Main input data: Vs 10 knots T 1080 kN RPM 1500 n= 25 Hz D 4m xboss 0.1 rboss
Resulting performance: Thrust Torque Power Vs
Circulation distribution parameters: k= 20 a= 0.1 m=
0.4
RPM KT
0.2 m
z
KQ
3 blades
JA η
Water Density Kin.viscosity
1025 kg/m3 0 m2/s
x=r/R r xx w t c Γ VA
0.2 0.41 0.12 0.149 0.219 1.29 12.17
0.28 0.57 0.2 0.137 0.198 1.49 15.19
0.36 0.73 0.29 0.129 0.178 1.64 17.34
0.44 0.89 0.38 0.123 0.158 1.74 18.87
0.52 1.05 0.47 0.118 0.138 1.8 19.82
0.6 1.21 0.56 0.113 0.118 1.8 20.15
0.68 1.37 0.65 0.110 0.097 1.76 19.78
0.76 1.53 0.74 0.107 0.077 1.64 18.59
4.379
4.440
4.482
4.514
4.540
4.561
4.579
4.594
UTmean
4.747
4.258
3.791
3.382
3.010
2.655
2.302
1.937
UAmean
20.219
23.152
25.062
26.349
27.124
27.398
27.120
26.180
βi
13.212
10.420
8.603
7.315
6.333
5.535
4.851
4.231
Χ(x,z,βi) UT UA βi V∞ [m/s] Lift [N/m] CL Rn CF CD dr dDrag [N] dTD [N] dQD [Nm] dT [N] dQ [Nm]
1
1
1
1
0.99
0.98
0.96
0.92
4.747
4.258
3.791
3.393
3.031
2.698
2.388
2.096
20.219
23.152
25.062
26.428
27.316
27.843
28.133
28.334
13.21 10.42 8.60 7.33 6.37 5.60 4.99 4.49 63.393 88.553 113.738 138.926 164.116 189.307 214.503 239.705 790647 1379162 2021860 2687343 3334341 3910284 4349566 4568563 0.099 0.077 0.062 0.052 0.045 0.039 0.035 0.031 6.87E+07 1.11E+08 1.57E+08 2.03E+08 2.48E+08 2.88E+08 3.17E+08 3.32E+08 2.20E-03 2.05E-03 1.95E-03 1.88E-03 1.83E-03 1.80E-03 1.77E-03 1.76E-03 5.90E-03 5.20E-03 4.76E-03 4.45E-03 4.23E-03 4.07E-03 3.94E-03 3.86E-03 0.37 0.16 0.16 0.16 0.16 0.16 0.16 0.16 17267 14917 24775 36759 50334 64666 78360 89561 3946
2698
3706
4691
5581
6313
6811
7010
6859 279311 33990
8333 214329 31002
17833 316152 53061
32375 421769 81099
52425 524624 114420
77743 616343 151531
106791 686485 189544
136429 721718 223847
0.009 0.065 1.075
0.007 0.055 1.063
0.006 0.047 1.054
Cavitation check: (This is just one of several possible methods) Draught at propeller: 10 m h= 8 Water vapour pressure: 1500 Atm.pressure101325 σ t/c v/V ∆v/V Vx
0.086 0.170 1.194
0.043 0.133 1.152
0.026 0.109 1.124
0.017 0.091 1.104
0.012 0.077 1.088
0.028
0.021
0.017
0.014
0.012
0.011
0.010
0.009
77.461
103.898
129.831
155.358
180.567
205.515
230.110
254.637
(Vx/V∞)2-1
0.493
Cavitation? Yes
0.377 Yes
0.303 Yes
0.251 Yes
0.211 Yes
0.179 Yes
0.151 Yes
0.128 Yes
Calculation of geometric pitch distribution: kc ka kt f/c αi3
1.668 1.0124 11.516 0.0108
1.614 1.0334 9.662 0.0081
1.557 1.0704 8.332 0.0063
1.509 1.1278 7.280 0.0051
1.483 1.2101 6.383 0.0043
1.494 1.3217 5.573 0.0038
1.553 1.4672 4.798 0.0035
1.675 1.6511 4.017 0.0034
0.1550
0.1223
0.1024
0.0905
0.0836
0.0801
0.0791
0.0801
αt P/D
1.9596 0.1756
1.2857 0.1868
0.9066 0.1937
0.6618 0.1981
0.4908 0.2004
0.3646 0.2010
0.2649 0.2005
0.1884 0.1998
Resulting performance: 5044.4 kN 1349.5 kNm 211984 kW 10 knots 1500
20.5
0.031
20
0.0021
19.5
0.045 0.108
19
1.544
1.082 Average induced tangential velocity. Calculated.
28.935 4.13 264.920 4446756 0.029 3.20E+08 1.77E-03
1.75
0.220
0.210 15 1.7eq. 20.844 Average induced axial velocity. Calculated by solving second degree 0.200 0.150 14.5 1.65 2.972 Initial hydrodynamic pitch angle. 0.190 0.148 14 0.66 Goldstein factor, from diagram 1.6 0.180 0.145 13.5 0.143 1.639 Induced tangential velocity at blade 1.55 0.170 13 0.140 31.581 Induced axial velocity at blade 1.5 0.160 0.138 12.5 4.03 0.150 1.45 0.135 290.182 12 0.140 3737034 Radial lift distribution. 0.1 0 0.2 0 0.30.133 0 1.4 0.130 0.130 .15 .25 .35 0.027 Blade section lift coefficient 1.35 0.120 2.62E+08 0.128 1.3 0.110 0.125 1.82E-03
3.83E-03 3.89E-03 0.16 0.15 94787 81993
1.25
1.2
6825
5767
1.15
159585 702809 246060
151148 560855 224981
1.1
Wake fraction w [-]
0.84 1.836
1.8
Blade max thickness [m]
3.631
1.85
Chord length [m]
24.334
Blade section circulation G
4.608
18.5 0.92 Dim.less radius. Selected. 18 1.85 0.92 17.5 0.102 Wake fraction. Empirical formula 17 0.037 Blade max thickness for each radius. Empirical formula 16.5 1.07 Chord length. Selected (designed) values 12.56 Circulation distribution. See parameters above 16 4.620 Local axial inflow velocity 15.5
0.84 1.69 0.83 0.104 0.057 1.44 16.38
0.4 0 .45
0.100 0.123 0.090 0.120 0.080 0.118 0.070 0.115
0.060 0.113 1.05 0.050 0.110 0.20.040 0.25 0.108 0.3
0.35
0.
0.030 0.105 0.103 0.2 0.25 0.3 0 0.100 0.2 0.25 0.005 0.040 1.045
0.004 0.035 1.039
0.008
0.007
279.049
303.814
v/V (12%)=
1.14
0.12
0.110 Yes
0.096 Yes
1.873 1.8778 3.180 0.0035
2.159 Correction factor for camber 2.1518 Correction factor for angle of attack 2.166 Correction factor due to thickness 0.0038 Camber distribution
0.0830
0.0894 Correction of ideal angle of attack due to 3-D effects
0.1263 0.2012
0.0749 Correction of ideal angle of attack due to thickness effects 0.2130 Resulting pitch distribution
1.85 1.8
1.75 1.7
1.65
0.220 0.210 0.200 0.150 0.190 0.148 0.180
1.55
0.170
1.5
1.45
0.2 1.4
1.35
0.145 0.143
0.140 0.138 0.150 0.135 0.140 0 0.30.133 0 0.130 0.130 .25 .35 0.120 0.128 0.160
Wake fraction w [-]
Blade max thickness [m]
1.6
0.4 0 .45
0.5
0 .55
xx
0 0.7 .65
0 .75
0.8
0 .85
0.9 0 .95
istribution f/c [-]
Radial thrust distribution dT [N]
Lift coefficient CL [-]
0.110 0.125 0.100 0.123
Velocities [m/s]
0.01 0.01 0.1 1.25 0.01 0.090 0.120 0.09 0.01 1.2 32.5 300 0.080 0.118 0.01 0.09 1.15 0.01 30 280 0.070 0.115 0.01 1.1 0.060 0.113 0.08 725000 250000 27.5 0.01 260 240000 700000 1.05 0.050 0.110 0.08 0.01 230000 675000 25 0.45 0.5 0.55 0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95 0.20.040 0.25 0.108 0.3 0.07 0.35 0.4 240 0.01 220000 650000 Dim.less radius x=r/R 0.01 0.030 0.105 0.06 22.5 625000 210000 0.103 0.2 0.25 0.3 0.35 600000 0.4 0.45 0.5 0.55 0.6 0.65 0.7 0.75 0.8 0.85 0.90 0.95 220 200000 0.06 20 0 Row 31 190000 0.100 Dim.less radius x=r/R 575000 200 0 Row 34 180000 0.2 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95 0.060.25 17.50.3 550000 0.01 0.22 0 170000 180 Row 21 Dim.less radius x=r/R 525000 0.05 0.01 0.21 0 15 160000 Row 26 500000 0 0.05 160 150000 Row 0.01 0.21 27 12.5 475000 0 140000 Row 29 0.04 4500000.01 0.21 0 140 130000 Row 39 10 425000 0 0.04 0.01 0.21Row 40 120000 120 0 110000 7.5 4000000.01 0.03 0.2 375000 0 100000 100 0.2 5 3500000.01 0.03 0 90000 0.2 0 0.3 0 0.01 0.4 0 0.5 0 0.6 0 0.7 0 0.8 0 0.9 0 325000 0.2 8080000 2.5 .25 300000 .35 .45 .55 .65 .75 .85 .95 70000 0.01 0.2 Dim.less radius x=r/R 0 275000 6060000 1.3
0.1
0.6
Row 21 0.21 Row 26 0.21 Row 27 Row 29 0.21 Row 39 0.21Row 40
Camber distribution f/c [-]
Radial thrust distributio
Velocitie
Lift
0 170000 180 5250000.01 0 15 160000 500000 0 0.05 160 150000 0.01 12.5 475000 0 140000 0.04 4500000.01 0 140 130000 10 425000 0 0.04 0.01 120000 120 400000 0 110000 7.5 0.03 3750000.01 0 100000 100 5 3500000.01 0.03 0 90000 0.2 0 0.3 0 0.01 0.4 0 0.5 0 0.6 0 0.7 0 0.8 0 0.9 0 325000 8080000 2.5 .25 300000 .35 .45 .55 .65 .75 .85 .95 70000 0.01 Dim.less radius x=r/R 0 275000 6060000 0.01 0 50000 0.2250000 0 0.3 0.4 0 0.5 0 0.6 0 0.7 0 0.8 0 0.9 0 .25 0.01 .35 .45 .55 .65 .75 .85 .95 40000 225000 200000 30000 Dim.less radius x=r/R 0.01 0.2 0 0.3 0 0.4 0 0.5 0 0.6 0 0.7 0 0.8 0 0.9 0 .35 .45 .55 .65 .75 .85 .95 0.01 .25 0.05
0
Dim.less radius x=r/R
0.2 0.2 0.2 0.2 0.19 0.19 0.19 0.19 0.18
0
0.18
0
0.18
0
0.18 0.2 0 0.3 0 0.4 0 0.5 0 0.6 0 0.7 0 0.8 0 0.9 0 .25 .35 .45 .55 .65 .75 .85 .95 Dim.less radius x=r/R
0.01 0.01 0.01 0.01 300 0.01 0.01 280 0.01 250000 0.01 260 240000 0.01 230000 240 0.01 220000 0.01 210000 220 0 200000 0 Row 31 190000 200 0 Row 34 180000 .85 0.9 0.95 0.22 0 170000 180 Row 21 0.21 0 160000 Row 26 0 160 150000 Row 0.21 27 0 140000 Row 29 0.21 0 140 130000 Row 39 0 0.21Row 40 120000 120 0 110000 0.2 0 100000 100 0.2 0 90000 0.2 8080000 5 70000 0.2 6060000
0 0 0 0 0 0 0 0 0
170000 180 160000 160 150000 140000 140 130000 120000 120 110000 100000 100 90000 8080000 5 70000 6060000 50000 0.9 0 .95 40000 30000 0 0.9 0 85 .95
Row 21 0.21 Row 26 0.21 Row 27 Row 29 0.21 Row 39 0.21Row 40
0 0.8 0 0.9 0 .75 .85 .95
0.2 0.2 0.2 0.2 0.19 0.19 0.19 0.19 0.18 0.18 0.18 0.18
Row 61 Row 64