the propeller design calculations
TRANSCRIPT
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: โ=54000๐3
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 ฯ = 0.25
Thrust Deduction Fraction t = 0.16
Relative Rotating Efficiency ๐๐ = 1.0
Ship Hull Efficiency ๐๐ป =1โ๐ก
1โ๐= 1.12
4. Maximum ship velocity
Power storage fraction 15% Shaft transmission efficiency ๐๐ = 0.97
The power propeller receive in open water๏ผ
๐๐ท = 33000 ร 0.85 ร ๐๐๐๐
= 33000 ร 0.85 ร 0.97 ร 1.0
= 27208.5(kW)
Torque receive under designed power and rated rotating speed:
Q =9550 ร ๐๐ท
๐=
9550 ร 27208.5
102= 2547462.5(N โ 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 ๐0
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: โ๐ = ๐ โ ๐๐ = 12.7 โ 4.7 = 8๐
๐0 = ๐๐ + ๐พโ๐ = 10330 + 1025 ร 8 = 18530๐๐๐/๐2
Calculating Temperature: t=15โ PD=37018.37hp ฯ=104.6kgfยทs2/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 ๐๐ด = 0.5144๐(1 โ ๐) m/s 8.9122 8.9329 8.9242 8.8531
3 (0.7๐๐๐ท
60)2
(๐/๐ )2 845.2170 866.0712 860.7790 828.8285
4 (๐/๐ )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 ๐2 28.86375930 28.93292304 28.95980656 27.93907281
9 ๐2 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, ๐0, D and P/D,
therefore, we can get the main parameters of the propeller.
๐0.7๐ 2 = ๐๐ด
2 + (0.7๐๐
60๐ท)
2
๐๐
๐ =145.6๐๐ธ
(1 โ ๐ก)๐(= 75
๐๐ท
๐๐ด
๐0)
๐ด๐ = ๐/๐๐ โ1
2๐๐0.7๐
2
๐ด๐ธ = ๐ด๐/(1.067 โ 0.229๐/๐ท)
๐ด๐ธ/๐ด๐
๐0.7๐ = ๐0/ (1
2๐๐0.7๐
2 )
3
Thus:
๐ด๐ธ/๐ด0 = 0.7543 P/D = 0.9463 D = 7.8196m ๐0 = 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 = โ๐
๐พโ๐ Y =
1.36๐ด1๐๐
๐๐๐๐ X =
๐ด2๐บ๐ด๐๐2
1010๐๐
Calculating power: ๐๐ = 33000 รท 0.735 ร 0.97 = 43551.02โp
๐ด๐ = ๐ด๐ธ/๐ด0 = 0.7543 P/D = 0.9463 ฮต = 10ยฐ
G = 7.6g/๐๐3 N = ๐๐ = 102๐/๐๐๐
4
๐0.66๐ =0.226๐ท๐ด๐
0.1๐=
0.226 ร 7.8196 ร 0.7543
0.5= 2.667m
๐0.25๐ = 0.7212๐0.66๐ = 1.9227๐
๐0.6๐ = 0.9911๐0.66๐ = 2.6433๐
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)โ=1.4/7.9=0.1772
dh/D=0.18
โ (๐
๐ท)
๐ต=
1
10[(
๐โ
D)
โฒ
โ ๐โ/D] = โ0.0001
2. Modification to pitch according to different thickness ratio:
5
Designed propeller(t
b)
0.7๐ =
0.14919
0.9964ร2.4424= 0.0579
Standard propeller(๐ก
๐)
0.7๐ =
0.0171ร๐ท
0.9964ร0.3409ร๐ท= 0.0503 ๏ผAccording to MAU5-80๏ผ
1 โ s =30.866๐๐ด
๐๐=
(1 โ ๐)๐ ร 30.866
๐๐=
0.75 ร 23.05 ร 30.866
102 ร 7.3997= 0.6868
๐๐ธ0 = 0.8 ๐โฒ๐ธ = {1 + 1.1 [(
๐โ
๐ท)
โฒ
โ (๐โ
๐ท)]}
๐ด๐ธ
๐ด0= 0.7535
โ (๐ก
๐)
0.7= [(
t
b)
0.7 ่ฎพโ (
t
b)
0.7 ๆ ร
0.8
0.7535] ร 0.75 = 0.00337
โ (๐
๐ท)
๐ก= โ2
๐
๐ท(1 โ ๐ )โ (
๐ก
๐)
0.7= โ0.00438
Pitch after modification:
๐
๐ท= (
๐
๐ท)
0+ โ (
๐
๐ท)
๐ต+ โ (
๐
๐ท)
๐ก= 0.9463 โ 0.0001 โ 0.00438 = 0.9418
8. Calculation of mass and moment of inertia
Mass of all blades ๐บ๐ = 35459.11๐๐
Mass of hub ๐บโ = 15091.78๐๐
Mass of the propeller ๐บ = 5055089 ๐๐
Moment of inertia of all blades ๐ผ๐ = 15522.61 ๐๐ ยท ๐ ยท ๐ 2
Moment of inertia of hub ๐ผโ = 1642.39๐๐ ยท ๐ ยท ๐ 2
Moment of inertia of the propeller ๐ผ = 17164๐๐ ยท ๐ ยท ๐ 2
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
๐
๐ท= 0.9418 J = 0ๆถ,KT=0.4603 KQ=0.06336
Calculating power P๐ท = 33000 รท 0.735 ร 0.97 = 43551.02โ๐
Thrust deduction fraction t=0.16
Moment of main engine
Q =๐๐ท ร 60 ร 75
2๐๐=
43551.02 ร 60 ร 75
2๐ ร 102= 305795.30๐๐๐ ยท ๐
Thrust of the bollard
T =๐พ๐ ร ๐
๐พ๐ ร ๐ท=
0.4603 ร 305795.3
0.06336 ร 7.8196= 284100.55๐๐๐
Rotating speed of the propeller
N = 60โ๐
๐๐ท4๐พ๐= 75.36๐/๐๐๐
11. Calculation of the nautical performance
Choose rotating speed as 82r/min๏ผ92r/min๏ผ102r/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 ๐ด๐ธ/๐ด0 = 0.7543
Trim angle 10
Efficiency of propeller ๐0 = 0.6715
Design ship speed ๐๐๐๐ฅ = 23.0501kn
Hub ratio ๐โ/D = 0.179
Sense of rotation clockwise
Material 3Cu yorcalnic
Weight ๐บ = 50550.89 ๐๐
Moment of inertia ๐ผ = 17164๐๐ ยท ๐ ยท ๐ 2
9
Appendix
Source Code for Open Water Characteristic Curve๏ผMATLAB๏ผ๏ผ
C=[];r=4;
V=[];u=4;
for a = 0.5:0.1:0.8;%็้ขๆฏ
B=[];m=11;
for d = 7.5:0.1:8.5;%็ดๅพๅๅ
A=[];n=5;
for v = 21:1:25;%้ๅบฆๅๅ
b = 0.4:0.1:1.6;%่บ่ทๅๅ
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;%ๆญ็ฉๅคงๅฐ
y0=kt*j/(kq*3.14*2);
bt = interp1(q,b,2547274,'spline');%ๆๅผ่ฎก็ฎ่บ่ทๆฏ
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);%ๆๆๆจๅ
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;%ๆๅผ่ฎก็ฎ้ปๅๆฒ็บฟๅๆๆๆจๅๅผ
%่ช้
break;
end
end
B=[B s];%่ช้้ๅ
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];%ๆไฝณ็ดๅพ
V=[V max_v];%ๆๅคง่ช้
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);%็ปๅฎ็็้ขๆฏ
disp(C);%ๆไฝณ็ดๅพ
disp(V);%ๆๅคง่ช้
disp(F);%่บ่ทๆฏ
disp(G);%่บๆๆกจๆ็
disp(ax);%่ฆๆฑ็็้ขๆฏ
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.