.continut Disertatie [627054]

1

CHAPTER 1

– INTRODUCTION –

2
1.1 INTRODUCTION

A bulk carrier, bulk freighter, or colloquially, bulker is
a merchant ship specially designed to transport unpackaged bulk cargo ,
such as grains, coal, ore, and cement in its cargo holds .
Since the first specialized bulk carrier was built in 1852, economic
forces have fuelled the development of these ships, causing them to grow in
size and sophistication. Today's bulk carriers are specially designed to
maximize capacity, safety, efficien cy, and durability.
Today, bulk carriers make up 40% of the world's merchant
fleets and range in size from single -hold mini -bulk carriers to mammoth ore
ships able to carry 400,000 metric tons of deadweight (DWT). A number of
specialized designs exist: some can unload their own cargo, some depend on
port facilities for unlo ading, and some even package the cargo as it is loaded.
Over half of all bulk carriers have Greek, Japanese, or Chinese
owners and more than a quarter are registered in Pana ma. South Korea is
the largest single builder of bulk carriers, and 82% of these ships were built
in Asia.
Bulk carriers are segregated into six major size categories :
– small
– Handysize is a naval architecture term for smaller bulk carriers or oil
tanker with deadweig ht of up to 50,000 tonnes, although there is no official
definition in terms of exact tonnages. Handysize is also sometimes used to refer to
the span of up to 60,000 tons, with the vessels above 35,000 tonnes referred to
as Handymax or Supramax .

3

-Handymax (or Supramax) is a naval architecture term for the larger bulk
carriers in the Handysize class. Handysize class consists of Supramax (50,000 to
60,000 DWT ), Handymax (40,000 to 50,000 DWT), and Handy (<40,000 DWT). The
ships are us ed for less voluminous cargos, even allowing for combining different
cargos in different holds.

4
-Panamax (New Panamax or Neopanamax ) are terms for the size limits for ships
travelling through the Panama Canal with a maximum length of 300 m and a width
of 32.2 m, which are constructed to respond to the limitations imposed by the
channel dimensions. They also ha ve to provide superior operating conditions for the
loading, transport and unloading of solid bulk cargoes.

-capesize are the largest dry cargo ships . They are too large to transit the Suez
Canal (Suezmax limits) or Panama Canal (Neopanamax limits), and so have to pass
either Cape Agulhas or Cape Horn to traverse between oceans.

5

-very large – Very large bulk and ore carriers fall into the capesize category but are
often consider ed separately .
1.2- PANAMAX ship
The chosen ship for the master thesis is a Panamax bulk -carrier,
designed for the bulk cargo transport such as iron ore, coal and phosphates. This
vessel is provided with a bulb and stern bulb and a continu ous main deck that
extends from aft to the fore.
The propulsion is achieved with a single propeller with a diameter
of … m. It is divided into 7 housings and a engine room, superstructure, the latter
being located in the aft of t he ship. The double bottom extends from the bulkhead
wall to the bulkhead of the engine compartment.
In the double bottom there is a central tunnel which extends over
the whole area of the housings, having the dimensions h = 1.8 [ m] and b = 3 [m],
allowing the passage of the ballast, bilge tubing, the location of the valves and
other components for the installations.

6
1.3. Ship description
The ship is built according to the German register Germanishe r
Lloyd Rules. + 100A5, + MC, BULK – CARRIER, BC -A, unrestricted navigation, ice class
E1(holds 2,4,6 may be empty)
Both the ship and the planned facilities were constructed under the
supervision and in accordance with the rules laid down in Germanischer
Lloyd by the shipyards;

+100 A5 – The ship was designed and constructed according to
Germanischer Lloyd arrangements or other rules considered equivalent.

1.3.1 MAIN DIMENSIONS

Marinestudy.net

7
 Maxim length Lmax = 225.13[m]
 Length between perpendiculars Lpp = 217.3[m]
 Length on waterline Lwl = 222.4 [m]
 Beam B = 32.2 [m]
 Depth D = 19.0 [m]
 Draft T = 13.8 [m]
 Deadweight Dw = 65700 [tdw]
 Speed v = 15 [Nd]
 Distance between frames = 900 [mm]
 Distance between frames on engine room = 750 [mm]
 Distance between frames on = 600 [mm]

1.4. Ship destination

The ship is designed to carry bulk cargoes with a maximum density
of 3 [t / m ^ 3] such as: -iron ore;
– coal;
– phosphates.
The ship may be loaded with any bulk cargo, as long as it does not
exceed Dw, or if the cargo density is low, the commander must use the ba llast tanks
to pro vide a minimum aft draft to ensure immersion of the propeller and proper
operation. The deadweight of bulk ship in sea water with density ρ = 1.025 [t / m ^
3] is 65700 [tdw] and has a draft of 13.8 [m].

8

CHAPTER 2

– SHIP RESISTANCE OF THE
PANAMAX BULKCARRIER –

9
2.1 Components of resistance

Overall ship resistance (RT) is the projection of the resultant hydro –
aerodynamic forces acting on the ship in the direction of the displacement speed
and opposed to the forward movement. Hydro -aerodynamic forces occur due to
tangential stresses and tensions acting on the immersed and emer – ging surfaces of
the moving body of the ship and are influenced by a number of factors: the sail ing
regime, the ship's shape, the speed of the ship, the direction of flow to the
diametrical plane, the presence o f winds, waves or sea currents.
The domain of navigation is defined based on the „nabla” Froude
number (Fn ), calculated with the volumetric displacement (
 ):

167.0
3.21781,9716.7
3/1

gvFn

May be possible three domains of navigations:
– if Fn  1, the ship there is in the displacement domain (the ship weight
force is eq ual with the buoyancy force);
– if 1  Fn  3, the ship there is in the transient domain (the draughts and the
trim are different at the design speed versus zero speed condition);
– if Fn  3, the ship there is in the planning domain ((the ship weight force is
equal with the planning force).
In this case,the Froude number is subunit, so the ship is in displacement mode
(the weight of the ship is balanced by the pushing force).

Total resistance of the ship has the following components:

10

AW A APP v w T R R RR R R 
where: Rw – wave resistance;
Rv – viscosity resistance;
RAPP – resistance of appendages;
RA – aerodynamic resistance of the emery part;
RAW – additional resistance in waves.

In the h ypothesis of the hull of the ship is presented the general shema of the
rotting of the hydrodynamic components of the resistance to advancement .

11

I

II

III

Fig. 2.1.1 Components of resistance

Bare hull resistance, R
Rezidual resistance, R R
Skin friction resistance, R F0 (equivalent flat plate)
Form effect on skin friction
Pressure resistance, R P
Friction resistance, R F
Wave resistance, R W
Viscous pressure resistance,
RPV
Wave making resistance,
RWM
Wave braking
resistance, R WB
Viscosity
resistance, R V
Bare hull resistance, R
(hydrodynamic part)

12
The components situated in the left part of the figu re depend of the Froude
number:
vFn
gL

The components situated in the right part of the figure depend of the
Reynolds number:
vLRe
On the first level (Froude hypo thesis), the bare hull resistance is determined
on the basis of the skin friction resistance
0FR and the rezidual resistance R R:
R FR RR
0

On the second level, the bare hull resistance is determined on the basis of the
friction resistance
FR and the pressure resistance R P:
FP R R R

On the third level (Hughes hypothesis), the bare hull resistance is determined
on the basis of the viscous resistance
VR and the wave resista nce R W:
F PV WB WM V W R R R R R RR 

The total resistance may be determined on the basis of the bare hull
resistance, appendages resistance, wind resistance and added wave resistance:
AW A APP V W T R R R R R R 

13
2.2. SHIP RESISTANCE
The method of Holtrop – Mennen

The Holtrop -Mennen method is a statistical method and has the following scope for
bulk carriers:

the application
domain of the
method
24,0Fn
16,0Fn 7
85,0 73,0pC

803,0pC
1,7 / 1,5  BLWL

9,62,32/4,222 /  BLWL
2,3 / 4,2 TB

33,2 /TB

Fig. 2.2.1 Applicability domains for Method Holtrop and Mennen

14

The total resistance will be calculated with the for mula below:
A APP TR B W F T R R R R R Rk R  ) 1(1

RT – Total resistance
1+k 1 – Form factor of bare hull
RF – Friction resistance from the ITTC 1957 line
RW – Wave resistance of bare hull
RB – Wave resistance of the bulbous bow
RTR – Additional resistance from the immersed transom
RAPP – Appendage resistance
RA – Correlation allowan ce
The general dimensions of the ship are:
General dimensions
LWL = 222.4 [m]

Lpp = 217.3 [m]
T = 13.8 [m]
B = 32.2 [m]

v = 7.716 [m/s]

15

Tabel 2.2 .1 General dimensions

Friction resistance (R F)
According ITTC -1957, the friction resistance will be calculated with the formula
below:
Sv C RF F 2
21

kN RF 98.493 1106271,7 025,1211046,12 3

Where
22Relog075,0
FC – frictional resistance coefficient
S – wetted surface
υ – kinematic viscosity of water

The Reynolds number will be determinated with the formula:

WLLvRe

9
61044,110191,17,22271,7Re 

3 = 1,025 [t m ]
CW = 0.855
CB = 0.789
CM = 0.981
CP = 0.803
Fn = 0.167
hb = 4.347 [m]

16


– water density (
3t/m 025,1 );
v – the speed of the ship (
m/s 71,7 5144,015 v );
S – wetted surface

B BT WM B M WL
CA C TBC C C BT LS
/ 38,2) 3696,0 / 003467,02862,0 4425,0 453,0( ) 2(
 

2 062 11 789,0/8.4538,2)855,0 3696,08,13/2,32 003467,0981,0 2862,0 789,0 4425,0 453,0( 981,0)2,328,132(7,222
mS
   

Where, LWL – Length on waterline
T – draught
B – beam
CB – Block coefficient
CM – Midship section coefficient
CW – Waterplane coefficient
ABT – Area of the bulbous bow

M BT A A *105.0

ABT = 0.105*436.26=45.8 [m2]

17
Form factor of bare hull (1+k 1)

604247,0 36486,0 3 121563,046106,0 06806,1
14 1
) 1( )/ ( )/ () /( ) /( 487118,093,0 1
    
p WL R WLWL WL
C L L LLT LB c k
221,1 )803,01( ) 76183/4,222( )101.63/4,222()4,222/8,13( )4,222/2,32(89,0 487118,093,0 1
604247,0 36486,0 3 121563,046106,0 06806,1
1
      
k

where :
89,0)10( 011,01 011,0114 ppc c

ppc = 0 for normal shapes of the ship's hull ;
LR – the distance from the stern perpendicular to the area from which
begins the cylindrical zone of the ship and can be calculated with the formula :

)]1 4/( 06.0 1[ p cb p p WL R C lC C L L
m 101.63)]1 803,04/()293,2( 803,006.0 803,01[4,222  RL

where lcb is the longitudinal distance of the center of the hull from the half of the
float length, expressed as a percentage of the LWL.

m 197.3 1004.2222/4.222 111.7cbl

1002/
WLWL B
cbLLxl

18

Appendage resistance (RAPP)

The resistance of the appendix is determined according to the surface area of the
SAPP appendices, with the relation:
eq APP F APP k SvC R ) 1(222


kN RAPP 951.24,121.47271,7 025,11046,12
3

Where :
4,1 ) 1(2eqk represents the rudder factor

cTLSWL
APP
SAPP = A T (the area of the rudder)
c=50…70 for fast cargo ships with a propeller
I adopted c =65
658.134.222APPS
=47.217 [m2].

Wave resistance (Rw)

The wave resistance will be determinated with the formula below(valid for
numbers Froude Fn  0,4) :

)] cos( [
5 2 12
4 1Fn mFm
Wd
ne g ccc R

19

)] 167,0953,0cos( 10308,3 167,0964,1[2 7 9,0
7618381,9 025,11707,0 686,2   e RW
kN Rw 253.80

Where:

37565,1 07961,1 78613,3
7 1 ) 90( )/( 2223105  Ei BT c c
 686,2 51.3990 2,32/8,13 144,0 222310537565,1 07961,1 78613,3
1     c

WLLBc /7

144,04,222/2,327  c

Ei
– the half -angle between the tangent to the float in the forward extremity;
. ] )L/ 100( )B/L()l 02251,0 C1( )C1( )B/L( exp[891i
16302,0 3
WL34574,0
R6367,0
cb p30484,0
W80856,0
WL E
  

51.39 ] )4,222/ 76183 100( )2,32/101.63()197.3 02251,0 803,01( )855,01( )2,32/4,222( exp[891
16302,03 34574,06367,0 30484,0 80856,0
     Ei

707,0033,089,1
2  ec

3 89,1
2cec

20

)]h T A 31,0(TB/[A56,0 cB F BT5,1
BT 3

033,0)] 347,48,13 807.45 31,0(8,132,32/[ 807,4556,05,1
3    c

m T hf B 347,4 315.0
, where hB is the elevation of the center of the bulb's
transverse surface.

) /( 8,015 M T CTBA c 

 1 981,08,132,32/08,015 c

/ 03,0 446,1 BL CWL p

953,032,2222,40,03- 0,803 1,446  

d = -0,9;

163/1
1 / 79323,4 / 75254,1/ 0140407,0 c LB L TL mWL WL WL  

964,1 162,14,222/2,3279323,44,222/ 76183 75254,18,13/4,222 0140407,03/1
1
    m

162,1 803,0 984388,6 803,0 8673,13 803,0 07981,83 2
16  c

3 2
p 16 C 984388,6 C 13,8673- C 07981,8P P c   

21

) 034,0(
15 429,34,0Fne c m
  7 167,0034,0
4 10308,3 4,0 169.029,3  e m

39.144 /L 512 /Lfor 69385,13
WL3
WL 15  c

Wave resistance of bulbous bow (RB)
The additional pressure resistance due to the presence of the bulb is calculated by:
) 1/( 11,02 5,1 3 ) 3(2
i BT ip
B Fn g A Fn e RB

][002,0) 167,01/(81,9 025,1 807,45 836,0 11,02 5,1 3 ) 520,03(2
kN Re R
BB
 

where:

52,0)347,45,18,13/( 807.4556,02/1 Bp

] 15,0) 25,0 (/[ Fn2/12 2/1
i v A hTgvBT B F 

836,0) ] 716,715,0) 807,4525,0 347,48,13(81,9/[716,7 Fn2/12 2/1
i    

Additional adhesion resistance between model and ship (RA)

Additional adhesion resistance between model and ship is the effect of the body
roughness and aerodynamic strength of the ship's emerge side at a zero wind spee d.
Determination of resistance is made according to the total wetted surface of the
ship's body, as follows:
)5,1 /( 56,02/1
B BT B h T A p 

22

) (22
APP A A SSvC R 
][29.112)217.47 11062(271,7 025,11033,02
3
kN RR
AA


Where:
) 04,0( )5,7/ ( 003,0 00205,0 )100 ( 006,04 24 2/1 16,0c cC L L CB WL WL A  

34 2/1 16,0
1033,0)04,0 04,0(707,0 789,0 )5,7/4,222( 003,0 00205,0 )1004,222( 006,0

  AC
0,04 /LT ; ,040 /LT pentru 0,04WL F WL F 4   c

RT components Symbol Calculate value [kN]
Friction resistance RF 493,98
Form factor of bare hull
without appendices (1+k1) 1,221
Appendage resistance RAPP 2,951
Wave resistance Rw 80,253
Wave resistance of bulbous bow RB 0,002
Additional adhesion resistance
between model and ship RA 112,29
Total resistance RT 798,944
Total resistance (without 1+k1) RT 689,485

Table 2.2 .2 Resistance components

23
Velocity Simbol [Nd ] 12 [Nd] 13 [N d] 14 [Nd] 15 [Nd] 16 [Nd] 17 [Nd] 18 [Nd]
Velocity [m/s] 6.173 6.687 7.202 7.716 8.230 8.745 9.259
Total resistance Rt [kN] 490.025 579.422 683.672 798.944 957.326 1139.694 1362.243

Table 2.2 .3 The forward resistance components calculated for a range of speeds

Fig. 2.2.2 Ship resistance 02004006008001000120014001600
10 11 12 13 14 15 16 17 18 19 20Rt[kN]

24

CHAPTER 3

– SHIP PROPULSION –

25

3.1. Calculation of propulsion coefficients

Calculation of the propulsion coefficient s is determined using the Holtrop –
Mennen method as follows:

 Wake fraction coefficient (w):

20 192/1
120111 20 9
) 1(27915,0) 1(93405,0 050776,0
ccC LBcCCcTLCccw
P wlPV
Awl
v


 

  

85,0 091,0777,04,2222,3285,0 27915,0)777,01(0018,0428,1 93405,0 050776,08,134,2220018,085,0 014,12
2/1




 w

w=0.288
where :
,8 9cc
for
014,12 288 8  c c

Ae wl TDLSBc  /8
, for
5 /aTB
014,128c

ppc c  015,0120

26

85,0)10( 015,0120 c

e ADTc /11
, for
2 /e ADT
428,1 428,1 /;11 c DTe A

P M C C c   38648,0 71276,0) 3571,1/( 18567,019 ,for
7,0,PC
c19= 0,18567/(1,3571 -0.981) -0.71276 + 0,38648· 0,803
c19 = 0,091

 Thrust deduction fraction (t):

)10( 0015,0]197,3 0225,0 803,01/[ )66.9/8,132,32( )4,222/2,32( 25014,001762,0 2624,0 28956,0
   t

) __ _ (164,0 calculein utilizata valoarea t

281,012,0 803,05,012,0 5,0

ttC tP

 Relative rotative efficiency
R :

)l 0225,0 C( 07424,0 A/A 05908,0 9922,0cb P 0 E R

013,1]197,3 0225,0 803,0[ 07424,0 55,0 05908,0 9922,0

RR


T – Thrust force
pp cb P e WL c l C DTB LB t    0015,0 ) 0225,0 1/( )/ ( )/( 25014,001762,0 2624,0 28956,0

27

kNtRT 674.9551
46,02,066,9) 2300 100000(674,955)43,03,1(
) ()3,03,1(
00 0

AAKDp pTZ
AA
ee ve

It is adopted
55,0
0AAe
where: Ae – the area of the propeller blades
A0 – The propeller disk area
Z = 4 blades
p0 = 100000 [Pa] ( atmosphe ric pressure )
pv = 2300 [Pa]
K = 0,2 (adopted )

 Advance velocity (vA):
) 1(w vvA

sm vA / 493,5)288,01(716,7 

 Relative rotative efficiency
H:

173,1288,01164,01
11wt
H

28
propulsion coefficients Symbol Value Unit
Wake fraction coefficient w 0.288
Thrust deduction fraction t 0.164
Relative rotative efficiency ηR 1.013
Advance velocity vA 5.493 [m/s]
Relative rotative efficiency ηH 1.173

Tab le 3.1 Propulsion coefficients

3.2 Hydrodynamics characteristics of
screw propulsion

The propeller design data is based on the results of open water
test w ith varied series of screw models. The screw series comprise models whose
geometrical characteristics such:
-pitch ratio P/D;
-number of blade Z;
-blade area ratio Ae/A0;
– blade sections ;
– blade thickness are systematically varied.
The most extensive and widely used propeller series is the Wageningen B
series,also known as the Troost,or NSMB B series.

29
The open water characteristics of series of propellers are available i n a variety of
forms including diagrams giving K T, KQ , ƞ0 as function of J =0.0001, 0.1 , 0.2…1 for
P/D = 0.6, … , 1.2
Also are used different diagrams for the different values of Z and Ae/A0.

Those values of torque coefficients (K Q) and thrust coefficients (K T) can be
expressed as polynomials usin g:
-advance ratio (J)
-number of blade (z)
-pitch ratio P/D
-blade area ratio Ae/A0




46
0038
00
)/()/()()()/()/()()(
kz
ey x Q
KQ Qkz
ey x Q
KT T
k k k kk k k K
AA DP J zA KAA DP J zA K

Where – Ak – regression coefficients
– xk, yk, zk, – correspondent exponents of the independent variable J, P/D,
Ae/A0.
Using the polynomial equations and the coefficients A KT and A KQ , xk, yk, zk, Q k
(Tables 3.2.1 and 3.2.2), it`s create a code and a diagram to calculate the open
water characteristics of B Wageningen screw series.

30
Using the computed codes based on standard serie s below(Tables 3.2.1 and
3.2.2),we can estimate the propeller of optimum efficiency.

k Akt xk yk zk Qk
1 0.008805 0 0 0 0
2 -0.20455 1 0 0 0
3 0.166351 0 1 0 0
4 0.158114 0 2 0 0
5 -0.14758 2 0 1 0
6 -0.4815 1 1 1 0
7 0.415437 0 2 1 0
8 0.01440 4 0 0 0 1
9 -0.05301 2 0 0 1
10 0.014388 0 1 0 1
11 0.060683 1 1 0 1
12 -0.01259 0 0 1 1
13 0.010969 1 0 1 1
14 -0.1337 0 3 0 0
15 0.006384 0 6 0 0
16 -0.00133 2 6 0 0
17 0.168496 3 0 1 0
18 -0.05072 0 0 2 0
19 0.085456 2 0 2 0
20 -0.05045 3 0 2 0
21 0.010465 1 6 2 0
22 -0.00648 2 6 2 0
23 -0.00842 0 3 0 1
24 0.016842 1 3 0 1
25 -0.00102 3 3 0 1
26 -0.03178 0 3 1 1
27 0.018604 1 0 2 1
28 -0.00411 0 2 2 1
29 -0.00061 0 0 0 2
30 -0.00498 1 0 0 2
31 0.002598 2 0 0 2
32 -0.00056 3 0 0 2
33 -0.00164 1 2 0 2
34 -0.00033 1 6 0 2
35 0.000117 2 6 0 2
36 0.000691 0 0 1 2
37 0.004217 0 3 1 2
38 5.65E -05 3 6 1 2
39 -0.00147 0 3 2 2
Table 3.2.1 Coefficients for K T Polynomial

31

k Akq xk yk zk Qk
1 0.003794 0 0 0 0
2 0.008865 2 0 0 0
3 -0.03224 1 1 0 0
4 0.003448 0 2 0 0
5 -0.04088 0 1 1 0
6 -0.10801 1 1 1 0
7 -0.08854 2 1 1 0
8 0.188561 0 2 1 0
9 -0.00371 1 0 0 1
10 0.005137 0 1 0 1
11 0.020945 1 1 0 1
12 0.004743 2 1 0 1
13 -0.00723 2 0 1 1
14 0.004 384 1 1 1 1
15 -0.02694 0 2 1 1
16 0.055808 3 0 1 0
17 0.016189 0 3 1 0
18 0.003181 1 3 1 0
19 0.015896 0 0 2 0
20 0.047173 1 0 2 0
21 0.019628 3 0 2 0
22 -0.05028 0 1 2 0
23 -0.03002 3 1 2 0
24 0.041712 2 2 2 0
25 -0.03977 0 3 2 0
26 -0.0035 0 6 2 0
27 -0.01069 3 0 0 1
28 0.001109 3 3 0 1
29 -0.00031 0 6 0 1
30 0.003599 3 0 1 1
31 -0.00142 0 6 1 1
32 -0.00384 1 0 2 1
33 0.01268 0 2 2 1
34 -0.00318 2 3 2 1
35 0.003343 0 6 2 1
36 -0.00183 1 1 0 2
37 0.000112 3 2 0 2
38 -2.97E -05 3 6 0 2
39 0.00027 1 0 1 2
40 0.000833 2 0 1 2
41 0.001553 0 2 1 2
42 0.000303 0 6 1 2
43 -0.00018 0 0 2 2
44 -0.00043 0 3 2 2
45 8.69E -05 3 3 2 2
46 -0.00047 0 6 2 2
47 5.54E -05 1 6 2 2
Table 3.2.2 Coefficients for K Q Poly nomial

Using the computed codes based on standard series below(Tables 3.2.1 and
3.2.2),we can estimate the propeller of optimum efficiency.

32
P/D=0.6
η J KT KQ
0.000 0.0001 0.247 0.024
0.160 0.1 0.220 0.022
0.308 0.2 0.189 0.020
0.436 0.3 0.155 0.017
0.531 0.4 0.117 0.014
0.564 0.5 0.076 0.011
0.439 0.6 0.033 0.007
-0.439 0.7 -0.013 0.003
6.764 0.8 -0.060 -0.001
2.664 0.9 -0.108 -0.006
2.301 1 -0.157 -0.011

P/D=0.9
η J KT KQ
0.000 0.0001 0.383 0.050
0.120 0.1 0.357 0.047
0.236 0.2 0.328 0.044
0.346 0.3 0.295 0.041
0.449 0.4 0.258 0.037
0.541 0.5 0.219 0.032
0.619 0.6 0.177 0.027
0.672 0.7 0.133 0.022
0.680 0.8 0.087 0.016
0.564 0.9 0.039 0.010
-0.420 1 -0.009 0.003

P/D=1.1
η J KT KQ
0.000 0.0001 0.463 0.073
0.100 0.1 0.440 0.070
0.198 0.2 0.413 0.066
0.294 0.3 0.382 0.062
0.385 0.4 0.348 0.058
0.471 0.5 0.310 0.052
0.550 0.6 0.270 0.047
0.620 0.7 0.228 0.041
0.678 0.8 0.184 0.034
0.717 0.9 0.138 0.028
0.718 1 0.091 0.020

P/D=0.7
η J KT KQ
0.000 0.0001 0.293 0.031
0.145 0.1 0.267 0.029
0.283 0.2 0.236 0.02 7
0.409 0.3 0.202 0.024
0.516 0.4 0.164 0.020
0.593 0.5 0.124 0.017
0.615 0.6 0.080 0.013
0.488 0.7 0.035 0.008
-0.458 0.8 -0.012 0.003
4.162 0.9 -0.060 -0.002
2.236 1 -0.109 -0.008
P/D=0.8
η J KT KQ
0.000 0.0001 0.339 0.040
0.132 0.1 0.313 0.038
0.258 0.2 0.283 0.035
0.377 0.3 0.249 0.031
0.484 0.4 0.212 0.028
0.575 0.5 0.171 0.024
0.639 0.6 0.129 0.019
0.652 0.7 0.084 0.014
0.529 0.8 0.037 0.009
-0.456 0.9 -0.010 0.003
3.157 1 -0.059 -0.003
P/D=1
η J KT KQ
0.000 0.0001 0.424 0.061
0.109 0.1 0.400 0.058
0.216 0.2 0.372 0.055
0.319 0.3 0.340 0.051
0.416 0.4 0.304 0.047
0.505 0.5 0.265 0.042
0.586 0.6 0.224 0.037
0.652 0.7 0.181 0.031
0.697 0.8 0.136 0.025
0.702 0.9 0.089 0.018
0.593 1 0.04 1 0.011

33

P/D=1.2
η J KT KQ
0.000 0.0001 0.499 0.086
0.092 0.1 0.477 0.083
0.183 0.2 0.452 0.079
0.272 0.3 0.422 0.074
0.358 0.4 0.389 0.069
0.439 0.5 0.353 0.064
0.516 0.6 0.315 0.058
0.587 0.7 0.274 0.052
0.649 0.8 0.231 0.045
0.700 0.9 0.186 0.038
0.732 1 0.140 0.030

Using the computed open water characteristics for a given propeller,I drawn a
diagram for each P/D=0.6…1.2.

Fig. 3.2.1 Diagram K T as function of P/D

-0.2-0.100.10.20.30.40.50.6
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1J
PD=0.6
PD=0.7
PD=0.8
PD=0.9
PD=1
PD=1.1
PD=1.2

34

Fig. 3.2.2 Diagram K Q as function of P /D

3.2.1 The engine selection

To determine open water characteristics it must to calculate :
– Delivered Power
– the rotation
using the values of the Th rust and Diameter .

-0.0200.020.040.060.080.1
0 0.15 0.3 0.45 0.6 0.75 0.9 1.05J
PD=0.6
PD=0.7
PD=0.8
PD=0.9
PD=1
PD=1.1
PD=1.2

35

INPUT DATA :
number of blade Z = 4
blade area ratio Ae/A0 = 0.55
density ρ = 1.025 t/m3
thrust T = 955.674 KN
speed v = 15 kn = 7.716 m/s
diameter D = 6.751 m
wake fraction coefficient w = 0.288
advance velocity vA = 5.493 m/s

OUTPUT DATA :
delivered power =?
rotat ion =?

First step is to draw two diagrams for P/D =0.6…1.2.

Fig. 3.2.1.1 KT = f(J) -0.200-0.1000.0000.1000.2000.3000.4000.5000.600
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1J
PD=0.6
PD=0.7
PD=0.8
PD=0.9
PD=1
PD=1.1
PD=1.2

36

Fig. 3.2.1.2 K Q = f(J)
ctJ KTDvK JDvJTKDDJvTKDnTKDJvnDnvJ
TA
T
ATAT TA A




22 2
2
2 2242 4 2



6778.0ct

For different values given to J 1, J2, J3, J 4 it`s obtained thrust
coefficients K T1, KT2, KT3, KT4.
J KT J KT
0.1 0.007 0.1 0.007
0.2 0.027 0.2 0.027
0.3 0.061 0.3 0.061
0.4 0.108 0.4 0.108
0.5 0.169 0.5 0.169
0.6 0.244 0.6 0.244
-0.0200.020.040.060.080.1
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1J
PD=0.6
PD=0.7
PD=0.8
PD=0.9
PD=1
PD=1.1
PD=1.2

37

Fig. 3.2.1.3 Advance ratio
P/D=0.6 J1= 0.41 KT1= 0.114 KQ1= 0.016
P/D=0.7 J2= 0.46 KT2= 0.143 KQ2= 0.019
P/D=0.8 J3= 0.52 KT3= 0.183 KQ3= 0.023
P/D=0.9 J4= 0.55 KT4= 0.205 KQ4= 0.03
P/D=1 J4= 0.58 KT5= 0.228 KQ5= 0.038
P/D=1.1 J4= 0.62 KT6= 0.261 KQ6= 0.048
P/D=1.2 J4= 0.65 KT7= 0.286 KQ7= 0.057

After K T and K Q are calculated, i t will determine open water efficiency η 0.

20J
KK
QT

38
J1= 0.41 Ƞ01= 0.464683524
J2= 0.46 Ƞ02= 0.552644155
J3= 0.52 Ƞ03= 0.659489495
J4= 0.55 Ƞ04= 0.598263491
J5= 0.58 Ƞ05= 0.553893248
J6= 0.62 Ƞ06= 0.535623371
J7= 0.65 Ƞ07= 0.51974569 6

Fig. 3.2.1.4 η 0 = f(J)

Analyzing the chart, corresponding to the maximum value of open water
efficiency ,we obtain the optimum advance ratio Jopt = 0.52 .
Then it will be calculate the rotation with formula:

rps rpm n nDJvnA564.1 89.93751.652.0493.5
 
0.30.350.40.450.50.550.60.650.7
0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7eta
eta

39
Then we make the chart of the pitch ratio P/D opt using the values below:
J P/D
0.41 0.6
0.46 0.7
0.52 0.8
0.55 0.9
0.58 1
0.62 1.1
0.65 1.2

Fig.3.2.1.5 P/D = f(J)

For J opt = 0.52, it will be used the pitch ratio P/D=0.8.
J KT KQ 10 KQ
0.0001 0.339 0.040 0.403
0.1 0.313 0.038 0.377
0.2 0.283 0.035 0.348
0.3 0.249 0.031 0.315
0.4 0.212 0.028 0.278
0.5 0.171 0.024 0.237
0.6 0.129 0.019 0.193
0.7 0.084 0.014 0.144
0.8 0.037 0.009 0.090
0.9 -0.010 0.003 0.032
1 -0.059 -0.003 -0.030
00.20.40.60.811.21.4
0.3 0.4 0.5 0.6 0.7P/D
P/D

40

Fig. 3.2.1.6 P/D =0.9

Using the chart 3.2.1.5 we can determine the Kq value .
So,for J = 0.52 , KQ it will be 0.023.

After that,t he Delivered Power will be calculated with formula below:
85.0198.032. 955285.01 98.008. 795708. 7957751.6 025.1 564.1 2 023.02
5 35 3

uredaxBB
u red axD
BDDQ D
cKW PPcPPKW PPD n K P


Knowing the PB = 9552.32 KW and n = 93.89 rpm,it were chosen two
engine s:
First engine from MAN B&W has : -0.010-0.0050.0000.0050.0100.0150.0200.0250.0300.0350.0400.045
0 0.2 0.4 0.6 0.8 1 1.2P/D
P/D

41
PB= 12460 KW
n= 117 rpm

Fig 3.2.1.7 Main engine [www.MAN B&W .com]

Fig 3.2.1.8 Main engine [www.MAN B&W.com]

42
3.2.2 Determining the optimum diameter

Using the characteristics of the engine like delivered power and
rotation,can be determinated the optimum diameter of the p ropeller
INPUT DATA:
Brake Power PB =12460 KW
Delivered Power PD = 10379.18 KW
Rotation n = 117 rpm = 1.95 rps
Number of blade z = 4
Blade area ratio Ae/A 0 = 0.55
Density ρ = 1.025 t/m3
Speed v = 15 kn = 7.716 m/s
Wake faction coefficient w = 0.28
Advance Velocity vA = 5.493 m/s

OUTPUT DATA:

Diameter = ?

For P/D = 0.6 , P/D = 0.7, P/D = 0.8, P/D = 0.9 , P/D = 1, P/D =
1.1, P/D = 1.2 we can draw two diagrams :

43

Fig. 3.2.2.1 K Q = f(J)

Fig. 3.2.2.2 K T = f(J)
-0.02-0.0100.010.020.030.040.050.060.070.08
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1P/D=0.6
P/D=0.7
P/D=0.8
P/D=0.9
P/D=1
P/D=1.1
P/D=1.2
J
-0.2-0.15-0.1-0.0500.050.10.150.20.250.30.350.40.450.50.55
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1P/D=0.6
P/D=0.7
P/D=0.8
P/D=0.9
P/D=1
Series6
Series7

44

225.12
222;2
5 5
52
5
35 3 5 25 2







ctJct K J
vnPK
nJvnPKnJvDDnvJDnPK
DnnP
KDnQKnPQ
Q
AD
Q
AD
QA AD
QD
QQD

 

For different values given to J 1, J2, J3, J4 it`s obtained thrust
coefficients K Q1, KQ2, KQ3, KQ4.

J KQ
0.3 0.003
0.4 0.013
0.5 0.038
0.6 0.095
0.7 0.206
0.8 0.401
0.9 0.723

45

Fig. 3.2.2.3 Advance ratio
J1= 0.4 KQ1= 0.013 KT1= 0.1
J2= 0.44 KQ2= 0.020 KT2= 0.15
J3= 0.46 KQ3= 0.025 KT3= 0.19
J4= 0.48 KQ4= 0.031 KT4= 0.22
J5= 0.51 KQ5= 0.042 KT5= 0.265
J6= 0.525 KQ6= 0.049 KT6= 0.285
J7= 0.55 KQ7= 0.062 KT7= 0.327

After K T and K Q are calculated, it will determine open water efficiency η 0.
20J
KK
QT

J1= 0.4 P/D=0.6 ƞ01 = 0.508
J2= 0.44 P/D=0 .7 ƞ02 = 0.520
J3= 0.46 P/D=0.8 ƞ03 = 0.552
J4= 0.48 P/D=0.9 ƞ04 = 0.539
J5= 0.51 P/D=1 ƞ05 = 0.509
J6= 0.525 P/D=1.1 ƞ06 = 0.488
J7= 0.55 P/D=1.2 ƞ07 = 0.464

46

Fig. 3.2.2.4 η 0 = f(J)

Using the maximum value of open water effici ency from the chart 3.2.2.4, we can
obtain the optimum advance ratio,J opt = 0.46.
Now,the value of the optimum advance ratio will be used to calculate the
diameter
m D DnJvDopt optA
opt 124.695.146.0493.5 .
This value must keep the condition below:
Dopt < 0.65 T
6.124<0.65*13.8 =>

It remains to calculate pitch ratio P/D opt.
J P/D
0.4 0.6
0.44 0.7
0.46 0.8
0.48 0.9
0.51 1
0.525 1.1
0.55 1.2 0.4500.5000.5500.600
0.3 0.4 0.5 0.6J
J
6.124<8 .97

47

Fig. 3.2.2.5 P/D = f(J)
For J opt = 0.46, pitch rati o P/D opt = 0.8 .

3.2.3 Propeller design using Wageningen B Series

Following the main dimensions below,will be designed a
propeller for a bulk -carrier:
 Length waterline (L wl) = 222.4 m
 Beam (B) = 32.2 m
 Draught(T) = 13.8 m
 Speed (v) = 15 kn
 Deadweight = 65700 tdw
 Displacement = 78087 m3
00.10.20.30.40.50.60.70.80.911.11.21.3
0.3 0.35 0.4 0.45 0.5 0.55 0.6P/D
P/D

48
Speed of the ship
V [Nd] 14 15 16
Ship resistance
RT [kN] 683.672 798.944 957.326
Thrust deduction
coefficient
t 0.164 0.164 0.164
Wake fraction coeff icient
w 0.288 0.288 0.288
Hull efficiency
ȠH 1.173 1.173 1.173
Relative rotate efficiency
ȠR 1.013 1.013 1.013

Table 3. 2.3.1 Performance characteristics of the ship

The main engine choose has: – Brake Power (Pb) = 12460 KW
-Engine rotation = 117 rpm
– No. Cyl. = 7

An optimum propeller must consume all the delivered power.To achieve such
performance,will be considered two cases:
1. when cu = 0.85 and n = n 0
2. when cu = 0.75 and n = 0.9655 * n 0

First case:
Propeller rotation= engine rotation=117 rpm=1.95 rps
Delivered Power is calculated with formula:
u red ax B D c P P  ,
where:
-Brake power (PB) = 12460 KW

49
-Shaft efficiency (ηax ) = 0.98
-Randament redactor (ηred )= 1
-Cu = 0.85
u red ax B D c P P 
=> PD = 10379.18 KW

Ae/A 0 = 0.55
z = 4 blades
Second step is to calculated the to rque coefficient:

5 32 D nPKD
Q

– Delivered Power P D = 10379.18 KW
– Engine rotation n = 1.95 rps
– Diameter D = 6.124 m
– KQ = 0.025
– Water density ρ = 1025 kg/m3
Name Formula UM V1 V2 V3
Speed of the ship V m/s 7.2016 7.716 8.2304
Speed of advance
) 1(wvvA m/s 5.128 5.494 5.860
Advance rati o
DnvJA
 –
0.43 0.46 0.49
Pitch ratio P/D – diag. K Q-J – 0.68 0.8 0.94

50
Open water
efficiency η0 –
0.515 0.552 0.53
Thrust coefficient KT- diag. K T-J – 0.13 0.17 0.185
Thrust
4 2Dn KTT KN 712.94 932.31 1014.57
Hull efficien cy
wt
H11 –
1.174 1.174 1.174
Relative rotative
efficiency ηR –
1.013 1.013 1.013
Propulsive efficiency
R H D  0 – 0.613 0.657 0.630
Effective Power PE = R * v KW 4923.53 6164.65 7879.18
Delivered Power
DE
DPP KW
8037.74 9389.31 12498.83

Table 3.2.3.2 Main characteristics of the propeller
when c u = 0.85 and n = n 0

To calculate the pitch ratio and the speed of the optimum propeller,we
must draw two charts,using the values obtain before.
1. P/D = f(v)
v1 = 14[Nd] P/D1 = 0.68
v2 = 15[Nd] P/D2 = 0.8
v3 = 16[Nd] P/D3 = 0.94

51

Fig. 3.2.3.1 P/D = f(v)
2. P D = f(v)
v1 = 14[Nd] PD1 = 8037.74[kW]
v2 = 15[Nd] PD2 = 9389.31[kW]
v3 = 16[Nd] PD3 = 12498.83[kW]

Fig. 3.2.3.2 P D = f(v)

00.10.20.30.40.50.60.70.80.91
13.5 14 14.5 15 15.5 16 16.5P/D
P/D
0.00500.001000.001500.002000.002500.003000.003500.004000.004500.005000.005500.006000.006500.007000.007500.008000.008500.009000.009500.0010000.0010500.0011000.0011500.0012000.0012500.0013000.0013500.00
13.5 14 14.5 15 15.5 16 16.5PD
PD

52
RESULTS FOR CASE 1:
V= 15.32 [Nd]
P/D= 0.83

Second case:
Propeller rotation= 0.9655* engine rotation=112.96 rpm=1.882 rps
Delivered Power is calculated with formula:
u red ax B D c P P  , where:
-Brake power (P B) = 12460 KW
-Shaft efficiency (η ax ) = 0.98
-Randament redactor (η red )= 1
-Cu = 0.75
u red ax B D c P P 
=> P D = 9158.1 KW
Ae/A 0 = 0.55
z = 4 blades
Next step is to calculated the torque coefficient:

5 32 D nPKD
Q

– Deliver ed Power P D = 9158.1 KW
– Engine rotation n = 1.88 2 rps
– Diameter D = 6.124 m
– KQ = 0.024

53
– Water density ρ = 1025 kg/m3
Name Formula UM V1 V2 V3
Speed of the
ship V m/s 7.202 7.716 8.230
Speed of
advance
) 1(wvvA m/s 5.128 5.494 5.860
Advance
ratio
DnvJA
 – 0.44 0.48 0.51
Pitch ratio P/D – diag. K Q-J – 0.7 0.87 1
Open water
efficiency η0 – 0.52 0.54 0.51
Thrust
coefficient KT- diag. K T-J – 0.14 0.22 0.27
Thrust
4 2Dn KTT KN 767.7860234 1206.520894 1480.73
Hull
efficiency
wt
H11 – 1.174 1.174 1.174
Relative
rotative
efficiency ηR – 1.013 1.013 1.013
Propulsive
efficiency
R H D  0 – 0.618 0.642 0.607
Effective
Power PE = R * v KW 4923.53 6164.65 7879.18
Delivered
Power
DE
DPP KW 7960.45 9597.96 12988.98
Table 3. 2.3.3 Main characteristics of the propeller
when c u = 0.85 and n = n 0
To calculate the pitch ratio and the speed of the optimum propeller,we must
draw two charts,using the values obtain before.
1. P/D = f(v)

54
v1 = 14[Nd] P/D1 = 0.7
v2 = 15[Nd] P/D2 = 0.87
v3 = 16[Nd] P/D3 = 1

Fig. 3.2.3.3 P/D = f(v)
2. P D = f(v)
v1 = 14[Nd] PD1 = 7960.45[kN]
v2 = 15[Nd] PD2 = 9597.96[kN]
v3 = 16[Nd] PD3 = 12988.98[kN]

Fig. 3.2.3.4 PD = f(v) 00.20.40.60.811.2
13.5 14 14.5 15 15.5 16 16.5P/D
P/D
0.002000.004000.006000.008000.0010000.0012000.0014000.00
13.5 14 14.5 15 15.5 16 16.5PD
PD

55

RESULTS FOR CASE 2 :
V= 14.8 [Nd]
P/D= 0.92

Next step is to verify the cavitation of the propeller.

3.2.3 Cavitation control propeller
– Schoenherr Criteria –

Cavitation is the f ormation of vapour cavities in a liquid, small
liquid -free zones ("bubbles" or "voids"), that are the consequence of forces acting
upon the liquid. It usually occurs when a liquid is subjected to rapid changes
of pressure that cause the formation of cavities in the liquid where the pressure
is relatively low. When subjected to higher pressure, the voids implode and can
generate an intense shock wave .

Damages made by cavitation:

56

http://www.cjrprop.com/consultancy/problem -solving/
http://gcaptain.com/propeller -cavitation -analysis/

The m ain dimensions are:
 Diameter D = 6.124 m
 Revolution rate n = 112.96 rpm = 1.8 82 rps
 Number of blade z = 4

57
 Blade area ratio A e/A 0 = 0.55
 Pitch ratio P/D = 0.92
 Speed v = 14.8 kn

2
0 ) ( 27.1 / DnPKf AA
SC
e 

Empirical coefficient f = 1.3
Cavitation characteristic K C = 0.29
Water density ρ = 1025 kg/m3
2 4
0 / 174759.721013.10 mN P pDhg pp PS v a v S 

 

Armospheric pr essure p 0 = 10.13 * 104 N/m2
Vapour pressure of water at 15 °C p v = 1707 N/m2
Height of shaft centre -line above base
mDTha 53.102.02


373.0) ( 27.12 DnPKf
SC

CONDITION: A e/A 0 =0.55 > 0.375

3.2.4 Propelle r blade geometry

The propeller geometry is characterized by:
– Beam of the blade b r
– Distance between leading edge and propeller generator line b ri

58
– Distance between trailing edge and propeller generator line b re
– Distance between leading edge and maxi mum thickness line c r
– Maximum thickness of the section blade e r

Rr

01/AAz
Dbx
er
rri
bbx2
rr
bcx3
Dexr4
0.2 1.662 0.617 0.35 0.0366
0.3 1.882 0.613 0.35 0.0324
0.4 2.05 0.601 0.35 0.0282
0.5 2.152 0.586 0.35 0.024
0.6 2.187 0.561 0.389 0.0198
0.7 2.144 0.524 0.443 0.0156
0.8 1.98 0.463 0.479 0.0114
0.9 1.582 0.351 0.5 0.0072
1 – 0 – 0.0030

Table 3.2.4.1 Dimensions of the blade contour

– Beam of the blade b r is calculated by:
10/xzAADbe
r 

– Distance between leading edge and propeller generator line b ri
2xbbr ri

– Distance between trailing edge and propeller generator line b re
ri r re bb b

59
– Distance betwe en leading edge and maximum thickness line c r
3xbcr r

– Maximum thickness of the section blade e r
4xDer

br bri bre cr er
1.400 0.000 1.400 0.490 0.224
1.585 0.978 0.607 0.555 0.198
1.726 1.058 0.668 0.604 0.173
1.812 1.089 0.723 0.634 0.147
1.842 1.033 0.809 0.716 0.121
1.806 0.946 0.859 0.800 0.096
1.667 0.772 0.895 0.799 0.070
1.332 0.468 0.865 0.666 0.044
– – – – 0.018

Table 3.2.4.2 Propeller geometr y characteristics

60
3.2.5 Calculation of resistance
of the blade propeller
At radius 0.6R, the value of the blade thicknes s of solid propeller must be
equal with the value of the formula (according to the rules Germanisher Ll oyd):
mm CCKkKtDyn G 3133.1101 0 

) (15062.32) ( 637.817 tan0076.115000cos1
00
normaland generatixfaceby included AnglemDRrake Blade mm Ren
HeK



mm HPR radiusat profileof angle Pitch radDH
65. 5634)6.0 ( 487.0 99.2553.0arctan0
6.0


k = 44 (Blade profile as for Wageningen B Series propeller)
44.2
cossin cos 2 10
25
1 






wmW
czBnHDP
K

PW = 12460 KW (Main engine power)
)() (
RBRBHHM
= 4677.198 mm

61
r/R R B=br %H H RBH RB
0.2 612.462876
3 1.400 0.822 4631.68925
5 3970385.45
5 857.2219
0.3 918.694314
4 1.585 0.887 4997.94205
5 7277200.35
8 1456.039
0.4 1224.92575
3 1.726 0.95 5352.92553
8 11319762.0
1 2114.687
0.5 1531.15719
1 1.812 0.992 5589.58119
4 15510428 2774.882
0.6 1837.388 62
9 1.842 1 5634.65846
2 19067768.5
6 3384.015
0.7 2143.62006
7 1.806 1 5634.65846
2 21808342.5
2 3870.393
0.8 2449.85150
5 1.667 1 5634.65846
2 23017333.7
9 4084.956
0.9 2756.08294
3 1.332 1 5634.65846
2 20689444.3
5 3671.819
1 3062.31438
1 – 1 5634.65846
2 – –
Ʃ(RBH) Ʃ(RB)
122660665 22214.01

Table 3. 2.5.1 Values corresponding t o the pitch at the various radius

Cw = 630 (Cast manganese aluminium broze)
CG – size factor
85.02.121.11Df
f1 = 7.2 for solid propeller
85.0 0921.1 1.1 GC

1 024.15.01
33max




ff
Cm
Dyn
(Dynamic factor)
f3 = 0.2
5.1 5579.112maxT
mEf

62

389.1) 1(103.43
9
TDw nVES
T
CONDITION : e r > t ( 121 mm
 110.313)
So,the blades of the propeller will resist.

3.2.6 The second engine

Know ing the P B = 9319.34 KW and n = 93.89 rpm,I chose the second engine.
The second engine from WARTSILA has :
PB= 11300 KW
n= 105 rpm

63

Fig 3.2. 6.1 Main engine [www.wartsila.com]

3.2.7 Determining the optimum diameter

Using the characteristics of the engine like delivered power and
rotation,can be determinated the optimum diameter of the propeller
INPUT DATA:
Brake Power PB = 11300 KW
Delivered Power PD = 9412.9 KW
Rotation n = 105 rpm = 1.7 5 rps
Number of blade z = 4
Blade area ratio Ae/A 0 = 0.55
Density ρ = 1.025 t/m3
Speed v = 15 kn = 7.716 m/s
Wake faction coefficient w = 0.28 8
Advance Velocity vA = 5.493 m/s

64
OUTPUT DATA:
Diameter = ?

For P/D = 0.6 , P/D = 0.7, P/D = 0.8, P/D = 0.9, P/D = 1, P/D =
1.1, P/D = 1.2 we ca n draw two diagrams :

Fig. 3.2. 7.1 K Q = f(J)

Fig. 3.2.7 .2 K T = f(J) -0.02-0.0100.010.020.030.040.050.060.070.08
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1P/D=0.
6
P/D=0.
7
P/D=0.
8
P/D=0.
9
P/D=1
P/D=1.
1
-0.2-0.100.10.20.30.40.50.6
0 0.2 0.4 0.6 0.8 1 1.2P/D=0.6
P/D=0.7
P/D=0.8
P/D=0.9
P/D=1
P/D=1.1
P/D=1.2

65

894.02
222;2
5 5
52
5
35 3 5 25 2







ctJct K J
vnPK
nJvnPKnJvDDnvJDnPK
DnnP
KDnQKnPQ
Q
AD
Q
AD
QA AD
QD
QQD

 

For different values given to J 1, J2, J3, J4 it`s obtained thrust
coefficients K Q1, KQ2, KQ3, KQ4.

J KQ
0.3 0.002
0.4 0.009
0.5 0.028
0.6 0.070
0.7 0.150
0.8 0.293
0.9 0.528

66

Fig. 3.2.7 .3 Advance ratio

0.43 KQ1= 0.013 KT1= 0.1
J2= 0.46 KQ2= 0.020 KT2= 0.14
J3= 0.485 KQ3= 0.025 KT3= 0.18
J4= 0.52 KQ4= 0.031 KT4= 0.21
J5= 0.54 KQ5= 0.042 KT5= 0.24
J6= 0.56 KQ6= 0.049 KT6= 0.28
J7= 0.58 KQ7= 0.062 KT7= 0.325

After K T and K Q are calculated, it will determine open water efficiency η 0.
20J
KK
QT

J1= 0.43 P/D=0.6 ƞ01 = 0.520
J2= 0.46 P/D=0.7 ƞ02= 0.556
J3= 0.49 P/D=0.8 ƞ03 = 0.579
J4= 0.51 P/D=0.9 ƞ04 = 0.511
J5= 0.54 P/D=1 ƞ05 = 0.502
J6= 0.56 P/D=1.1 ƞ06 = 0.507
J7= 0.55 P/D=1.2 ƞ07 = 0.511

67

Fig. 3.2.7.4 η0 = f(J)

Using the maximum value of open water efficienc y from the chart 3.2.2.4, we can
obtain the optimum advance ratio,J opt = 0.485 .
Now,the value of the optimum advance ratio will be used to calculate the
diameter
m D DnJvDopt optA
opt 472.675.1 485.0493.5 .
This value must keep the condition below:
Dopt < 0.65 * T
6.472 <0.65*13.8 =>

It remains to calculate pitch ratio P/D opt. 0.4000.5000.600
0.3 0.4 0.5 0.6J
J
6.472 <8.97

68
J P/D
0.43 0.6
0.46 0.7
0.485 0.8
0.52 0.9
0.54 1
0.56 1.1
0.58 1.2

Fig. 3.2.7.5 P/D = f(J)
For J opt = 0.485 , pitc h ratio P/D opt = 0.8 .

3.2.8 Propeller design using Wageningen B Series

Following the main dimensions below,will be designed a
propeller for a bulk -carrier:
 Length waterline (L wl) = 222.4 m 00.10.20.30.40.50.60.70.80.911.11.21.3
0.3 0.35 0.4 0.45 0.5 0.55 0.6P/D
P/D

69
 Beam (B) = 32.2 m
 Draught(T) = 13.8 m
 Speed(v) = 15 kn
 Deadweight = 65700 tdw
 Displacement = 78087 m3

Speed of the ship
V [Nd] 14 15 16
Ship resistance
RT [kN] 683.672 798.944 957.326
Thrust deduction
coefficient
t 0.164 0.164 0.164
Wake fraction
coeffincient
w 0.288 0.288 0.288
Hull efficiency
ȠH 1.173 1.173 1.173
Relative rotate efficiency
ȠR 1.013 1.013 1.013

Table 3.2. 8.1 Performance characteristics of the ship

The main engine choose has: – Brake Power (Pb) = 11300 KW
-Engine rotation = 105 rpm
– No. Cyl. = 6

An optimum propeller must consume all the delivered power.To achieve such
performance,will be considered two cases:
3. when cu = 0.8 5 and n = n 0
4. when cu = 0.75 and n = 0.9655 * n 0

70
First case:
Propeller rotation= engine rotation=105 rpm=1.7 5 rps
Delivered Power is calculated with formula:
u red ax B D c P P  ,
where:
-Brake power (P B) = 11300 KW
-Shaft efficiency (ηax ) = 0.98
-Randament redactor (η red )= 1
-Cu = 0.85
u red ax B D c P P 
=> P D = 9412.9 KW

Ae/A 0 = 0.55
z = 4 blades
Second step is to calculated the torque coefficient:

5 32 D nPKD
Q

– Delivered Power P D = 9412.9 KW
– Engine rotation n = 1.7 5 rps
– Diameter D = 6.472 m
– KQ = 0.024
– Water density ρ = 1025 kg/m3

71
Name Formula UM V1 V2 V3
Speed of the ship V m/s 7.2016 7.716 8.2304
Speed of advance
) 1(wvvA m/s 5.128 5.494 5.860
Advance ratio
DnvJA
 –
0.45 0.485 0.52
Pitch ratio P/D – diag. K Q-J – 0.66 0.82 0.9
Open water
efficiency η0 –
0.554 0.579 0.52
Thrust coefficient KT- diag. K T-J – 0.13 0.18 0.21
Thrust
4 2Dn KTT KN 716.33 991.84 1157.15
Hull efficiency
wt
H11 –
1.174 1.174 1.174
Relative rotative
efficiency ηR –
1.013 1.013 1.013
Propulsive efficiency
R H D  0 – 0.659 0.689
Effective Power PE = R * v KW 0.659 4923.53 6164.65
Delivered Power
DE
DPP KW
4923.53 7471.90 8951.47

Table 3.2. 8.2 Main characteristics of the propeller
when c u = 0.85 and n = n 0
To calculate the pitch ratio and the speed of the optimum propeller,we
must draw two charts,using the values obtain before.

72
1. P/D = f(v)
v1 = 14[Nd] P/D1 = 0.66
v2 = 15[Nd] P/D2 = 0.82
v3 = 16[Nd] P/D3 = 0.9

Fig. 3.2.8 .1 P/D = f(v)
2. P D = f(v)
v1 = 14[Nd] PD1 = 7471.90 [kW]
v2 = 15[Nd] PD2 = 8951.47 [kW]
v3 = 16[Nd] PD3 = 12739.19 [kW]
00.10.20.30.40.50.60.70.80.91
13.5 14 14.5 15 15.5 16 16.5P/D
P/D

73

Fig. 3.2.8 .2 P D = f(v)
RESULTS FOR CASE 1:
V= 15.1 [Nd]
P/D= 0.93

Second case:
Propeller rotation = 0.9655* engine rotation=101.37 rpm=1.689 rps
Delivered Power is calculated with formula:
u red ax B D c P P  , where:
-Brake power (P B) = 11300 KW
-Shaft eff iciency (η ax ) = 0.98
-Randament redactor (η red )= 1
-Cu = 0.75
u red ax B D c P P 
=> P D = 8305.5 KW 0.00500.001000.001500.002000.002500.003000.003500.004000.004500.005000.005500.006000.006500.007000.007500.008000.008500.009000.009500.0010000.0010500.0011000.0011500.0012000.0012500.0013000.0013500.00
13.5 14 14.5 15 15.5 16 16.5PD
PD

74
Ae/A 0 = 0.55
z = 4 blades

Next step is to calculated the torque coefficient:

5 32 D nPKD
Q

– Delivered Power PD = 8305.5 KW
– Engine rotation n = 1.689 rps
– Diameter D = 6.472 m
– KQ = 0.023
– Water density ρ = 1025 kg/m3

Name Formula UM V1 V2 V3
Speed of the
ship V m/s 7.202 7.716 8.230
Speed of
advance
) 1(wvvA m/s 5.128 5.494 5.860
Advance
ratio
DnvJA
 – 0.47 0.50 0.54
Pitch ratio P/D – diag. K Q-J – 0.72 0.85 1
Open water
efficiency η0 – 0.56 0.54 0.502
Thrust
coefficient KT- diag. K T-J – 0.15 0.2 0.25
Thrust
4 2Dn KTT KN 826.5343803 1102.04584 1377.56

75
Hull
efficiency
wt
H11 – 1.174 1.174 1.174
Relative
rotative
efficiency ηR – 1.013 1.013 1.013
Propulsive
efficiency
R H D  0 –
Effective
Power PE = R * v KW 0.666 0.642 0.597
Delivered
Power
DE
DPP KW 4923. 53 6164.65 7879.18
Table 3. 2.8.3 Main characteristics of the propeller
when c u = 0.85 and n = n 0
To calculate the pitch ratio and the speed of the optimum propeller,we must
draw two charts,using the values obtain before.
1. P/D = f(v)
v1 = 14[Nd] P/D1 = 0.72
v2 = 15[Nd] P/D2 = 0.85
v3 = 16[Nd] P/D3 = 1

Fig. 3.2.8 .3 P/D = f(v) 00.20.40.60.811.2
13.5 14 14.5 15 15.5 16 16.5P/D
P/D

76
2. P D = f(v)
v1 = 14[Nd] PD1 = 7391.85 [kN]
v2 = 15[Nd] PD2 = 9597.96[kN]
v3 = 16[Nd] PD3 = 13195.97 .98[kN]

Fig. 3.2.8.4 PD = f(v)
RESULTS FOR CASE 2:
V= 14.8 [Nd]
P/D= 0.82

Next step is to verify the cavitation of the propeller.
3.2.9 Cavitation control propeller
– Schoenherr Criteria –
The main dimensions are:
 Diameter D = 6.472 m
 Revolution rate n = 1 01.377 rpm = 1.689 rps 0.002000.004000.006000.008000.0010000.0012000.0014000.00
13.5 14 14.5 15 15.5 16 16.5PD
PD

77
 Number of blade z = 4
 Blade area ratio A e/A 0 = 0.55
 Pitch ratio P/D = 0.8 2
 Speed v = 14.8 kn
2
0 ) ( 27.1 / DnPKf AA
SC
e 

Empirical coefficient f = 1.3
Cavitation characteristic K C = 0.29
Water density ρ = 1025 kg/m3
2 4
0 / 171258.721013.10 mN P pDhg pp PS v a v S 

 

Armospheric pressure p 0 = 10.13 * 104 N/m2
Vapour pressure of water at 15 °C p v = 1707 N/m2
Height of shaft centre -line above base
mDTha 36.102.02


342.0) ( 27.12 DnPKf
SC

CONDITION: A e/A 0 =0.55 > 0.342
3.2.10 Propeller blade geometry
The propeller geometry is characterized by:
– Beam of the blade b r
– Distance between leading edge and propeller generator line b ri
– Distance between trailing edge and prop eller generator line b re
– Distance between leading edge and maximum thickness line c r
– Maximum thickness of the section blade e r

78

Rr

01/AAz
Dbx
er
rri
bbx2
rr
bcx3
Dexr4
0.2 1.662 0.617 0.35 0.0366
0.3 1.882 0.613 0.35 0.0324
0.4 2.05 0.601 0.35 0.0282
0.5 2.152 0.586 0.35 0.024
0.6 2.187 0.561 0.389 0.0198
0.7 2.144 0.524 0.443 0.0156
0.8 1.98 0.463 0.479 0.0114
0.9 1.582 0.351 0.5 0.0072
1 – 0 – 0.0030

Table 3.2.10 .1 Dimensions of the blade contour

– Beam of the blade b r is calculated by:
10/xzAADbe
r 

– Distance between leading edge and propeller generator line b ri
2xbbr ri

– Distance between trailing edge and pr opeller generator line b re
ri r re bb b

– Distance between leading edge and maximum thickness line c r
3xbcr r

79
– Maximum thickness of the section blade e r
4xDer

br bri bre cr er
1.479 0.000 1.479 0.518 0.237
1.675 1.033 0.642 0.586 0.210
1.825 1.118 0.706 0.639 0.183
1.915 1.151 0.764 0.670 0.155
1.946 1.092 0.854 0.757 0.128
1.908 1.000 0.908 0.845 0.101
1.762 0.816 0.946 0.844 0.074
1.408 0.494 0.914 0.704 0.047
– – – – 0.019
Table 3.2.10 .2 Propeller geometry characteristics

Calculation of resistance of the blade propeller
At radius 0.6R, the value of the blade thickness of solid propeller must be
equal with the value of the formula (according to the rules Germanisher Lloyd ):
mm CCKkKtDyn G 608.941 0 

) (15236.32) ( 119.864 tan0067.115000cos1
00
normaland generatixfaceby included AnglemDRrake Blade mm Ren
HeK



80

mm HPR radiusat profileof angle Pitch radDH
69. 5307)6.0 ( 4346.0 489.2353.0arctan0
6.0
 
k = 44 (Blade profile as for Wageningen B Series propeller)
679.1
cossin cos 2 10
25
1 






wmW
czBnHDP
K

PW = 11300 KW (Main engine power)
)() (
RBRBHHM
= 5201.360 mm

r/R R B=br %H H RBH RB
0.2 647.2803535 1.479 0.822 4362.928494 4177309.595 957.4554
0.3 970.9205302 1.675 0.887 4707.928923 7656465.404 1626.292
0.4 1294.560707 1.825 0.95 5042.313953 11909712.8 2361.954
0.5 1618.200884 1.915 0.992 5265.237307 16318783.26 3099.344
0.6 1941.8410 6 1.946 1 5307.698898 20061521.35 3779.702
0.7 2265.481237 1.908 1 5307.698898 22944925.5 4322.952
0.8 2589.121414 1.762 1 5307.698898 24216925.63 4562.604
0.9 2912.761591 1.408 1 5307.698898 21767713.84 4101.158
1 3236.401767 – 1 5307.698898 – –
Ʃ(RBH) Ʃ(RB)
129053357.4 24811.46

Table 3.2.10 .3 Values corresponding to the pitch at the various radius
Cw = 630 (Cast manganese aluminium broze)
CG – size factor
85.02.121.11Df

81
f1 = 7.2 for solid propeller
85.005.1 1.1 GC

1 254.15.01
33max




ff
Cm
Dyn
(Dynamic factor)
f3 = 0.2
5.1 678.112maxT
mEf

130.1) 1(103.43
9
TDw nVES
T

CONDITION : e r > t ( 128 mm
 94.608 )
So,the blades of the propeller will resist.

3.2.11 analogy between the man engine
and wartsila engin e
The main characteristics of the propeller are exposed below:
PROPELLER
PB= 9319.343 KW
n= 93.89706 rot/min
PD= 7763.013 KW

The final results calculated to chose the suitable engine, are exposed below:

82
WARTSILA RT -flex58T MAN B&W
PB=11300 kW PB=12460 kW
n=105 rpm n=117 rpm
5 cylinders 7 cylinders
Dopt=6.472 m Dopt=6.124 m
PD=9412.9
[kW] PD=8305.5
[kW] PD=10379.18
[kW] PD=9158.1
[kW]
V=15.1 [Nd] V=14.8 [Nd] V=15.32 [Nd] V=14.8 [Nd]
P/D=0.93 P/D=0.82 P/D=0.83 P/D=0.92

ADVANTAGES AND DISADVAN TAGES
DISADVANTAGE ADVANTAGE
D = 6.124 [m] => Due to the small
diameter, the propeller efficiency
decreases and the speed increases:
D  => h => n D =6.472 [m]=> a large diameter of the
propeller ensures good yield and low
speed : D =>h  => n
Because of the small diameter and
high speed ( D  si n) there is a
risk of high noise and vibrations on
the board of the ship. Due to its large diameter and low
speed (D si n ) low noise and
vibrations are produced compared to
the 6.124 m diameter prop eller.
Due to the small diameter of the
yield ( D  =>h) there is the risk
of cavitation . Because of the large diameter, the
default yield (D  =>h ) ,there is a
lower risk of cavitation.
Fuel consumption = 170 [g / kWh]
=> a high consumption Fuel con sumption = 161 [g / kWh] =>
lower consumption than the other
engine
ADVANTAGE DISADVANTAGE
High fuel consumption can result in
lower engine costs. Low fuel consumption can result in
higher engine costs.
Due to the small diameter, the costs
for designing , manufacturing and
operating the propeller are lower. Due to the large diameter, the costs
for designing, manufacturing and
operating the propeller are higher.

83
The choice of the diameter of the propeller is made from energy and
constructive considerati ons. From an efficiency point of view, it is preferable
to have a diameter as large as the diameter reduction decreases the diameter
and influences the cavitation performance of the propeller. A decrease in yield
leads to increased cavitation risk.
When we choose the diameter of the propeller, a number of
constructive considerations must be taken into consideration like:
– the shape of the aft extremity ;
-draft;
-the dist ance from the propeller to the ship's body .
Taking into account the above aspects, De / T <0.7 ratio is
recommended in the preliminary design. In the case of bulk -carriers,this De /
T ratio should be less than 0.65.
For the diameter of the propeller De = 6.124 m and T = 13.8 m,
the ratio is De / T = 0.44 <0.65. For propeller diameter De = 6.472 m and draft
T = 13.8 m, De / T ratio = 0.46 <0.65. that the De / T ratio is less than 0.65.
Howe ver, if a propeller with the optimal diameter in terms of yield
can not be placed in the ship's stern for constructive reasons, choosing the
diameter may become a compromise problem.
In such cases, if it’s possible from a financial point o f view, other
types of propulsion can be chosen.
Conclusions
Based on the results of the above comparative analysis and the
propeller positioning calculations, it has agreed that the propeller with an
optimal diameter of 6.472 m has the most a dvantages and can be located in
the aft of the vessel, which proves a good choice for achieving good propeller
efficiency, low engine power that engages the propeller, low noise and
vibrations on board, and low cavitation risk.

84

CHAPTER 4

-HYDRODINAMI C
INVESTIGATION OF
BEARING FORCES INDUCED
BY A BULK -CARRIER
PROPELLER –

85

4.1 HYDRODINAMIC
INVESTIGATION OF BEARING FORCES
The speed,power per shaft of modern ships and the
increase of dimensions has lead to a ru sh of propeller -induced vibrations.
The vibration performances of a new built ship have the
same level of importance,as speed performance and fuel consumption,since they
may cause mechanical damage and may reduc e comfort on board.

The propeller induc ed vibration as primary source of excitations
constitute a very complex problem and many efforts have been devoted by
improving model experiments and numerical methods.

86
The total unsteady forces exerted by a propeller are mainly
generated by unsteadiness of the flow field. This is usually described throught
the distribution of axial and tangential velocities at the propeller disc -plane.
The resultant harmonic velocity experienced by each propeller
blade is the complex weighted sum of the actual axial and tangential velocities
(radial variations are ignored). From the viewpoint of properties two kinds of
propeller ex citing forces are known, namely:
– surface forces
-bearing forces.
The former fo rces are transmitted from the propeller to the
hull surfaces as radiated pressure whose main causes are the violent unsteady
variations of cavitation bubbles and sheets, while the latter are exerted from the
propeller to the ship structure throught the pr opeller shaft and bearings because
of spatially wake non -uniformity.
The bearing forces comprises the fluctuating forces and
moments developed on the propeller blade and transmitted to the hull structure
via the stern tube beari ng and thrust block.

Fig. 4.1.1 Bearing forces transmitted to the hull

87
The quasi -steady method assumes that the characteristics of a propeller in
each phase of unsteady motion are approximated by those in uniform flow at the
same phase.

Fig. 4.1.2 Schematic presentation of quasi -steady method
Thus, if the non -uniform flow field is known around a propeller,
the flow speed and the angle of attack at each phase are calculated according to
the diagram of velociti es.
The propeller characteristics at eatch phase of the unsteady
motion are obtained either using the lifting line theory which gives the loading
distribution along the radius or considering the total blade loading calculated
from t he experimental open -water characteristics of the propeller, which is to be
distributed along the radius using weight functions.
Using the first variant, the radial application point of the resulting
forces on the bla de can be accurately calculated by integration along the radius.
Considering the blade in an instantaneous angular position θ (Fig.4.1.3), for a
blade element dr situated at radius r, the instantaneous advance coefficient J(r,θ)
and the hydrodynamic pitch angle β(r,θ) may be worked off by the following
relations:

88

),( tan1),( 1
`)],( 1[),(
0 rwrwJDnrwvrJ
ta
Sa

Rrr
rJ
nDvJrwJrrw Jr
S
St Sa S
  

; tan ;),()],( 1[tan),(
1
01
 

– n` is the instantaneous revolutions of propeller, corresponding to the real valu e
of the tangential velocity og the inflow to the given element, give n as:
rrwvnrnt
 
2),( 2`

Fig.4.1.3 Coordinate system of propeller blade

89
The previous relations which give the instantaneous advance
coefficient and hydrodynamic pitch angle for a certain blade position, are valid
only for a single p oint of the blade element, namely for the point corresponding
to the angle Ɵ and radius r.
Due to the three -dimensional unsteady effects, the wake distribution
changes along the chord and, consequently, in order to remove this deficienc y,
the velocities across the chord are averaged using the flat plate type weight
function according to Sasajima:
xx
cxf112)(

-c is the chord length
– x is the adimentional position of the point along the chord.
The wake distribution, av eraged with weight function, corresponding
to the position of the blade element is given by the relations:


  
1
11
1
)(])( )( ,[1),()(])( )( ,[1),(
dxxfxr r rw rwdxxfxr r rw rw
b g t tb g a a


Where :
– x = -1 for the leading edge
– x =1 for the trailing edge.
By using the averaged wake comp onents at eath phase of the
propeller rotation, the corrected local advance coefficient is obtained.
The wake distribution used in bearing forces calculations is the
effective full scale wake distribution. The nominal wake measured behind th e

90
ship model is corrected for scale effect using the three -dimensional contraction
method proposed by Hoekstra. The contraction factor C is the sum of three parts:
C = iC + jC + kC
i + j + |k| = 1
i – concentric contraction factor to th e centre of the pr opeller shaft
j – horizontal contra ction factor to the centerplane
k – vertical contraction factor to the hull stern above the propeller or to the
water surface if the latter is lower.
Their values depend s on the harmonic content of the model wake
distribution. Additional corrections are made for the diffusion effect on the wake
peak, which acts to lower the sharp wake zone.
In order to derive the effective wake distribution from he scaled
nominal wake distribution, a computer program was developed based on
Huang`s work. This method is more realistic that the simple radial contraction
procedure for the flow approaching the propeller, given by the simple
momentum theory according to the relati on:
) 1 1(21
TnewC

Where ρ new is the radius of nominal wake, ρ is the contracted radius and C T is the
thrust load coefficient.
By evaluating the thrust and torque distribution values in terms of
the corrected instantaneous advance coefficient J(r, Ɵ), the instantaneous values
of thrust and torque generated by the blade element are easily calculated as
follows:
Zdr D rwnrvndrdKr dFt
rJT
bx1),(2`1 ),(42
2
),(


  


91

Zdr D rwnrvndrdKr dMt
rJQ
bx1),(2`1 ),(52
2
),(



  

The other components of forces and moments on th e propeller
shaft can be writte n as:
  cos),( ),(   r r dF r dMbx by

  sin),( ),(   r r dF r dMbx bz

 cos),(),(  rr dMr dFbx
by

 sin),(),(  rr dMr dFbx
bz

At each phase the force and moment components acting on the
whole blade are calculated by integrating between hub an d blade tip:
R
rbx bx
hr dF F ),( )(  
;
R
rby by
hr dF F ),( )(   ;
R
rbz bz
hr dF F ),( )(  
R
rbx bx
hr dM M ),( )(  
;
R
rby by
hr dM M ),( )(   ;
R
rbz bz
hr dM M ),( )(  
The total periodic forces and moments acting on the whole
propeller at each phase are the sum over all Z blades. They are often presented as
simplitudes and phases of the blade harmonics.



 Z
ibx xZiF F
1)1(2)( 
;


 Z
ibx xZiM M
1)1(2)( 



 Z
iby yZiM M
1)1(2)( 



 Z
iby yZiF F
1)1(2)( 

92



 Z
ibz zZiF F
1)1(2)(  ;


 Z
ibz zZiM M
1)1(2)( 
The whole calculation process of propeller bearing forces by quasi –
steady method is presented through the flow -chart shown in Fig.4.1.4. The main
goal of the process is to allow a rati onal design of the propeller in order to
minimize entity of excitation sources.

Fig.4.1.4 Flow chart of bearing forces code

93
4.2 Bearing forces calculation
To calculate the bearing forces,will be used an program
which comprise the fluctuating forces and moments developed on the propeller
blade and in propeller shaft.
The input data contains the values below: :
 Axial wake distribution
Relative radius
Angle
[deg] 0.2 0.4 0.5 0.6 0.7 0.8 0.9 1
0 0.1989 0.1989 0.2414 0.2072 0.19 0.2226 0.0667 0.1
12 0.0634 0.0634 0.2854 0.3062 0.3514 0.3433 0.3609 0.392
24 0.2795 0.2795 0.2879 0.3207 0.2793 0.3 0.3054 0.324
36 0.2976 0.2976 0.2738 0.235 0.1471 0.1749 0.2966 0.316
48 0.3231 0.3231 0.2084 0.0716 0.1439 0.1822 0.391 0.486
60 0.2915 0.2915 0.1975 0.1143 0.2108 0.2924 0.512 0.652
72 0.2732 0.2732 0.1876 0.2361 0.2817 0.4943 0.6744 0.773
84 0.256 0.256 0.1541 0.3116 0.4763 0.5953 0.7803 0.834
96 0.2217 0.2217 0.2085 0.4157 0.4278 0.7056 0.8205 0.876
108 0.2062 0.2062 0.0697 0.3174 0.5129 0.7022 0.8599 0.869
120 0.1891 0.1891 0.1451 0.2897 0.5041 0.6638 0.7772 0.884
132 0.1334 0.1334 0.1418 0.2513 0.4843 0.64 0.8197 0.829
144 0.1888 0.1888 0.1363 0.1726 0.3864 0.4924 0.8018 0.861
156 0.1373 0.1373 0.0813 0.0693 0.1221 0.4106 0.7116 0.822
168 0.1245 0.1245 0.1124 0.0879 0.099 0.4108 0.5858 0.802
180 0.106 0.106 0.1291 0.0746 0.2344 0.2981 0.5813 0.854
192 0.1245 0.1245 0.1124 0.0879 0.099 0.4108 0.5858 0.802
204 0.1373 0.1373 0.0813 0.0693 0.1221 0.4106 0.7116 0.822
216 0.1888 0.1888 0.1363 0.1726 0.3864 0.4924 0.8018 0.861
228 0.1334 0.1334 0.1418 0.2513 0.4843 0.64 0.8197 0.829
240 0.1891 0.1891 0.1451 0.2897 0.5041 0.6638 0.7772 0.884
252 0.2062 0.2062 0.0697 0.3174 0.5129 0.7022 0.8599 0.869
264 0.2217 0.2217 0.2085 0.4157 0.4278 0.7056 0.8205 0.876
276 0.256 0.256 0.1541 0.3116 0.4763 0.5953 0.7803 0.834
288 0.2732 0.2732 0.1876 0.2361 0.2817 0.4943 0.6744 0.773
300 0.2915 0.2915 0.1975 0.1143 0.2108 0.2924 0.512 0.652
312 0.3231 0.3231 0.2084 0.0716 0.1439 0.1822 0.391 0.486
324 0.2976 0.2976 0.2738 0.235 0.1471 0.1749 0.2966 0.316
336 0.2795 0.2795 0.2879 0.3207 0.2793 0.3 0.3054 0.324
348 0.0634 0.0634 0.2854 0.3062 0.3514 0.3433 0.3609 0.392
360 0.1989 0.1989 0.2414 0.2072 0.19 0.2226 0.0667 0.1
Table 4.2 .1 Axial wake distribution

94

Fig. 4.2.1 Axial wake diagram
 Propeller geometry parameters
r/R c bri P
[-] [m] [m] [m]
0.2 1.4786 0.9125 4.9461
0.3 1.6743 1.0242 5.3371
0.4 1.8237 1.0958 5.7162
0.5 1.9145 1.1207 5.969
0.6 1.9456 1.0911 6.0171
0.7 1.9074 1 6.0171
0.8 1.7526 0.8103 6.0171
0.9 1.4074 0.4932 6.0171

Table 4.2 .2 Geometrical characteristics

00.10.20.30.40.50.60.70.80.91
-40 10 60 110 160 210 260 310 3600.2
0.4
0.5
0.6
0.7
0.8
0.9
1
Angle
(deg)
Axial wake

95
r/R – Relative Radius
c – Chord
bri – Distance between leading edge and propeller generator line b ri
P – Pitch

 Hydrodynamics c haracteristics of the propeller (For P/D = 0.93 )

J KT 10KQ η
0.0001 0.3955 0.5346 0.0001
0.1 0.3705 0.5058 0.1166
0.2 0.3413 0.4729 0.2298
0.3 0.3084 0.4359 0.3378
0.4 0.2722 0.3948 0.4389
0.5 0.2330 0.3494 0.5307
0.6 0.1912 0.2996 0.6094
0.7 0.1473 0.2454 0.6685
0.8 0.1015 0.1867 0.6925
0.9 0.0544 0.1233 0.6319
1 0.0063 0.0553 0.1809
Table 4.2.3 Hydrodynamics characteristics
J – Advance
Kt – Thrust coefficient
Kq – Torque coefficient

96

Fig. 4.2. 2 Hydrodynamics characteristics
The output data contains :
 Forces and Moments on propeller blade
Angle[deg
] Fx[kN] Fy[kN] Fz[kN] Mx[kNm
] My[kNm
] Mz[kNm]
0 -305.33 -132.12 0 299.19 -691.41 0
6 -303.71 -130.87 13.75 297.98 -683.98 71.89
12 -322.4 -134.78 28.65 312.02 -714.13 151.79
18 -349.82 -139.81 45.43 332.88 -753.4 244.79
24 -370.51 -140.62 62.61 348.58 -766.48 341.26
30 -378.68 -135.65 78.32 354.71 -742.64 428.76
36 -374.77 -125.68 91.31 351.78 -686.58 498.83
42 -361.73 -112.22 101.04 341.94 -608.74 548.11
48 -338.67 -95.85 106.45 324.37 -513.16 569.93
54 -299.84 -76.59 105.42 295.08 -399.1 549.31
60 -249.9 -56.65 98.12 256.57 -282.95 490.08
66 -207.22 -39.84 89.47 221.78 -190.86 428.67
72 -179.57 -27.2 83.71 199.32 -125.66 386.73
78 -157.36 -16.64 78.27 181.19 -74.09 348.55
84 -135.79 -7.53 71.66 163.17 -32.14 305.81
90 -120.15 0 66.12 149.74 0 272.09
96 -113.04 6.63 63.04 143.54 26.76 254.58
102 -114.03 13.26 62.37 144.4 53.69 252.57
108 -122.75 20.74 63.83 151.99 85.89 264.36
114 -137.91 29.63 66.55 164.97 127.02 285.3
120 -161.77 40.81 70.68 184.82 183.17 317.25
126 -197.03 55.41 76.27 213.49 262.26 360.97
132 -236.42 72.59 80.62 245.67 358.24 397.86
138 -269.34 89.24 80.35 271.92 453.26 408.11 0.00000.10000.20000.30000.40000.50000.60000.70000.8000
0 0.2 0.4 0.6 0.8 1 1.2KT
10KQ
eta

97
144 -291.73 103.24 75.01 288.98 534.45 388.3
150 -305.64 114.51 66.11 299.43 599.4 346.06
156 -319.32 124.94 55.63 309.69 660.59 294.11
162 -337.82 135.96 44.18 323.72 727.55 236.39
168 -353.22 144.91 30.8 335.47 782.39 166.3
174 -357.78 148.86 15.65 338.94 805.75 84.69
180 -351.87 147.69 0 334.44 796.81 0
186 -333.69 140.79 -14.8 320.58 751.5 -78.99
192 -300.97 127.83 -27.17 295.93 666.66 -141.7
198 -258.9 110.77 -35.99 263.74 557.59 -181.17
204 -214.69 91.94 -40.93 227.9 444.14 -197.75
210 -174.74 74.73 -43.15 195.4 342.69 -197.85
216 -143.72 60.69 -44.09 169.86 263.3 -191.3
222 -117.84 48.48 -43.65 147.72 198.3 -178.55
228 -92.34 37 -41.09 125.21 139 .92 -155.4
234 -71.89 27.72 -38.15 106.8 95.69 -131.71
240 -60.5 21.3 -36.89 96.45 68.5 -118.64
246 -54.32 16.31 -36.64 90.82 50.03 -112.38
252 -55.12 12.49 -38.45 91.55 38.57 -118.7
258 -71.82 9.8 -46.1 106.73 33.81 -159.08
264 -103.55 6.24 -59.37 135.18 24.51 -233.22
270 -141.93 0 -74.35 168.36 0 -321.4
276 -185.22 -9.41 -89.55 203.91 -43.84 -417.14
282 -231.42 -22.18 -104.35 241.59 -108.96 -512.59
288 -271.64 -37.35 -114.95 273.7 -190.09 -585.02
294 -301.88 -53.27 -119.66 296.61 -278.05 -624.5 1
300 -324.78 -69.29 -120.01 313.82 -367.73 -636.93
306 -338.65 -84.19 -115.88 324.36 -450.75 -620.41
312 -340.06 -96.16 -106.8 325.44 -515.28 -572.28
318 -335.59 -105.68 -95.15 322.03 -564.75 -508.5
324 -340.17 -116.3 -84.49 325.52 -623.2 -452.78
330 -362.65 -131.04 -75.66 342.64 -711.2 -410.61
336 -399.33 -149.23 -66.44 369.92 -826.1 -367.8
342 -441.88 -168.35 -54.7 400.84 -951.66 -309.21
348 -481.48 -185.6 -39.45 429.68 -1066.48 -226.69
354 -510.08 -197.91 -20.8 450.64 -1148.76 -120.74
360 -305.33 -132.12 0 299.19 -691.41 0

Table 4. 2.4 Forces and moments on propeller blade

98

Fig. 4.2.3 Fx on propeller blade

Fig. 4.2.4 Fy on propeller blade
-600-500-400-300-200-1000
0 100 200 300 400Fx [kN]
Fx
-250-200-150-100-50050100150200
0 100 200 300 400Fy [kN]
Fy
Angle
(deg)
Angle (deg)

99

Fig. 4.2.5 Fz on propeller blade

Fig. 4.2.6 Mx on propeller blade

-150-100-50050100150
0 50 100 150 200 250 300 350 400Fz[kN]
Fz
050100150200250300350400450500
0 100 200 300 400Mx[kNm]
Mx
Angle(deg)
Angle(deg)

100

Fig. 4.2.7 My on propeller blade

Fig. 4.2.8 Mz on propeller blade

-1500-1000-50005001000
0 100 200 300 400My[kNm]
My
-800-600-400-2000200400600800
0 100 200 300 400Mz
Mz
Angle(deg)
Angle(deg)

101
 Forces and Moments in propeller shaft

Angle[deg] Fx[kN] Fy[kN] Fz[kN] Mx[kNm] My[kNm] Mz[kNm]
0 -919.28 15.57 -8.22 951.73 105.4 -49.31
6 -935.67 7.14 -27.56 966 50.43 -169.66
12 -968.82 -15.87 -40.5 993.93 -102.74 -249.93
18 -1003.11 -45.65 -41.68 1022.31 -300 -257.04
24 -1024.99 -72.33 -31.43 1038.06 -473.36 -195.69
30 -1039.98 -89.4 -14.16 1048.75 -584.52 -88.76
36 -1054.17 -93.77 7.61 1059.49 -611. 78 48.09
42 -1056.05 -87.31 31.21 1060.77 -567.48 195.14
48 -1035.94 -75.3 50.55 1043.52 -484.73 314.14
54 -1003.63 -61.92 57.78 1016.38 -392.16 353.11
60 -978.69 -51.88 51.69 995.09 -326.25 306.9
66 -980.19 -47.82 42.01 992.22 -306.34 242.6
72 -1014 .38 -47.1 34.74 1015.44 -311.2 195.21
78 -1063.87 -47.53 23.52 1053.07 -324.36 129.09
84 -1107.21 -50.35 7.14 1087.93 -350.63 36.55
90 -919.28 15.57 -8.22 951.73 105.4 -49.31

Table 4. 2.5 Forces and moments in propeller shaft

102

Fig. 4.2.9 Fx in pro peller shaft

Fig. 4.2.10 Fy in propeller shaft
-1200-1150-1100-1050-1000-950-900-850-800
0 20 40 60 80 100Fx[kN]
Fx
-100-80-60-40-2002040
0 20 40 60 80 100Fy[kN]
Fy
Angle
(deg)
Angle(deg)

103

Fig. 4.2.11 Fz in propeller shaft

Fig. 4.2.12 Mx in propeller shaft

-60-40-20020406080
0 20 40 60 80 100Fz[kN]
Fz
940960980100010201040106010801100
0 20 40 60 80 100Mx[kNm]
Mx
Angle(deg)
Angle(deg)

104

Fig. 4.2.13 My in propeller shaft

Fig. 4.2.14 Mz in propeller shaft

 Medium values of bearing forces and moments
Fxm = -1013.85kN
-700-600-500-400-300-200-1000100200
0 20 40 60 80 100My[kNm]
My
-300-200-1000100200300400
0 20 40 60 80 100Mz[kNm]
Mz
Angle(deg)
Angle(deg)

105
Fym = -51.40 kN
Fzm = 9.48 kN
Mxm = 1024.05 kNm
Mym = -335.42 kNm
Mzm = 53.78kNm

Many theoretical methods were developed for propeller vibration
calculations, i.e, quasi -steady methods, vortex lattice methods, lifting surfa ce
methods and surface panel methods. Theoretical comparative results for the
same design condition with different methods reflect differences up to about
(20-40)% for thrust and torque fluctuation at blade frequency; for the other
components they can be h ighter. The conclusion is that computer codes have
been not rigorously validated.
The experimental procedures on models are hardly used for the prediction
of propeller forces and moments. Accuracy of the experimental results are
determided by a lot of fac tors depending on the own properties of the
measuring system and on the hydrodynamic phenomena.
The error due to scale effects on the wake distribution dominates the
experimental and theoreti cal predictions in most cases.A n amount of about
30% for the blade frequency is reported. The error for the higher h armonics
can even be greater up to about 50%. If the cavitation behaviour is normal ,
it’s effect on the bearing forces can be neglected.