This document summarizes the design calculations for key components of a ship's rudder based on classification society rules and reference books. It provides dimensions for the rudder area, rudder force and torque, rudder stock, couplings, frames, plates, webs, pintle, bearings, and steering arrangement based on ship particulars including length, breadth, draft and speed. Calculations are shown for rudder area, force, torque and structural component sizing based on formulas from classification rules.

1. Bangladesh University of
Engineering and Technology
Rudder
Design
Only calculation
Ashifur Rahaman Roll: 1312029

2. PRINCIPAL PARTICULARS
1. Length of ship 𝑳 = 𝟏𝟏𝟓 𝒎
2. Breadth of ship 𝑩 = 𝟏𝟔. 𝟒 𝒎
3. Draft 𝑻 = 𝟔. 𝟓 𝒎
4. Depth 𝑯 = 𝟏𝟎. 𝟒𝟕 𝒎
5. Block coefficient 𝑪 𝑩 = 𝟎. 𝟕
6. Speed of the ship= 12 knot
Nominal upper yield strength of forged steel 𝑅 𝑒𝐻 = 280 𝑁/𝑚𝑚2
Material factor 𝑘 𝑅 = (
235
𝑅 𝑒𝐻
)
0.75
in case of 𝑅 𝑒𝐻 ≥ 235 𝑁/𝑚𝑚2
= (
235
235
)
0.75
= 𝟏

3. RUDDER AREA
 The classification society Det norske Veritas (DnV) calls for rudder area to be
at least the size of (according to their 1975 rules):
𝐴 =
𝑇𝐿
100
{1 + 25(
𝐵
𝐿
)
2
}
So we have,
𝐴 =
𝑇𝐿
100
{1 + 25(
𝐵
𝐿
)
2
}
=
6.5 × 115
100
{1 + 25(
16.4
115
)
2
}
= 7.6 𝑚2
 From the reference book Applied Naval Architecture by Munroe Smith the
rudder area can be determined by,
𝐴 =
𝐿𝑇
60
So we have,
𝐴 =
𝐿𝑇
60
=
115 × 6.5
60
= 12.45 𝑚2
 According to Germanischer Lloyd the size of movable rudder area is
recommended to be not less than,
𝐴 = 𝑐1 × 𝑐2 × 𝑐3 × 𝑐4 ×
1.75 × 𝐿𝑇
100
Where,
𝑐1 = Factor for the ship type = 1.0 (in general)
𝑐2 = Factor for the rudder type = 1.0 (in general)
𝑐3 = Factor for the rudder profile = 1.0 (for NACA profile and plate rudder)
𝑐4 = Factor for the rudder arrangement = 1.0 (for rudders in the propeller jet)
So we have,

4. 𝐴 = 𝑐1 × 𝑐2 × 𝑐3 × 𝑐4 ×
1.75 × 𝐿𝑇
100
= 1.0 × 1.0 × 1.0 × 1..0 ×
1.75 × 115𝑋6.5
100
= 13.08 𝑚2
So we take the rudder area as 13 𝑚2
Aspect ratio:
Mean breadth of rudder=
3.3+2.5
2
=2.9 m (Data collected from actual ship stern shape)
Mean height, h=Rudder area/mean breadth=
12.45
2.9
= 4.29 m
Let, Aspect ratio, 𝑎 = h2/Ar = 1.48
Where
Rudder area Ar=12.45 𝑚2
Mean height of rudder h=4.29 m
Mean Breadth of rudder b= 2.9 m
RUDDER FORCE & TORQUE
 From the Germanischer Lloyd the rudder force is to be determined form the
following formula,
𝐶 𝑅 = 132 × 𝐴𝑣2
× 𝜅1 × 𝜅2 × 𝜅3 × 𝜅 𝑡
Where,
𝐶 𝑅 = Normal force acting on rudder
𝜅1 = Coefficient depending on the aspect ratio
=
1.48+2
3
= 1.16
𝜅2 = Coefficient depending on the type of the rudder and rudder
profile
= 1.1 (For NACA profile and ahead condition)
=1.4 for astern condition
𝜅3 = Coefficient depending on the location of the rudder
= 1.0 (For rudders including those within the propeller jet)
𝜅4 = Coefficient depending on the thrust coefficient
= 1.0 (Normally)
𝑣 = Ship speed (kn) = 12 kn for ahead condition
= 7 kn for astern condition
𝐴 = Movable rudder area
So we have,
𝐶 𝑅 = 132 × 𝐴𝑣2
× 𝜅1 × 𝜅2 × 𝜅3 × 𝜅 𝑡
= 132 × 12.45 × (12)2
× 1.16 × 1.1 × 1.0 × 1.0

5. = 301964.88 𝑁 (ahead)
𝐶 𝑅 = 132 × 𝐴𝑣2
× 𝜅1 × 𝜅2 × 𝜅3 × 𝜅 𝑡
= 132 × 12.45 × (12)2
∗ 1.16 × 1.4 × 1.0 × 1.0
= 384318.9 𝑁 (astern)
The distance of centre of pressure from the turning axis is given by,
𝑟 = 𝑏( 𝛼 − 𝑘 𝑏)
Where,
𝛼 = 0.33 (For ahead condition) and
= 0.66 (for astern condition)
𝑘 𝑏 = Balance factor
= Af/A = 0.25
𝑏 = Mean breadth of rudder
So we have,
𝑟 = 𝑏( 𝛼 − 𝑘 𝑏)
= 2.9(0.33 − 0.25)
= 0.232 𝑚
but, r min = (0.1×b) for ahead condition.
so, r = 0.1×2.9=0.29m
So we take r as 0.33m for ahead condition
r =2.9(0.66 – 0.25) = 1.189 m for astern condition
The torque on rudder is to be determined by using this formula,
𝑄 𝑅 = 𝐶 𝑅 × 𝑟
= 384318.9 × 0.29
= 𝟏𝟏𝟏𝟒𝟓𝟐. 𝟒 𝑁𝑚( ahead)
𝑄 𝑅 = 301964.88 ×1.189 = 359036.24 Nm ( astern)
The load on rudder is to be calculated by,
𝑝 𝑅 =
𝐶 𝑅
103 × ℎ
=
384318.9
103 × 4.29
= 𝟖𝟗. 𝟓𝟖 𝑘𝑁/𝑚2

6. RUDDER STOCK
 According to Germanischer Lloyd the diameter of rudder stock for transmitting
the rudder torque is not to be less than,
𝐷𝑡 = 4.2 × √𝑄 𝑅 × 𝑘 𝑅
3
Where,
𝑘 𝑅 = Material factor for rudder
= 0.88
So we have,
𝐷𝑡 = 4.2 × √𝑄 𝑅 × 𝑘 𝑅
3
= 4.2 × √ 359036.24 × .88
3
= 327.55 𝑚𝑚
We take diameter of the rudder stock as 𝐷𝑡 = 328 𝑚𝑚
RUDDER COUPLINGS
 The diameter of horizontal coupling bolts is not to be less than,
𝑑 𝑏 = 0.62 × √
𝐷3 × 𝑘 𝑏
𝑘 𝑅 × 𝑛 × 𝑒
Where,
𝐷 = Rudder stock diameter
𝑛 = Total number of bolts
= 6
𝑘 𝑅 = Material factor for rudder
= 0.88
𝑘 𝑏 = Material factor for bolt
= 𝑘 𝑅
= 1
𝑒 = Mean distance of the bolt axis form the centre of bolt system
= Rudder stock radius + distance of bolt axis from outer surface of
rudder stock
= (164 + 80)
= 244 𝑚𝑚
So we have,
𝑑 𝑏 = 0.62 × √
𝐷3 × 𝑘 𝑏
𝑘 𝑅 × 𝑛 × 𝑒
= 0.62 × √
(328)3 × 1
1 × 6 × 244
= 96.25 𝑚𝑚
So we take the diameter of horizontal coupling bolts as 𝑑 𝑏 = 96 𝑚𝑚

7.  The thickness of coupling flanges is not to be less than,
0.9𝑑 𝑏
So we take the thickness of coupling flanges as 𝑡𝑓 = 𝟖𝟕 𝑚𝑚
RUDDER FRAMES
 According to NKK rules for construction of ships, the standard spacing of
horizontal rudder frames is to be obtained from the following formula,
𝑎ℎ = 0.2 ×
𝐿
100
+ 0.4
= 0.2 ×
115
100
+ 0.4
= 0.63 𝑚
= 630 𝑚𝑚
So we take the spacing of horizontal rudder frames 𝑎ℎ = 𝟔𝟓𝟎 𝑚𝑚
 The standard distance from the vertical rudder frame forming the rudder main
piece to the adjacent vertical frame is to be obtained by,
𝑎 𝑣 = 1.5 × 𝑎ℎ
= 1.5 × 650
= 975 𝑚𝑚
So, we take the spacing of horizontal rudder frames 𝑎 𝑣 = 𝟏𝟎𝟎𝟎 𝑚𝑚
RUDDER PLATES & WEB
 According to Germanischer Lloyd, the thickness of rudder plating is to
determined from the following formula,
𝑡 𝑝 = 1.74 × 𝑎 × √ 𝑝 𝑅 × 𝑘 + 2.5
Where,
𝑎 = Smaller unsupported width of a plate panel
= 1 𝑚
𝑝 𝑅 = 10𝑇 +
𝐶 𝑅
103 ×𝐴
= 10 × 6.5 +
384318.9
1000 ×12.45
= 95.86 𝑘𝑁/𝑚2
𝑘 = Material factor
= 𝟏

8. So we have,
𝑡 𝑝 = 1.74 × 𝑎 × √𝑝 𝑅 × 𝑘 + 2.5
= 1.74 × 1 × √95.86× 1 + 2.5
= 19.53 𝑚𝑚
Hence we take the thickness of rudder plating as 𝑡 𝑝 = 𝟐𝟎 𝑚𝑚
 The thickness of the webs is not to be less than,
𝑡 𝑤 = 0.7 × 𝑡 𝑝
= 0.7 × 20
= 13.6 𝑚𝑚
So, we take thickness of webs as 𝑡 𝑤 = 𝟏𝟒 𝑚𝑚
PINTLE
The diameter of pintle is not to be less than,
𝑑 𝑝 = 0.35 × √𝐵1 × 𝑘 𝑅
Where,
𝐵1 = Support reaction at the pintle
= CR× 1
= 384318.9× 1 = 384318.9 𝑁
𝑘 𝑅 = Material factor
= 1
So we have,
𝑑 𝑝 = 0.35 × √𝐵1 × 𝑘 𝑅
= 0.35 × √384318.9 × 1
= 216.9 𝑚𝑚
we take pintle diameter as 𝒅 𝒑 = 𝟐𝟏𝟕 𝑚𝑚

9. BEARING
 In way of bearings liners and bushes are to be fitted. Their minimum thickness
is given as,
𝒕 𝒎𝒊𝒏 = 𝟐𝟐 𝑚𝑚 , for lignum materials.
So we take thickness of liner 𝒕𝒍 = 𝟐𝟐 𝑚𝑚
The projected bearing surface at the neck bearing,
𝐀 𝐛𝐧 =
B2
q
Where,
B2 = Supportreaction at neck bearing and carrier bearing = CR/1
= 384318.9 N
q = Permissible surface pressure
= 2.5 N/mm2
(For lignum vitae)
So we have,
Abn =
B2
q
=
384318.9
2.5
= 153727.56 mm2
Again,
𝐀 𝐛𝐧 = 𝐛𝐞𝐚𝐫𝐢𝐧𝐠 𝐡𝐞𝐢𝐠𝐡𝐭 × 𝐞𝐱𝐭𝐞𝐫𝐧𝐚𝐥 𝐝𝐢𝐚𝐦𝐞𝐭𝐞𝐫 𝐨𝐟 𝐥𝐢𝐧𝐞𝐫
External diameter of liner, = (250 + 80) mm
= 330 mm
So we have, Bearing height,
hb =
177078
330
= 465.8 mm
Again, the bearing height shall be equal to the bearing diameter, or, not
exceeding 1.2 times to the bearing diameter.
So we take bearing height as, 𝐡 𝐛 = 𝟓𝟎𝟎 𝐦𝐦

10. Sleeve:
Thickness = 8 mm , for metallic sleeve
Steering Arrangement:
From NKK Rulebook, sectional Area of the tiller
𝑨 𝒕 = 𝟎. 𝟒 × 𝒅 𝒖
𝟐
Here,
𝒅 𝒖 = Diameter of the upper stock in cm
= 25 cm
So we have,
𝑨 𝒕 = 𝟎. 𝟒 × 𝒅 𝒖
𝟐
= 𝟎. 𝟒 × 𝟐𝟓 𝟐
= 𝟐𝟓𝟎
If diameter of the tiller is d then,
𝒅 = √
𝑨 𝒕 × 𝟒
𝝅
= √
𝟐𝟓𝟎 × 𝟒
𝝅
= 𝟏𝟕. 𝟖𝟒 𝒄𝒎
= 𝟏𝟕𝟖 𝒎𝒎
So we take diameter of tiller as 𝒅 = 𝟏𝟖𝟎 𝒎𝒎
Diameter of the link chain is not to be less than 9.55 mm.
So, we take diameter of link chain as 𝒅 𝒄 = 𝟐𝟎𝒎𝒎
Diameter of the steering rod,
𝒅 𝒔 = 𝟏. 𝟐𝟓 × 𝒅 𝒄
= 𝟏. 𝟐𝟓 × 𝟐𝟎
= 𝟐𝟓𝒎𝒎
So we take diameter of steering rod 𝒅 𝒔 = 𝟐𝟓𝒎𝒎

11. Various ruddercomponents and their corresponding dimensions
Items Dimensions Material
Rudder stock Diameter 328 mm Hot rolled steel
Coupling bolts Diameter 96 mm Hot rolled steel
Coupling flanges Thickness 87 mm Hot rolled steel
Horizontal web Spacing 650 mm Hot rolled steel
Vertical web Spacing 1000 mm Hot rolled steel
Web plate Thickness 14 mm Hot rolled steel
Rudder plate Thickness 20 mm Hot rolled steel
Pintle Diameter 217 mm Hot rolled steel
Liner/Bush Thickness 330 mm Lignum Vitae
Sleeve Thickness 8 mm Aluminum brass (Cu+
Zn+ Al)