Ur s10 Rev.7 Feb 2023ul

S10
S10
S10 Rudders, Sole Pieces and Rudder Horns
(cont)
(1986)
(Rev.1 S10.1 General
1990)
(Corr.1 1.1 Basic assumptions
July 1999)
(Corr.2 1.1.1 This UR applies to ordinary profile rudders, and to some enhanced profile rudders with
July 2003) special arrangements for increasing the rudder force.
(Rev.2
May 2010) 1.1.2 This UR applies to rudders made of steel for ships with L ≥ 24m.
(Rev.3
Mar 2012) 1.2 Design considerations
(Corr.1
May 2015) 1.2.1 Effective means are to be provided for supporting the weight of the rudder without
(Rev.4 excessive bearing pressure, e.g. by a rudder carrier attached to the upper part of the rudder
Apr 2015) stock. The hull structure in way of the rudder carrier is to be suitably strengthened.
(Corr.1
Dec 2015) 1.2.2 Suitable arrangements are to be provided to prevent the rudder from lifting.
(Rev.5
May 2018) 1.2.3 In rudder trunks which are open to the sea, a seal or stuffing box is to be fitted above
(Rev.6 the deepest load waterline, to prevent water from entering the steering gear compartment and
Sep 2019) the lubricant from being washed away from the rudder carrier. If the top of the rudder trunk is
(Rev.7 below the deepest waterline at scantling draught (without trim), two separate watertight seals /
Feb 2023) stuffing boxes are to be provided.
1.3 Materials
1.3.1 Welded parts of rudders are to be made of approved rolled hull materials.
Note:
1. Changes introduced in Rev.3 are to be uniformly implemented by IACS Members for

ships contracted for construction on or after 1 January 2013.
2. The “contracted for construction” date means the date on which the contract to build the
vessel is signed between the prospective owner and the shipbuilder. For further details
regarding the date of “contract for construction”, refer to IACS Procedural Requirement
(PR) No. 29.

ships contracted for construction on or after 1 July 2016.


ships contracted for construction on or after 1 January 2021.

Page 1 of 43 IACS Req. 1986/Rev.7 2023

S10
S10 1.3.2 Material factor k for normal and high tensile steel plating may be taken into account
when specified in each individual rule requirement. The material factor k is to be taken as
(cont) defined in UR S4, unless otherwise specified.
1.3.3 Steel grade of plating materials for rudders and rudder horns are to be in accordance
with UR S6.
1.3.4 Rudder stocks, pintles, coupling bolts, keys and cast parts of rudders are to be made of
rolled, forged or cast carbon manganese steel in accordance with UR W7, W8 and W11.
1.3.5 For rudder stocks, pintles, keys and bolts the specified minimum yield stress is not to
be less than 200 N/mm2. The requirements of this UR are based on a material's specified
minimum yield stress of 235 N/mm2. If material is used having a specified minimum yield stress
differing from 235 N/mm2 the material factor k is to be determined as follows:
𝟐𝟐𝟐𝟐𝟐𝟐 𝒆𝒆
𝒌𝒌 = � �
𝑹𝑹𝒆𝒆𝒆𝒆
with
e = 0.75 for ReH > 235 N/mm2
e = 1.00 for ReH ≤ 235 N/mm2
ReH = specified minimum yield stress, in N/mm2, of material used, and is not to be
taken greater than 0.7σT or 450 N/mm2, whichever is the smaller value.
σT = tensile strength, in N/mm2, of material used.
1.4 Welding and design details
1.4.1 Slot-welding is to be limited as far as possible. Slot welding is not to be used in areas
with large in-plane stresses transversely to the slots or in way of cut-out areas of semi-spade
rudders.
When slot welding is applied, the length of slots is to be minimum 75 mm with breadth of 2 t,
where t is the rudder plate thickness, in mm. The distance between ends of slots is not to be
more than 125 mm. The slots are to be fillet welded around the edges and filled with a suitable
compound, e.g. epoxy putty. Slots are not to be filled with weld.
Continuous slot welds are to be used in lieu of slot welds. When continuous slot welding is
applied, the root gap is to be between 6-10 mm. The bevel angle is to be at least 15°.
1.4.2 In way of the rudder horn recess of semi-spade rudders, the radii in the rudder plating
except in way of solid part in cast steel are not to be less than 5 times the plate thickness, but
in no case less than 100 mm. Welding in side plate is to be avoided in or at the end of the radii.
Edges of side plate and weld adjacent to radii are to be ground smooth.
1.4.3 Welds in the rudder side plating subjected to significant stresses from rudder bending
and welds between plates and heavy pieces (solid parts in forged or cast steel or very thick
plating) are to be made as full penetration welds. In way of highly stressed areas e.g. cut-out
of semi-spade rudder and upper part of spade rudder, cast or welding on ribs is to be arranged.
Two sided full penetration welding is normally to be arranged. Where back welding is
impossible welding is to be performed against ceramic backing bars or equivalent. Steel
backing bars may be used and are to be fitted with continuously welded on one side to the

S10
S10 heavy piecebevelled edge, see Figure 1. The bevel angle is to be at least 15° for one sided
welding.
(cont)
Figure 1: Use of steel backing bar in way of full penetration welding of rudder side
plating
1.4.4 Requirements for welding and design details of rudder trunks are described in S10.9.3.
1.4.5 Requirements for welding and design details when the rudder stock is connected to the
rudder by horizontal flange coupling are described in S10.6.1.4.
1.4.6 Requirements for welding and design details of rudder horns are described in S10.9.2.3.
1.5 Equivalence
1.5.1 The Society may accept alternatives to requirements given in this UR, provided they
are deemed to be equivalent.
1.5.2 Direct analyses adopted to justify an alternative design are to take into consideration all
relevant modes of failure, on a case by case basis. These failure modes may include, amongst
others: yielding, fatigue, buckling and fracture. Possible damages caused by cavitation are also
to be considered.
1.5.3 If deemed necessary by the Society, lab tests, or full scale tests may be requested to
validate the alternative design approach.
S10.2 Rudder force and rudder torque
2.1 Rudder blades without cut-outs
2.1.1 The rudder force upon which the rudder scantlings are to be based is to be
determined from the following formula:

S10
S10 CR = K1 K2 K3 132 AV2 [N]

(cont) where:
CR = rudder force [N]
A = area of rudder blade [m2]
V = maximum service speed, in knots, with the ship on summer load waterline.
When the speed is less than 10 knots, V is to be replaced by the expression:
Vmin = (V + 20) / 3
For the astern condition the maximum astern speed as defined in SOLAS
Regulation II-1/3.15 is to be used, however, in no case taken less than:
Vastern = 0.5 V
K1 = factor depending on the aspect ratio λ of the rudder area.
K1 = (λ + 2) / 3, with λ not to be taken greater than 2.
λ = b2 / At
b = mean height of the rudder area, in m. Mean breadth and mean height of rudder
are calculated according to the coordinate system in Fig. 12.
At = sum of rudder blade area A and area of rudder post or rudder horn, if any, within
the height b, in m2.
K2 = coefficient depending on the type of the rudder and the rudder profile according
to Table 1.
K3 = 0.8 for rudders outside the propeller jet.

= 1.15 for rudders behind a fixed propeller nozzle.
= 1.0 otherwise.

S10
S10
(cont)
Figure 12
Table 1
K2
Profile Type
Ahead condition Astern condition
NACA-00 series Göttingen
1.10 0.80
Flat side
1.10 0.90
Hollow
1.35 0.90
High lift rudders

1.70 1.30
Fish tail
1.40 0.80
Single plate
1.00 1.00
Mixed profiles (e.g. HSVA) 1.21 0.90

S10
S10 2.1.2 The rudder torque is to be calculated for both the ahead and astern condition according
(cont) to the formula:
QR = CR r [Nm]
r = c (α – k1) [m]
c = mean breadth of rudder area, in m, see Fig. 12.
α = 0.33 for ahead condition.
α = 0.66 for astern condition.
k1 = Af / A
Af = portion of the rudder blade area situated ahead of the centre line of the rudder
stock.
rmin = 0.1c for ahead condition, in m.
2.2 Rudder blades with cut-outs (semi-spade rudders)
The total rudder force CR is to be calculated according to S10.2.1.1. The pressure distribution
over the rudder area, upon which the determination of rudder torque and rudder blade strength
is to be based, is to be derived as follows:
The rudder area may be divided into two rectangular or trapezoidal parts with areas A1 and A2,
so that A = A1 + A2 (see Figure 23).
Figure 23
The levers r1 and r2 are to be determined as follows:
r1 = c1 (α – k1) [m]
r2 = c2 (α – k2) [m]
c1, c2 = mean breadth of partial areas A1, A2 determined, where applicable, in

accordance with Figure 12.

S10
S10 k1 = A1f / A1
(cont)
k2 = A2f / A2
A1a = portion of A1 situated aft of the centre line of the rudder stock.
A1f = portion of A1 situated ahead of the centre line of the rudder stock.
A2a = portion of A2 situated aft of the centre line of the rudder stock.
A2f = portion of A2 situated ahead of the centre line of the rudder stock.
For parts of a rudder behind a fixed structure such as the rudder horn:
The resulting force of each part may be taken as:

𝑨𝑨𝟏𝟏
CR1 = CR [N]
𝑨𝑨
𝑨𝑨
CR2 = CR 𝑨𝑨𝟐𝟐 [N]
The resulting torque of each part may be taken as:
QR1 = CR1 r1 [Nm]
QR2 = CR2 r2 [Nm]
The total rudder torque is to be calculated for both the ahead and astern condition according
to the formula:
QR = QR1 + QR2 [Nm]
For ahead condition QR is not to be taken less than:
A1c1 + A2c2
QR min = 0.1CR
A

S10
S10 S10.3 Rudder strength calculation

(cont) 3.1 The rudder force and resulting rudder torque as given in S10.2 causes bending
moments and shear forces in the rudder body, bending moments and torques in the rudder
stock, supporting forces in pintle bearings and rudder stock bearings and bending moments,
shear forces and torques in rudder horns and heel pieces. The rudder body is to be stiffened
by horizontal and vertical webs enabling it to act as a bending girder.
3.2 The bending moments, shear forces and torques as well as the reaction forces are to
be determined by a direct calculation or by an approximate simplified method considered
appropriate by each individual society. For rudders supported by sole pieces or rudder horns
these structures are to be included in the calculation model in order to account for the elastic
support of the rudder body. Guidelines for calculation of bending moment and shear force
distribution are given in an annex to this UR.
S10.4 Rudder stock scantlings
4.1 The rudder stock diameter required for the transmission of the rudder torque is to be
dimensioned such that the torsional stress is not exceeding the following value:
𝜏𝜏 𝑇𝑇 = 68 / k [N/mm2]
The rudder stock diameter for the transmission of the rudder torque is therefore not to be less
than:
𝟑𝟑
𝒅𝒅𝒕𝒕 = 𝟒𝟒. 𝟐𝟐�𝑸𝑸𝑹𝑹 𝒌𝒌 [mm]
QR = total rudder torque, in Nm, as calculated in S10.2.1.2 and/or S10.2.2.
k = material factor for the rudder stock as given in S10.1.3.5.
4.2 Rudder stock scantlings due to combined loads
If the rudder stock is subjected to combined torque and bending, the equivalent stress in the
rudder stock is not to exceed 118 / k, in N/mm2.
k = material factor for the rudder stock as given in S10.1.3.5.
The equivalent stress is to be determined by the formula:
𝝈𝝈𝒄𝒄 = �𝝈𝝈𝟐𝟐𝒃𝒃 + 𝟑𝟑𝝉𝝉𝟐𝟐𝒕𝒕 [N/mm2]
Bending stress: 𝝈𝝈𝒃𝒃 = 𝟏𝟏𝟏𝟏. 𝟐𝟐 × 𝟏𝟏𝟎𝟎𝟑𝟑 𝑴𝑴⁄𝒅𝒅𝟑𝟑𝒄𝒄 [N/mm2]
Torsional stress: 𝝉𝝉𝒕𝒕 = 𝟓𝟓. 𝟏𝟏 × 𝟏𝟏𝟎𝟎𝟑𝟑 𝑸𝑸𝑹𝑹 ⁄𝒅𝒅𝟑𝟑𝒄𝒄 [N/mm2]
The rudder stock diameter is therefore not to be less than:
𝟔𝟔 𝟒𝟒
𝒅𝒅𝒄𝒄 = 𝒅𝒅𝒕𝒕 �𝟏𝟏 + [mm]
𝟑𝟑(𝑴𝑴⁄𝑸𝑸𝑹𝑹 )𝟐𝟐
M = bending moment, in Nm, at the station of the rudder stock considered.

S10
S10 For a spade rudder with trunk extending inside the rudder, the rudder stock scantlings shall be
checked against the two cases defined in Annex S10.3.
(cont)
4.3 Before significant reduction in rudder stock diameter are granted due to the application
of steel with specified minimum yield stress exceeding 235 N/mm2, the Society may require the
evaluation of the rudder stock deformations. Large deformations of the rudder stock are to be
avoided in order to avoid excessive edge pressures in way of bearings.
S10.5 Rudder blade
5.1 Permissible stresses
The section modulus and the web area of a horizontal section of the rudder blade are to be
such that the following stresses will not be exceeded:
a) In general, except in way of rudder recess sections where b) applies
(i) bending stress σb 110/k [N/mm2]
(ii) shear stress 𝜏𝜏 50/k [N/mm2]

(iii) equivalent stress 𝜎𝜎𝑒𝑒 = �𝜎𝜎𝑏𝑏2 + 3𝜏𝜏 2 120/k [N/mm2]
k = material factor for the rudder plating as given in S10.1.3.2.
b) In way of the recess for the rudder horn pintle on semi-spade rudders
(i) bending stress σb 75 [N/mm2]
(ii) shear stress 𝜏𝜏 50 [N/mm2]

(iii) equivalent stress 𝜎𝜎𝑒𝑒 = �𝜎𝜎𝑏𝑏2 + 3𝜏𝜏 2 100 [N/mm2]
Note: The stresses in b) apply equally to high tensile and ordinary steels.
5.2 Rudder plating
The thickness of the rudder side, top and bottom plating is not to be less than:
𝑡𝑡 = 5.5𝑠𝑠𝑠𝑠√𝑘𝑘�𝑇𝑇𝑇𝑇𝑇𝑇𝑑𝑑 + 𝐶𝐶𝑅𝑅 10−4 ⁄𝐴𝐴 + 2.5 [mm]
Tscd = summer scantling loadline draught, in m.
CR = rudder force, in N, according to S10.2.1.1.
A = rudder area, in m2.
𝛽𝛽 = �1.1 − 0.5(𝑠𝑠⁄𝑏𝑏)2 max. 1.00 if b/s ≥ 2.5.
s = smallest unsupported width of plating, in m.
b = greatest unsupported width of plating, in m.

S10
S10 The thickness of the nose plates may be increased to the discretion of each Society. The
(cont) thickness of web plates is not to be less than the greater of 70% of the rudder side plating
thickness and 8 mm.
The rudder plating in way of the solid part is to be of increased thickness per S10.5.3.4.
5.3 Connections of rudder blade structure with solid parts
5.3.1 Solid parts in forged or cast steel, which house the rudder stock or the pintle, are to be
provided with protrusions, except where not required as indicated below.
These protrusions are not required when the web plate thickness is less than:
- 10 mm for web plates welded to the solid part on which the lower pintle of a semi-spade
rudder is housed and for vertical web plates welded to the solid part of the rudder stock
coupling of spade rudders.
- 20 mm for other web plates.
5.3.2 The solid parts are in general to be connected to the rudder structure by means of two
horizontal web plates and two vertical web plates.
5.3.3 Minimum section modulus of the connection with the rudder stock housing.
The section modulus of the cross-section of the structure of the rudder blade, in cm3, formed
by vertical web plates and rudder plating, which is connected with the solid part where the
rudder stock is housed is to be not less than:
𝐻𝐻𝐸𝐸 −𝐻𝐻𝑥𝑥 2 𝑘𝑘
𝑊𝑊𝑠𝑠 = 𝑐𝑐𝑠𝑠 𝑑𝑑𝑐𝑐 3 � � 10−4 [cm3]
𝐻𝐻𝐸𝐸 𝑘𝑘𝑠𝑠
where:
cs = coefficient, to be taken equal to:
= 1.0 if there is no opening in the rudder plating or if such openings are closed by
a full penetration welded plate.
= 1.5 if there is an opening in the considered cross-section of the rudder.
dc = rudder stock diameter, in mm.
HE = vertical distance between the lower edge of the rudder blade and the upper edge
of the solid part, in m.
HX = vertical distance between the considered cross-section and the upper edge of
the solid part, in m.
k = material factor for the rudder blade plating as given in S10.1.3.2.
ks = material factor for the rudder stock as given in S10.1.3.5.
The actual section modulus of the cross-section of the structure of the rudder blade is to be
calculated with respect to the symmetrical axis of the rudder.

S10
S10 The breadth of the rudder plating, in m, to be considered for the calculation of section modulus
(cont) is to be not greater than:
b = sV + 2 Hx / 3 [m]
where:
sV = spacing between the two vertical webs, in m, (see Figure 34).
Where openings for access to the rudder stock nut are not closed by a full penetration welded
plate, they are to be deducted.
Figure 3 4 Cross-section of the connection between rudder blade structure and rudder
stock housing, example with opening in only one side shown
5.3.4 The thickness of the horizontal web plates connected to the solid parts, in mm, as well
as that of the rudder blade plating between these webs, is to be not less than the greater of the
following values:
tH = 1.2 t [mm]
tH = 0.045 ds² / sH [mm]

S10
S10 where:
(cont)
t = defined in S10.5.2.
dS = diameter, in mm, to be taken equal to:
= dc, as per S10.4.2, for the solid part housing the rudder stock.
= dp, as per S10.7.1, for the solid part housing the pintle.
sH = spacing between the two horizontal web plates, in mm.
The increased thickness of the horizontal webs is to extend fore and aft of the solid part at least
to the next vertical web.
5.3.5 The thickness of the vertical web plates welded to the solid part where the rudder stock
is housed as well as the thickness of the rudder side plating under this solid part is to be not
less than the values obtained, in mm, from Table 2.
Table 2 Thickness of side plating and vertical web plates
Thickness of vertical web Thickness of rudder plating, in

plates, in mm mm
Type of rudder Rudder blade Rudder blade
Rudder blade Area with
without without
with opening opening
opening opening
Rudder supported by
1.2 t 1.6 t 1.2 t 1.4 t
sole piece
Semi-spade and spade
1.4 t 2.0 t 1.3 t 1.6 t
rudders
t = thickness of the rudder plating, in mm, as defined in S10.5.2
The increased thickness is to extend below the solid piece at least to the next horizontal web.
5.4 Single plate rudders
5.4.1 Mainpiece diameter
The mainpiece diameter is calculated according to S10.4.1 and S10.4.2 respectively. For spade
rudders the lower third may taper down to 0.75 times stock diameter.

S10
S10 5.4.2 Blade thickness

(cont) The blade thickness is not to be less than:
𝑡𝑡𝑏𝑏 = 1.5𝑠𝑠𝑠𝑠√𝑘𝑘 + 2.5 [mm]
where:
s = spacing of stiffening arms, in m, not to exceed 1 m.
V = speed, in knots, see S10.2.1.1.
5.4.3 Arms
The thickness of the arms is not to be less than the blade thickness
ta = tb [mm]
The section modulus is not to be less than:
Za = 0.5 s C12 V2 k [cm3]
C1 = horizontal distance from the aft edge of the rudder to the centreline of the rudder
stock, in m.
k = material factor as given in S10.1.3.2 or S10.1.3.5 respectively.
S10.6 Rudder stock couplings
6.1 Horizontal flange couplings
6.1.1 The diameter of the coupling bolts is not to be less than:
𝒅𝒅𝒃𝒃 = 𝟎𝟎. 𝟔𝟔𝟔𝟔�𝒅𝒅𝟑𝟑 𝒌𝒌𝒃𝒃 ⁄𝒏𝒏 𝒆𝒆𝒎𝒎 𝒌𝒌𝒔𝒔 [mm]
d = stock diameter, taken equal to the greater of the diameters dt or dc according to

S10.4.1 and S10.4.2, in mm.
n = total number of bolts, which is not to be less than 6.
em = mean distance, in mm, of the bolt axes from the centre of the bolt system.
ks = material factor for the stock as given in S10.1.3.5.
kb = material factor for the bolts as given in S10.1.3.5.
6.1.2 The thickness of the coupling flanges, in mm, is not to be less than the greater of the
following formulae:
𝑡𝑡𝑓𝑓 = 𝑑𝑑𝑏𝑏 �𝑘𝑘𝑓𝑓 ⁄𝑘𝑘𝑏𝑏

S10
S10 t f = 0.9d b
(cont)
kf = material factor for flange as given in S10.1.3.5.
kb = material factor for the bolts as given in S10.1.3.5.
db = bolt diameter, in mm, calculated for a number of bolts not exceeding 8.
6.1.3 The width of material between the perimeter of the bolt holes and the perimeter of the
flange is not to be less than 0.67 db.
6.1.4 The welded joint between the rudder stock and the flange is to be made in accordance
with Figure 4 5 or equivalent.
Figure 4 5 Welded joint between rudder stock and coupling flange
6.1.5 Coupling bolts are to be fitted bolts and their nuts are to be locked effectively.
6.2 Vertical flange couplings
6.2.1 The diameter of the coupling bolts, in mm, is not to be less than:
𝑑𝑑𝑏𝑏 = 0.81 𝑑𝑑⁄√𝑛𝑛 × �𝑘𝑘𝑏𝑏 ⁄𝑘𝑘𝑠𝑠
where:
d = stock diameter, in mm, in way of coupling flange.
n = total number of bolts, which is not to be less than 8.
kb = material factor for bolts as given in S10.1.3.5.

S10
S10 ks = material factor for stock as given in S10.1.3.5.

(cont)
6.2.2 The first moment of area of the bolts about the centre of the coupling, m, is to be not
less than:
m = 0.00043 d3 [cm3]
6.2.3 The thickness of the coupling flanges is to be not less than the bolt diameter, and the
width of the flange material between the perimeter of the bolt holes and the perimeter of the
flange is to be not less than 0.67 db.
6.2.4 Coupling bolts are to be fitted bolts and their nuts are to be locked effectively.
6.3 Cone couplings with key
6.3.1 Tapering and coupling length
Cone couplings without hydraulic arrangements for mounting and dismounting the coupling
should have a taper c on diameter of 1:8 - 1:12.
where:
c = (d0 − du ) / ℓc (see Figure 5 6 and 5b7b)
The diameters d0, in mm, and du, in mm, are shown in Figure 5 6 and the cone length, ℓc, in
mm, is defined in Figure 5b7b.
The cone coupling is to be secured by a slugging nut. The nut is to be secured, e.g. by a
securing plate.
The cone shapes are to fit exactly. The coupling length ℓ, in mm, is to be, in general, not less
than 1.5d0.

S10
S10 Figure 5 6 Cone coupling with key

(cont)
Figure 5a 7a – Gudgeon outer diameter(da) measurement
Figure 5b 7b Cone length and coupling length
6.3.2 Dimensions of key
For couplings between stock and rudder a key is to be provided, the shear area of which, in
cm2, is not to be less than:
17.55𝑄𝑄𝐹𝐹
𝑎𝑎𝑠𝑠 =
𝑑𝑑𝑘𝑘 𝑅𝑅𝑒𝑒𝑒𝑒1
where:
QF = design yield moment of rudder stock, in Nm.
𝑑𝑑𝑡𝑡 3
𝑄𝑄𝐹𝐹 = 0.02664
𝑘𝑘
Where the actual diameter dta is greater than the calculated diameter dt, the diameter dta is to
be used. However, dta applied to the above formula need not be taken greater than 1.145 dt.
dt = stock diameter, in mm, according to S10.4.1.

S10
S10 k = material factor for stock as given in S10.1.3.5.

(cont) dk = mean diameter of the conical part of the rudder stock, in mm, at the key.
ReH1 = specified minimum yield stress of the key material, in N/mm2.
The effective surface area, in cm2, of the key (without rounded edges) between key and rudder
stock or cone coupling is not to be less than:
5𝑄𝑄𝐹𝐹
𝑎𝑎𝑘𝑘 =
𝑑𝑑𝑘𝑘 𝑅𝑅𝑒𝑒𝑒𝑒2
where:
ReH2 = specified minimum yield stress of the key, stock or coupling material, in N/mm2,
whichever is less.
6.3.3 The dimensions of the slugging nut are to be as follows (see Figure 56):
external thread diameter: dg ≥ 0.65 do
height: hn ≥ 0.6 dg
outer diameter: dn ≥ 1.2 du, or 1.5 dg
whichever is the greater.
6.3.4 Push up
It is to be proved that 50% of the design yield moment is solely transmitted by friction in the
cone couplings. This can be done by calculating the required push-up pressure and push-up
length according to S10.6.4.2 and S10.6.4.3 for a torsional moment Q'F = 0.5QF.
6.3.5 Notwithstanding the requirements in S10.6.3.2 and S10.6.3.4, where a key is fitted to
the coupling between stock and rudder and it is considered that the entire rudder torque is
transmitted by the key at the couplings, the scantlings of the key as well as the push-up force
and push-up length are to be at the discretion of the Society.
6.4 Cone couplings with special arrangements for mounting and dismounting the
couplings
6.4.1 Where the stock diameter exceeds 200 mm, the press fit is recommended to be effected
by a hydraulic pressure connection. In such cases the cone is to be more slender, c ≈1:12 to
≈1:20.
In case of hydraulic pressure connections, the nut is to be effectively secured against the rudder
stock or the pintle.
For the safe transmission of the torsional moment by the coupling between rudder stock and
rudder body the push-up pressure and the push-up length are to be determined according to
S10.6.4.2 and S10.6.4.3 respectively.

S10
S10
(cont)
Figure 6 8 Cone coupling without key
6.4.2 Push-up pressure
The push-up pressure is not to be less than the greater of the two following values:
2QF
preq1 = 2
10 3 [N/mm²]
d πμ0
m
6M b 3
preq 2 = 10
 2d m
𝑝𝑝𝑟𝑟𝑟𝑟𝑟𝑟2= 6𝑀𝑀𝑐𝑐
103
[N/mm²]
2
𝑙𝑙 𝑑𝑑𝑚𝑚
where:
QF = design yield moment of rudder stock, as defined in S10.6.3.2 in Nm.
dm = mean cone diameter, in mm, see Figure 56.
ℓ = coupling length, in mm.
µ0 = frictional coefficient, equal to 0.15.
Mbc = bending moment in rudder stock at the top of the cone coupling (e.g. in case of
spade rudders), in Nm.
For spade rudder with trunk extending inside the rudder, the coupling shall be checked against
the two cases defined in Annex S10.3

S10
S10 It has to be proved by the designer that the push-up pressure does not exceed the permissible
surface pressure in the cone. The permissible surface pressure, in N/mm², is to be determined
(cont) by the following formula:
0.95R eH (1 − 𝛼𝛼 2 )
𝑝𝑝perm = − 𝑝𝑝𝑏𝑏 [N/mm²]
√3 + 𝛼𝛼 4

S10
S10 where:
(cont) 3.5𝑀𝑀𝑏𝑏𝑐𝑐
𝑝𝑝𝑏𝑏 = 103 [N/mm²]
𝑑𝑑𝑚𝑚 ℓ2
ReH = specified minimum yield stress of the material of the gudgeon, in N/mm2.
α = dm /da
dm = diameter, in mm, see Figure 56.
da = outer diameter of the gudgeon, in mm, see Figure 5 6 and Figure 5a7a. (The
least diameter is to be considered).
The outer diameter of the gudgeon in mm shall not be less than 1.25 d0, with d0 defined in
Figure 56.
6.4.3 Push-up length
The push-up length𝛥𝛥ℓ, in mm, 𝛥𝛥ℓ is to comply with the following formula:
𝛥𝛥ℓ1 ≤ 𝛥𝛥ℓ ≤ 𝛥𝛥ℓ2
where:
𝑝𝑝𝑟𝑟𝑟𝑟𝑟𝑟 𝑑𝑑𝑚𝑚 0.8𝑅𝑅𝑡𝑡𝑡𝑡

∆ℓ1 = + [mm]
1 − 𝛼𝛼 2 𝑐𝑐
𝐸𝐸 � 2 � 𝑐𝑐
𝑝𝑝perm 𝑑𝑑𝑚𝑚 0.8𝑅𝑅𝑡𝑡𝑡𝑡

Δℓ2 = + [mm]
1 − 𝛼𝛼 2 𝑐𝑐
𝐸𝐸 � 2 � 𝑐𝑐
Rtm = mean roughness, in mm, taken equal to 0.01.
c = taper on diameter defined in S10.6.3.1.
Note: In case of hydraulic pressure connections the required push-up force Pe, in N, for the
cone may be determined by the following formula:
𝑐𝑐
𝑃𝑃𝑒𝑒 = 𝑝𝑝𝑟𝑟𝑟𝑟𝑟𝑟 𝑑𝑑𝑚𝑚 𝜋𝜋 ℓ � + 0.02�
2
The value 0.02 is a reference for the friction coefficient using oil pressure. It varies and depends
on the mechanical treatment and roughness of the details to be fixed. Where due to the fitting
procedure a partial push-up effect caused by the rudder weight is given, this may be taken into
account when fixing the required push-up length, subject to approval by the Society.

S10
S10 S10.7 Pintles

(cont) 7.1 Scantlings
The pintle diameter, in mm, is not to be less than:
𝑑𝑑𝑝𝑝 = 0.35�𝐵𝐵𝑘𝑘𝑝𝑝
where:
B = relevant bearing force, in N.
kp = material factor for pintle as given in S10.1.3.5.
7.2 Couplings
7.2.1 Tapering
Pintles are to have a conical attachment to the gudgeons with a taper on diameter not greater
than:
1:8 - 1:12 for keyed and other manually assembled pintles applying locking by slugging nut.
1:12 - 1:20 on diameter for pintles mounted with oil injection and hydraulic nut.
7.2.2 Push-up pressure for pintle
The required push-up pressure for pintle in case of dry fitting, in N/mm², is to be determined by
preq1 as given below.
The required push-up pressure for pintle in case of oil injection fitting, in N/mm², is to be
determined by the maximum pressure of preq1 and preq2 as given belowfollowing formula:
𝐵𝐵1 𝐵𝐵𝑑𝑑0
𝑝𝑝𝑟𝑟𝑟𝑟𝑟𝑟1 = 0.4 2 ℓ [N/mm²]
𝑑𝑑𝑚𝑚
6𝑀𝑀𝑏𝑏𝑏𝑏
𝑝𝑝𝑟𝑟𝑟𝑟𝑟𝑟2 = 103 [N/mm²]
ℓ2 𝑑𝑑𝑚𝑚
where:
B1 = Supporting force in the pintle, in N, e.g. B1 as defined in figure A4 for semi-spade

rudder.
d0 = Pintle diameter, in mm, see Figure 59.
Mbp = bending moment in the pintle cone coupling to be determined by:
𝑀𝑀𝑏𝑏𝑏𝑏 = 𝐵𝐵ℓ𝑎𝑎 [Nm]
ℓa = length between middle of pintle-bearing and top of contact surface between cone
coupling and pintle in m, see Figure 79)

S10
S10 The required push-up length, Δℓ1, is to be calculated similarly as in S10.6.4.3, using the required
(cont) push-up pressure as defined above, and properties for the pintle.
Figure 79 pintle cone coupling indicating ℓa
7.3 The minimum dimensions of threads and nuts are to be determined according to
S10.6.3.3.
7.4 Pintle housing
The length of the pintle housing in the gudgeon is not to be less than the pintle diameter dp. dp
is to be measured on the outside of liners.
The thickness of the pintle housing is not to be less than 0.25 dp.
S10.8 Rudder stock bearing, rudder shaft bearing and pintle bearing
8.1 Liners and bushes
8.1.1 Rudder stock bearing
Liners and bushes are to be fitted in way of bearings. For rudder stocks and pintles having
diameter less than 200 mm, liners in way of bushes may be provided optionally. The minimum
thickness of liners and bushes is to be equal to:
• tmin = 8 mm for metallic materials and synthetic material.

• tmin = 22 mm for lignum material.
8.1.2 Pintle bearing

S10
S10 The thickness of any liner or bush, in mm, is neither to be less than:
(cont)
𝑡𝑡 = 0.01√𝐵𝐵
where:
B = relevant bearing force, in N.
nor than the minimum thickness defined in S10.8.1.1.
8.2 Minimum bearing surface
An adequate lubrication is to be provided.
The bearing surface Ab (defined as the projected area: length x outer diameter of liner) is not
to be less than:
Ab = P / qa [mm2]
where:
P = reaction force, in N, in bearing as determined in S10.3.2.
qa = allowable surface pressure according to the table below.
The allowable surface pressure qa for the various combinations is to be taken as reported in
Table 3. Higher values than given in the table may be taken in accordance with makers’
specifications if they are verified by tests:
Table 3 Allowable surface pressure qa
Bearing material qa [N/mm2]

lignum vitae 2.5
white metal, oil lubricated 4.5
synthetic material with hardness greater than
5.52)
60 Shore D1)
steel3) and bronze and hot-pressed bronze-
7.0
graphite materials
Notes:
1) Indentation hardness test at 23°C and with 50% moisture, are to be carried out according
to a recognized standard. Synthetic bearing materials are to be of an approved type.
2) Surface pressures exceeding 5.5 N/mm2 may be accepted in accordance with bearing
manufacturer's specification and tests, but in no case more than 10 N/mm2.
3) Stainless and wear-resistant steel in an approved combination with stock liner.
8.3 Bearing Dimensions
The length/diameter ratio of the bearing surface is not to be greater than 1.2.

S10
S10 The bearing length Lp of the pintle, in mm, is to be such that:

(cont) Dp ≤ Lp ≤ 1.2 Dp
where:
Dp = Actual pintle diameter, in mm, measured on the outside of liners.
8.4 Bearing clearances
With metal bearings, clearances should not be less than db / 1000 + 1.0, in mm, on the diameter.
If non-metallic bearing material is applied, the bearing clearance is to be specially determined

considering the material’s swelling and thermal expansion properties. This clearance is not to
be taken less than 1.5 mm on bearing diameter unless a smaller clearance is supported by the
manufacturer’s recommendation and there is documented evidence of satisfactory service
history with a reduced clearance.
S10.9 Strength of sole pieces and of rudder horns
9.1 Sole piece
Figure 7 810 Sole piece
The section modulus around the vertical z-axis is not to be less than:
Zz = Mb k / 80 [cm3]
The section modulus around the transverse y-axis is not to be less than:
Zy = 0.5 Zz
The sectional area is not to be less than:
As = B1 k / 48 [mm2]

S10
S10 9.1.1 Equivalent stress

(cont)
At no section within the length ℓ50 is the equivalent stress to exceed 115 / k, in N/mm2. The
equivalent stress is to be determined by the following formula:
𝜎𝜎𝑒𝑒 = �𝜎𝜎𝑏𝑏2 + 3𝜏𝜏 2 [N/mm2]
where:
σb = Mb / Zz(x) [N/mm2]
𝜏𝜏 = B1 / As [N/mm2]
Mb = bending moment at the section considered [Nm].
Mb = B1 x [Nm]
Mbmax = B1 ℓ50 [Nm]
B1 = supporting force in the pintle bearing, in N, (normally B1 = CR / 2).
9.2 Rudder horn
When the connection between the rudder horn and the hull structure is designed as a curved
transition into the hull plating, special consideration is to be given to the effectiveness of the
rudder horn plate in bending and to the stresses in the transverse web plates.
The bending moments and shear forces are to be determined by a direct calculation or in line
with the guidelines given in Annex S10.5 and Annex S10.6 for semi spade rudder with one
elastic support and semi spade rudder with 2-conjugate elastic support respectively.
The section modulus around the horizontal x-axis is not to be less than:
Zx = Mb k / 67 [cm3]
Mb = bending moment at the section considered, in Nm.

S10
S10 The shear stress is not to be larger than:

(cont)
𝜏𝜏 τ = 48 / k [N/mm2]
9.2.1 Equivalent stress
At no section within the height of the rudder horn is the equivalent stress to exceed 120 / k, in
N/mm2. The equivalent stress is to be calculated by the following formula:
𝜎𝜎𝑒𝑒 = �𝜎𝜎𝑏𝑏2 + 3(𝜏𝜏 2 + 𝜏𝜏 𝑇𝑇2 ) [N/mm2]
σb = Mb / Zx [N/mm2]
𝜏𝜏 = B1 / Ah [N/mm2]
B1 = supporting force in the pintle bearing, in N.
Ah = effective shear area of rudder horn in y-direction, in mm2.
𝜏𝜏 𝑇𝑇 = MT 103 / 2 AT th [N/mm2]
MT = torsional moment, in Nm.
AT = area in the horizontal section enclosed by the rudder horn, in mm2.
th = plate thickness of rudder horn, in mm.
9.2.2 Rudder horn plating
The thickness of the rudder horn side plating is not to be less than:
t = 2.4 Lk [mm]
where:
L = Rule length as defined in UR S2, in m.
9.2.3 Welding and connection to hull structure
The rudder horn plating is to be effectively connected to the aft ship structure, e.g. by
connecting the plating to side shell and transverse/ longitudinal girders, in order to achieve a
proper transmission of forces, see Figure 8911.
Brackets or stringer are to be fitted internally in horn, in line with outside shell plate, as shown
in Figure 8911.

S10
S10
(cont)
Figure 8 911 Connection of rudder horn to aft ship structure
Transverse webs of the rudder horn are to be led into the hull up to the next deck in a sufficient
number.
Strengthened plate floors are to be fitted in line with the transverse webs in order to achieve a
sufficient connection with the hull.
The centre line bulkhead (wash-bulkhead) in the after peak is to be connected to the rudder
horn.
Scallops are to be avoided in way of the connection between transverse webs and shell plating.
The weld at the connection between the rudder horn plating and the side shell is to be full
penetration. The welding radius is to be as large as practicable and may be obtained by
grinding.
9.3 Rudder trunk
The requirements in this section apply to trunk configurations which are extended below stern
frame and arranged in such a way that the trunk is stressed by forces due to rudder action.
9.3.1 Materials, welding and connection to hull
The steel used for the rudder trunk is to be of weldable quality, with a carbon content not
exceeding 0.23% on ladle analysis or a carbon equivalent CEQ not exceeding 0.41%.
Plating materials for rudder trunks are in general not to be of lower grades than corresponding
to class II as defined in UR S6.

S10
S10 The weld at the connection between the rudder trunk and the shell or the bottom of the skeg is
(cont) to be full penetration.
For rudder trunks extending below shell or skeg, tThe fillet shoulder radius r, in mm, (see Figure
91012) is to be as large as practicable and to comply with the following formulae:
r = 0.1dc / k
without being less than:
r = 60 [mm] when σ ≥ 40 / k [N/mm²]

r = 30 [mm] when σ < 40 / k [N/mm²]
where:
dc = rudder stock diameter axis defined in S10.4.2.
σ = bending stress in the rudder trunk, in N/mm².
k = material factor for the rudder trunk as given in S10.1.3.2 or S10.1.3.5

respectively.
The radius may be obtained by grinding. If disk grinding is carried out, score marks are to be
avoided in the direction of the weld. The radius is to be checked with a template for accuracy.
Four profiles at least are to be checked. A report is to be submitted to the Surveyor.
Rudder trunks comprising of materials other than steel are to be specially considered by the
Society.
Figure 9 1012 Fillet shoulder radius

S10
S10 9.3.2 Scantlings

(cont) The scantlings of the trunk are to be such that:
- the equivalent stress due to bending and shear does not exceed 0.35 ReH.
- the bending stress on welded rudder trunk is to be in compliance with the following
formula:
σ ≤ 80 / k [N/mm²]
with:
σ = bending stress in the rudder trunk, as defined in S10.9.3.1.
k = material factor for the rudder trunk as given in S10.1.3.2 or S10.1.3.5

respectively, not to be taken less than 0.7.
ReH = specified minimum yield stress, in N/mm2, of the material used.
For calculation of bending stress, the span to be considered is the distance between the mid-
height of the lower rudder stock bearing and the point where the trunk is clamped into the shell
or the bottom of the skeg.

S10
S10 Annex
(cont)
Guidelines for calculation of bending moment

and shear force distribution
AnnexS10.1 General
The evaluation of bending moments, shear forces and support forces for the system rudder–
rudder stock may be carried out for some basic rudder types as outlined in AnnexS10.2-
AnnexS10.6.

S10
S10 AnnexS10.2 Spade rudder

(cont) Data for the analysis
ℓ10 - ℓ30 = Lengths of the individual girders of the system, in m.
I10 – I30 = Moments of inertia of these girders, in cm4.
Load of rudder body:
PR = CR / (ℓ10 103) [kN/m]
Moments and forces
The moments and forces may be determined by the following formulae:
Mb = CR (ℓ20 + (ℓ10 (2 c1 + c2) / 3 (c1 + c2))) [Nm]
B3 = Mb / ℓ30 [N]
B2 = CR + B3 [N]
The maximum moment, MRC, in top of the cone coupling as shown in Figure A1 is applicable
for the connection between the rudder and the rudder stock.
Figure A 1

S10
S10
(cont)

S10
S10 AnnexS10.3 Spade rudder with trunk

PR = CR / ((ℓ10 + ℓ20)103) [kN/m]
Moments and forces

For a spade rudder with trunk extending inside the rudder, the strength shall be checked
withagainst the following two cases:
a) pressure applied on the entire rudder area
b) pressure applied only on rudder area below the middle of neck bearing.
For spade rudders with rudders trunks The moments, in Nm, and forces, in N, for the two
cases defined above may be determined according to Figure A2 a) and b), respectively.
Figure A2 a)
Full rudder force CR = CR1+CR2 and total rudder torque QR = QR1 + QR2 with rudders
stock bending moment Mb = MCR2 - MCR1

S10
S10
(cont)
Figure A2 b)
Rudder force CR2 corresponding to rudder torque QR2 acting at rudder blade area A2
with rudders stock bending moment Mb = MCR2
MR is the greatest of the following values:
MCR1 = CR1 (CG1Z – ℓ10)
MCR2 = CR2 (ℓ10 – CG2Z)
where:
CR1 : Rudder force over the rudder blade area A1.
CR2 : Rudder force over the rudder blade area A2.
CG1Z : Vertical position of the centre of gravity of the rudder blade area A1 from base.
CG2Z : Vertical position of the centre of gravity of the rudder blade area A2 from base.
CR = CR1 + CR2
B3 = (MCR2 - MCR1) / (ℓ20 + ℓ30)
B2 = CR + B3

S10
S10
(cont)
Figure A 2
AnnexS10.4 Rudder supported by sole piece
Data for the analysis
For rudders supported by a sole piece the length ℓ20 is the distance between lower edge of
rudder body and centre of sole piece and I20 the moment of inertia of the pintle in the sole piece.
I50 = moment of inertia of sole piece around the z-axis, in cm4.
ℓ50 = effective length of sole piece, in m.
PR = CR / (ℓ10 103) [kN/m]
Z = spring constant of support in the sole piece.
Z = 6.18 x I50 / ℓ503 [kN/m]
Moments and forces
Moments and shear forces are indicated in Figure A 3

S10
S10
(cont)
Figure A 3

S10
S10 AnnexS10.5 Semi spade rudder with one elastic support

I10 – I50 =Moments of inertia of these girders, in cm4.
Z = spring constant of support in the rudder horn.
Z = 1 / (fb + ft) [kN/m] for the support in the rudder horn (Figure A 4).
fb = unit displacement of rudder horn, in m, due to a unit force of 1 kN acting in the

centre of support.
fb = 1.3 d3 / (6.18 In) [m/kN] (guidance value)
In = moment of inertia of rudder horn around the x-axis, in cm4, (see also Figure A
4).
ft = unit displacement due to torsion.
ft =
(
de 2 ∑ u i t i 3.14 × 10 8 FT2 ) [m/kN]
FT = mean sectional area of rudder horn, in m2.
ui = breadth, in mm, of the individual plates forming the mean horn sectional area.
ti = thickness within the individual breadth ui, in mm.
d = Height of the rudder horn, in m, defined in Figure A 4. This value is measured

downwards from the upper rudder horn end, at the point of curvature
transition, to the mid-line of the lower rudder horn pintle.
e(z) = distance as defined in Figure A 5, in m.
PR10 = CR2 / (ℓ10 x 103) [kN/m]
PR20 = CR1 / (ℓ20 x 103) [kN/m]
for CR, CR1, CR2, see S10.2.
Moments and forces
Moments and shear forces are indicated in Figure A 4.
Rudder horn
The loads on the rudder horn are as follows:
Mb = bending moment = B1 z [Nm], Mbmax = B1 d [Nm]

S10
S10 q = shear force = B1 [N]

(cont) MT(z) = torsional moment = B1 e(z) [Nm]
An estimate for B1 is:
B1 = CR b / (ℓ20 + ℓ30) [N]
Figure A 4
Figure A 5

S10
S10 Annex S10.6 Semi spade rudder with 2-conjugate elastic support
K11, K22, K12 : Rudder horn compliance constants calculated for rudder horn with 2-conjugate
elastic supports (Figure A 6).The 2-conjugate elastic supports are defined in terms of horizontal
displacements, yi, by the following equations:
at the lower rudder horn bearing:
y1 = - K12 B2 - K22 B1
at the upper rudder horn bearing:
y2 = - K11 B2 - K12 B1
where:
y1, y2 : Horizontal displacements, in m, at the lower and upper rudder horn bearings,
respectively.
B1, B2 : Horizontal support forces, in kN, at the lower and upper rudder horn bearings,
respectively.
K11, K22, K12 : Obtained, in m/kN, from the following formulae:
λ3 e2 λ
K11 = 1.3 +
3EJ1h GJ th
 λ3 λ2 (d λ ) e 2 λ
K 22 = 1.3  + +
 3EJ 1h 2 EJ 1h  GJ th
 λ3 λ2 (d λ ) λ(d λ ) (d λ)3  + e 2d
2
K12 = 1.3  + + + 
 3EJ1h EJ1h EJ1h 3EJ 2h  GJ th
d : Height of the rudder horn, in m, defined in Figure A 6. This value is measured

downwards from the upper rudder horn end, at the point of curvature transition, to the
mid-line of the lower rudder horn pintle.
λ : Length, in m, as defined in Figure A 6. This length is measured downwards from the

upper rudder horn end, at the point of curvature transition, to the mid-line of the upper
rudder horn bearing. For λ = 0, the above formulae converge to those of spring constant
Z for a rudder horn with 1-elastic support, and assuming a hollow cross section for this
part.
e : Rudder-horn torsion lever, in m, as defined in Figure A 6 (value taken at z = d/2).
J1h : Moment of inertia of rudder horn about the x axis, in m4, for the region above the
upper rudder horn bearing. Note that J1h is an average value over the length λ (see Figure
A 6).

S10
S10 J2h : Moment of inertia of rudder horn about the x axis, in m4, for the region between the
upper and lower rudder horn bearings. Note that J2h is an average value over the length
(cont) d - λ (see Figure A 6).
Jth : Torsional stiffness factor of the rudder horn, in m4.
For any thin wall closed section:
2
4FT
J th =
∑ ut i
i i
FT : Mean of areas enclosed by outer and inner boundaries of the thin walled section of
rudder horn, in m2.
ui : Length, in mm, of the individual plates forming the mean horn sectional area.
ti : Thickness, in mm, of the individual plates mentioned above.
Note that the Jth value is taken as an average value, valid over the rudder horn height.
PR10 = CR2 / (ℓ10 x 103) [kN/m]
PR20 = CR1 / (ℓ20 x 103) [kN/m]
for CR, CR1, CR2, see S10.2.2.
Moments and forces
Moments and shear forces are indicated in Figure A 6.
Rudder horn bending moment
The bending moment acting on the generic section of the rudder horn is to be obtained, in Nm,
from the following formulae:
• between the lower and upper supports provided by the rudder horn:
MH = FA1 z
• above the rudder horn upper-support:
MH = FA1 z + FA2 (z - dlu)
where:
FA1 : Support force at the rudder horn lower-support, in N, to be obtained according to

Figure A 6, and taken equal to B1.
FA2 : Support force at the rudder horn upper-support, in N, to be obtained according to

Figure A 6, and taken equal to B2.

S10
S10 z : Distance, in m, defined in Figure A 7, to be taken less than the distance d, in m, defined
in the same figure.
(cont)
dlu : Distance, in m, between the rudder-horn lower and upper bearings (according to
Figure A 6, dlu = d - λ ).
Rudder horn shear force
The shear force QH acting on the generic section of the rudder horn is to be obtained, in N,
from the following formulae:
• between the lower and upper rudder horn bearings:
QH = FA1
• above the rudder horn upper-bearing:
QH = FA1 + FA2
where:
FA1, FA2 : Support forces, in N.
The torque acting on the generic section of the rudder horn is to be obtained, in Nm, from the
following formulae:
• between the lower and upper rudder horn bearings:
MT = FA1 e(z)
• above the rudder horn upper-bearing:
MT = FA1 e(z) + FA2 e(z)
where:
e(z) : Torsion lever, in m, defined in Figure A 7.
Rudder horn shear stress calculation
For a generic section of the rudder horn, located between its lower and upper bearings, the
following stresses are to be calculated:
𝜏𝜏𝑆𝑆 : Shear stress, in N/mm2, to be obtained from the following formula:

𝐹𝐹𝐴𝐴1
𝜏𝜏𝑆𝑆 =
𝐴𝐴𝐻𝐻
𝜏𝜏 𝑇𝑇 : Torsional stress, in N/mm2, to be obtained for hollow rudder horn from the following
formula:
𝑀𝑀𝑇𝑇 10−3
𝜏𝜏 𝑇𝑇 =
2F 𝑇𝑇 𝑡𝑡𝐻𝐻

S10
S10 For solid rudder horn, 𝜏𝜏 𝑇𝑇 is to be considered by the Society on a case by case basis.
(cont)
For a generic section of the rudder horn, located in the region above its upper bearing, the
following stresses are to be calculated:
𝜏𝜏𝑆𝑆 : Shear stress, in N/mm2, to be obtained from the following formula:
𝐹𝐹𝐴𝐴1 + 𝐹𝐹𝐴𝐴2
𝜏𝜏𝑆𝑆 =
𝐴𝐴𝐻𝐻
𝜏𝜏 𝑇𝑇 : Torsional stress, in N/mm2, to be obtained for hollow rudder horn from the following
formula:
𝑀𝑀𝑇𝑇 10−3
𝜏𝜏 𝑇𝑇 =
2𝐹𝐹𝑇𝑇 𝑡𝑡𝐻𝐻
For solid rudder horn, 𝜏𝜏 𝑇𝑇 is to be considered by the Society on a case by case basis where:
AH : Effective shear sectional area of the rudder horn, in mm2, in y-direction.
MT : Torque, in Nm.
FT : Mean of areas enclosed by outer and inner boundaries of the thin walled section of
rudder horn, in m2.
tH : Plate thickness of rudder horn, in mm. For a given cross section of the rudder horn,
the maximum value of 𝜏𝜏 𝑇𝑇 is obtained at the minimum value of tH.
Rudder horn bending stress calculation
For the generic section of the rudder horn within the length d, the following stresses are to be
calculated:
σB : Bending stress, in N/mm2, to be obtained from the following formula:
MH
σB =
WX
where:
MH : Bending moment at the section considered, in Nm.
WX : Section modulus, in cm3, around the x-axis (see Figure A 7).

S10
S10
(cont)
Figure A 6
Figure A 7
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S10

1. Changes introduced in Rev.3 are to be uniformly implemented by IACS Members for

3. Changes introduced in Rev.4 are to be uniformly implemented by IACS Members for

4. Changes introduced in Rev.5 are to be uniformly implemented by IACS Members for

5. Changes introduced in Rev.6 are to be uniformly implemented by IACS Members for

6. Changes introduced in Rev.7 are to be uniformly implemented by IACS Members for

Page 1 of 43 IACS Req. 1986/Rev.7 2023

e = 0.75 for ReH > 235 N/mm2

e = 1.00 for ReH ≤ 235 N/mm2

σT = tensile strength, in N/mm2, of material used.

1.4 Welding and design details

Page 2 of 43 IACS Req. 1986/Rev.7 2023

S10.2 Rudder force and rudder torque

2.1 Rudder blades without cut-outs

Page 3 of 43 IACS Req. 1986/Rev.7 2023

S10 CR = K1 K2 K3 132 AV2 [N]

When the speed is less than 10 knots, V is to be replaced by the expression:

K1 = (λ + 2) / 3, with λ not to be taken greater than 2.

K3 = 0.8 for rudders outside the propeller jet.

Page 4 of 43 IACS Req. 1986/Rev.7 2023

High lift rudders

Mixed profiles (e.g. HSVA) 1.21 0.90

Page 5 of 43 IACS Req. 1986/Rev.7 2023

c = mean breadth of rudder area, in m, see Fig. 12.

α = 0.33 for ahead condition.

α = 0.66 for astern condition.

rmin = 0.1c for ahead condition, in m.

2.2 Rudder blades with cut-outs (semi-spade rudders)

The levers r1 and r2 are to be determined as follows:

c1, c2 = mean breadth of partial areas A1, A2 determined, where applicable, in

Page 6 of 43 IACS Req. 1986/Rev.7 2023

α = 0.33 for ahead condition.

α = 0.66 for astern condition.

α = 0.25 for ahead condition.

α = 0.55 for astern condition.

The resulting force of each part may be taken as:

The resulting torque of each part may be taken as:

QR1 = CR1 r1 [Nm]

QR2 = CR2 r2 [Nm]

QR = QR1 + QR2 [Nm]

For ahead condition QR is not to be taken less than:

Page 7 of 43 IACS Req. 1986/Rev.7 2023

S10 S10.3 Rudder strength calculation

S10.4 Rudder stock scantlings

QR = total rudder torque, in Nm, as calculated in S10.2.1.2 and/or S10.2.2.

k = material factor for the rudder stock as given in S10.1.3.5.

4.2 Rudder stock scantlings due to combined loads

k = material factor for the rudder stock as given in S10.1.3.5.

The equivalent stress is to be determined by the formula:

𝝈𝝈𝒄𝒄 = �𝝈𝝈𝟐𝟐𝒃𝒃 + 𝟑𝟑𝝉𝝉𝟐𝟐𝒕𝒕 [N/mm2]

Bending stress: 𝝈𝝈𝒃𝒃 = 𝟏𝟏𝟏𝟏. 𝟐𝟐 × 𝟏𝟏𝟎𝟎𝟑𝟑 𝑴𝑴⁄𝒅𝒅𝟑𝟑𝒄𝒄 [N/mm2]

Torsional stress: 𝝉𝝉𝒕𝒕 = 𝟓𝟓. 𝟏𝟏 × 𝟏𝟏𝟎𝟎𝟑𝟑 𝑸𝑸𝑹𝑹 ⁄𝒅𝒅𝟑𝟑𝒄𝒄 [N/mm2]

The rudder stock diameter is therefore not to be less than:

M = bending moment, in Nm, at the station of the rudder stock considered.

Page 8 of 43 IACS Req. 1986/Rev.7 2023

S10.5 Rudder blade

5.1 Permissible stresses

a) In general, except in way of rudder recess sections where b) applies