Rudder Calculation

RUDDER CALCULATION LOA (m) LBP (m) 69.63

B(m) 61

D(m) 15.4

No of Screw Step 1

1

5.07

V (Knots) 13

Type

Spade Rudder

RUDDER AREA For normal supply vessels the range of rudder area is 3-4 % of (L*T) Taking the rudder area to be 3.5 % of (L*T)

a

Ar b

T(m) 6.04

5.26 m2

Using DNV Rule A = TL/100 [1+25 (B/L) 2]

For normal seagoing ships Where

A c

8.02 m2

Average of Above two areas are taken as a Rudder Area Ar

Step 2

7 m2

RUDDER GEOMETRY Area = b * c

T = 1.4b+X

b

3.43 m

c

1.94 m

Aspect Ratio = Span / Chord Step 3

RUDDER MAXIMUM ANGLE

a

αmax = (5/7)*ԃmax

25 deg

Rudder Deflection Rate ԃmin = (24 * V)/L ԃmin

X = 0.05D-.0055D X 0.26878 b - Span C - Chord

AR

1.77

Where,

αmax b

A - Rudder area (m2) T - Ships Draught (m) LBP - Ships Length (m)

5.11 deg/sec

αmax - Angle of Attack ԃmax - Rudder deflection Angle ԃmax = 33 - 35 for sea-going with conventional rudder

Step 4

RUDDER PROFILE Taper Ratio is taken as C = (Ct + Cr)/2

0.5

Taper Ratio = Ct/Cr

Cr

2.58 m

Ct

1.29 m

Sweep back angle is taken to be

7 deg

Step 5

LOCATION OF RUDDER TURNING AXIS

a

For Tip

b

c

(Apporx)

0.122173

BC = b/2 tan 7

BC

0.2105413 m

BD = ct/4

BD

0.3226511 m

AC = EF = C/4

AC = EF

0.4839767 m

AD = AB+BD

AD

0.5960865 m

IJ = b/2 tan7

IJ

0.2105413 m

JL = Cr/4

JL

0.6453023 m

HI = EF = C/4

HI = EF

0.4839767 m

HL = HI+IJ+JL

HL

1.3398203 m

KL = HL-HK

KL

0.7437338 m

For Root

Let's take 25% of Area to be at forward part of the rudder Stock Ar/4

1.6597705 m2

Step 6

RUDDER CONSTRUCTION

a

Rudder Stock

ds = 83.3 Kr (FR(V+3)2(AR2XPF2+N2)1/2)1/3 Where,

ds

158.885 mm

Kr - Rudder coefficient FR - Rudder profile coefficient

0.248

Xpf = (0.12 * Ar)/6

0.133

1

Step 7

RUDDER BEARING

a

Depth ZB = 1.25 ds

Zb

198.61 mm

T= 0.2ds

T

31.78 mm

b

Clearance = 0.001*ds + 1 but not less than 1.5 mm Clearance

1.2 mm

Step 8

RUDDER SCANTLING

a

Plate Thickness t= K(0.001Yw+0.61)[4-Yw /Xw](1.45+0.1(ds) 1/2) Where, 1 K Yw = Vertical spacing between the horizontal web in mm. Xw = horizontal spacing of the vertical web in mm ds = the basic stock diameter, mm Yw t

600 mm 10.93 mm

Xw

900 mm

step 8

Rudder Construction 1

Rudder Stock

Basic stock diameter ds ds = 83.3 Kr (FR(V+3)2(AR2XPF2+N2)1/2)1/3 ԃs

where

Kr=Rudder coefficient = 0.248 FR= Rudder profile coefficient =1.0 V= Service speed =16 Kn AR = Rudder area =10.5 m2

XPF = 0.12 AR / YR YR =Depth of rudder at the center line of stock

step2 Rudder Bearing

Depth ZB = 1.2 ds

Zb=

mm

Minimum thickness of the wall for the lower bearing is to be taken as the lesser of 0.2ԃ or 100mm

T= 0.2ds

T=

mm

minimum7.0N/mm^2given bearing pressure on the projected area of the lowest main bearing for metal

RUDDER CALCULATION

LOA (m) LBP (m) B(m) D(m) T(m) V (Knots) 322.26 305.4 50.9 25.45 18.97 13 No of Screw Step 1

98.49 m2

Using DNV Rule A = TL/100 [1+25 (B/L) 2] Where

A

98.17 m2

For normal seagoing ships A - Rudder area (m2) T - Ships Draught (m) LBP - Ships Length (m)

Average of Above two areas are taken as a Rudder Area Ar

Step 2

Spade Rudder

For normal supply vessels the range of rudder area is 3-4 % of (L*T) Taking the rudder area to be 3.5 % of (L*T) Ar

c

Type

RUDDER AREA

a

b

2

98 m2

RUDDER GEOMETRY Area = b * c b

T = 1.4b+X

X = 0.05D-.0055D X 1.132525

12.74 m

b - Span C - Chord

c

7.72 m

Aspect Ratio = Span / Chord Step 3

RUDDER MAXIMUM ANGLE

a

αmax = (5/7)*ԃmax

AR

1.65

Where, αmax - Angle of Attack ԃmax - Rudder deflection Angle

αmax b

25 deg

Rudder Deflection Rate

ԃmax = 33 - 35 for sea-going with conventional rudder

ԃmin = (24 * V)/L ԃmin

Step 4

1.02 deg/sec

RUDDER PROFILE Taper Ratio is taken as C = (Ct + Cr)/2

0.5

Taper Ratio = Ct/Cr

Cr

10.29 m

Ct

5.14 m

Sweep back angle is taken to be

7 deg

(Apporx)

Step 5

LOCATION OF RUDDER TURNING AXIS

a

For Tip

b

c

0.122173

BC = b/2 tan 7

BC

0.7822023 m

BD = ct/4

BD

1.2862295 m

AC = EF = C/4

AC = EF

1.9293443 m

AD = AB+BD

AD

2.4333715 m

IJ = b/2 tan7

IJ

0.7822023 m

JL = Cr/4

JL

2.5724591 m

HI = EF = C/4

HI = EF

1.9293443 m

HL = HI+IJ+JL

HL

5.2840057 m

KL = HL-HK

KL

2.8506342 m

For Root

Let's take 25% of Area to be at forward part of the rudder Stock Ar/4

24.581879 m2

Step 6

RUDDER CONSTRUCTION

a

Rudder Stock

ds = 83.3 Kr (FR(V+3)2(AR2XPF2+N2)1/2)1/3 Where,

ds

1414.525 mm

Kr - Rudder coefficient FR - Rudder profile coefficient

0.248

Xpf = (0.12 * Ar)/6

0.360

Step 7

RUDDER BEARING

a

Depth ZB = 1.25 ds

Zb

1768.16 mm

T= 0.2ds

T

282.90 mm

b

Clearance = 0.001*ds + 1 but not less than 1.5 mm Clearance

2.4 mm

Step 8

RUDDER SCANTLING

a

Plate Thickness t= K(0.001Yw+0.61)[4-Yw /Xw](1.45+0.1(ds) 1/2) Where, K 1 Yw = Vertical spacing between the horizontal web in mm. Xw = horizontal spacing of the vertical web in mm ds = the basic stock diameter, mm Yw t

600 mm 21.02 mm

Xw

900 mm

1