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Concept & Formula
Concept & Formula
Inputs
Stocks Diameter
Description
Unit
Remarks
S
N
_{u}
^{3}
Ö Q
_{R }
K
_{s}
mm
Upper Stock Diameter
Q
_{R}
Total rudder torque
kNm
K
_{s}
Material factor for upper stock

Q
_{R}
C
_{R}
r
kNm
C
_{R}
rudder force
kN
r
c(a  A
_{f}
/A)
m
> 0.1c for ahead condition
c
mean breadth of rudder area
m
a

Ahead
a
0.66

Astern
A
_{f}
Area of rudder blade situated forward
of the centerline of the rudder stock
m
^{2}
C
_{R}
nK
_{T}
AV
^{2}
kN
A
total projected area of ruder
m
^{2}
V
V
_{d}
for the ahead condition but is not to
taken as less than V
_{min}
knots
V
V
_{a}
for the astern condition but is not to
taken as less than 0.5V
_{d }
or 0.5V
_{min}
, whichever is greater
knots
V
_{d}
the design speed with the vessel running
ahead at the maximum continuous rated
shaft rpm and at the summer load line
knots
V
_{a}
maximum astern speed
knots
V
_{min}
(V
_{a}
+ 20)/3
knots
K
_{T}
1.463

Ahead
K
_{T}
1.682

Ahead behind fixed propeller nozzle
K
_{T}
1.063

Astern
K
_{T}
1.2

flat sided rudders Astern
K
_{T}
1.222

Astern behind fixed propeller nozzle
K
_{T}
1.38

Flat sided rudders astern behind
fixed propeller nozzle
A
_{t}
sum of rudder blade area A and the rudder
post or rudder horn area within the
extension of the rudder profile
m
^{2}
n

K
(n
_{y}
/Y)
^{e}

U
minumum tensile strength of material used
N/mm
^{2}
^{e}
1
for Y £ 235 N/mm
^{2}
^{e}
0.75
for Y > 235 N/mm
^{2}
c
mean breadth of rudder area
m
A
_{f}
Area of rudder blade situated forward
of the centerline of the rudder stock
m
^{2}
A
total projected area of ruder
m
^{2}
V
_{d}
the design speed with the vessel running
ahead at the maximum continuous rated
shaft rpm and at the summer load line
knots
V
_{a}
maximum astern speed
knots
A
_{t}
sum of rudder blade area A and the rudder
post or rudder horn area within the
extension of the rudder profile
m
^{2}
Y
Specified minimum yield strength of the
material, but is not to be taken as greater
than 0.7U or 450 N/mm
^{2}
, whichever is lesser
N/mm
^{2}
n
_{y}
N/mm
^{2}
U
minimum tensile strength of material used
N/mm
^{2}
l
_{n}
distance from center of neck bearing to the
centroid of rudder area
m
Kt
Location of Propeller
Ahead
Ahead behind fixed propeller nozzle
Astern
flat sided rudders Astern
Astern behind fixed propeller nozzle
Flat sided rudders astern behind fixed propeller nozzle
Symbol
Formula Expression/ Definition
Value
Unit
S
N
_{u}
^{3}
Ö Q
_{R }
K
_{s}
mm
Q
_{R}
Total rudder torque
K
_{s}
Material factor for upper stock

Q
_{R}
C
_{R}
r
kNm
r
c(a  A
_{f}
/A)
m
C
_{R}
Design Rudder force nK
_{T}
AV
^{2 }
kN
V
V
_{d}
for the ahead condition but is not to
taken as less than V
_{min}
knots
K
_{T}

A
_{t}
sum of rudder blade area A and the rudder
post or rudder horn area within the
extension of the rudder profile
m
^{2}
K
(n
_{y}
/Y)
^{e}

n
_{y}
N/mm
^{2}
U
minimum tensile strength of material used
N/mm
^{2}
Minimum Required Lower Rudder Stock Diameter
Symbol
Formula Expression/ Definition
Value
Unit
S
_{1}
S
^{6}
Ö 1 + (4/ 3) (M/ Q
_{R}
)
^{2}
mm
S
upper stock required diameter
mm
Q
_{R}
rudder torque
kNm
M
bending moment at the station of the
rudder stock
M
C
_{R}
l
_{n}
kNm
C
_{R}
rudder force
kN
l
_{n}
distance from center of neck bearing to the
centroid of rudder area
m
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