Main input data:Vs 10 knots Resulting performance:T 1080 kN ThrustRPM 1500 Circulation distribution parameters: Torquen= 25 Hz k= 20 PowerD 4 m a= 0.1 Vs

0.1 m= 0.4 RPM

0.2 m

z 3 blades

Water Densi 1025

Kin.viscosit 1.19E-06 h

x=r/R 0.204 0.284 0.364 0.444 0.524 0.604 0.684 0.764r 0.408 0.568 0.728 0.888 1.048 1.208 1.368 1.528xx 0.115556 0.204444 0.293333 0.382222 0.471111 0.56 0.648889 0.737778w 0.149 0.137 0.129 0.123 0.118 0.113 0.110 0.107t 0.219 0.198 0.178 0.158 0.138 0.118 0.097 0.077c 1.287 1.488 1.636 1.738 1.795 1.804 1.757 1.642G 12.17 15.19 17.34 18.87 19.82 20.15 19.78 18.59

4.379 4.440 4.482 4.514 4.540 4.561 4.579 4.594

4.747 4.258 3.791 3.382 3.010 2.655 2.302 1.937

20.219 23.152 25.062 26.349 27.124 27.398 27.120 26.180

13.212 10.420 8.603 7.315 6.333 5.535 4.851 4.2311 1 1 0.997 0.993 0.984 0.964 0.924

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 4.4963.393 88.553 113.738 138.926 164.116 189.307 214.503 239.705

Lift [N/m] 790647 1379162 2021860 2687343 3334341 3910284 4349566 4568563

0.099 0.077 0.062 0.052 0.045 0.039 0.035 0.031Rn 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-03dr 0.368 0.16 0.16 0.16 0.16 0.16 0.16 0.16dDrag [N] 17267 14917 24775 36759 50334 64666 78360 89561

3946 2698 3706 4691 5581 6313 6811 7010

6859 8333 17833 32375 52425 77743 106791 136429dT [N] 279311 214329 316152 421769 524624 616343 686485 721718dQ [Nm] 33990 31002 53061 81099 114420 151531 189544 223847

Cavitation check: (This is just one of several possible methods)Draught at propeller: 10 m h= 8Water vapour pressure 1500 Atm.press 101325

s 0.086 0.043 0.026 0.017 0.012 0.009 0.007 0.006t/c 0.170 0.133 0.109 0.091 0.077 0.065 0.055 0.047v/V 1.194 1.152 1.124 1.104 1.088 1.075 1.063 1.054

0.028 0.021 0.017 0.014 0.012 0.011 0.010 0.009

xboss

rboss KT

KQ

kg/m3 JA

m2/s

VA

UTmean

UAmean

bi

C(x,z,bi)

UT

UA

bi

V∞ [m/s]

CL

CF

CD

dTD [N]

dQD [Nm]

Dv/V

77.461 103.898 129.831 155.358 180.567 205.515 230.110 254.637

0.493 0.377 0.303 0.251 0.211 0.179 0.151 0.128Cavitation? Yes Yes Yes Yes Yes Yes Yes Yes

Calculation of geometric pitch distribution:

kc 1.668 1.614 1.557 1.509 1.483 1.494 1.553 1.675ka 1.0124 1.0334 1.0704 1.1278 1.2101 1.3217 1.4672 1.6511kt 11.516 9.662 8.332 7.280 6.383 5.573 4.798 4.017f/c 0.0108 0.0081 0.0063 0.0051 0.0043 0.0038 0.0035 0.0034

0.1550 0.1223 0.1024 0.0905 0.0836 0.0801 0.0791 0.0801

1.9596 1.2857 0.9066 0.6618 0.4908 0.3646 0.2649 0.1884P/D 0.1756 0.1868 0.1937 0.1981 0.2004 0.2010 0.2005 0.1998

Vx

(Vx/V∞)2-1

ai3

at

Resulting performance:5044.4 kN1349.5 kNm

211984 kW10 knots

1500

0.031

0.0021

0.045

0.108

0.844 0.924 Dim.less radius. Selected.1.688 1.848

0.826666667 0.9155560.104 0.102 Wake fraction. Empirical formula0.057 0.037 Blade max thickness for each radius. Empirical formula1.435 1.07 Chord length. Selected (designed) values16.38 12.56 Circulation distribution. See parameters above

4.608 4.620 Local axial inflow velocity

1.544 1.082 Average induced tangential velocity. Calculated.

24.334 20.844 Average induced axial velocity. Calculated by solving second degree eq.

3.631 2.972 Initial hydrodynamic pitch angle.0.841 0.66 Goldstein factor, from diagram

1.836 1.639 Induced tangential velocity at blade

28.935 31.581 Induced axial velocity at blade

4.13 4.03264.920 290.182

4446756 3737034 Radial lift distribution.

0.029 0.027 Blade section lift coefficient3.20E+08 2.62E+08

1.77E-03 1.82E-03

3.83E-03 3.89E-030.16 0.152

94787 81993

6825 5767

159585 151148702809 560855246060 224981

0.005 0.0040.040 0.0351.045 1.039 v/V (12%)= 1.137 0.120.008 0.007

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

5

10

15

20

25

xx

Bla

de s

ecti

on

cir

cu

lati

on

G

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

Dim.less radius x=r/R

Ch

ord

len

gth

[m

]

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10.000

0.050

0.100

0.150

0.200

0.250

Dim.less radius x=r/R

Bla

de

max

th

ickn

ess

[m]

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10.000

0.020

0.040

0.060

0.080

0.100

0.120

0.140

0.160

Dim.less radius x=r/R

Wak

e fr

acti

on

w [

-]

279.049 303.814

0.110 0.096Yes Yes

1.873 2.159 Correction factor for camber1.8778 2.1518 Correction factor for angle of attack

3.180 2.166 Correction factor due to thickness0.0035 0.0038 Camber distribution

0.0830 0.0894 Correction of ideal angle of attack due to 3-D effects

0.1263 0.0749 Correction of ideal angle of attack due to thickness effects0.2012 0.2130 Resulting pitch distribution

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

5

10

15

20

25

xx

Bla

de s

ecti

on

cir

cu

lati

on

G

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

Dim.less radius x=r/R

Ch

ord

len

gth

[m

]

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10.000

0.050

0.100

0.150

0.200

0.250

Dim.less radius x=r/R

Bla

de

max

th

ickn

ess

[m]

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10.000

0.020

0.040

0.060

0.080

0.100

0.120

0.140

0.160

Dim.less radius x=r/R

Wak

e fr

acti

on

w [

-]

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

0.02

0.04

0.06

0.08

0.1

0.12

0

0.001

0.002

0.003

0.004

0.005

0.006

0.007

Lift coef.

Drag coef.

Dim.less radius x=r/R

Lif

t co

effi

cien

t C

L [

-]

Dra

g c

oef

fici

ent

CD

[-]

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

5

10

15

20

25

30

35

0

50

100

150

200

250

300

350

VA=V(1-w)

UT

UA

Vinf

Dim.less radius x=r/R

Vel

oci

ties

[m

/s]

To

tal

velo

city

Vin

f [m

/s]

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

100000

200000

300000

400000

500000

600000

700000

800000

0

50000

100000

150000

200000

250000

300000

dT

dQ

Dim.less radius x=r/R

Rad

ial

thru

st

dis

trib

uti

on

dT

[N

]

Rad

ial

torq

ue d

istr

ibu

tio

n d

Q [

Nm

]

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

0.002

0.004

0.006

0.008

0.01

0.012

0

0.05

0.1

0.15

0.2

0.25

f/c

P/D

Dim.less radius x=r/R

Cam

ber

dis

trib

uti

on

f/c

[-]

Pit

ch d

istr

ibu

tio

n P

/D [

-]

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

0.02

0.04

0.06

0.08

0.1

0.12

0

0.001

0.002

0.003

0.004

0.005

0.006

0.007

Lift coef.

Drag coef.

Dim.less radius x=r/R

Lif

t co

effi

cien

t C

L [

-]

Dra

g c

oef

fici

ent

CD

[-]

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

5

10

15

20

25

30

35

0

50

100

150

200

250

300

350

VA=V(1-w)

UT

UA

Vinf

Dim.less radius x=r/R

Vel

oci

ties

[m

/s]

To

tal

velo

city

Vin

f [m

/s]

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

100000

200000

300000

400000

500000

600000

700000

800000

0

50000

100000

150000

200000

250000

300000

dT

dQ

Dim.less radius x=r/R

Rad

ial

thru

st

dis

trib

uti

on

dT

[N

]

Rad

ial

torq

ue d

istr

ibu

tio

n d

Q [

Nm

]

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

0.002

0.004

0.006

0.008

0.01

0.012

0

0.05

0.1

0.15

0.2

0.25

f/c

P/D

Dim.less radius x=r/R

Cam

ber

dis

trib

uti

on

f/c

[-]

Pit

ch d

istr

ibu

tio

n P

/D [

-]

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10.000

0.020

0.040

0.060

0.080

0.100

0.120

0.140

0.160

Dim.less radius x=r/R

Wak

e fr

acti

on

w [

-]

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

0.02

0.04

0.06

0.08

0.1

0.12

0

0.001

0.002

0.003

0.004

0.005

0.006

0.007

Lift coef.

Drag coef.

Dim.less radius x=r/R

Lif

t co

effi

cien

t C

L [

-]

Dra

g c

oef

fici

ent

CD

[-]

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

5

10

15

20

25

30

35

0

50

100

150

200

250

300

350

VA=V(1-w)

UT

UA

Vinf

Dim.less radius x=r/R

Vel

oci

ties

[m

/s]

To

tal

velo

city

Vin

f [m

/s]

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

100000

200000

300000

400000

500000

600000

700000

800000

0

50000

100000

150000

200000

250000

300000

dT

dQ

Dim.less radius x=r/R

Rad

ial

thru

st

dis

trib

uti

on

dT

[N

]

Rad

ial

torq

ue d

istr

ibu

tio

n d

Q [

Nm

]

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

0.002

0.004

0.006

0.008

0.01

0.012

0

0.05

0.1

0.15

0.2

0.25

f/c

P/D

Dim.less radius x=r/R

Cam

ber

dis

trib

uti

on

f/c

[-]

Pit

ch d

istr

ibu

tio

n P

/D [

-]

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

0.02

0.04

0.06

0.08

0.1

0.12

0

0.001

0.002

0.003

0.004

0.005

0.006

0.007

Lift coef.

Drag coef.

Dim.less radius x=r/R

Lif

t co

effi

cien

t C

L [

-]

Dra

g c

oef

fici

ent

CD

[-]

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

5

10

15

20

25

30

35

0

50

100

150

200

250

300

350

VA=V(1-w)

UT

UA

Vinf

Dim.less radius x=r/R

Vel

oci

ties

[m

/s]

To

tal

velo

city

Vin

f [m

/s]

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

100000

200000

300000

400000

500000

600000

700000

800000

0

50000

100000

150000

200000

250000

300000

dT

dQ

Dim.less radius x=r/R

Rad

ial

thru

st

dis

trib

uti

on

dT

[N

]

Rad

ial

torq

ue d

istr

ibu

tio

n d

Q [

Nm

]

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

0.002

0.004

0.006

0.008

0.01

0.012

0

0.05

0.1

0.15

0.2

0.25

f/c

P/D

Dim.less radius x=r/R

Cam

ber

dis

trib

uti

on

f/c

[-]

Pit

ch d

istr

ibu

tio

n P

/D [

-]