The Propeller Design Calculations

Name: Hanqing Cai

Student ID: 5130809037

Major: Naval Architecture and Ocean Engineering

Contents Main parameters of the ship........................................................................ 1

Main parameters of the main engine .......................................................... 1

Propulsion factors ....................................................................................... 1

Maximum ship velocity .............................................................................. 1

Check for cavitation .................................................................................... 2

Check for propeller strength ....................................................................... 3

Modification to pitch .................................................................................. 4

Calculation of mass and moment of inertia ................................................ 5

Calculation of open-water characteristics of the designed propeller.......... 5

Calculation of the bollard performance ...................................................... 6

Calculation of the nautical performance ..................................................... 6

Summary of the design for ship propeller .................................................. 7

Appendix ..................................................................................................... 8

1

1. Main parameters of the ship

Length of Design Waterline: LWl=215m

Length between Perpendiculars: LPP=210m

Breadth: B=32m

Design Draft: T=12.7m

Block Coefficient: CB=0.655

Displacement of Volume: ∇=54000𝑚3

Height between Axle and Baseline: Zp=4.7m

Boss Diameter dh=1.4m

2. Main parameters of the main engine

Maximum Continuous Power 33000kW

Rated Rotating Speed 102r/min

Sense of Rotation Clockwise

3. Propulsion factors

Wake fraction ω = 0.25

Thrust Deduction Fraction t = 0.16

Relative Rotating Efficiency 𝜂𝑅 = 1.0

Ship Hull Efficiency 𝜂𝐻 =1−𝑡

1−𝜔= 1.12

4. Maximum ship velocity

Power storage fraction 15% Shaft transmission efficiency 𝜂𝑆 = 0.97

The power propeller receive in open water：

𝑃𝐷 = 33000 × 0.85 × 𝜂𝑆𝜂𝑅

= 33000 × 0.85 × 0.97 × 1.0

= 27208.5(kW)

Torque receive under designed power and rated rotating speed:

Q =9550 × 𝑃𝐷

𝑛=

9550 × 27208.5

102= 2547462.5(N ∙ m)

The process of deciding the maximum ship velocity:

Assume several value of extended area ratio of blade which range from 0.5 to 0.8,

calculating each extended area ratio of blade in the following process:

1. Assume several diameters of the propeller (7.5m~8.5m, interval is 0.1m);

2. For each diameter, assume several ship velocity (21Kn~25Kn, interval is

1Kn);

3. For every diameter and ship velocity, calculate the thrust and moment of the

propeller using regression formula in different advance coefficient, and decide the

proper pitch and effective thrust and efficiency of propeller by interpolation or

method of dichotomy.

2

4. For each diameter, decide the ship velocity which makes the effective thrust

and resistance the same, the pitch and the efficiency of propeller by interpolation

according to the curve of resistance and effective thrusts in different ship velocities.

5. Decide the proper diameter, which is the best diameter in the assumed

extended area of blade in the max ship velocity according to the relationship between

ship velocity and diameter.

EAR D/m V/kn P/D 𝜂0

0.5 7.7805 23.11848 0.9126 0.6639

0.6 7.8759 23.17218 0.9076 0.673

0.7 7.8518 23.14981 0.9231 0.6691

0.8 7.7047 22.96518 0.9552 0.6392

5. Check for cavitation

Use the Burill cavitation line to calculate the minimal extended area of blades which

there is no cavitation.

Depth of the boss axis: ℎ𝑠 = 𝑇 − 𝑍𝑃 = 12.7 − 4.7 = 8𝑚

𝑝0 = 𝑝𝑎 + 𝛾ℎ𝑠 = 10330 + 1025 × 8 = 18530𝑘𝑔𝑓/𝑚2

Calculating Temperature: t=15℃ PD=37018.37hp ρ=104.6kgf·s2/m4

Order Item Unit Value

EAR=0.5 EAR=0.6 EAR=0.7 EAR=0.8

1 V kn 23.12 23.17 23.15 22.97

2 𝑉𝐴 = 0.5144𝑉(1 − 𝜔) m/s 8.9122 8.9329 8.9242 8.8531

3 (0.7𝜋𝑁𝐷

60)2

(𝑚/𝑠)2 845.2170 866.0712 860.7790 828.8285

4 (𝑚/𝑠)2 924.6439 945.8675 940.4213 907.2055

5 0.38306695 0.37447161 0.37664026 0.39043032

6 0.146 0.144 0.144 0.149

7 kgf 203848.0118 206163.2844 205166.6745 197574.1581

8 𝑚2 28.86375930 28.93292304 28.95980656 27.93907281

9 𝑚2 36.34627177 36.36490620 36.61195852 35.75536785

10 0.76484811 0.74681396 0.75651030 0.76729104

Then we can map according to the blanket above among EAR, V, 𝜂0, D and P/D,

therefore, we can get the main parameters of the propeller.

𝑉0.7𝑅2 = 𝑉𝐴

2 + (0.7𝜋𝑁

60𝐷)

2

𝜏𝑐

𝑇 =145.6𝑃𝐸

(1 − 𝑡)𝑉(= 75

𝑃𝐷

𝑉𝐴

𝜂0)

𝐴𝑃 = 𝑇/𝜏𝑐 ∙1

2𝜌𝑉0.7𝑅

2

𝐴𝐸 = 𝐴𝑃/(1.067 − 0.229𝑃/𝐷)

𝐴𝐸/𝐴𝑂

𝜎0.7𝑅 = 𝑝0/ (1

2𝜌𝑉0.7𝑅

2 )

3

Thus:

𝐴𝐸/𝐴0 = 0.7543 P/D = 0.9463 D = 7.8196m 𝜂0 = 0.6715 V = 23.0501kn

6. Check for propeller strength

According to specification in 2001, check and, which should be no less than the

following parameters:

t = √𝑌

𝐾−𝑋 Y =

1.36𝐴1𝑁𝑒

𝑍𝑏𝑛𝑒 X =

𝐴2𝐺𝐴𝑑𝑁2

1010𝑍𝑏

Calculating power: 𝑁𝑒 = 33000 ÷ 0.735 × 0.97 = 43551.02ℎp

𝐴𝑑 = 𝐴𝐸/𝐴0 = 0.7543 P/D = 0.9463 ε = 10°

G = 7.6g/𝑐𝑚3 N = 𝑛𝑒 = 102𝑟/𝑚𝑖𝑛

4

𝑏0.66𝑅 =0.226𝐷𝐴𝑑

0.1𝑍=

0.226 × 7.8196 × 0.7543

0.5= 2.667m

𝑏0.25𝑅 = 0.7212𝑏0.66𝑅 = 1.9227𝑚

𝑏0.6𝑅 = 0.9911𝑏0.66𝑅 = 2.6433𝑚

Item Unit Value

0.25R 0.6R

b m 1.9227 2.6433

K1 634 207

K2 250 151

K3 1410 635

K4 4 34

A1 1876.8 7687.2

y 111735.1 29759.06

K5 82 23

K6 34 12

K7 41 65

K8 380 330

A2 1235.95 1131.11

K 1.38 1.38

X 0.3667 0.2441

t^2 110268.4879 26198.66082

t mm 332.0669931 161.8600038

MAU standard blade thickness mm 315.13 170.46

Consequence Not satisfied Satisfied

Practical blade thickness mm 332.07 189.83

So we can get the value of thickness by linearize the t1.0R=0.0035D=27.27mm between

t0.25R=332.07mm:

t0.2=352.39mm t0.3=311.75mm

t0.4=271.11mm t0.5=230.47mm

t0.6=189.83mm t0.7=149.19mm

t0.8=108.55mm t0.9= 67.91mm

7. Modification to pitch

1. Modification to pitch according to different hub diameter ratio:

(dh/D)’=1.4/7.9=0.1772

dh/D=0.18

∆ (𝑃

𝐷)

𝐵=

1

10[(

𝑑ℎ

D)

′

− 𝑑ℎ/D] = −0.0001

2. Modification to pitch according to different thickness ratio:

5

Designed propeller(t

b)

0.7𝑅=

0.14919

0.9964×2.4424= 0.0579

Standard propeller(𝑡

𝑏)

0.7𝑅=

0.0171×𝐷

0.9964×0.3409×𝐷= 0.0503 （According to MAU5-80）

1 − s =30.866𝑉𝐴

𝑁𝑃=

(1 − 𝜔)𝑉 × 30.866

𝑁𝑃=

0.75 × 23.05 × 30.866

102 × 7.3997= 0.6868

𝑎𝐸0 = 0.8 𝑎′𝐸 = {1 + 1.1 [(

𝑑ℎ

𝐷)

′

− (𝑑ℎ

𝐷)]}

𝐴𝐸

𝐴0= 0.7535

∆ (𝑡

𝑏)

0.7= [(

t

b)

0.7 设− (

t

b)

0.7 标×

0.8

0.7535] × 0.75 = 0.00337

∆ (𝑃

𝐷)

𝑡= −2

𝑃

𝐷(1 − 𝑠)∆ (

𝑡

𝑏)

0.7= −0.00438

Pitch after modification:

𝑃

𝐷= (

𝑃

𝐷)

0+ ∆ (

𝑃

𝐷)

𝐵+ ∆ (

𝑃

𝐷)

𝑡= 0.9463 − 0.0001 − 0.00438 = 0.9418

8. Calculation of mass and moment of inertia

Mass of all blades 𝐺𝑏 = 35459.11𝑘𝑔

Mass of hub 𝐺ℎ = 15091.78𝑘𝑔

Mass of the propeller 𝐺 = 5055089 𝑘𝑔

Moment of inertia of all blades 𝐼𝑏 = 15522.61 𝑘𝑔 · 𝑚 · 𝑠2

Moment of inertia of hub 𝐼ℎ = 1642.39𝑘𝑔 · 𝑚 · 𝑠2

Moment of inertia of the propeller 𝐼 = 17164𝑘𝑔 · 𝑚 · 𝑠2

9. Calculation of open-water characteristics of the designed propeller

The open water data of the design propeller:

6

J 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

Kt 0.463 0.431 0.396 0.357 0.316 0.271 0.224 0.175 0.123 0.069 0.014

Kq 0.064 0.060 0.056 0.051 0.046 0.041 0.035 0.029 0.023 0.016 0.08

10. Calculation of the bollard performance

𝑃

𝐷= 0.9418 J = 0时,KT=0.4603 KQ=0.06336

Calculating power P𝐷 = 33000 ÷ 0.735 × 0.97 = 43551.02ℎ𝑝

Thrust deduction fraction t=0.16

Moment of main engine

Q =𝑃𝐷 × 60 × 75

2𝜋𝑁=

43551.02 × 60 × 75

2𝜋 × 102= 305795.30𝑘𝑔𝑓 · 𝑚

Thrust of the bollard

T =𝐾𝑇 × 𝑄

𝐾𝑄 × 𝐷=

0.4603 × 305795.3

0.06336 × 7.8196= 284100.55𝑘𝑔𝑓

Rotating speed of the propeller

N = 60√𝑇

𝜌𝐷4𝐾𝑇= 75.36𝑟/𝑚𝑖𝑛

11. Calculation of the nautical performance

Choose rotating speed as 82r/min，92r/min，102r/min.

Item Unit Value

V kn 21.00 22.00 23.00 24.00 25.00

VA m/s 8.1018 8.4876 8.8734 9.2592 9.6450

N=92r/min

J 0.6757 0.7079 0.7401 0.7722 0.8044

KT 0.1868 0.1706 0.1542 0.1375 0.1207

KQ 0.0306 0.0286 0.0265 0.0244 0.0222

PE kw 15258.5 14599.6 13794.7 12841.5 11737.6

PS kw 21397.7 19987.1 18545.8 17072.7 15566.1

N=97r/min

J 0.6409 0.6714 0.7019 0.7324 0.7630

KT 0.6409 0.6714 0.7019 0.7324 0.7630

KQ 0.0327 0.0308 0.0289 0.0270 0.0250

PE kw 18530.2 17974.6 17267.9 16407.6 15391.6

PS kw 26830.2 25298.4 23735.6 22140.8 20512.6

N=102r/min

J 0.6095 0.6385 0.6675 0.6965 0.7256

KT 0.2194 0.2052 0.1909 0.1763 0.1616

KQ 0.0346 0.0329 0.0311 0.0293 0.0274

PE kw 22030.1 21589.2 20992.0 20236.1 19319.2

PS kw 32993.9 31335.0 29644.6 27921.9 26165.6

7

As we can get from figure above:

In preloading stage, the maximum of ship speed V=23.9kn, the power of main engine

28050kw.

In 110% fully loaded stage, the maximum of ship speed V=22.5kn, the power of main

engine 30428kw.

In loaded stage, the maximum of ship speed V=23.2kn, the power of main engine

29287kw, which is satisfied by the design condition.

12. Summary of the design for ship propeller

Propeller diameter D = 7.8196m

Pitch ratio P/D = 0.9463

Form MAU

Number of blades Z = 5

8

Area ratio 𝐴𝐸/𝐴0 = 0.7543

Trim angle 10

Efficiency of propeller 𝜂0 = 0.6715

Design ship speed 𝑉𝑚𝑎𝑥 = 23.0501kn

Hub ratio 𝑑ℎ/D = 0.179

Sense of rotation clockwise

Material 3Cu yorcalnic

Weight 𝐺 = 50550.89 𝑘𝑔

Moment of inertia 𝐼 = 17164𝑘𝑔 · 𝑚 · 𝑠2

9

Appendix

Source Code for Open Water Characteristic Curve（MATLAB）：

C=[];r=4;

V=[];u=4;

for a = 0.5:0.1:0.8;%盘面比

B=[];m=11;

for d = 7.5:0.1:8.5;%直径变化

A=[];n=5;

for v = 21:1:25;%速度变化

b = 0.4:0.1:1.6;%螺距变化

j=v*0.5144*0.75/1.7/d;

kt = getkt(a,b,j);

kq = getkq(a,b,j);

t = kt*1025*1.7*1.7*d.^4;

q = kq*1025*1.7*1.7*d.^5;%扭矩大小

y0=kt*j/(kq*3.14*2);

bt = interp1(q,b,2547274,'spline');%插值计算螺距比

kt1 = getkt(a,bt,j);

kq1 = getkq(a,bt,j);

q1 = kq1*1025*1.7.^2*d.^5;

t1 = 0.84*kt1*q1/(kq1*d);%有效推力

A=[A t1];

end

v_res =

[9.766,10.023,10.28,10.537,10.794,11.051,11.308,11.565,11.822,12.079,12.336,12.593,12.85];

t_res =

[987917,1035419,1101167.315,1173863.529,1248378.729,1325762.374,1412274.496,1518633.809,16

59871.426,1854706.515,2125000,2495751.608,2994630.35];

v1=[10.794,11.308,11.822,12.336,12.85];

for s=9.766:0.001:12.89;

t2=interp1(v_res,t_res,s,'spline');

t3=interp1(v1,A,s,'spline');

delta=t2-t3;

if abs(delta)<1000;%插值计算阻力曲线和有效推力值

%航速

break;

end

end

B=[B s];%航速集合

end

D=7.5:0.1:8.5;

pd=polyfit(D,B,2);

10

ad=pd(1,1);

bd=pd(1,2);

cd=pd(1,3);

optimal_d = -bd/(2*ad);

max_v = (4*ad*cd-bd*bd)/(4*ad);

C=[C optimal_d];%最佳直径

V=[V max_v];%最大航速

end

F=[];w=4;

G=[];i=4;

H=[];c=4;

a = 0.5;

d=7.7805;

v=11.8829/0.5144;

b = 0.4:0.1:1.6;

j=v*0.5144*0.75/1.7/d;

kt = getkt(a,b,j);

kq = getkq(a,b,j);

t = kt*1025*1.7*1.7*d.^4;

q = kq*1025*1.7*1.7*d.^5;

bt = interp1(q,b,2547274,'spline');

kt1 = getkt(a,bt,j);

kq1 = getkq(a,bt,j);

t1 = 0.84*kt1*q1/(kq1*d);

y0=kt1*j/(kq1*3.14*2);

pe=t1*v*0.514/735;

F=[F bt];

G=[G y0];

H=[H pe];

a = 0.6;

d=7.8759;

v=11.9105/0.5144;

b = 0.4:0.1:1.6;

j=v*0.5144*0.75/1.7/d;

kt = getkt(a,b,j);

kq = getkq(a,b,j);

t = kt*1025*1.7*1.7*d.^4;

q = kq*1025*1.7*1.7*d.^5;

bt = interp1(q,b,2547274,'spline');

kt1 = getkt(a,bt,j);

kq1 = getkq(a,bt,j);

t1 = 0.84*kt1*q1/(kq1*d);

y0=kt1*j/(kq1*3.14*2);

pe=t1*v*0.514/735;

11

F=[F bt];

G=[G y0];

H=[H pe];

a = 0.7;

d=7.8518;

v=11.8990/0.5144;

b = 0.4:0.1:1.6;

j=v*0.5144*0.75/1.7/d;

kt = getkt(a,b,j);

kq = getkq(a,b,j);

t = kt*1025*1.7*1.7*d.^4;

q = kq*1025*1.7*1.7*d.^5;

bt = interp1(q,b,2547274,'spline');

kt1 = getkt(a,bt,j);

kq1 = getkq(a,bt,j);

t1 = 0.84*kt1*q1/(kq1*d);

y0=kt1*j/(kq1*3.14*2);

pe=t1*v*0.514/735;

F=[F bt];

G=[G y0];

H=[H pe];

a = 0.8;

d=7.7047;

v=11.8041/0.5144;

b = 0.4:0.1:1.6;

j=v*0.5144*0.75/1.7/d;

kt = getkt(a,b,j);

kq = getkq(a,b,j);

t = kt*1025*1.7*1.7*d.^4;

q = kq*1025*1.7*1.7*d.^5;

bt = interp1(q,b,2547274,'spline');

kt1 = getkt(a,bt,j);

kq1 = getkq(a,bt,j);

t1 = 0.84*kt1*q1/(kq1*d);

y0=kt1*j/(kq1*3.14*2);

pe=t1*v*0.514/735;

F=[F bt];

G=[G y0];

H=[H pe];

bx=[0.5,0.6,0.7,0.8];

hs=8;

p0=10330+1025*hs;

12

V1=[11.8829,11.9105,11.8990,11.8041];

D1=[7.7805,7.8759,7.8518,7.7047];

F1=[0.9126,0.9076,0.9231,0.9552];

Y0=[0.6639,0.6730,0.6691,0.6392];

VA=V1*0.75;

P=(0.7*3.14*102*D1/60).^2;

V7=VA.^2+P;

g=p0./(0.5*104.63*V7);

tc=[0.146,0.144,0.144,0.149];

T=75*36486*Y0./VA;

Ap=T./(0.5*104.63*V7.*tc);

Ae=Ap./(1.067-0.299*F1);

ax=Ae./(0.785*D1.^2);

disp(bx);%给定的盘面比

disp(C);%最佳直径

disp(V);%最大航速

disp(F);%螺距比

disp(G);%螺旋桨效率

disp(ax);%要求的盘面比

Screenshoot of the partial source code:

Screenshoot of the consequence:

13

The first to sixth line stand for assumed EAR, D, Maximal Velocity, Pitch Ratio,

Efficiency of the Propeller, Required EAR respectively.