAULT  (unquoted  string)  [used only when CurrMo 
  20.0       CurrNSRef    ‐  Near‐surface  current  reference  depth (meters)  [used only when CurrMod=1]  
   0.0       CurrNSV0     ‐  Near‐surface  current  velocity  at still water level (m/s) [used only when CurrMod=1]  
   0.0       CurrNSDir    ‐  Near‐surface  current  heading  direction  (degrees)  [used only when CurrMod=1]  
   0.0       CurrDIV      ‐  Depth‐independent  current  velocity  (m/s) [used only when CurrMod=1]  
   0.0       CurrDIDir    ‐  Depth‐independent  current  heading  direction  (degrees)  [used only when CurrMod=1]  
‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐  OUTPUT (CONT) ‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐ 
   1         NWaveKin     ‐  Number of points where the incident  wave kinematics  can be output [0 to 9] (‐) 
   8         WaveKinNd    ‐  List of platform  nodes that have wave kinematics  sensors  [1 to PtfmNodes]  (‐) [unused  if NWaveKin=0  
185

D.2 WAMIT Input File – CONFIG.WAM
CONFIGuration  file for WAMIT v6.3PC.  
IALTFRC          =     1                         IALTFRC        ‐  Alternative  form of the .FRC file {1: use alternative  form #1, 2 
IALTFRCN         = 1  1  etc.                   IALTFRCN       ‐  Alternative  form of the .FRC file {1: use alternative  form #1, 2 
IALTPOT          =     1                         IALTPOT        ‐  Alternative  form of the .POT file {1: use alternative  form #1, 2 
ICTRSURF         =     0                         ICTRSURF       ‐  Alternative  form to evaluate  the drift forces over a user‐define 
IDIAG†         POT                             IDIAG†        ‐  Control  index for increasing  the precision  of the panel integrat  
IFIELD_ARRAYS   =     0                         IFIELD_ARRAYS  ‐ Additional  uniform  field point data {0: none, 1: using compresse  
IFORCE          =     1                         IFORCE        ‐  Execute  FORCE subprogram  {0: do not execute,  1: do execute}  (swi 
IGENMDS          =     0                         IGENMDS        ‐  Option to input geometric  data associated  with mode shapes of ge 
ILOWGDF          =     0                         ILOWGDF        ‐  Generate  low‐order _LOW.GDF  file based on input geometry  {0: no,  
ILOWHI          =     0                         ILOWHI        ‐  Order of panel method {0: low‐order, 1: high‐order} (switch)  
ILOG†          POT                             ILOG†         ‐  Control  index for increasing  the precision  of the panel integrat  
INUMOPT5         =     0                         INUMOPT5       ‐  Option to output separate  body pressure  and velocity  {0: as in v 
INUMOPT6         =     0                         INUMOPT6       ‐  Option to output separate  pressure  at field points {0: as in v6. 
INUMOPT7         =     0                         INUMOPT7       ‐  Option to output separate  fluid velocity  at field points {0: as  
IPERIO          =     2                         IPERIO        ‐  Input data option for PER in the .POT file {1: period in sec, 2:  
IPLTDAT          =     0                         IPLTDAT        ‐  Generate  _PAN.DAT  and _PAT.DAT  files for plotting  panel and patc 
IPNLBPT          =     0                         IPNLBPT        ‐  Option to evaluate  the body pressure  at specified  points in the  
IPOTEN          =     1                         IPOTEN        ‐  Execute  POTEN subprogram  {0: do not execute,  1: do execute}  (swi 
IQUAD†         POT   0                         IQUAD†        ‐  Control  index for increasing  the precision  of the panel integrat  
IQUADI†         SPL   4                         IQUADI†        ‐  Order of Guass quadrature  in the inner integration  (‐) [unused  w 
IQUADO†         SPL   3                         IQUADO†        ‐  Order of Guass quadrature  in the outer integration  (‐) [unused  w 
IRR†           POT                             IRR†          ‐  Irregular  frequency  removal  {0: do not remove,  1: remove by repr 
ISCATT          =     0                         ISCATT        ‐  Solve for the diffraction  potential  from the diffraction  or scat 
ISOLVE          =     1                         ISOLVE        ‐  Method of solution  for the linear systems  in POTEN {0: iterative   
ISOR†          POT                             ISOR†         ‐  Source strength  evaluation  {0: do not evaluate,  1: do evaluate}   
ITANKFPT         =     0                         ITANKFPT       ‐  Format for specifying  input field point coordinates  {0: conventi  
KSPLIN         SPL   3                         KSPLIN        ‐  Order of B‐spline for potential  in high‐order method {3: quadrat  
MAXITT          =   35                         MAXITT        ‐  Maximum  number of iterations  in the iterative  solver of POTEN (‐ 
MAXMIT          =     8                         MAXMIT        ‐  Maximum  number of iterations  in the adaptive  integration  used to  
MAXSCR          = 8192                         MAXSCR        ‐  Available  RAM for scratch  storage  in POTEN = 8*MAXSCR^2  bytes (‐ 
MODLST          =     0                         MODLST        ‐  Order in which the added mass and damping  coefficients,  exciting   
MONITR          =     0                         MONITR        ‐  Mode for  displaying  output to the monitor  during execution  of FO 
NEWMDS(n)†      POT2  0                         NEWMDS(n)†     ‐  Number of generalized  modes for body n (‐) 
NOOUT           = 1  1  1  1  1  1  1  1  1   NOOUT         ‐  Omit/include  output in the .OUT file for each of the 9 output op 
NPTANK(n)                                      NPTANK(n)      ‐  List of panel or patch index ranges of internal  tanks for body n  
NUMHDR          =     0                         NUMHDR        ‐  Omit/include  one‐line header in the numeric  output files {0: omi 
NUMNAM          =     0                         NUMNAM        ‐  Numeric  output filename  convention  {0: use rootname  of the .FRC  
PANEL_SIZE       =   ‐ 1.0                       PANEL_SIZE     ‐  Automatic  subdivision  of patches  in the higher‐order panel metho 
RHOTANK                                        RHOTANK        ‐  List of fluid densities  in internal  tanks relative  to the densit 
SCRATCH_PATH    = C:\WAMITv6                    SCRATCH_PATH   ‐  Path of directory  for storage  of some scratch  arrays (unquoted  s 
USERID_PATH      = C:\WAMITv6                    USERID_PATH    ‐  Path of directory  where USERID.WAM  is stored (unquoted  string)  
XBODY(n)†  POT or GGDF                         XBODY(n)†      ‐  X‐, Y‐, and Z‐coordinates  and the Z‐axis rotation  of the body‐fi 
D.3 WAMIT Input File – Barge.POT
POTential  control  file in alternative  form #1 for WAMIT v6.3PC.  
   0                                          ISOR†         ‐  Source strength  evaluation  {0: do not evaluate,  1: do evaluate}   
   2                                          IRR†          ‐  Irregular  frequency  removal  {0: do not remove,  1: remove by repr 
‐1.0  0.0  0.0  0.0  0.0                      HBOT          ‐  Water depth {‐1.0: infinite}  (meters)   &  XBODY†        ‐  X‐, Y‐ 
   0     1     0                                IQUAD†        ‐  Control  index for increasing  the precision  of the panel integrat  
   1     1                                     IRAD          ‐  Control  index for radiation  modes {1: use all 6 rigid‐body modes  
   1     1     1     1     1     1                 MODE          ‐  List of radiation  modes and diffraction  components  required  {0:  
‐102                                          NPER          ‐  Number of wave periods  to be analyzed  {0: evaluate  hydrostatics   
  ‐0.05 0.05                                  PER           ‐  List of wave periods  [IPERIO  = 1] or wave frequencies  [IPERIO  =  
  37                                          NBETA         ‐  Number of wave heading  angles to be analyzed  {0: do not solve th 
‐180.0 
‐170.0 
‐160.0 
‐150.0 
‐140.0 
‐130.0 
‐120.0 
‐110.0 
‐100.0 
 ‐90.0 
 ‐80.0 
 ‐70.0 
 ‐60.0 
 ‐50.0 
 ‐40.0 
 ‐30.0 
 ‐20.0 
 ‐10.0 
   0.0 
  10.0 
  20.0 
  30.0 
  40.0 
186

50.0 
  60.0 
  70.0 
  80.0 
  90.0 
 100.0 
 110.0 
 120.0 
 130.0 
 140.0 
 150.0 
 160.0 
 170.0 
 180.0                                        BETA          ‐  List of wave heading  angles relative  to the global coordinate  sy 
D.4 WAMIT Input File – Barge.FRC
FoRCe control  file in alternative  form #1 for WAMIT v6.3PC.  
   1     0     1     0     0     0     0     0     0 IOPTN         ‐  Switches  for generating  numerical  output files [1]{0: do not out 
   0.0                                        VCG           ‐  Vertical  location  of the center of gravity  of the body relative   
   0.0  0.0  0.0 
   0.0  0.0  0.0 
   0.0  0.0  0.0                              XPRDCT        ‐  Matrix of body radii of gyration  about the body‐fixed coordinate   
   0                                          NBETAH        ‐  Number of wave heading  angles to be analyzed  by the Haskind  rela 
   0                                          NFIELD        ‐  Number of points in the fluid domain where the hydrodynamic  pres 
                                              XFIELD        ‐  Global X‐, Y‐, Z‐ coordinates  of field points where the pressure   
D.5 WAMIT Input File – Barge.GDF
Geometric  Data File for WAMIT v6.3PC.   Barge: Half‐Length=20.000000,  Half‐Width=20.000000,  Draft=4.000000;   NL=  41, NW=  41,  
  1.0      9.806650                    ULEN          ‐  Length scale (meters)   &  GRAV          ‐  Gravitational  acceleration  (m/s 
     1             1                   ISX           ‐  Geometric  plane of symmetry  switch for the x=0 plane {0: x=0 plane is not  
 2400                                NPAN(C)        ‐  Number of (conventional)  panels defined  in this file.  Each panel has 4 v 
       5.0000000        20.0000000         0.0000000  
       5.5000000        20.0000000         0.0000000  
       5.5000000        20.0000000       ‐ 0.5000000  
       5.0000000        20.0000000       ‐ 0.5000000  
       5.0000000        20.0000000       ‐ 0.5000000  
       5.5000000        20.0000000       ‐ 0.5000000  
       5.5000000        20.0000000       ‐ 1.0000000  
       5.0000000        20.0000000       ‐ 1.0000000  
 
[lines deleted]  
 
       0.5000000        0.5000000       ‐ 0.0100000  
       0.5000000         0.0000000       ‐ 0.0100000  
       0.0000000         0.0000000       ‐ 0.0100000  
       0.0000000         0.5000000       ‐ 0.0100000  
     0                                NPAND         ‐  Number of dipole panels defined  in this file.  Each panel has 4 vertices   
D.6 WAMIT Output File – Barge.hst
      1      1   0.000000E+00  
      1      2   0.000000E+00  
      1      3   0.000000E+00  
      1      4   0.000000E+00  
      1      5   0.000000E+00  
      1      6   0.000000E+00  
      2      1   0.000000E+00  
      2      2   0.000000E+00  
      2      3   0.000000E+00  
      2      4   0.000000E+00  
      2      5   0.000000E+00  
      2      6   0.000000E+00  
      3      1   0.000000E+00  
      3      2   0.000000E+00  
      3      3   1.600000E+03  
      3      4   0.000000E+00  
      3      5   0.000000E+00  
      3      6   0.000000E+00  
      4      1   0.000000E+00  
      4      2   0.000000E+00  
      4      3   0.000000E+00  
      4      4   2.013000E+05  
      4      5   0.000000E+00  
      4      6   0.000000E+00  
      5      1   0.000000E+00  
187

5      2   0.000000E+00  
      5      3   0.000000E+00  
      5      4   0.000000E+00  
      5      5   2.013000E+05  
      5      6   0.000000E+00  
      6      1   0.000000E+00  
      6      2   0.000000E+00  
      6      3   0.000000E+00  
      6      4   0.000000E+00  
      6      5   0.000000E+00  
      6      6   0.000000E+00  
D.7 WAMIT Output File – Barge.1
 ‐0.100000E+01       1      1  1.776617E+03  
 ‐0.100000E+01       1      5  1.297780E+04  
 ‐0.100000E+01       2      2  1.776618E+03  
 ‐0.100000E+01       2      4 ‐1.297781E+04  
 ‐0.100000E+01       3      3  2.880441E+04  
 ‐0.100000E+01       4      2 ‐1.295660E+04  
 ‐0.100000E+01       4      4  1.413279E+06  
 ‐0.100000E+01       5      1  1.295662E+04  
 ‐0.100000E+01       5      5  1.413279E+06  
 ‐0.100000E+01       6      6  2.434394E+05  
  0.000000E+00       1      1  7.308306E+02  
  0.000000E+00       1      5  1.668855E+03  
  0.000000E+00       2      2  7.308387E+02  
  0.000000E+00       2      4 ‐1.668626E+03  
  0.000000E+00       3      3  1.817598E+04  
  0.000000E+00       4      2 ‐1.734576E+03  
  0.000000E+00       4      4  1.229522E+06  
  0.000000E+00       5      1  1.734658E+03  
  0.000000E+00       5      5  1.229520E+06  
  0.000000E+00       6      6  1.152173E+05  
  0.125664E+03       1      1  1.779421E+03   2.548481E ‐04 
  0.125664E+03       1      5  1.302383E+04   7.084972E ‐03 
  0.125664E+03       2      2  1.779422E+03   2.465041E ‐04 
  0.125664E+03       2      4 ‐1.302386E+04  ‐6.601011E ‐03 
  0.125664E+03       3      3  2.920453E+04   3.226425E+02  
  0.125664E+03       4      2 ‐1.300262E+04  ‐7.034077E ‐03 
  0.125664E+03       4      4  1.414163E+06   1.920742E ‐01 
  0.125664E+03       5      1  1.300266E+04   6.788456E ‐03 
  0.125664E+03       5      5  1.414163E+06   1.771003E ‐01 
  0.125664E+03       6      6  2.435710E+05  ‐3.525452E ‐05 
  0.628319E+02       1      1  1.788056E+03   1.595723E ‐02 
  0.628319E+02       1      5  1.316680E+04   4.356846E ‐01 
  0.628319E+02       2      2  1.788058E+03   1.595903E ‐02 
  0.628319E+02       2      4 ‐1.316683E+04  ‐4.365759E ‐01 
  0.628319E+02       3      3  2.978440E+04   1.246353E+03  
  0.628319E+02       4      2 ‐1.314521E+04  ‐4.359398E ‐01 
  0.628319E+02       4      4  1.416919E+06   1.187046E+01  
  0.628319E+02       5      1  1.314526E+04   4.359777E ‐01 
  0.628319E+02       5      5  1.416920E+06   1.196969E+01  
  0.628319E+02       6      6  2.439680E+05  ‐2.121533E ‐05 
 
[lines deleted]  
 
  0.125664E+01       1      1  4.383039E+02   3.095645E+01  
  0.125664E+01       1      5  2.853315E+03  ‐7.720968E+00  
  0.125664E+01       2      2  4.383042E+02   3.095489E+01  
  0.125664E+01       2      4 ‐2.853380E+03   7.708005E+00  
  0.125664E+01       3      3  1.271407E+04   1.630128E ‐01 
  0.125664E+01       4      2 ‐2.882646E+03  ‐3.207071E+01  
  0.125664E+01       4      4  1.187890E+06  ‐3.894744E+00  
  0.125664E+01       5      1  2.882619E+03   3.220637E+01  
  0.125664E+01       5      5  1.187889E+06  ‐5.182734E+00  
  0.125664E+01       6      6  9.052984E+04   8.109989E+03  
D.8 WAMIT Output File – Barge.3
  0.125664E+03  ‐0.180000E+03       1  1.983066E+00  ‐9.000000E+01  ‐6.338097E ‐08 ‐1.983066E+00  
  0.125664E+03  ‐0.180000E+03       2  4.825996E ‐08 ‐9.000000E+01  ‐1.542444E ‐15 ‐4.825996E ‐08 
  0.125664E+03  ‐0.180000E+03       3  1.591020E+03   2.962686E ‐03  1.591020E+03   8.226946E ‐02 
  0.125664E+03  ‐0.180000E+03       4  1.325606E ‐06  9.000000E+01   4.236804E ‐14  1.325606E ‐06 
  0.125664E+03  ‐0.180000E+03       5  5.447115E+01  ‐9.000000E+01  ‐1.740960E ‐06 ‐5.447115E+01  
  0.125664E+03  ‐0.180000E+03       6  5.515950E ‐15  9.000000E+01   5.515950E ‐15  4.165130E ‐24 
  0.125664E+03  ‐0.170000E+03       1  1.952940E+00  ‐9.000000E+01  ‐6.241811E ‐08 ‐1.952940E+00  
  0.125664E+03  ‐0.170000E+03       2  3.443574E ‐01 ‐9.000000E+01  ‐1.100605E ‐08 ‐3.443574E ‐01 
  0.125664E+03  ‐0.170000E+03       3  1.591020E+03   2.962686E ‐03  1.591020E+03   8.226946E ‐02 
  0.125664E+03  ‐0.170000E+03       4  9.458789E+00   9.000000E+01   3.023152E ‐07  9.458789E+00  
188

0.125664E+03  ‐0.170000E+03       5  5.364359E+01  ‐9.000000E+01  ‐1.714512E ‐06 ‐5.364359E+01  
  0.125664E+03  ‐0.170000E+03       6  4.453025E ‐08  3.766301E ‐08  4.453025E ‐08  2.927167E ‐17 
  0.125664E+03  ‐0.160000E+03       1  1.863475E+00  ‐9.000000E+01  ‐5.955869E ‐08 ‐1.863475E+00  
  0.125664E+03  ‐0.160000E+03       2  6.782514E ‐01 ‐9.000000E+01  ‐2.167768E ‐08 ‐6.782514E ‐01 
  0.125664E+03  ‐0.160000E+03       3  1.591020E+03   2.962687E ‐03  1.591020E+03   8.226947E ‐02 
  0.125664E+03  ‐0.160000E+03       4  1.863024E+01   9.000000E+01   5.954440E ‐07  1.863024E+01  
  0.125664E+03  ‐0.160000E+03       5  5.118615E+01  ‐9.000000E+01  ‐1.635966E ‐06 ‐5.118615E+01  
  0.125664E+03  ‐0.160000E+03       6  6.214594E ‐08  5.072097E ‐08  6.214594E ‐08  5.501456E ‐17 
  0.125664E+03  ‐0.150000E+03       1  1.717387E+00  ‐9.000000E+01  ‐5.488958E ‐08 ‐1.717387E+00  
  0.125664E+03  ‐0.150000E+03       2  9.915367E ‐01 ‐9.000000E+01  ‐3.169064E ‐08 ‐9.915367E ‐01 
  0.125664E+03  ‐0.150000E+03       3  1.591020E+03   2.962686E ‐03  1.591020E+03   8.226946E ‐02 
  0.125664E+03  ‐0.150000E+03       4  2.723551E+01   9.000000E+01   8.704816E ‐07  2.723551E+01  
  0.125664E+03  ‐0.150000E+03       5  4.717344E+01  ‐9.000000E+01  ‐1.507716E ‐06 ‐4.717344E+01  
  0.125664E+03  ‐0.150000E+03       6  6.074003E ‐08  6.990674E ‐08  6.074003E ‐08  7.410908E ‐17 
  0.125664E+03  ‐0.140000E+03       1  1.519122E+00  ‐9.000000E+01  ‐4.855279E ‐08 ‐1.519122E+00  
  0.125664E+03  ‐0.140000E+03       2  1.274695E+00  ‐9.000000E+01  ‐4.074073E ‐08 ‐1.274695E+00  
  0.125664E+03  ‐0.140000E+03       3  1.591020E+03   2.962686E ‐03  1.591020E+03   8.226946E ‐02 
  0.125664E+03  ‐0.140000E+03       4  3.501334E+01   9.000000E+01   1.119071E ‐06  3.501334E+01  
  0.125664E+03  ‐0.140000E+03       5  4.172728E+01  ‐9.000000E+01  ‐1.333655E ‐06 ‐4.172728E+01  
  0.125664E+03  ‐0.140000E+03       6  3.637167E ‐08  1.327815E ‐07  3.637167E ‐08  8.429042E ‐17 
  0.125664E+03  ‐0.130000E+03       1  1.274693E+00  ‐9.000000E+01  ‐4.074061E ‐08 ‐1.274693E+00  
  0.125664E+03  ‐0.130000E+03       2  1.519122E+00  ‐9.000000E+01  ‐4.855287E ‐08 ‐1.519122E+00  
  0.125664E+03  ‐0.130000E+03       3  1.591020E+03   2.962686E ‐03  1.591020E+03   8.226947E ‐02 
  0.125664E+03  ‐0.130000E+03       4  4.172725E+01   9.000000E+01   1.333656E ‐06  4.172725E+01  
  0.125664E+03  ‐0.130000E+03       5  3.501333E+01  ‐9.000000E+01  ‐1.119070E ‐06 ‐3.501333E+01  
  0.125664E+03  ‐0.130000E+03       6  9.002664E ‐09  5.364467E ‐07  9.002664E ‐09  8.428979E ‐17 
  0.125664E+03  ‐0.120000E+03       1  9.915339E ‐01 ‐9.000000E+01  ‐3.169052E ‐08 ‐9.915339E ‐01 
  0.125664E+03  ‐0.120000E+03       2  1.717391E+00  ‐9.000000E+01  ‐5.488981E ‐08 ‐1.717391E+00  
  0.125664E+03  ‐0.120000E+03       3  1.591020E+03   2.962686E ‐03  1.591020E+03   8.226947E ‐02 
  0.125664E+03  ‐0.120000E+03       4  4.717342E+01   9.000000E+01   1.507717E ‐06  4.717342E+01  
  0.125664E+03  ‐0.120000E+03       5  2.723554E+01  ‐9.000000E+01  ‐8.704814E ‐07 ‐2.723554E+01  
  0.125664E+03  ‐0.120000E+03       6  1.997914E ‐08  1.800000E+02  ‐1.997914E ‐08  7.410738E ‐17 
  0.125664E+03  ‐0.110000E+03       1  6.782510E ‐01 ‐9.000000E+01  ‐2.167763E ‐08 ‐6.782510E ‐01 
  0.125664E+03  ‐0.110000E+03       2  1.863477E+00  ‐9.000000E+01  ‐5.955889E ‐08 ‐1.863477E+00  
  0.125664E+03  ‐0.110000E+03       3  1.591020E+03   2.962686E ‐03  1.591020E+03   8.226948E ‐02 
  0.125664E+03  ‐0.110000E+03       4  5.118610E+01   9.000000E+01   1.635968E ‐06  5.118610E+01  
  0.125664E+03  ‐0.110000E+03       5  1.863021E+01  ‐9.000000E+01  ‐5.954436E ‐07 ‐1.863021E+01  
  0.125664E+03  ‐0.110000E+03       6  1.964059E ‐08  1.800000E+02  ‐1.964059E ‐08  5.501368E ‐17 
  0.125664E+03  ‐0.100000E+03       1  3.443568E ‐01 ‐9.000000E+01  ‐1.100603E ‐08 ‐3.443568E ‐01 
  0.125664E+03  ‐0.100000E+03       2  1.952945E+00  ‐9.000000E+01  ‐6.241831E ‐08 ‐1.952945E+00  
  0.125664E+03  ‐0.100000E+03       3  1.591021E+03   2.962685E ‐03  1.591021E+03   8.226947E ‐02 
  0.125664E+03  ‐0.100000E+03       4  5.364361E+01   9.000000E+01   1.714512E ‐06  5.364361E+01  
  0.125664E+03  ‐0.100000E+03       5  9.458813E+00  ‐9.000000E+01  ‐3.023147E ‐07 ‐9.458813E+00  
  0.125664E+03  ‐0.100000E+03       6  1.732498E ‐08  1.800000E+02  ‐1.732498E ‐08  2.927118E ‐17 
  0.125664E+03  ‐0.900000E+02       1  2.412994E ‐08  9.000000E+01   7.712198E ‐16  2.412994E ‐08 
  0.125664E+03  ‐0.900000E+02       2  1.983073E+00  ‐9.000000E+01  ‐6.338124E ‐08 ‐1.983073E+00  
  0.125664E+03  ‐0.900000E+02       3  1.591021E+03   2.962686E ‐03  1.591021E+03   8.226948E ‐02 
  0.125664E+03  ‐0.900000E+02       4  5.447108E+01   9.000000E+01   1.740961E ‐06  5.447108E+01  
  0.125664E+03  ‐0.900000E+02       5  6.628035E ‐07  9.000000E+01   2.118402E ‐14  6.628035E ‐07 
  0.125664E+03  ‐0.900000E+02       6  1.249348E ‐15 ‐9.000000E+01   1.249348E ‐15 ‐2.082531E ‐24 
  0.125664E+03  ‐0.800000E+02       1  3.443569E ‐01  9.000000E+01   1.100603E ‐08  3.443569E ‐01 
  0.125664E+03  ‐0.800000E+02       2  1.952945E+00  ‐9.000000E+01  ‐6.241831E ‐08 ‐1.952945E+00  
  0.125664E+03  ‐0.800000E+02       3  1.591021E+03   2.962685E ‐03  1.591021E+03   8.226947E ‐02 
  0.125664E+03  ‐0.800000E+02       4  5.364361E+01   9.000000E+01   1.714512E ‐06  5.364361E+01  
  0.125664E+03  ‐0.800000E+02       5  9.458814E+00   9.000000E+01   3.023147E ‐07  9.458814E+00  
  0.125664E+03  ‐0.800000E+02       6  1.799070E ‐08 ‐9.322196E ‐08  1.799070E ‐08 ‐2.927141E ‐17 
  0.125664E+03  ‐0.700000E+02       1  6.782510E ‐01  9.000000E+01   2.167763E ‐08  6.782510E ‐01 
  0.125664E+03  ‐0.700000E+02       2  1.863477E+00  ‐9.000000E+01  ‐5.955889E ‐08 ‐1.863477E+00  
  0.125664E+03  ‐0.700000E+02       3  1.591020E+03   2.962686E ‐03  1.591020E+03   8.226948E ‐02 
  0.125664E+03  ‐0.700000E+02       4  5.118610E+01   9.000000E+01   1.635968E ‐06  5.118610E+01  
  0.125664E+03  ‐0.700000E+02       5  1.863021E+01   9.000000E+01   5.954436E ‐07  1.863021E+01  
  0.125664E+03  ‐0.700000E+02       6  1.993885E ‐08 ‐1.580865E ‐07  1.993885E ‐08 ‐5.501388E ‐17 
  0.125664E+03  ‐0.600000E+02       1  9.915339E ‐01  9.000000E+01   3.169052E ‐08  9.915339E ‐01 
  0.125664E+03  ‐0.600000E+02       2  1.717391E+00  ‐9.000000E+01  ‐5.488981E ‐08 ‐1.717391E+00  
  0.125664E+03  ‐0.600000E+02       3  1.591020E+03   2.962686E ‐03  1.591020E+03   8.226947E ‐02 
  0.125664E+03  ‐0.600000E+02       4  4.717342E+01   9.000000E+01   1.507717E ‐06  4.717342E+01  
  0.125664E+03  ‐0.600000E+02       5  2.723554E+01   9.000000E+01   8.704814E ‐07  2.723554E+01  
  0.125664E+03  ‐0.600000E+02       6  1.997914E ‐08 ‐2.125237E ‐07  1.997914E ‐08 ‐7.410738E ‐17 
  0.125664E+03  ‐0.500000E+02       1  1.274693E+00   9.000000E+01   4.074062E ‐08  1.274693E+00  
  0.125664E+03  ‐0.500000E+02       2  1.519122E+00  ‐9.000000E+01  ‐4.855287E ‐08 ‐1.519122E+00  
  0.125664E+03  ‐0.500000E+02       3  1.591020E+03   2.962686E ‐03  1.591020E+03   8.226947E ‐02 
  0.125664E+03  ‐0.500000E+02       4  4.172725E+01   9.000000E+01   1.333656E ‐06  4.172725E+01  
  0.125664E+03  ‐0.500000E+02       5  3.501334E+01   9.000000E+01   1.119070E ‐06  3.501334E+01  
  0.125664E+03  ‐0.500000E+02       6  4.064337E ‐09 ‐1.800000E+02  ‐4.064337E ‐09 ‐8.428993E ‐17 
  0.125664E+03  ‐0.400000E+02       1  1.519122E+00   9.000000E+01   4.855279E ‐08  1.519122E+00  
  0.125664E+03  ‐0.400000E+02       2  1.274695E+00  ‐9.000000E+01  ‐4.074073E ‐08 ‐1.274695E+00  
  0.125664E+03  ‐0.400000E+02       3  1.591020E+03   2.962686E ‐03  1.591020E+03   8.226946E ‐02 
  0.125664E+03  ‐0.400000E+02       4  3.501334E+01   9.000000E+01   1.119071E ‐06  3.501334E+01  
  0.125664E+03  ‐0.400000E+02       5  4.172728E+01   9.000000E+01   1.333655E ‐06  4.172728E+01  
  0.125664E+03  ‐0.400000E+02       6  3.637167E ‐08 ‐1.800000E+02  ‐3.637167E ‐08 ‐8.429042E ‐17 
  0.125664E+03  ‐0.300000E+02       1  1.717387E+00   9.000000E+01   5.488958E ‐08  1.717387E+00  
  0.125664E+03  ‐0.300000E+02       2  9.915367E ‐01 ‐9.000000E+01  ‐3.169064E ‐08 ‐9.915367E ‐01 
  0.125664E+03  ‐0.300000E+02       3  1.591020E+03   2.962686E ‐03  1.591020E+03   8.226946E ‐02 
  0.125664E+03  ‐0.300000E+02       4  2.723551E+01   9.000000E+01   8.704816E ‐07  2.723551E+01  
189

0.125664E+03  ‐0.300000E+02       5  4.717344E+01   9.000000E+01   1.507716E ‐06  4.717344E+01  
  0.125664E+03  ‐0.300000E+02       6  6.074003E ‐08 ‐1.800000E+02  ‐6.074003E ‐08 ‐7.410908E ‐17 
  0.125664E+03  ‐0.200000E+02       1  1.863475E+00   9.000000E+01   5.955869E ‐08  1.863475E+00  
  0.125664E+03  ‐0.200000E+02       2  6.782514E ‐01 ‐9.000000E+01  ‐2.167768E ‐08 ‐6.782514E ‐01 
  0.125664E+03  ‐0.200000E+02       3  1.591020E+03   2.962687E ‐03  1.591020E+03   8.226947E ‐02 
  0.125664E+03  ‐0.200000E+02       4  1.863024E+01   9.000000E+01   5.954440E ‐07  1.863024E+01  
  0.125664E+03  ‐0.200000E+02       5  5.118615E+01   9.000000E+01   1.635966E ‐06  5.118615E+01  
  0.125664E+03  ‐0.200000E+02       6  6.214594E ‐08 ‐1.800000E+02  ‐6.214594E ‐08 ‐5.501456E ‐17 
  0.125664E+03  ‐0.100000E+02       1  1.952940E+00   9.000000E+01   6.241811E ‐08  1.952940E+00  
  0.125664E+03  ‐0.100000E+02       2  3.443574E ‐01 ‐9.000000E+01  ‐1.100605E ‐08 ‐3.443574E ‐01 
  0.125664E+03  ‐0.100000E+02       3  1.591020E+03   2.962686E ‐03  1.591020E+03   8.226946E ‐02 
  0.125664E+03  ‐0.100000E+02       4  9.458788E+00   9.000000E+01   3.023151E ‐07  9.458788E+00  
  0.125664E+03  ‐0.100000E+02       5  5.364359E+01   9.000000E+01   1.714512E ‐06  5.364359E+01  
  0.125664E+03  ‐0.100000E+02       6  4.114693E ‐08 ‐1.800000E+02  ‐4.114693E ‐08 ‐2.927184E ‐17 
  0.125664E+03   0.000000E+00       1  1.983066E+00   9.000000E+01   6.338097E ‐08  1.983066E+00  
  0.125664E+03   0.000000E+00       2  0.000000E+00   9.000000E+01   0.000000E+00   0.000000E+00  
  0.125664E+03   0.000000E+00       3  1.591020E+03   2.962686E ‐03  1.591020E+03   8.226946E ‐02 
  0.125664E+03   0.000000E+00       4  0.000000E+00   9.000000E+01   0.000000E+00   0.000000E+00  
  0.125664E+03   0.000000E+00       5  5.447115E+01   9.000000E+01   1.740960E ‐06  5.447115E+01  
  0.125664E+03   0.000000E+00       6  0.000000E+00   9.000000E+01   0.000000E+00   0.000000E+00  
  0.125664E+03   0.100000E+02       1  1.952940E+00   9.000000E+01   6.241811E ‐08  1.952940E+00  
  0.125664E+03   0.100000E+02       2  3.443574E ‐01  9.000000E+01   1.100605E ‐08  3.443574E ‐01 
  0.125664E+03   0.100000E+02       3  1.591020E+03   2.962686E ‐03  1.591020E+03   8.226946E ‐02 
  0.125664E+03   0.100000E+02       4  9.458788E+00  ‐9.000000E+01  ‐3.023151E ‐07 ‐9.458788E+00  
  0.125664E+03   0.100000E+02       5  5.364359E+01   9.000000E+01   1.714512E ‐06  5.364359E+01  
  0.125664E+03   0.100000E+02       6  4.114693E ‐08  4.076011E ‐08  4.114693E ‐08  2.927184E ‐17 
  0.125664E+03   0.200000E+02       1  1.863475E+00   9.000000E+01   5.955869E ‐08  1.863475E+00  
  0.125664E+03   0.200000E+02       2  6.782514E ‐01  9.000000E+01   2.167768E ‐08  6.782514E ‐01 
  0.125664E+03   0.200000E+02       3  1.591020E+03   2.962687E ‐03  1.591020E+03   8.226947E ‐02 
  0.125664E+03   0.200000E+02       4  1.863024E+01  ‐9.000000E+01  ‐5.954440E ‐07 ‐1.863024E+01  
  0.125664E+03   0.200000E+02       5  5.118615E+01   9.000000E+01   1.635966E ‐06  5.118615E+01  
  0.125664E+03   0.200000E+02       6  6.214594E ‐08  5.072097E ‐08  6.214594E ‐08  5.501456E ‐17 
  0.125664E+03   0.300000E+02       1  1.717387E+00   9.000000E+01   5.488958E ‐08  1.717387E+00  
  0.125664E+03   0.300000E+02       2  9.915367E ‐01  9.000000E+01   3.169064E ‐08  9.915367E ‐01 
  0.125664E+03   0.300000E+02       3  1.591020E+03   2.962686E ‐03  1.591020E+03   8.226946E ‐02 
  0.125664E+03   0.300000E+02       4  2.723551E+01  ‐9.000000E+01  ‐8.704816E ‐07 ‐2.723551E+01  
  0.125664E+03   0.300000E+02       5  4.717344E+01   9.000000E+01   1.507716E ‐06  4.717344E+01  
  0.125664E+03   0.300000E+02       6  6.074003E ‐08  6.990674E ‐08  6.074003E ‐08  7.410908E ‐17 
  0.125664E+03   0.400000E+02       1  1.519122E+00   9.000000E+01   4.855279E ‐08  1.519122E+00  
  0.125664E+03   0.400000E+02       2  1.274695E+00   9.000000E+01   4.074073E ‐08  1.274695E+00  
  0.125664E+03   0.400000E+02       3  1.591020E+03   2.962686E ‐03  1.591020E+03   8.226946E ‐02 
  0.125664E+03   0.400000E+02       4  3.501334E+01  ‐9.000000E+01  ‐1.119071E ‐06 ‐3.501334E+01  
  0.125664E+03   0.400000E+02       5  4.172728E+01   9.000000E+01   1.333655E ‐06  4.172728E+01  
  0.125664E+03   0.400000E+02       6  3.637167E ‐08  1.327815E ‐07  3.637167E ‐08  8.429042E ‐17 
  0.125664E+03   0.500000E+02       1  1.274693E+00   9.000000E+01   4.074062E ‐08  1.274693E+00  
  0.125664E+03   0.500000E+02       2  1.519122E+00   9.000000E+01   4.855287E ‐08  1.519122E+00  
  0.125664E+03   0.500000E+02       3  1.591020E+03   2.962686E ‐03  1.591020E+03   8.226947E ‐02 
  0.125664E+03   0.500000E+02       4  4.172725E+01  ‐9.000000E+01  ‐1.333656E ‐06 ‐4.172725E+01  
  0.125664E+03   0.500000E+02       5  3.501334E+01   9.000000E+01   1.119070E ‐06  3.501334E+01  
  0.125664E+03   0.500000E+02       6  4.064337E ‐09  1.188252E ‐06  4.064337E ‐09  8.428993E ‐17 
  0.125664E+03   0.600000E+02       1  9.915339E ‐01  9.000000E+01   3.169052E ‐08  9.915339E ‐01 
  0.125664E+03   0.600000E+02       2  1.717391E+00   9.000000E+01   5.488981E ‐08  1.717391E+00  
  0.125664E+03   0.600000E+02       3  1.591020E+03   2.962686E ‐03  1.591020E+03   8.226947E ‐02 
  0.125664E+03   0.600000E+02       4  4.717342E+01  ‐9.000000E+01  ‐1.507717E ‐06 ‐4.717342E+01  
  0.125664E+03   0.600000E+02       5  2.723554E+01   9.000000E+01   8.704814E ‐07  2.723554E+01  
  0.125664E+03   0.600000E+02       6  1.997914E ‐08  1.800000E+02  ‐1.997914E ‐08  7.410738E ‐17 
  0.125664E+03   0.700000E+02       1  6.782510E ‐01  9.000000E+01   2.167763E ‐08  6.782510E ‐01 
  0.125664E+03   0.700000E+02       2  1.863477E+00   9.000000E+01   5.955889E ‐08  1.863477E+00  
  0.125664E+03   0.700000E+02       3  1.591020E+03   2.962686E ‐03  1.591020E+03   8.226948E ‐02 
  0.125664E+03   0.700000E+02       4  5.118610E+01  ‐9.000000E+01  ‐1.635968E ‐06 ‐5.118610E+01  
  0.125664E+03   0.700000E+02       5  1.863021E+01   9.000000E+01   5.954436E ‐07  1.863021E+01  
  0.125664E+03   0.700000E+02       6  1.993885E ‐08  1.800000E+02  ‐1.993885E ‐08  5.501388E ‐17 
  0.125664E+03   0.800000E+02       1  3.443569E ‐01  9.000000E+01   1.100603E ‐08  3.443569E ‐01 
  0.125664E+03   0.800000E+02       2  1.952945E+00   9.000000E+01   6.241831E ‐08  1.952945E+00  
  0.125664E+03   0.800000E+02       3  1.591021E+03   2.962685E ‐03  1.591021E+03   8.226947E ‐02 
  0.125664E+03   0.800000E+02       4  5.364361E+01  ‐9.000000E+01  ‐1.714512E ‐06 ‐5.364361E+01  
  0.125664E+03   0.800000E+02       5  9.458814E+00   9.000000E+01   3.023147E ‐07  9.458814E+00  
  0.125664E+03   0.800000E+02       6  1.799070E ‐08  1.800000E+02  ‐1.799070E ‐08  2.927141E ‐17 
  0.125664E+03   0.900000E+02       1  2.412994E ‐08  9.000000E+01   7.712198E ‐16  2.412994E ‐08 
  0.125664E+03   0.900000E+02       2  1.983073E+00   9.000000E+01   6.338124E ‐08  1.983073E+00  
  0.125664E+03   0.900000E+02       3  1.591021E+03   2.962686E ‐03  1.591021E+03   8.226948E ‐02 
  0.125664E+03   0.900000E+02       4  5.447108E+01  ‐9.000000E+01  ‐1.740961E ‐06 ‐5.447108E+01  
  0.125664E+03   0.900000E+02       5  6.628035E ‐07  9.000000E+01   2.118402E ‐14  6.628035E ‐07 
  0.125664E+03   0.900000E+02       6  1.249348E ‐15  9.000000E+01  ‐1.249348E ‐15  2.082531E ‐24 
  0.125664E+03   0.100000E+03       1  3.443568E ‐01 ‐9.000000E+01  ‐1.100603E ‐08 ‐3.443568E ‐01 
  0.125664E+03   0.100000E+03       2  1.952945E+00   9.000000E+01   6.241831E ‐08  1.952945E+00  
  0.125664E+03   0.100000E+03       3  1.591021E+03   2.962685E ‐03  1.591021E+03   8.226947E ‐02 
  0.125664E+03   0.100000E+03       4  5.364361E+01  ‐9.000000E+01  ‐1.714512E ‐06 ‐5.364361E+01  
  0.125664E+03   0.100000E+03       5  9.458813E+00  ‐9.000000E+01  ‐3.023147E ‐07 ‐9.458813E+00  
  0.125664E+03   0.100000E+03       6  1.732498E ‐08 ‐9.680328E ‐08  1.732498E ‐08 ‐2.927118E ‐17 
  0.125664E+03   0.110000E+03       1  6.782510E ‐01 ‐9.000000E+01  ‐2.167763E ‐08 ‐6.782510E ‐01 
  0.125664E+03   0.110000E+03       2  1.863477E+00   9.000000E+01   5.955889E ‐08  1.863477E+00  
  0.125664E+03   0.110000E+03       3  1.591020E+03   2.962686E ‐03  1.591020E+03   8.226948E ‐02 
  0.125664E+03   0.110000E+03       4  5.118610E+01  ‐9.000000E+01  ‐1.635968E ‐06 ‐5.118610E+01  
190

0.125664E+03   0.110000E+03       5  1.863021E+01  ‐9.000000E+01  ‐5.954436E ‐07 ‐1.863021E+01  
  0.125664E+03   0.110000E+03       6  1.964059E ‐08 ‐1.604866E ‐07  1.964059E ‐08 ‐5.501368E ‐17 
  0.125664E+03   0.120000E+03       1  9.915339E ‐01 ‐9.000000E+01  ‐3.169052E ‐08 ‐9.915339E ‐01 
  0.125664E+03   0.120000E+03       2  1.717391E+00   9.000000E+01   5.488981E ‐08  1.717391E+00  
  0.125664E+03   0.120000E+03       3  1.591020E+03   2.962686E ‐03  1.591020E+03   8.226947E ‐02 
  0.125664E+03   0.120000E+03       4  4.717342E+01  ‐9.000000E+01  ‐1.507717E ‐06 ‐4.717342E+01  
  0.125664E+03   0.120000E+03       5  2.723554E+01  ‐9.000000E+01  ‐8.704814E ‐07 ‐2.723554E+01  
  0.125664E+03   0.120000E+03       6  1.997914E ‐08 ‐2.125237E ‐07  1.997914E ‐08 ‐7.410738E ‐17 
  0.125664E+03   0.130000E+03       1  1.274693E+00  ‐9.000000E+01  ‐4.074061E ‐08 ‐1.274693E+00  
  0.125664E+03   0.130000E+03       2  1.519122E+00   9.000000E+01   4.855287E ‐08  1.519122E+00  
  0.125664E+03   0.130000E+03       3  1.591020E+03   2.962686E ‐03  1.591020E+03   8.226947E ‐02 
  0.125664E+03   0.130000E+03       4  4.172725E+01  ‐9.000000E+01  ‐1.333656E ‐06 ‐4.172725E+01  
  0.125664E+03   0.130000E+03       5  3.501333E+01  ‐9.000000E+01  ‐1.119070E ‐06 ‐3.501333E+01  
  0.125664E+03   0.130000E+03       6  9.002664E ‐09 ‐1.800000E+02  ‐9.002664E ‐09 ‐8.428979E ‐17 
  0.125664E+03   0.140000E+03       1  1.519122E+00  ‐9.000000E+01  ‐4.855279E ‐08 ‐1.519122E+00  
  0.125664E+03   0.140000E+03       2  1.274695E+00   9.000000E+01   4.074073E ‐08  1.274695E+00  
  0.125664E+03   0.140000E+03       3  1.591020E+03   2.962686E ‐03  1.591020E+03   8.226946E ‐02 
  0.125664E+03   0.140000E+03       4  3.501334E+01  ‐9.000000E+01  ‐1.119071E ‐06 ‐3.501334E+01  
  0.125664E+03   0.140000E+03       5  4.172728E+01  ‐9.000000E+01  ‐1.333655E ‐06 ‐4.172728E+01  
  0.125664E+03   0.140000E+03       6  3.637167E ‐08 ‐1.800000E+02  ‐3.637167E ‐08 ‐8.429042E ‐17 
  0.125664E+03   0.150000E+03       1  1.717387E+00  ‐9.000000E+01  ‐5.488958E ‐08 ‐1.717387E+00  
  0.125664E+03   0.150000E+03       2  9.915367E ‐01  9.000000E+01   3.169064E ‐08  9.915367E ‐01 
  0.125664E+03   0.150000E+03       3  1.591020E+03   2.962686E ‐03  1.591020E+03   8.226946E ‐02 
  0.125664E+03   0.150000E+03       4  2.723551E+01  ‐9.000000E+01  ‐8.704816E ‐07 ‐2.723551E+01  
  0.125664E+03   0.150000E+03       5  4.717344E+01  ‐9.000000E+01  ‐1.507716E ‐06 ‐4.717344E+01  
  0.125664E+03   0.150000E+03       6  6.074003E ‐08 ‐1.800000E+02  ‐6.074003E ‐08 ‐7.410908E ‐17 
  0.125664E+03   0.160000E+03       1  1.863475E+00  ‐9.000000E+01  ‐5.955869E ‐08 ‐1.863475E+00  
  0.125664E+03   0.160000E+03       2  6.782514E ‐01  9.000000E+01   2.167768E ‐08  6.782514E ‐01 
  0.125664E+03   0.160000E+03       3  1.591020E+03   2.962687E ‐03  1.591020E+03   8.226947E ‐02 
  0.125664E+03   0.160000E+03       4  1.863024E+01  ‐9.000000E+01  ‐5.954440E ‐07 ‐1.863024E+01  
  0.125664E+03   0.160000E+03       5  5.118615E+01  ‐9.000000E+01  ‐1.635966E ‐06 ‐5.118615E+01  
  0.125664E+03   0.160000E+03       6  6.214594E ‐08 ‐1.800000E+02  ‐6.214594E ‐08 ‐5.501456E ‐17 
  0.125664E+03   0.170000E+03       1  1.952940E+00  ‐9.000000E+01  ‐6.241811E ‐08 ‐1.952940E+00  
  0.125664E+03   0.170000E+03       2  3.443574E ‐01  9.000000E+01   1.100605E ‐08  3.443574E ‐01 
  0.125664E+03   0.170000E+03       3  1.591020E+03   2.962686E ‐03  1.591020E+03   8.226946E ‐02 
  0.125664E+03   0.170000E+03       4  9.458789E+00  ‐9.000000E+01  ‐3.023152E ‐07 ‐9.458789E+00  
  0.125664E+03   0.170000E+03       5  5.364359E+01  ‐9.000000E+01  ‐1.714512E ‐06 ‐5.364359E+01  
  0.125664E+03   0.170000E+03       6  4.453025E ‐08 ‐1.800000E+02  ‐4.453025E ‐08 ‐2.927167E ‐17 
  0.125664E+03   0.180000E+03       1  1.983066E+00  ‐9.000000E+01  ‐6.338097E ‐08 ‐1.983066E+00  
  0.125664E+03   0.180000E+03       2  4.825996E ‐08  9.000000E+01   1.542444E ‐15  4.825996E ‐08 
  0.125664E+03   0.180000E+03       3  1.591020E+03   2.962686E ‐03  1.591020E+03   8.226946E ‐02 
  0.125664E+03   0.180000E+03       4  1.325606E ‐06 ‐9.000000E+01  ‐4.236804E ‐14 ‐1.325606E ‐06 
  0.125664E+03   0.180000E+03       5  5.447115E+01  ‐9.000000E+01  ‐1.740960E ‐06 ‐5.447115E+01  
  0.125664E+03   0.180000E+03       6  5.515950E ‐15 ‐9.000000E+01  ‐5.515950E ‐15 ‐4.165130E ‐24 
  0.628319E+02  ‐0.180000E+03       1  7.915568E+00  ‐9.000011E+01  ‐1.576742E ‐05 ‐7.915568E+00  
  0.628319E+02  ‐0.180000E+03       2  1.926374E ‐07 ‐9.000000E+01  ‐3.837255E ‐13 ‐1.926374E ‐07 
  0.628319E+02  ‐0.180000E+03       3  1.563453E+03   4.658011E ‐02  1.563452E+03   1.271050E+00  
  0.628319E+02  ‐0.180000E+03       4  5.262239E ‐06  8.999989E+01   1.048258E ‐11  5.262239E ‐06 
  0.628319E+02  ‐0.180000E+03       5  2.162391E+02  ‐9.000011E+01  ‐4.307330E ‐04 ‐2.162391E+02  
  0.628319E+02  ‐0.180000E+03       6  1.158811E ‐12  9.000000E+01   1.158811E ‐12  2.892725E ‐23 
  0.628319E+02  ‐0.170000E+03       1  7.795320E+00  ‐9.000011E+01  ‐1.552790E ‐05 ‐7.795320E+00  
  0.628319E+02  ‐0.170000E+03       2  1.374557E+00  ‐9.000011E+01  ‐2.738060E ‐06 ‐1.374557E+00  
  0.628319E+02  ‐0.170000E+03       3  1.563453E+03   4.658012E ‐02  1.563452E+03   1.271050E+00  
  0.628319E+02  ‐0.170000E+03       4  3.754856E+01   8.999989E+01   7.479774E ‐05  3.754856E+01  
  0.628319E+02  ‐0.170000E+03       5  2.129541E+02  ‐9.000011E+01  ‐4.241891E ‐04 ‐2.129541E+02  
  0.628319E+02  ‐0.170000E+03       6  7.781527E ‐06  1.831370E ‐09  7.781527E ‐06  2.487243E ‐16 
  0.628319E+02  ‐0.160000E+03       1  7.438222E+00  ‐9.000011E+01  ‐1.481658E ‐05 ‐7.438222E+00  
  0.628319E+02  ‐0.160000E+03       2  2.707342E+00  ‐9.000011E+01  ‐5.392911E ‐06 ‐2.707342E+00  
  0.628319E+02  ‐0.160000E+03       3  1.563451E+03   4.658017E ‐02  1.563451E+03   1.271050E+00  
  0.628319E+02  ‐0.160000E+03       4  7.395633E+01   8.999989E+01   1.473225E ‐04  7.395633E+01  
  0.628319E+02  ‐0.160000E+03       5  2.031979E+02  ‐9.000011E+01  ‐4.047586E ‐04 ‐2.031979E+02  
  0.628319E+02  ‐0.160000E+03       6  1.178375E ‐05  2.250318E ‐09  1.178375E ‐05  4.628120E ‐16 
  0.628319E+02  ‐0.150000E+03       1  6.855124E+00  ‐9.000011E+01  ‐1.365508E ‐05 ‐6.855124E+00  
  0.628319E+02  ‐0.150000E+03       2  3.957861E+00  ‐9.000011E+01  ‐7.883886E ‐06 ‐3.957861E+00  
  0.628319E+02  ‐0.150000E+03       3  1.563449E+03   4.658022E ‐02  1.563449E+03   1.271050E+00  
  0.628319E+02  ‐0.150000E+03       4  1.081174E+02   8.999989E+01   2.153707E ‐04  1.081174E+02  
  0.628319E+02  ‐0.150000E+03       5  1.872679E+02  ‐9.000011E+01  ‐3.730287E ‐04 ‐1.872679E+02  
  0.628319E+02  ‐0.150000E+03       6  1.025948E ‐05  2.787099E ‐09  1.025948E ‐05  4.990625E ‐16 
  0.628319E+02  ‐0.140000E+03       1  6.063741E+00  ‐9.000011E+01  ‐1.207868E ‐05 ‐6.063741E+00  
  0.628319E+02  ‐0.140000E+03       2  5.088108E+00  ‐9.000011E+01  ‐1.013529E ‐05 ‐5.088108E+00  
  0.628319E+02  ‐0.140000E+03       3  1.563451E+03   4.658015E ‐02  1.563450E+03   1.271049E+00  
  0.628319E+02  ‐0.140000E+03       4  1.389937E+02   8.999989E+01   2.768744E ‐04  1.389937E+02  
  0.628319E+02  ‐0.140000E+03       5  1.656466E+02  ‐9.000011E+01  ‐3.299649E ‐04 ‐1.656466E+02  
  0.628319E+02  ‐0.140000E+03       6  4.580391E ‐06  8.884777E ‐09  4.580391E ‐06  7.102749E ‐16 
  0.628319E+02  ‐0.130000E+03       1  5.088099E+00  ‐9.000011E+01  ‐1.013527E ‐05 ‐5.088099E+00  
  0.628319E+02  ‐0.130000E+03       2  6.063747E+00  ‐9.000011E+01  ‐1.207870E ‐05 ‐6.063747E+00  
  0.628319E+02  ‐0.130000E+03       3  1.563450E+03   4.658020E ‐02  1.563450E+03   1.271050E+00  
  0.628319E+02  ‐0.130000E+03       4  1.656468E+02   8.999989E+01   3.299647E ‐04  1.656468E+02  
  0.628319E+02  ‐0.130000E+03       5  1.389937E+02  ‐9.000011E+01  ‐2.768741E ‐04 ‐1.389937E+02  
  0.628319E+02  ‐0.130000E+03       6  3.366579E ‐06  1.800000E+02  ‐3.366579E ‐06  7.103030E ‐16 
  0.628319E+02  ‐0.120000E+03       1  3.957853E+00  ‐9.000011E+01  ‐7.883853E ‐06 ‐3.957853E+00  
  0.628319E+02  ‐0.120000E+03       2  6.855131E+00  ‐9.000011E+01  ‐1.365513E ‐05 ‐6.855131E+00  
  0.628319E+02  ‐0.120000E+03       3  1.563448E+03   4.658024E ‐02  1.563448E+03   1.271050E+00  
  0.628319E+02  ‐0.120000E+03       4  1.872677E+02   8.999989E+01   3.730291E ‐04  1.872677E+02  
191

0.628319E+02  ‐0.120000E+03       5  1.081174E+02  ‐9.000011E+01  ‐2.153705E ‐04 ‐1.081174E+02  
  0.628319E+02  ‐0.120000E+03       6  9.737923E ‐06  1.800000E+02  ‐9.737923E ‐06  5.062944E ‐16 
  0.628319E+02  ‐0.110000E+03       1  2.707341E+00  ‐9.000011E+01  ‐5.392900E ‐06 ‐2.707341E+00  
  0.628319E+02  ‐0.110000E+03       2  7.438230E+00  ‐9.000011E+01  ‐1.481663E ‐05 ‐7.438230E+00  
  0.628319E+02  ‐0.110000E+03       3  1.563451E+03   4.658015E ‐02  1.563451E+03   1.271050E+00  
  0.628319E+02  ‐0.110000E+03       4  2.031977E+02   8.999989E+01   4.047584E ‐04  2.031977E+02  
  0.628319E+02  ‐0.110000E+03       5  7.395638E+01  ‐9.000011E+01  ‐1.473225E ‐04 ‐7.395638E+01  
  0.628319E+02  ‐0.110000E+03       6  1.101663E ‐05  1.800000E+02  ‐1.101663E ‐05  4.711616E ‐16 
  0.628319E+02  ‐0.100000E+03       1  1.374556E+00  ‐9.000011E+01  ‐2.738055E ‐06 ‐1.374556E+00  
  0.628319E+02  ‐0.100000E+03       2  7.795338E+00  ‐9.000011E+01  ‐1.552795E ‐05 ‐7.795338E+00  
  0.628319E+02  ‐0.100000E+03       3  1.563453E+03   4.658010E ‐02  1.563453E+03   1.271050E+00  
  0.628319E+02  ‐0.100000E+03       4  2.129536E+02   8.999989E+01   4.241898E ‐04  2.129536E+02  
  0.628319E+02  ‐0.100000E+03       5  3.754859E+01  ‐9.000011E+01  ‐7.479772E ‐05 ‐3.754859E+01  
  0.628319E+02  ‐0.100000E+03       6  7.200288E ‐06  1.800000E+02  ‐7.200288E ‐06  2.515480E ‐16 
  0.628319E+02  ‐0.900000E+02       1  9.631858E ‐08  9.000000E+01   1.918623E ‐13  9.631858E ‐08 
  0.628319E+02  ‐0.900000E+02       2  7.915587E+00  ‐9.000011E+01  ‐1.576749E ‐05 ‐7.915587E+00  
  0.628319E+02  ‐0.900000E+02       3  1.563453E+03   4.658009E ‐02  1.563453E+03   1.271050E+00  
  0.628319E+02  ‐0.900000E+02       4  2.162391E+02   8.999989E+01   4.307332E ‐04  2.162391E+02  
  0.628319E+02  ‐0.900000E+02       5  2.631120E ‐06  8.999989E+01   5.241285E ‐12  2.631120E ‐06 
  0.628319E+02  ‐0.900000E+02       6  5.470291E ‐13 ‐9.000000E+01   5.470291E ‐13 ‐1.498696E ‐23 
  0.628319E+02  ‐0.800000E+02       1  1.374556E+00   8.999989E+01   2.738056E ‐06  1.374556E+00  
  0.628319E+02  ‐0.800000E+02       2  7.795338E+00  ‐9.000011E+01  ‐1.552795E ‐05 ‐7.795338E+00  
  0.628319E+02  ‐0.800000E+02       3  1.563453E+03   4.658010E ‐02  1.563453E+03   1.271050E+00  
  0.628319E+02  ‐0.800000E+02       4  2.129536E+02   8.999989E+01   4.241898E ‐04  2.129536E+02  
  0.628319E+02  ‐0.800000E+02       5  3.754860E+01   8.999989E+01   7.479774E ‐05  3.754860E+01  
  0.628319E+02  ‐0.800000E+02       6  7.190672E ‐06 ‐1.999489E ‐09  7.190672E ‐06 ‐2.509377E ‐16 
  0.628319E+02  ‐0.700000E+02       1  2.707341E+00   8.999989E+01   5.392901E ‐06  2.707341E+00  
  0.628319E+02  ‐0.700000E+02       2  7.438230E+00  ‐9.000011E+01  ‐1.481663E ‐05 ‐7.438230E+00  
  0.628319E+02  ‐0.700000E+02       3  1.563451E+03   4.658015E ‐02  1.563451E+03   1.271050E+00  
  0.628319E+02  ‐0.700000E+02       4  2.031977E+02   8.999989E+01   4.047584E ‐04  2.031977E+02  
  0.628319E+02  ‐0.700000E+02       5  7.395638E+01   8.999989E+01   1.473225E ‐04  7.395638E+01  
  0.628319E+02  ‐0.700000E+02       6  1.094496E ‐05 ‐2.450852E ‐09  1.094496E ‐05 ‐4.681757E ‐16 
  0.628319E+02  ‐0.600000E+02       1  3.957853E+00   8.999989E+01   7.883853E ‐06  3.957853E+00  
  0.628319E+02  ‐0.600000E+02       2  6.855131E+00  ‐9.000011E+01  ‐1.365513E ‐05 ‐6.855131E+00  
  0.628319E+02  ‐0.600000E+02       3  1.563448E+03   4.658024E ‐02  1.563448E+03   1.271050E+00  
  0.628319E+02  ‐0.600000E+02       4  1.872677E+02   8.999989E+01   3.730291E ‐04  1.872677E+02  
  0.628319E+02  ‐0.600000E+02       5  1.081174E+02   8.999989E+01   2.153705E ‐04  1.081174E+02  
  0.628319E+02  ‐0.600000E+02       6  9.737923E ‐06 ‐2.978924E ‐09  9.737923E ‐06 ‐5.062944E ‐16 
  0.628319E+02  ‐0.500000E+02       1  5.088100E+00   8.999989E+01   1.013527E ‐05  5.088100E+00  
  0.628319E+02  ‐0.500000E+02       2  6.063747E+00  ‐9.000011E+01  ‐1.207870E ‐05 ‐6.063747E+00  
  0.628319E+02  ‐0.500000E+02       3  1.563450E+03   4.658020E ‐02  1.563450E+03   1.271050E+00  
  0.628319E+02  ‐0.500000E+02       4  1.656468E+02   8.999989E+01   3.299647E ‐04  1.656468E+02  
  0.628319E+02  ‐0.500000E+02       5  1.389937E+02   8.999989E+01   2.768741E ‐04  1.389937E+02  
  0.628319E+02  ‐0.500000E+02       6  3.283122E ‐06 ‐1.234711E ‐08  3.283122E ‐06 ‐7.075052E ‐16 
  0.628319E+02  ‐0.400000E+02       1  6.063741E+00   8.999989E+01   1.207868E ‐05  6.063741E+00  
  0.628319E+02  ‐0.400000E+02       2  5.088108E+00  ‐9.000011E+01  ‐1.013529E ‐05 ‐5.088108E+00  
  0.628319E+02  ‐0.400000E+02       3  1.563451E+03   4.658015E ‐02  1.563450E+03   1.271049E+00  
  0.628319E+02  ‐0.400000E+02       4  1.389937E+02   8.999989E+01   2.768744E ‐04  1.389937E+02  
  0.628319E+02  ‐0.400000E+02       5  1.656466E+02   8.999989E+01   3.299649E ‐04  1.656466E+02  
  0.628319E+02  ‐0.400000E+02       6  4.580391E ‐06 ‐1.800000E+02  ‐4.580391E ‐06 ‐7.102749E ‐16 
  0.628319E+02  ‐0.300000E+02       1  6.855124E+00   8.999989E+01   1.365508E ‐05  6.855124E+00  
  0.628319E+02  ‐0.300000E+02       2  3.957861E+00  ‐9.000011E+01  ‐7.883886E ‐06 ‐3.957861E+00  
  0.628319E+02  ‐0.300000E+02       3  1.563449E+03   4.658022E ‐02  1.563449E+03   1.271050E+00  
  0.628319E+02  ‐0.300000E+02       4  1.081174E+02   8.999989E+01   2.153707E ‐04  1.081174E+02  
  0.628319E+02  ‐0.300000E+02       5  1.872679E+02   8.999989E+01   3.730287E ‐04  1.872679E+02  
  0.628319E+02  ‐0.300000E+02       6  1.025948E ‐05 ‐1.800000E+02  ‐1.025948E ‐05 ‐4.990625E ‐16 
  0.628319E+02  ‐0.200000E+02       1  7.438222E+00   8.999989E+01   1.481658E ‐05  7.438222E+00  
  0.628319E+02  ‐0.200000E+02       2  2.707342E+00  ‐9.000011E+01  ‐5.392911E ‐06 ‐2.707342E+00  
  0.628319E+02  ‐0.200000E+02       3  1.563451E+03   4.658017E ‐02  1.563451E+03   1.271050E+00  
  0.628319E+02  ‐0.200000E+02       4  7.395633E+01   8.999989E+01   1.473225E ‐04  7.395633E+01  
  0.628319E+02  ‐0.200000E+02       5  2.031979E+02   8.999989E+01   4.047586E ‐04  2.031979E+02  
  0.628319E+02  ‐0.200000E+02       6  1.178375E ‐05 ‐1.800000E+02  ‐1.178375E ‐05 ‐4.628120E ‐16 
  0.628319E+02  ‐0.100000E+02       1  7.795320E+00   8.999989E+01   1.552790E ‐05  7.795320E+00  
  0.628319E+02  ‐0.100000E+02       2  1.374557E+00  ‐9.000011E+01  ‐2.738060E ‐06 ‐1.374557E+00  
  0.628319E+02  ‐0.100000E+02       3  1.563453E+03   4.658012E ‐02  1.563452E+03   1.271050E+00  
  0.628319E+02  ‐0.100000E+02       4  3.754856E+01   8.999989E+01   7.479774E ‐05  3.754856E+01  
  0.628319E+02  ‐0.100000E+02       5  2.129541E+02   8.999989E+01   4.241891E ‐04  2.129541E+02  
  0.628319E+02  ‐0.100000E+02       6  7.794393E ‐06 ‐1.800000E+02  ‐7.794393E ‐06 ‐2.503381E ‐16 
  0.628319E+02   0.000000E+00       1  7.915568E+00   8.999989E+01   1.576742E ‐05  7.915568E+00  
  0.628319E+02   0.000000E+00       2  0.000000E+00   9.000000E+01   0.000000E+00   0.000000E+00  
  0.628319E+02   0.000000E+00       3  1.563453E+03   4.658011E ‐02  1.563452E+03   1.271050E+00  
  0.628319E+02   0.000000E+00       4  0.000000E+00   9.000000E+01   0.000000E+00   0.000000E+00  
  0.628319E+02   0.000000E+00       5  2.162391E+02   8.999989E+01   4.307330E ‐04  2.162391E+02  
  0.628319E+02   0.000000E+00       6  0.000000E+00   9.000000E+01   0.000000E+00   0.000000E+00  
  0.628319E+02   0.100000E+02       1  7.795320E+00   8.999989E+01   1.552790E ‐05  7.795320E+00  
  0.628319E+02   0.100000E+02       2  1.374557E+00   8.999989E+01   2.738060E ‐06  1.374557E+00  
  0.628319E+02   0.100000E+02       3  1.563453E+03   4.658012E ‐02  1.563452E+03   1.271050E+00  
  0.628319E+02   0.100000E+02       4  3.754856E+01  ‐9.000011E+01  ‐7.479774E ‐05 ‐3.754856E+01  
  0.628319E+02   0.100000E+02       5  2.129541E+02   8.999989E+01   4.241891E ‐04  2.129541E+02  
  0.628319E+02   0.100000E+02       6  7.794393E ‐06  1.840210E ‐09  7.794393E ‐06  2.503381E ‐16 
  0.628319E+02   0.200000E+02       1  7.438222E+00   8.999989E+01   1.481658E ‐05  7.438222E+00  
  0.628319E+02   0.200000E+02       2  2.707342E+00   8.999989E+01   5.392911E ‐06  2.707342E+00  
  0.628319E+02   0.200000E+02       3  1.563451E+03   4.658017E ‐02  1.563451E+03   1.271050E+00  
  0.628319E+02   0.200000E+02       4  7.395633E+01  ‐9.000011E+01  ‐1.473225E ‐04 ‐7.395633E+01  
192

0.628319E+02   0.200000E+02       5  2.031979E+02   8.999989E+01   4.047586E ‐04  2.031979E+02  
  0.628319E+02   0.200000E+02       6  1.178375E ‐05  2.250318E ‐09  1.178375E ‐05  4.628120E ‐16 
  0.628319E+02   0.300000E+02       1  6.855124E+00   8.999989E+01   1.365508E ‐05  6.855124E+00  
  0.628319E+02   0.300000E+02       2  3.957861E+00   8.999989E+01   7.883886E ‐06  3.957861E+00  
  0.628319E+02   0.300000E+02       3  1.563449E+03   4.658022E ‐02  1.563449E+03   1.271050E+00  
  0.628319E+02   0.300000E+02       4  1.081174E+02  ‐9.000011E+01  ‐2.153707E ‐04 ‐1.081174E+02  
  0.628319E+02   0.300000E+02       5  1.872679E+02   8.999989E+01   3.730287E ‐04  1.872679E+02  
  0.628319E+02   0.300000E+02       6  1.025948E ‐05  2.787099E ‐09  1.025948E ‐05  4.990625E ‐16 
  0.628319E+02   0.400000E+02       1  6.063741E+00   8.999989E+01   1.207868E ‐05  6.063741E+00  
  0.628319E+02   0.400000E+02       2  5.088108E+00   8.999989E+01   1.013529E ‐05  5.088108E+00  
  0.628319E+02   0.400000E+02       3  1.563451E+03   4.658015E ‐02  1.563450E+03   1.271049E+00  
  0.628319E+02   0.400000E+02       4  1.389937E+02  ‐9.000011E+01  ‐2.768744E ‐04 ‐1.389937E+02  
  0.628319E+02   0.400000E+02       5  1.656466E+02   8.999989E+01   3.299649E ‐04  1.656466E+02  
  0.628319E+02   0.400000E+02       6  4.580391E ‐06  8.884777E ‐09  4.580391E ‐06  7.102749E ‐16 
  0.628319E+02   0.500000E+02       1  5.088100E+00   8.999989E+01   1.013527E ‐05  5.088100E+00  
  0.628319E+02   0.500000E+02       2  6.063747E+00   8.999989E+01   1.207870E ‐05  6.063747E+00  
  0.628319E+02   0.500000E+02       3  1.563450E+03   4.658020E ‐02  1.563450E+03   1.271050E+00  
  0.628319E+02   0.500000E+02       4  1.656468E+02  ‐9.000011E+01  ‐3.299647E ‐04 ‐1.656468E+02  
  0.628319E+02   0.500000E+02       5  1.389937E+02   8.999989E+01   2.768741E ‐04  1.389937E+02  
  0.628319E+02   0.500000E+02       6  3.283122E ‐06  1.800000E+02  ‐3.283122E ‐06  7.075052E ‐16 
  0.628319E+02   0.600000E+02       1  3.957853E+00   8.999989E+01   7.883853E ‐06  3.957853E+00  
  0.628319E+02   0.600000E+02       2  6.855131E+00   8.999989E+01   1.365513E ‐05  6.855131E+00  
  0.628319E+02   0.600000E+02       3  1.563448E+03   4.658024E ‐02  1.563448E+03   1.271050E+00  
  0.628319E+02   0.600000E+02       4  1.872677E+02  ‐9.000011E+01  ‐3.730291E ‐04 ‐1.872677E+02  
  0.628319E+02   0.600000E+02       5  1.081174E+02   8.999989E+01   2.153705E ‐04  1.081174E+02  
  0.628319E+02   0.600000E+02       6  9.737923E ‐06  1.800000E+02  ‐9.737923E ‐06  5.062944E ‐16 
  0.628319E+02   0.700000E+02       1  2.707341E+00   8.999989E+01   5.392901E ‐06  2.707341E+00  
  0.628319E+02   0.700000E+02       2  7.438230E+00   8.999989E+01   1.481663E ‐05  7.438230E+00  
  0.628319E+02   0.700000E+02       3  1.563451E+03   4.658015E ‐02  1.563451E+03   1.271050E+00  
  0.628319E+02   0.700000E+02       4  2.031977E+02  ‐9.000011E+01  ‐4.047584E ‐04 ‐2.031977E+02  
  0.628319E+02   0.700000E+02       5  7.395638E+01   8.999989E+01   1.473225E ‐04  7.395638E+01  
  0.628319E+02   0.700000E+02       6  1.094496E ‐05  1.800000E+02  ‐1.094496E ‐05  4.681757E ‐16 
  0.628319E+02   0.800000E+02       1  1.374556E+00   8.999989E+01   2.738056E ‐06  1.374556E+00  
  0.628319E+02   0.800000E+02       2  7.795338E+00   8.999989E+01   1.552795E ‐05  7.795338E+00  
  0.628319E+02   0.800000E+02       3  1.563453E+03   4.658010E ‐02  1.563453E+03   1.271050E+00  
  0.628319E+02   0.800000E+02       4  2.129536E+02  ‐9.000011E+01  ‐4.241898E ‐04 ‐2.129536E+02  
  0.628319E+02   0.800000E+02       5  3.754860E+01   8.999989E+01   7.479774E ‐05  3.754860E+01  
  0.628319E+02   0.800000E+02       6  7.190672E ‐06  1.800000E+02  ‐7.190672E ‐06  2.509377E ‐16 
  0.628319E+02   0.900000E+02       1  9.631858E ‐08  9.000000E+01   1.918623E ‐13  9.631858E ‐08 
  0.628319E+02   0.900000E+02       2  7.915587E+00   8.999989E+01   1.576749E ‐05  7.915587E+00  
  0.628319E+02   0.900000E+02       3  1.563453E+03   4.658009E ‐02  1.563453E+03   1.271050E+00  
  0.628319E+02   0.900000E+02       4  2.162391E+02  ‐9.000011E+01  ‐4.307332E ‐04 ‐2.162391E+02  
  0.628319E+02   0.900000E+02       5  2.631120E ‐06  8.999989E+01   5.241285E ‐12  2.631120E ‐06 
  0.628319E+02   0.900000E+02       6  5.470291E ‐13  9.000000E+01  ‐5.470291E ‐13  1.498696E ‐23 
  0.628319E+02   0.100000E+03       1  1.374556E+00  ‐9.000011E+01  ‐2.738055E ‐06 ‐1.374556E+00  
  0.628319E+02   0.100000E+03       2  7.795338E+00   8.999989E+01   1.552795E ‐05  7.795338E+00  
  0.628319E+02   0.100000E+03       3  1.563453E+03   4.658010E ‐02  1.563453E+03   1.271050E+00  
  0.628319E+02   0.100000E+03       4  2.129536E+02  ‐9.000011E+01  ‐4.241898E ‐04 ‐2.129536E+02  
  0.628319E+02   0.100000E+03       5  3.754859E+01  ‐9.000011E+01  ‐7.479772E ‐05 ‐3.754859E+01  
  0.628319E+02   0.100000E+03       6  7.200288E ‐06 ‐2.001675E ‐09  7.200288E ‐06 ‐2.515480E ‐16 
  0.628319E+02   0.110000E+03       1  2.707341E+00  ‐9.000011E+01  ‐5.392900E ‐06 ‐2.707341E+00  
  0.628319E+02   0.110000E+03       2  7.438230E+00   8.999989E+01   1.481663E ‐05  7.438230E+00  
  0.628319E+02   0.110000E+03       3  1.563451E+03   4.658015E ‐02  1.563451E+03   1.271050E+00  
  0.628319E+02   0.110000E+03       4  2.031977E+02  ‐9.000011E+01  ‐4.047584E ‐04 ‐2.031977E+02  
  0.628319E+02   0.110000E+03       5  7.395638E+01  ‐9.000011E+01  ‐1.473225E ‐04 ‐7.395638E+01  
  0.628319E+02   0.110000E+03       6  1.101663E ‐05 ‐2.450438E ‐09  1.101663E ‐05 ‐4.711616E ‐16 
  0.628319E+02   0.120000E+03       1  3.957853E+00  ‐9.000011E+01  ‐7.883853E ‐06 ‐3.957853E+00  
  0.628319E+02   0.120000E+03       2  6.855131E+00   8.999989E+01   1.365513E ‐05  6.855131E+00  
  0.628319E+02   0.120000E+03       3  1.563448E+03   4.658024E ‐02  1.563448E+03   1.271050E+00  
  0.628319E+02   0.120000E+03       4  1.872677E+02  ‐9.000011E+01  ‐3.730291E ‐04 ‐1.872677E+02  
  0.628319E+02   0.120000E+03       5  1.081174E+02  ‐9.000011E+01  ‐2.153705E ‐04 ‐1.081174E+02  
  0.628319E+02   0.120000E+03       6  9.737923E ‐06 ‐2.978924E ‐09  9.737923E ‐06 ‐5.062944E ‐16 
  0.628319E+02   0.130000E+03       1  5.088099E+00  ‐9.000011E+01  ‐1.013527E ‐05 ‐5.088099E+00  
  0.628319E+02   0.130000E+03       2  6.063747E+00   8.999989E+01   1.207870E ‐05  6.063747E+00  
  0.628319E+02   0.130000E+03       3  1.563450E+03   4.658020E ‐02  1.563450E+03   1.271050E+00  
  0.628319E+02   0.130000E+03       4  1.656468E+02  ‐9.000011E+01  ‐3.299647E ‐04 ‐1.656468E+02  
  0.628319E+02   0.130000E+03       5  1.389937E+02  ‐9.000011E+01  ‐2.768741E ‐04 ‐1.389937E+02  
  0.628319E+02   0.130000E+03       6  3.366579E ‐06 ‐1.208864E ‐08  3.366579E ‐06 ‐7.103030E ‐16 
  0.628319E+02   0.140000E+03       1  6.063741E+00  ‐9.000011E+01  ‐1.207868E ‐05 ‐6.063741E+00  
  0.628319E+02   0.140000E+03       2  5.088108E+00   8.999989E+01   1.013529E ‐05  5.088108E+00  
  0.628319E+02   0.140000E+03       3  1.563451E+03   4.658015E ‐02  1.563450E+03   1.271049E+00  
  0.628319E+02   0.140000E+03       4  1.389937E+02  ‐9.000011E+01  ‐2.768744E ‐04 ‐1.389937E+02  
  0.628319E+02   0.140000E+03       5  1.656466E+02  ‐9.000011E+01  ‐3.299649E ‐04 ‐1.656466E+02  
  0.628319E+02   0.140000E+03       6  4.580391E ‐06 ‐1.800000E+02  ‐4.580391E ‐06 ‐7.102749E ‐16 
  0.628319E+02   0.150000E+03       1  6.855124E+00  ‐9.000011E+01  ‐1.365508E ‐05 ‐6.855124E+00  
  0.628319E+02   0.150000E+03       2  3.957861E+00   8.999989E+01   7.883886E ‐06  3.957861E+00  
  0.628319E+02   0.150000E+03       3  1.563449E+03   4.658022E ‐02  1.563449E+03   1.271050E+00  
  0.628319E+02   0.150000E+03       4  1.081174E+02  ‐9.000011E+01  ‐2.153707E ‐04 ‐1.081174E+02  
  0.628319E+02   0.150000E+03       5  1.872679E+02  ‐9.000011E+01  ‐3.730287E ‐04 ‐1.872679E+02  
  0.628319E+02   0.150000E+03       6  1.025948E ‐05 ‐1.800000E+02  ‐1.025948E ‐05 ‐4.990625E ‐16 
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0.628319E+02   0.160000E+03       5  2.031979E+02  ‐9.000011E+01  ‐4.047586E ‐04 ‐2.031979E+02  
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  0.628319E+02   0.180000E+03       1  7.915568E+00  ‐9.000011E+01  ‐1.576742E ‐05 ‐7.915568E+00  
  0.628319E+02   0.180000E+03       2  1.926374E ‐07  9.000000E+01   3.837255E ‐13  1.926374E ‐07 
  0.628319E+02   0.180000E+03       3  1.563453E+03   4.658011E ‐02  1.563452E+03   1.271050E+00  
  0.628319E+02   0.180000E+03       4  5.262239E ‐06 ‐9.000011E+01  ‐1.048258E ‐11 ‐5.262239E ‐06 
  0.628319E+02   0.180000E+03       5  2.162391E+02  ‐9.000011E+01  ‐4.307330E ‐04 ‐2.162391E+02  
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  0.125664E+01  ‐0.120000E+03       5  9.214829E ‐01  9.406966E+01  ‐6.539704E ‐02  9.191594E ‐01 
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  0.125664E+01  ‐0.110000E+03       4  2.977684E ‐01  3.155189E+01   2.537483E ‐01  1.558134E ‐01 
  0.125664E+01  ‐0.110000E+03       5  9.130183E ‐01  1.281776E+02  ‐5.643375E ‐01  7.177225E ‐01 
  0.125664E+01  ‐0.110000E+03       6  2.462352E+01   1.382522E+00   2.461636E+01   5.940970E ‐01 
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194

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  0.125664E+01  ‐0.300000E+02       6  1.234953E+01   7.589193E+01   3.010217E+00   1.197704E+01  
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  0.125664E+01  ‐0.200000E+02       3  9.174211E ‐02  5.319652E+01   5.496015E ‐02  7.345745E ‐02 
  0.125664E+01  ‐0.200000E+02       4  9.207801E ‐01 ‐5.153143E+01   5.728037E ‐01 ‐7.209243E ‐01 
  0.125664E+01  ‐0.200000E+02       5  2.876672E ‐01  3.091370E+01   2.468017E ‐01  1.477880E ‐01 
  0.125664E+01  ‐0.200000E+02       6  2.462325E+01   1.380886E+00   2.461610E+01   5.933877E ‐01 
  0.125664E+01  ‐0.100000E+02       1  2.361786E+00  ‐4.219011E+00   2.355386E+00  ‐1.737545E ‐01 
  0.125664E+01  ‐0.100000E+02       2  4.178132E ‐01  1.494453E+02  ‐3.597974E ‐01  2.123997E ‐01 
  0.125664E+01  ‐0.100000E+02       3  3.654533E ‐01  2.633396E+00   3.650674E ‐01  1.679085E ‐02 
  0.125664E+01  ‐0.100000E+02       4  1.113104E+00   9.029066E+01  ‐5.646759E ‐03  1.113090E+00  
  0.125664E+01  ‐0.100000E+02       5  2.462962E+00   9.499172E+00   2.429190E+00   4.064710E ‐01 
  0.125664E+01  ‐0.100000E+02       6  6.406702E+01  ‐8.336032E+01   7.407757E+00  ‐6.363732E+01  
  0.125664E+01   0.000000E+00       1  3.723658E+01   4.667451E+01   2.554958E+01   2.708840E+01  
  0.125664E+01   0.000000E+00       2  0.000000E+00   9.000000E+01   0.000000E+00   0.000000E+00  
  0.125664E+01   0.000000E+00       3  5.366601E+00   4.634993E+01   3.704308E+00   3.883106E+00  
  0.125664E+01   0.000000E+00       4  0.000000E+00   9.000000E+01   0.000000E+00   0.000000E+00  
  0.125664E+01   0.000000E+00       5  3.827606E+01   4.592707E+01   2.662381E+01   2.749963E+01  
  0.125664E+01   0.000000E+00       6  0.000000E+00   9.000000E+01   0.000000E+00   0.000000E+00  
  0.125664E+01   0.100000E+02       1  2.361786E+00  ‐4.219011E+00   2.355386E+00  ‐1.737545E ‐01 
  0.125664E+01   0.100000E+02       2  4.178132E ‐01 ‐3.055469E+01   3.597974E ‐01 ‐2.123997E ‐01 
  0.125664E+01   0.100000E+02       3  3.654533E ‐01  2.633396E+00   3.650674E ‐01  1.679085E ‐02 
  0.125664E+01   0.100000E+02       4  1.113104E+00  ‐8.970934E+01   5.646759E ‐03 ‐1.113090E+00  
  0.125664E+01   0.100000E+02       5  2.462962E+00   9.499172E+00   2.429190E+00   4.064710E ‐01 
  0.125664E+01   0.100000E+02       6  6.406702E+01   9.663969E+01  ‐7.407757E+00   6.363732E+01  
  0.125664E+01   0.200000E+02       1  2.006404E+00   5.394589E+01   1.180867E+00   1.622101E+00  
  0.125664E+01   0.200000E+02       2  4.484448E ‐01  9.896774E+01  ‐6.990276E ‐02  4.429632E ‐01 
  0.125664E+01   0.200000E+02       3  9.174211E ‐02  5.319652E+01   5.496015E ‐02  7.345745E ‐02 
  0.125664E+01   0.200000E+02       4  9.207801E ‐01  1.284686E+02  ‐5.728037E ‐01  7.209243E ‐01 
  0.125664E+01   0.200000E+02       5  2.876672E ‐01  3.091370E+01   2.468017E ‐01  1.477880E ‐01 
  0.125664E+01   0.200000E+02       6  2.462325E+01  ‐1.786191E+02  ‐2.461610E+01  ‐5.933877E ‐01 
  0.125664E+01   0.300000E+02       1  5.178185E ‐01  5.169857E+01   3.209431E ‐01  4.063637E ‐01 
  0.125664E+01   0.300000E+02       2  3.095861E ‐01  9.268608E+01  ‐1.450839E ‐02  3.092460E ‐01 
  0.125664E+01   0.300000E+02       3  4.604926E ‐02 ‐1.596816E+02  ‐4.318395E ‐02 ‐1.599002E ‐02 
  0.125664E+01   0.300000E+02       4  9.021725E ‐01  9.414983E+01  ‐6.528568E ‐02  8.998072E ‐01 
  0.125664E+01   0.300000E+02       5  5.112429E ‐01 ‐1.115042E+02  ‐1.874063E ‐01 ‐4.756556E ‐01 
  0.125664E+01   0.300000E+02       6  1.234953E+01  ‐1.041081E+02  ‐3.010217E+00  ‐1.197704E+01  
  0.125664E+01   0.400000E+02       1  1.203053E+00   8.637856E+01   7.598975E ‐02  1.200650E+00  
  0.125664E+01   0.400000E+02       2  1.029077E+00   8.726032E+01   4.918807E ‐02  1.027901E+00  
  0.125664E+01   0.400000E+02       3  5.575266E ‐02  9.972774E+01  ‐9.420332E ‐03  5.495103E ‐02 
  0.125664E+01   0.400000E+02       4  4.508249E ‐01  1.413024E+02  ‐3.518492E ‐01  2.818602E ‐01 
  0.125664E+01   0.400000E+02       5  4.077001E ‐01 ‐4.692863E+01   2.784220E ‐01 ‐2.978264E ‐01 
  0.125664E+01   0.400000E+02       6  3.266479E ‐01 ‐3.970305E+01   2.513117E ‐01 ‐2.086656E ‐01 
  0.125664E+01   0.500000E+02       1  1.029144E+00   8.725648E+01   4.926003E ‐02  1.027964E+00  
  0.125664E+01   0.500000E+02       2  1.203070E+00   8.637492E+01   7.606713E ‐02  1.200663E+00  
  0.125664E+01   0.500000E+02       3  5.628183E ‐02  9.891718E+01  ‐8.724050E ‐03  5.560157E ‐02 
  0.125664E+01   0.500000E+02       4  4.014029E ‐01  1.361869E+02  ‐2.896531E ‐01  2.778945E ‐01 
  0.125664E+01   0.500000E+02       5  4.588585E ‐01 ‐3.740073E+01   3.645203E ‐01 ‐2.787042E ‐01 
  0.125664E+01   0.500000E+02       6  3.258539E ‐01  1.402543E+02  ‐2.505456E ‐01  2.083450E ‐01 
  0.125664E+01   0.600000E+02       1  3.095530E ‐01  9.267338E+01  ‐1.443828E ‐02  3.092161E ‐01 
  0.125664E+01   0.600000E+02       2  5.177627E ‐01  5.169791E+01   3.209133E ‐01  4.063162E ‐01 
  0.125664E+01   0.600000E+02       3  4.579637E ‐02 ‐1.591669E+02  ‐4.280223E ‐02 ‐1.628732E ‐02 
  0.125664E+01   0.600000E+02       4  5.006751E ‐01  6.879288E+01   1.811145E ‐01  4.667688E ‐01 
  0.125664E+01   0.600000E+02       5  9.214829E ‐01 ‐8.593034E+01   6.539704E ‐02 ‐9.191594E ‐01 
  0.125664E+01   0.600000E+02       6  1.234955E+01   7.589134E+01   3.010346E+00   1.197703E+01  
  0.125664E+01   0.700000E+02       1  4.484869E ‐01  9.897969E+01  ‐7.000179E ‐02  4.429901E ‐01 
195

0.125664E+01   0.700000E+02       2  2.006445E+00   5.394504E+01   1.180915E+00   1.622116E+00  
  0.125664E+01   0.700000E+02       3  9.283326E ‐02  5.308544E+01   5.575783E ‐02  7.422317E ‐02 
  0.125664E+01   0.700000E+02       4  2.975250E ‐01 ‐1.486025E+02  ‐2.539594E ‐01 ‐1.550024E ‐01 
  0.125664E+01   0.700000E+02       5  9.139579E ‐01 ‐5.182080E+01   5.649385E ‐01 ‐7.184452E ‐01 
  0.125664E+01   0.700000E+02       6  2.462373E+01   1.382357E+00   2.461657E+01   5.940315E ‐01 
  0.125664E+01   0.800000E+02       1  4.177332E ‐01 ‐3.053241E+01   3.598111E ‐01 ‐2.122191E ‐01 
  0.125664E+01   0.800000E+02       2  2.361580E+00  ‐4.222116E+00   2.355171E+00  ‐1.738670E ‐01 
  0.125664E+01   0.800000E+02       3  3.644951E ‐01  2.648255E+00   3.641058E ‐01  1.684125E ‐02 
  0.125664E+01   0.800000E+02       4  2.427344E+00  ‐1.706497E+02  ‐2.395093E+00  ‐3.943709E ‐01 
  0.125664E+01   0.800000E+02       5  1.125469E+00   8.999937E+01   1.252509E ‐05  1.125469E+00  
  0.125664E+01   0.800000E+02       6  6.406771E+01  ‐8.336099E+01   7.407092E+00  ‐6.363809E+01  
  0.125664E+01   0.900000E+02       1  2.792875E ‐07  7.986827E+01   4.913002E ‐08  2.749323E ‐07 
  0.125664E+01   0.900000E+02       2  3.723647E+01   4.667456E+01   2.554948E+01   2.708835E+01  
  0.125664E+01   0.900000E+02       3  5.365805E+00   4.635458E+01   3.703443E+00   3.882830E+00  
  0.125664E+01   0.900000E+02       4  3.828696E+01  ‐1.341008E+02  ‐2.664477E+01  ‐2.749449E+01  
  0.125664E+01   0.900000E+02       5  1.103154E ‐05  1.369071E+02  ‐8.055748E ‐06  7.536565E ‐06 
  0.125664E+01   0.900000E+02       6  1.552969E ‐04 ‐4.026945E+01   1.184936E ‐04 ‐1.003813E ‐04 
  0.125664E+01   0.100000E+03       1  4.177965E ‐01  1.494610E+02  ‐3.598411E ‐01  2.122929E ‐01 
  0.125664E+01   0.100000E+03       2  2.361629E+00  ‐4.221781E+00   2.355221E+00  ‐1.738568E ‐01 
  0.125664E+01   0.100000E+03       3  3.645604E ‐01  2.653809E+00   3.641694E ‐01  1.687956E ‐02 
  0.125664E+01   0.100000E+03       4  2.427364E+00  ‐1.706587E+02  ‐2.395175E+00  ‐3.939986E ‐01 
  0.125664E+01   0.100000E+03       5  1.125051E+00  ‐8.993605E+01   1.255705E ‐03 ‐1.125051E+00  
  0.125664E+01   0.100000E+03       6  6.406738E+01   9.663930E+01  ‐7.407373E+00   6.363773E+01  
  0.125664E+01   0.110000E+03       1  4.484580E ‐01 ‐8.101905E+01   7.000703E ‐02 ‐4.429600E ‐01 
  0.125664E+01   0.110000E+03       2  2.006438E+00   5.394444E+01   1.180928E+00   1.622098E+00  
  0.125664E+01   0.110000E+03       3  9.282635E ‐02  5.310986E+01   5.572205E ‐02  7.424140E ‐02 
  0.125664E+01   0.110000E+03       4  2.977684E ‐01 ‐1.484481E+02  ‐2.537483E ‐01 ‐1.558134E ‐01 
  0.125664E +01  0.110000E+03       5  9.130183E ‐01  1.281776E+02  ‐5.643375E ‐01  7.177225E ‐01 
  0.125664E+01   0.110000E+03       6  2.462352E+01  ‐1.786175E+02  ‐2.461636E+01  ‐5.940970E ‐01 
  0.125664E+01   0.120000E+03       1  3.095530E ‐01 ‐8.732662E+01   1.443828E ‐02 ‐3.092161E ‐01 
  0.125664E+01   0.120000E+03       2  5.177627E ‐01  5.169791E+01   3.209133E ‐01  4.063162E ‐01 
  0.125664E+01   0.120000E+03       3  4.579637E ‐02 ‐1.591669E+02  ‐4.280223E ‐02 ‐1.628732E ‐02 
  0.125664E+01   0.120000E+03       4  5.006751E ‐01  6.879288E+01   1.811145E ‐01  4.667688E ‐01 
  0.125664E+01   0.120000E+03       5  9.214829E ‐01  9.406966E+01  ‐6.539704E ‐02  9.191594E ‐01 
  0.125664E+01   0.120000E+03       6  1.234955E+01  ‐1.041087E+02  ‐3.010346E+00  ‐1.197703E+01  
  0.125664E+01   0.130000E+03       1  1.029152E+00  ‐9.274391E+01  ‐4.926759E ‐02 ‐1.027972E+00  
  0.125664E+01   0.130000E+03       2  1.203075E+00   8.637505E+01   7.606444E ‐02  1.200668E+00  
  0.125664E+01   0.130000E+03       3  5.619531E ‐02  9.880749E+01  ‐8.604339E ‐03  5.553268E ‐02 
  0.125664E+01   0.130000E+03       4  4.013925E ‐01  1.360051E+02  ‐2.887626E ‐01  2.788048E ‐01 
  0.125664E+01   0.130000E+03       5  4.572874E ‐01  1.427535E+02  ‐3.640184E ‐01  2.767713E ‐01 
  0.125664E+01   0.130000E+03       6  3.257516E ‐01 ‐3.972321E+01   2.505489E ‐01 ‐2.081812E ‐01 
  0.125664E+01   0.140000E+03       1  1.203053E+00  ‐9.362145E+01  ‐7.598975E ‐02 ‐1.200650E+00  
  0.125664E+01   0.140000E+03       2  1.029077E+00   8.726032E+01   4.918807E ‐02  1.027901E+00  
  0.125664E+01   0.140000E+03       3  5.575266E ‐02  9.972774E+01  ‐9.420332E ‐03  5.495103E ‐02 
  0.125664E+01   0.140000E+03       4  4.508249E ‐01  1.413024E+02  ‐3.518492E ‐01  2.818602E ‐01 
  0.125664E+01   0.140000E+03       5  4.077001E ‐01  1.330714E+02  ‐2.784220E ‐01  2.978264E ‐01 
  0.125664E+01   0.140000E+03       6  3.266479E ‐01  1.402970E+02  ‐2.513117E ‐01  2.086656E ‐01 
  0.125664E+01   0.150000E+03       1  5.178185E ‐01 ‐1.283014E+02  ‐3.209431E ‐01 ‐4.063637E ‐01 
  0.125664E+01   0.150000E+03       2  3.095861E ‐01  9.268608E+01  ‐1.450839E ‐02  3.092460E ‐01 
  0.125664E+01   0.150000E+03       3  4.604926E ‐02 ‐1.596816E+02  ‐4.318395E ‐02 ‐1.599002E ‐02 
  0.125664E+01   0.150000E+03       4  9.021725E ‐01  9.414983E+01  ‐6.528568E ‐02  8.998072E ‐01 
  0.125664E+01   0.150000E+03       5  5.112429E ‐01  6.849577E+01   1.874063E ‐01  4.756556E ‐01 
  0.125664E+01   0.150000E+03       6  1.234953E+01   7.589193E+01   3.010217E+00   1.197704E+01  
  0.125664E+01   0.160000E+03       1  2.006404E+00  ‐1.260541E+02  ‐1.180867E+00  ‐1.622101E+00  
  0.125664E+01   0.160000E+03       2  4.484448E ‐01  9.896774E+01  ‐6.990276E ‐02  4.429632E ‐01 
  0.125664E+01   0.160000E+03       3  9.174211E ‐02  5.319652E+01   5.496015E ‐02  7.345745E ‐02 
  0.125664E+01   0.160000E+03       4  9.207801E ‐01  1.284686E+02  ‐5.728037E ‐01  7.209243E ‐01 
  0.125664E+01   0.160000E+03       5  2.876672E ‐01 ‐1.490863E+02  ‐2.468017E ‐01 ‐1.477880E ‐01 
  0.125664E+01   0.160000E+03       6  2.462325E+01   1.380886E+00   2.461610E+01   5.933877E ‐01 
  0.125664E+01   0.170000E+03       1  2.361607E+00   1.757810E+02  ‐2.355207E+00   1.737394E ‐01 
  0.125664E+01   0.170000E+03       2  4.178357E ‐01 ‐3.055589E+01   3.598124E ‐01 ‐2.124187E ‐01 
  0.125664E+01   0.170000E+03       3  3.655501E ‐01  2.623623E+00   3.651669E ‐01  1.673300E ‐02 
  0.125664E+01   0.170000E+03       4  1.113482E+00  ‐8.973499E+01   5.150314E ‐03 ‐1.113470E+00  
  0.125664E+01   0.170000E+03       5  2.462513E+00  ‐1.704853E+02  ‐2.428637E+00  ‐4.070565E ‐01 
  0.125664E+01   0.170000E+03       6  6.406735E+01  ‐8.336049E+01   7.407608E+00  ‐6.363767E+01  
  0.125664E+01   0.180000E+03       1  3.723658E+01  ‐1.333255E+02  ‐2.554958E+01  ‐2.708840E+01  
  0.125664E+01   0.180000E+03       2  5.587313E ‐07  7.987847E+01   9.818955E ‐08  5.500359E ‐07 
  0.125664E+01   0.180000E+03       3  5.366601E+00   4.634993E+01   3.704308E+00   3.883106E+00  
  0.125664E+01   0.180000E+03       4  2.209019E ‐05 ‐4.312394E+01   1.612312E ‐05 ‐1.510039E ‐05 
  0.125664E+01   0.180000E+03       5  3.827606E+01  ‐1.340729E+02  ‐2.662381E+01  ‐2.749963E+01  
  0.125664E+01   0.180000E+03       6  3.105944E ‐04 ‐4.026929E+01   2.369881E ‐04 ‐2.007623E ‐04
196

Appendix E Input Files for the MIT / NREL Barge
E.1 FAST Platform / HydroDyn Input File
‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐ 
‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐  FAST PLATFORM  FILE ‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐ 
NREL 5.0 MW offshore  baseline  floating  platform  input properties  for the MIT/NREL  shallow  drafted  barge (SDB). 
‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐  FEATURE  FLAGS (CONT) ‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐ 
True         PtfmSgDOF    ‐  Platform  horizontal  surge translation  DOF (flag) 
True         PtfmSwDOF    ‐  Platform  horizontal  sway translation  DOF (flag) 
True         PtfmHvDOF    ‐  Platform  vertical  heave translation  DOF (flag) 
True         PtfmRDOF     ‐  Platform  roll tilt rotation  DOF (flag) 
True         PtfmPDOF     ‐  Platform  pitch tilt rotation  DOF (flag) 
True         PtfmYDOF     ‐  Platform  yaw rotation  DOF (flag) 
‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐  INITIAL  CONDITIONS  (CONT) ‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐ 
   0.0       PtfmSurge    ‐  Initial  or fixed horizontal  surge translational  displacement  of platform  (meters)  
   0.0       PtfmSway     ‐  Initial  or fixed horizontal  sway translational  displacement  of platform  (meters)  
   0.0       PtfmHeave    ‐  Initial  or fixed vertical  heave translational  displacement  of platform  (meters)  
   0.0       PtfmRoll     ‐  Initial  or fixed roll tilt rotational  displacement  of platform  (degrees)  
   0.0       PtfmPitch    ‐  Initial  or fixed pitch tilt rotational  displacement  of platform  (degrees)  
   0.0       PtfmYaw      ‐  Initial  or fixed yaw rotational  displacement  of platform  (degrees)  
‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐  TURBINE  CONFIGURATION  (CONT) ‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐ 
   0.0       TwrDraft     ‐  Downward  distance  from the ground level [onshore]  or MSL [offshore]  to the tower base platform  conn 
   3.88238   PtfmCM      ‐  Downward  distance  from the ground level [onshore]  or MSL [offshore]  to the platform  CM (meters)  
   0.0       PtfmRef      ‐  Downward  distance  from the ground level [onshore]  or MSL [offshore]  to the platform  reference  point  
‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐  MASS AND INERTIA  (CONT) ‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐ 
4519.15E3    PtfmMass     ‐  Platform  mass (kg) 
 390.147E6   PtfmRIner    ‐  Platform  inertia  for roll tilt rotation  about the platform  CM (kg m^2) 
 390.147E6   PtfmPIner    ‐  Platform  inertia  for pitch tilt rotation  about the platform  CM (kg m^2) 
 750.866E6   PtfmYIner    ‐  Platfrom  inertia  for yaw rotation  about the platform  CM (kg m^2) 
‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐  PLATFORM  (CONT) ‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐ 
FltngPtfmLd  PtfmLdMod    ‐  Platform  loading  model {0: none, 1: user‐defined  from routine  UserPtfmLd}  (switch)  
"PlatformDesigns\WAMIT\SDB\Cylinder"               WAMITFile    ‐  Root name of WAMIT output files containing  the linear,  nondime  
5089.38       PtfmVol0     ‐  Displaced  volume of water when the platform  is in its undisplaced  position  (m^3) [USE THE SAME VALU 
   0         PtfmNodes    ‐  Number of platform  nodes used in calculation  of viscous  drag term from Morison's  equation  (‐) 
   5.0       PtfmDraft    ‐  Effective  platform  draft     in calculation  of viscous  drag term from Morison's  equation  (meters)  
  36.0       PtfmDiam     ‐  Effective  platform  diameter  in calculation  of viscous  drag term from Morison's  equation  (meters)  
   0.0       PtfmCD      ‐  Effective  platform  normalized  hydrodynamic  viscous  drag coefficient  in calculation  of viscous  drag  
  60.0       RdtnTMax     ‐  Analysis  time for  wave radiation  kernel calculations  (sec) [determines  RdtnDOmega=Pi/RdtnTMax  in th 
   0.025     RdtnDT      ‐  Time step for  wave radiation  kernel calculations  (sec) [DT<=RdtnDT<=0.1  recommended]  [determines  Rd 
‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐  MOORING  LINES ‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐ 
   8         NumLines     ‐  Number of mooring  lines (‐) 
   1         LineMod      ‐  Mooring  line model {1: standard  quasi‐static,  2: user‐defined  from routine  UserLine}  (switch)  [used  
LRadAnch   LAngAnch   LDpthAnch   LRadFair   LAngFair    LDrftFair   LUnstrLen   LDiam   LMassDen   LEAStff   LSeabedCD   LTenTol  [used  
(m)        (deg)      (m)         (m)        (deg)       (m)         (m)         (m)      (kg/m)     (N)       (‐)         (‐)      [used  
 218.0       0.0      200.0       18.0         0.0       5.0         279.3       0.127   116.027    1.5E9     1.0         0.0001 
 218.0       0.0      200.0       18.0         0.0       5.0         279.3       0.127   116.027    1.5E9     1.0         0.0001 
 218.0      90.0      200.0       18.0        90.0       5.0         279.3       0.127   116.027    1.5E9     1.0         0.0001 
 218.0      90.0      200.0       18.0        90.0       5.0         279.3       0.127   116.027    1.5E9     1.0         0.0001 
 218.0     180.0      200.0       18.0       180.0       5.0         279.3       0.127   116.027    1.5E9     1.0         0.0001 
 218.0     180.0      200.0       18.0       180.0       5.0         279.3       0.127   116.027    1.5E9     1.0         0.0001 
 218.0     270.0      200.0       18.0       270.0       5.0         279.3       0.127   116.027    1.5E9     1.0         0.0001 
 218.0     270.0      200.0       18.0       270.0       5.0         279.3       0.127   116.027    1.5E9     1.0         0.0001 
‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐  WAVES ‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐ 
1025.0       WtrDens      ‐  Water density  (kg/m^3)  
 200.0       WtrDpth      ‐  Water depth (meters)  [USE THE SAME VALUE SPECIFIED  IN THE  WAMIT .POT FILE!] 
   2         WaveMod      ‐  Incident  wave kinematics  model {0: none=still  water, 1: plane progressive  (regular),  2: JONSWAP/Pie  
3630.0       WaveTMax     ‐  Analysis  time for  incident  wave calculations  (sec) [unused  when WaveMod=0]  [determines  WaveDOmega=2  
   0.25      WaveDT      ‐  Time step for  incident  wave calculations  (sec) [unused  when WaveMod=0]  [0.1<=WaveDT<=1.0  recommende  
   5.49      WaveHs      ‐  Significant  wave height of incident  waves (meters)  [used only when WaveMod=1  or 2] 
  14.6563    WaveTp      ‐  Peak spectral  period of incident  waves (sec) [used only when WaveMod=1  or 2] 
   1.0       WavePkShp    ‐  Peak shape parameter  of incident  wave spectrum  (‐) or DEFAULT  (unquoted  string)  [used only when Wav 
   0.0       WaveDir      ‐  Incident  wave propagation  heading  direction  (degrees)  [unused  when WaveMod=0]  
123456789    WaveSeed(1)  ‐ First  random seed of incident  waves [‐2147483648  to 2147483647]  (‐) [unused  when WaveMod=0]  
1011121314   WaveSeed(2)  ‐ Second random seed of incident  waves [‐2147483648  to 2147483647]  (‐) [unused  when WaveMod=0]  
‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐  CURRENT  ‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐ 
   0         CurrMod      ‐  Current  profile  model {0: none=no  current,  1: standard,  2: user‐defined  from routine  UserCurrent}  ( 
   0.0       CurrSSV0     ‐  Sub‐surface  current  velocity  at still water level (m/s) [used only when CurrMod=1]  
DEFAULT       CurrSSDir    ‐  Sub‐surface  current  heading  direction  (degrees)  or DEFAULT  (unquoted  string)  [used only when CurrMo 
  20.0       CurrNSRef    ‐  Near‐surface  current  reference  depth (meters)  [used only when CurrMod=1]  
   0.0       CurrNSV0     ‐  Near‐surface  current  velocity  at still water level (m/s) [used only when CurrMod=1]  
   0.0       CurrNSDir    ‐  Near‐surface  current  heading  direction  (degrees)  [used only when CurrMod=1]  
   0.0       CurrDIV      ‐  Depth‐independent  current  velocity  (m/s) [used only when CurrMod=1]  
   0.0       CurrDIDir    ‐  Depth‐independent  current  heading  direction  (degrees)  [used only when CurrMod=1]  
‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐  OUTPUT (CONT) ‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐ 
   0         NWaveKin     ‐  Number of points where the incident  wave kinematics  can be output [0 to 9] (‐) 
             WaveKinNd    ‐  List of platform  nodes that have wave kinematics  sensors  [1 to PtfmNodes]  (‐) [unused  if NWaveKin=0  
197

E.2 WAMIT Input File – CONFIG.WAM
CONFIGuration  file for WAMIT v6.3PC.  
IALTFRC          =     1                         IALTFRC        ‐  Alternative  form of the .FRC file {1: use alternative  form #1, 2 
IALTFRCN         = 1  1  etc.                   IALTFRCN       ‐  Alternative  form of the .FRC file {1: use alternative  form #1, 2 
IALTPOT          =     1                         IALTPOT        ‐  Alternative  form of the .POT file {1: use alternative  form #1, 2 
ICTRSURF         =     0                         ICTRSURF       ‐  Alternative  form to evaluate  the drift forces over a user‐define 
IDIAG†         POT                             IDIAG†        ‐  Control  index for increasing  the precision  of the panel integrat  
IFIELD_ARRAYS   =     0                         IFIELD_ARRAYS  ‐ Additional  uniform  field point data {0: none, 1: using compresse  
IFORCE          =     1                         IFORCE        ‐  Execute  FORCE subprogram  {0: do not execute,  1: do execute}  (swi 
IGENMDS          =     0                         IGENMDS        ‐  Option to input geometric  data associated  with mode shapes of ge 
ILOWGDF          =     0                         ILOWGDF        ‐  Generate  low‐order _LOW.GDF  file based on input geometry  {0: no,  
ILOWHI          =     0                         ILOWHI        ‐  Order of panel method {0: low‐order, 1: high‐order} (switch)  
ILOG†          POT                             ILOG†         ‐  Control  index for increasing  the precision  of the panel integrat  
INUMOPT5         =     0                         INUMOPT5       ‐  Option to output separate  body pressure  and velocity  {0: as in v 
INUMOPT6         =     0                         INUMOPT6       ‐  Option to output separate  pressure  at field points {0: as in v6. 
INUMOPT7         =     0                         INUMOPT7       ‐  Option to output separate  fluid velocity  at field points {0: as  
IPERIO          =     2                         IPERIO        ‐  Input data option for PER in the .POT file {1: period in sec, 2:  
IPLTDAT          =     0                         IPLTDAT        ‐  Generate  _PAN.DAT  and _PAT.DAT  files for plotting  panel and patc 
IPNLBPT          =     0                         IPNLBPT        ‐  Option to evaluate  the body pressure  at specified  points in the  
IPOTEN          =     1                         IPOTEN        ‐  Execute  POTEN subprogram  {0: do not execute,  1: do execute}  (swi 
IQUAD†         POT   0                         IQUAD†        ‐  Control  index for increasing  the precision  of the panel integrat  
IQUADI†         SPL   4                         IQUADI†        ‐  Order of Guass quadrature  in the inner integration  (‐) [unused  w 
IQUADO†         SPL   3                         IQUADO†        ‐  Order of Guass quadrature  in the outer integration  (‐) [unused  w 
IRR†           POT                             IRR†          ‐  Irregular  frequency  removal  {0: do not remove,  1: remove by repr 
ISCATT          =     0                         ISCATT        ‐  Solve for the diffraction  potential  from the diffraction  or scat 
ISOLVE          =     0                         ISOLVE        ‐  Method of solution  for the linear systems  in POTEN {0: iterative   
ISOR†          POT                             ISOR†         ‐  Source strength  evaluation  {0: do not evaluate,  1: do evaluate}   
ITANKFPT         =     0                         ITANKFPT       ‐  Format for specifying  input field point coordinates  {0: conventi  
KSPLIN         SPL   3                         KSPLIN        ‐  Order of B‐spline for potential  in high‐order method {3: quadrat  
MAXITT          =   35                         MAXITT        ‐  Maximum  number of iterations  in the iterative  solver of POTEN (‐ 
MAXMIT          =     8                         MAXMIT        ‐  Maximum  number of iterations  in the adaptive  integration  used to  
MAXSCR          = 8192                         MAXSCR        ‐  Available  RAM for scratch  storage  in POTEN = 8*MAXSCR^2  bytes (‐ 
MODLST          =     0                         MODLST        ‐  Order in which the added mass and damping  coefficients,  exciting   
MONITR          =     0                         MONITR        ‐  Mode for  displaying  output to the monitor  during execution  of FO 
NEWMDS(n)†      POT2  0                         NEWMDS(n)†     ‐  Number of generalized  modes for body n (‐) 
NOOUT           = 1  1  1  1  1  1  1  1  1   NOOUT         ‐  Omit/include  output in the .OUT file for each of the 9 output op 
NPTANK(n)                                      NPTANK(n)      ‐  List of panel or patch index ranges of internal  tanks for body n  
NUMHDR          =     0                         NUMHDR        ‐  Omit/include  one‐line header in the numeric  output files {0: omi 
NUMNAM          =     0                         NUMNAM        ‐  Numeric  output filename  convention  {0: use rootname  of the .FRC  
PANEL_SIZE       =   ‐ 1.0                       PANEL_SIZE     ‐  Automatic  subdivision  of patches  in the higher‐order panel metho 
RHOTANK                                        RHOTANK        ‐  List of fluid densities  in internal  tanks relative  to the densit 
SCRATCH_PATH    = C:\WAMITv6                    SCRATCH_PATH   ‐  Path of directory  for storage  of some scratch  arrays (unquoted  s 
USERID_PATH      = C:\WAMITv6                    USERID_PATH    ‐  Path of directory  where USERID.WAM  is stored (unquoted  string)  
XBODY(n)†  POT or GGDF                         XBODY(n)†      ‐  X‐, Y‐, and Z‐coordinates  and the Z‐axis rotation  of the body‐fi 
E.3 WAMIT Input File – Cylinder.POT
POTential  control  file in alternative  form #1 for WAMIT v6.3PC.  
   0                                          ISOR†         ‐  Source strength  evaluation  {0: do not evaluate,  1: do evaluate}   
   0                                          IRR†          ‐  Irregular  frequency  removal  {0: do not remove,  1: remove by repr 
 200.0  0.0  0.0  0.0  0.0                    HBOT          ‐  Water depth {‐1.0: infinite}  (meters)   &  XBODY†        ‐  X‐, Y‐ 
   0     0     0                                IQUAD†        ‐  Control  index for increasing  the precision  of the panel integrat  
   1     1                                     IRAD          ‐  Control  index for radiation  modes {1: use all 6 rigid‐body modes  
   1     1     1     1     1     1                 MODE          ‐  List of radiation  modes and diffraction  components  required  {0:  
‐102                                          NPER          ‐  Number of wave periods  to be analyzed  {0: evaluate  hydrostatics   
  ‐0.05 0.05                                  PER           ‐  List of wave periods  [IPERIO  = 1] or wave frequencies  [IPERIO  =  
   1                                          NBETA         ‐  Number of wave heading  angles to be analyzed  {0: do not solve th 
   0.0                                        BETA          ‐  List of wave heading  angles relative  to the global coordinate  sy 
E.4 WAMIT Input File – Cylinder.FRC
FoRCe control  file in alternative  form #1 for WAMIT v6.3PC.  
   1     0     1     0     0     0     0     0     0 IOPTN         ‐  Switches  for generating  numerical  output files [1]{0: do not out 
   0.0                                        VCG           ‐  Vertical  location  of the center of gravity  of the body relative   
   0.0  0.0  0.0 
   0.0  0.0  0.0 
   0.0  0.0  0.0                              XPRDCT        ‐  Matrix of body radii of gyration  about the body‐fixed coordinate   
   0                                          NBETAH        ‐  Number of wave heading  angles to be analyzed  by the Haskind  rela 
   0                                          NFIELD        ‐  Number of points in the fluid domain where the hydrodynamic  pres 
                                              XFIELD        ‐  Global X‐, Y‐, Z‐ coordinates  of field points where the pressure   
198

E.5 WAMIT Input File – Cylinder.GDF
Geometric  Data File for WAMIT v6.3PC.   Circular  cylinder:  Radius=18.000000,  Draft=5.000000;   NA=  58, NR=  37, ND=  11  
  1.0      9.806650                    ULEN          ‐  Length scale (meters)   &  GRAV          ‐  Gravitational  acceleration  (m/s 
     1             1                   ISX           ‐  Geometric  plane of symmetry  switch for the x=0 plane {0: x=0 plane is not  
 2622                                NPAN(C)        ‐  Number of (conventional)  panels defined  in this file.  Each panel has 4 v 
      17.9931655         0.4959782         0.0000000  
      18.0000000         0.0000000         0.0000000  
      18.0000000         0.0000000       ‐ 0.5000000  
      17.9931655         0.4959782       ‐ 0.5000000  
      17.9931655         0.4959782       ‐ 0.5000000  
      18.0000000         0.0000000       ‐ 0.5000000  
      18.0000000         0.0000000       ‐ 1.0000000  
      17.9931655         0.4959782       ‐ 1.0000000  
 
[lines deleted]  
 
       0.0000000        18.0000000       ‐ 5.0000000  
       0.4959782        17.9931655       ‐ 5.0000000  
       0.4822010        17.4933554       ‐ 5.0000000  
       0.0000000        17.5000000       ‐ 5.0000000  
     0                                NPAND         ‐  Number of dipole panels defined  in this file.  Each panel has 4 vertices   
E.6 WAMIT Output File – Cylinder.hst
      1      1   0.000000E+00  
      1      2   0.000000E+00  
      1      3   0.000000E+00  
      1      4   0.000000E+00  
      1      5   0.000000E+00  
      1      6   0.000000E+00  
      2      1   0.000000E+00  
      2      2   0.000000E+00  
      2      3   0.000000E+00  
      2      4   0.000000E+00  
      2      5   0.000000E+00  
      2      6   0.000000E+00  
      3      1   0.000000E+00  
      3      2   0.000000E+00  
      3      3   1.017745E+03  
      3      4   0.000000E+00  
      3      5   0.000000E+00  
      3      6   0.000000E+00  
      4      1   0.000000E+00  
      4      2   0.000000E+00  
      4      3   0.000000E+00  
      4      4   6.968945E+04  
      4      5   0.000000E+00  
      4      6   0.000000E+00  
      5      1   0.000000E+00  
      5      2   0.000000E+00  
      5      3   0.000000E+00  
      5      4   0.000000E+00  
      5      5   6.968947E+04  
      5      6   0.000000E+00  
      6      1   0.000000E+00  
      6      2   0.000000E+00  
      6      3   0.000000E+00  
      6      4   0.000000E+00  
      6      5   0.000000E+00  
      6      6   0.000000E+00  
E.7 WAMIT Output File – Cylinder.1
 ‐0.100000E+01       1      1  1.489954E+03  
 ‐0.100000E+01       1      5  6.071913E+03  
 ‐0.100000E+01       2      2  1.489951E+03  
 ‐0.100000E+01       2      4 ‐6.071907E+03  
 ‐0.100000E+01       3      3  1.365988E+04  
 ‐0.100000E+01       4      2 ‐6.064123E+03  
 ‐0.100000E+01       4      4  4.238899E+05  
 ‐0.100000E+01       5      1  6.064096E+03  
 ‐0.100000E+01       5      5  4.238900E+05  
 ‐0.100000E+01       6      6  6.802706E ‐08 
  0.000000E+00       1      1  5.318895E+02  
  0.000000E+00       1      5  1.837424E+03  
  0.000000E+00       2      2  5.318895E+02  
199

0.000000E+00       2      4 ‐1.837423E+03  
  0.000000E+00       3      3  9.698843E+03  
  0.000000E+00       4      2 ‐1.848423E+03  
  0.000000E+00       4      4  3.975065E+05  
  0.000000E+00       5      1  1.848424E+03  
  0.000000E+00       5      5  3.975065E+05  
  0.000000E+00       6      6  6.618992E ‐08 
  0.125664E+03       1      1  1.492564E+03   3.627036E ‐02 
  0.125664E+03       1      5  6.089232E+03   4.171622E ‐01 
  0.125664E+03       2      2  1.492562E+03   3.618027E ‐02 
  0.125664E+03       2      4 ‐6.089223E+03  ‐4.171455E ‐01 
  0.125664E+03       3      3  1.504551E+04   1.326158E+03  
  0.125664E+03       4      2 ‐6.081390E+03  ‐4.176246E ‐01 
  0.125664E+03       4      4  4.240218E+05   4.771546E+00  
  0.125664E+03       5      1  6.081377E+03   4.159448E ‐01 
  0.125664E+03       5      5  4.240217E+05   4.774776E+00  
  0.125664E +03      6      6  6.802735E ‐08 ‐2.658206E ‐16 
  0.628319E+02       1      1  1.500499E+03   1.688199E ‐01 
  0.628319E+02       1      5  6.141928E+03   1.929863E+00  
  0.628319E+02       2      2  1.500498E+03   1.688323E ‐01 
  0.628319E+02       2      4 ‐6.141922E+03  ‐1.929951E+00  
  0.628319E+02       3      3  1.461348E+04   1.427834E+03  
  0.628319E+02       4      2 ‐6.133953E+03  ‐1.927234E+00  
  0.628319E+02       4      4  4.244209E+05   2.202481E+01  
  0.628319E+02       5      1  6.133940E+03   1.927675E+00  
  0.628319E+02       5      5  4.244209E+05   2.202487E+01  
  0.628319E+02       6      6  6.802819E ‐08 ‐9.891171E ‐16 
 
[lines deleted]  
 
  0.125664E+01       1      1  4.398125E+02   1.828869E+01  
  0.125664E+01       1      5  1.690897E+03  ‐7.049192E+00  
  0.125664E+01       2      2  4.398125E+02   1.828869E+01  
  0.125664E+01       2      4 ‐1.690901E+03   7.049183E+00  
  0.125664E+01       3      3  9.633591E+03   2.642366E ‐02 
  0.125664E+01       4      2 ‐1.706354E+03   9.886565E+00  
  0.125664E+01       4      4  3.966836E+05   3.810670E+00  
  0.125664E+01       5      1  1.706357E+03  ‐9.886564E+00  
  0.125664E+01       5      5  3.966838E+05   3.810673E+00  
  0.125664E+01       6      6  6.784203E ‐08  9.183608E ‐10 
E.8 WAMIT Output File – Cylinder.3
  0.125664E+03   0.000000E+00       1  7.489913E+00   8.999969E+01   4.113390E ‐05  7.489913E+00  
  0.125664E+03   0.000000E+00       2  0.000000E+00   9.000000E+01   0.000000E+00   0.000000E+00  
  0.125664E+03   0.000000E+00       3  1.012577E+03   1.912910E ‐02  1.012577E+03   3.380647E ‐01 
  0.125664E+03   0.000000E+00       4  0.000000E+00   9.000000E+01   0.000000E+00   0.000000E+00  
  0.125664E+03   0.000000E+00       5  8.600130E+01   8.999969E+01   4.723112E ‐04  8.600130E+01  
  0.125664E+03   0.000000E+00       6  0.000000E+00   9.000000E+01   0.000000E+00   0.000000E+00  
  0.628319E+02   0.000000E+00       1  1.534577E+01   8.999855E+01   3.881812E ‐04  1.534577E+01  
  0.628319E+02   0.000000E+00       2  0.000000E+00   9.000000E+01   0.000000E+00   0.000000E+00  
  0.628319E+02   0.000000E+00       3  9.976350E+02   8.361685E ‐02  9.976340E+02   1.455937E+00  
  0.628319E+02   0.000000E+00       4  0.000000E+00   9.000000E+01   0.000000E+00   0.000000E+00  
  0.628319E+02   0.000000E+00       5  1.752071E+02   8.999855E+01   4.431981E ‐03  1.752071E+02  
  0.628319E+02   0.000000E+00       6  0.000000E+00   9.000000E+01   0.000000E+00   0.000000E+00  
 
[lines deleted]  
 
  0.125664E+01   0.000000E+00       1  5.488204E+00   6.842252E+01   2.018336E+00   5.103597E+00  
  0.125664E+01   0.000000E+00       2  0.000000E+00   9.000000E+01   0.000000E+00   0.000000E+00  
  0.125664E+01   0.000000E+00       3  5.635286E ‐02 ‐1.303021E+02  ‐3.645004E ‐02 ‐4.297720E ‐02 
  0.125664E+01   0.000000E+00       4  0.000000E+00   9.000000E+01   0.000000E+00   0.000000E+00  
  0.125664E+01   0.000000E+00       5  2.966837E+00  ‐1.115774E+02  ‐1.091078E+00  ‐2.758925E+00  
  0.125664E+01   0.000000E+00       6  0.000000E+00   9.000000E+01   0.000000E+00   0.000000E+00
200

Appendix F Extreme-Event Tables for Normal Operation
F.1 Land-Based Wind Turbine Loads
 
 
 
 
 
 
 
201

202

203

F.2 Sea-Based Wind Turbine Loads
 
 
 
204

205

206

207

208

F1147-E(09/2007) REPORT DOCUMENTATION PAGE Form Approved
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5a. CONTRACT NUMBER
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4. TITLE AND SUBTITLE
Dynamics Modeling and Loads Analysis of an Offshore Floating
Wind Turbine
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5d. PROJECT NUMBER
NREL/TP-500-41958
5e. TASK NUMBER
WER7.5001 6. AUTHOR(S)
J.M. Jonkman
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National Renewable Energy Laboratory 1617 Cole Blvd.
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14. ABSTRACT (Maximum 200 Words)
The objectives of the work described in this report are to develop a comprehensive simulation tool that can model the
coupled dynamic response of offshore floating wind turbines, verify the simulation capability through model-to-model
comparisons, and apply the simulation tool in an integrated loads analysis for one of the promising floating support platform concepts.
15. SUBJECT TERMS
offshore wind energy development; modeling; wind turbine design analysis
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