SIST EN ISO 12215-8:2018

SLOVENSKI STANDARD
01-december-2018
1DGRPHãþD
SIST EN ISO 12215-8:2009
SIST EN ISO 12215-8:2009/AC:2011
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YNOMXþXMHSRSUDYHN&RU
Small craft - Hull construction and scantlings - Part 8: Rudders (ISO 12215-8:2009,
including Cor 1:2010)
Kleine Wasserfahrzeuge - Rumpfbauweise und Dimensionierung - Teil 8: Ruder (ISO
12215-8:2009, einschließlich Cor 1:2010)
Petits navires - Construction de coques et échantillonnage - Partie 8: Gouvernails (ISO
12215-8:2009; y compris Cor 1:2010)
Ta slovenski standard je istoveten z: EN ISO 12215-8:2018
ICS:
47.020.10 Ladijski trupi in njihovi Hulls and their structure
konstrukcijski elementi elements
47.080 ýROQL Small craft
2003-01.Slovenski inštitut za standardizacijo. Razmnoževanje celote ali delov tega standarda ni dovoljeno.

EN ISO 12215-8
EUROPEAN STANDARD
NORME EUROPÉENNE
October 2018
EUROPÄISCHE NORM
ICS 47.080 Supersedes EN ISO 12215-8:2009
English Version
Small craft - Hull construction and scantlings - Part 8:
Rudders (ISO 12215-8:2009, including Cor 1:2010)
Petits navires - Construction de coques et Kleine Wasserfahrzeuge - Rumpfbauweise und
échantillonnage - Partie 8: Gouvernails (ISO 12215- Dimensionierung - Teil 8: Ruder (ISO 12215-8:2009,
8:2009; y compris Cor 1:2010) einschließlich Cor 1:2010)
This European Standard was approved by CEN on 16 April 2018.

CEN members are bound to comply with the CEN/CENELEC Internal Regulations which stipulate the conditions for giving this
European Standard the status of a national standard without any alteration. Up-to-date lists and bibliographical references
concerning such national standards may be obtained on application to the CEN-CENELEC Management Centre or to any CEN
member.
This European Standard exists in three official versions (English, French, German). A version in any other language made by
translation under the responsibility of a CEN member into its own language and notified to the CEN-CENELEC Management
Centre has the same status as the official versions.

CEN members are the national standards bodies of Austria, Belgium, Bulgaria, Croatia, Cyprus, Czech Republic, Denmark, Estonia,
Finland, Former Yugoslav Republic of Macedonia, France, Germany, Greece, Hungary, Iceland, Ireland, Italy, Latvia, Lithuania,
Luxembourg, Malta, Netherlands, Norway, Poland, Portugal, Romania, Serbia, Slovakia, Slovenia, Spain, Sweden, Switzerland,
Turkey and United Kingdom.
EUROPEAN COMMITTEE FOR STANDARDIZATION
COMITÉ EUROPÉEN DE NORMALISATION

EUROPÄISCHES KOMITEE FÜR NORMUNG

CEN-CENELEC Management Centre: Rue de la Science 23, B-1040 Brussels
© 2018 CEN All rights of exploitation in any form and by any means reserved Ref. No. EN ISO 12215-8:2018 E
worldwide for CEN national Members.

Contents Page
European foreword . 3
Annex ZA (informative) Relationship between this European Standard and the Essential
Requirements of Directive 2013/53/EU aimed to be covered . 4
European foreword
The text of ISO 12215-8:2009, including Cor 1:2010 has been prepared by Technical Committee
ISO/TC 188 “Small craft” of the International Organization for Standardization (ISO) and has been taken
over as EN ISO 12215-8:2018.
This European Standard shall be given the status of a national standard, either by publication of an
identical text or by endorsement, at the latest by April 2019, and conflicting national standards shall be
withdrawn at the latest by April 2019.
Attention is drawn to the possibility that some of the elements of this document may be the subject of
patent rights. CEN shall not be held responsible for identifying any or all such patent rights.
This document supersedes EN ISO 12215-8:2009.
This document has been prepared under a mandate given to CEN by the European Commission and the
European Free Trade Association, and supports essential requirements of EU Directive 2013/53/EU.
For relationship with EU Directive 2013/53/EU, see informative Annex ZA, which is an integral part of
this document.
According to the CEN-CENELEC Internal Regulations, the national standards organizations of the
following countries are bound to implement this European Standard: Austria, Belgium, Bulgaria, Croatia,
Cyprus, Czech Republic, Denmark, Estonia, Finland, Former Yugoslav Republic of Macedonia, France,
Germany, Greece, Hungary, Iceland, Ireland, Italy, Latvia, Lithuania, Luxembourg, Malta, Netherlands,
Norway, Poland, Portugal, Romania, Serbia, Slovakia, Slovenia, Spain, Sweden, Switzerland, Turkey and
the United Kingdom.
Endorsement notice
The text of ISO 12215-8:2009, including Cor 1:2010 has been approved by CEN as EN ISO 12215-8:2018
without any modification.
Annex ZA
(informative)
Relationship between this European Standard and the Essential
Requirements of Directive 2013/53/EU aimed to be covered
This European standard has been prepared under a Commission’s standardization request M/542
C(2015) 8736 final to provide one voluntary means of conforming to Essential Requirements of Directive
2013/53/EU.
Once this standard is cited in the Official Journal of the European Union under that Directive, compliance
with the normative clauses of this standard given in Table ZA.1 confers, within the limits of the scope of
this standard, a presumption of conformity with the corresponding Essential Requirements of that
Directive and associated EFTA regulations.
Table ZA.1 — Correspondence between this European Standard and Annex I of Directive
2013/53/EU
Essential Requirements Clause(s)/sub- Remarks/Notes
of Directive 2013/53/EU clause(s) of
this EN
Annex I, Part A, 2.5 – 7.2, 7.3, 12.1 These clauses specify warnings and information to
Owner’s manual be included in the owner’s manual, if relevant.
Annex I, Part A, 3.1 - All clauses This part of this standard provides scantling
Structure requirements applicable to five types of rudder

configuration: Type I to Type V, as shown in Figures
2 and 3 of clause 6.2. It applies only to monohulls.
The application of this part of this standard does not
ensure proper steering capabilities.
Single bearing spade rudders and single hull bearing
skeg rudders are not addressed by this standard.
Annex I, Part A, 5.4.2 - 6.1.6 In respect of the ability of emergency tiller
Steering system – components to transmit rudder torque.
Emergency arrangements
WARNING 1 — Presumption of conformity stays valid only as long as a reference to this European
Standard is maintained in the list published in the Official Journal of the European Union. Users of this
standard should consult frequently the latest list published in the Official Journal of the European Union.
WARNING 2 — Other Union legislation may be applicable to the product(s) falling within the scope of
this standard.
INTERNATIONAL ISO
STANDARD 12215-8
First edition
2009-05-15
Small craft — Hull construction and
scantlings —
Part 8:
Rudders
Petits navires — Construction de coques et échantillonnage —
Partie 8: Gouvernails
Reference number
ISO 12215-8:2009(E)
©
ISO 2009
ISO 12215-8:2009(E)
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ii © ISO 2009 – All rights reserved

ISO 12215-8:2009(E)
Contents Page
Foreword. v
Introduction . vi
1 Scope . 1
2 Normative references . 1
3 Terms and definitions. 1
4 Symbols . 2
5 Design stresses . 4
5.1 Rudder material. 4
6 Rudder and steering arrangement, rudder types . 5
6.1 General. 5
6.2 Rudder types . 6
7 Design rudder force calculation. 10
7.1 General. 10
7.2 Force F and corresponding load case . 11
7.3 Force F and corresponding load case . 12
8 Rudder bending moment and reactions at bearings . 13
8.1 General. 13
8.2 Analysis of spade rudder (Type I). 13
8.3 Analysis of skeg rudders (Types II to V) . 14
9 Rudder design torque, T . 16
10 Rudder and rudder stock design . 17
10.1 Load bearing parts of the rudder . 17
10.2 Metal rudder stock material . 17
10.3 Design stress for metal rudder stock . 18
10.4 Required diameter for solid circular metal rudder stocks . 18
10.5 Vertical variation of the diameter of a Type I rudder (spade). 18
10.6 Round tubular stocks. 19
10.7 Non-circular metal rudder stocks . 20
10.8 Simple non-isotropic rudder stocks (e.g. wood or FRP). 21
10.9 Complex structural rudders and rudder stocks in composite. 21
10.10 Check of deflection of Type I rudder stocks between bearings . 21
11 Equivalent diameter at the level of notches.22
12 Rudder bearings, pintles and gudgeons. 22
12.1 Bearing arrangement. 22
12.2 Clearance between stock and bearings . 23
13 Rudder stock structure and rudder construction . 24
13.1 Rudder stock structure . 24
13.2 Rudder construction. 24
13.3 FRP rudder blades. 24
13.4 Non-FRP rudder blades. 25
14 Skeg structure. 25
14.1 General. 25
14.2 Design stress . 25
Annex A (normative) Metal for rudder stock . 26
ISO 12215-8:2009(E)
Annex B (normative) Complex composite rudder stock design . 30
Annex C (normative) Complete calculation for rudders with skeg . 32
Annex D (informative) Geometrical properties of some typical rudder blade shapes . 36
Annex E (informative) Vertical variation of diameter for Type I rudders . 39
Annex F (informative) Type I rudders — Deflection of stock between bearings . 41
Bibliography . 44

iv © ISO 2009 – All rights reserved

ISO 12215-8:2009(E)
Foreword
ISO (the International Organization for Standardization) is a worldwide federation of national standards bodies
(ISO member bodies). The work of preparing International Standards is normally carried out through ISO
technical committees. Each member body interested in a subject for which a technical committee has been
established has the right to be represented on that committee. International organizations, governmental and
non-governmental, in liaison with ISO, also take part in the work. ISO collaborates closely with the
International Electrotechnical Commission (IEC) on all matters of electrotechnical standardization.
International Standards are drafted in accordance with the rules given in the ISO/IEC Directives, Part 2.
The main task of technical committees is to prepare International Standards. Draft International Standards
adopted by the technical committees are circulated to the member bodies for voting. Publication as an
International Standard requires approval by at least 75 % of the member bodies casting a vote.
Attention is drawn to the possibility that some of the elements of this document may be the subject of patent
rights. ISO shall not be held responsible for identifying any or all such patent rights.
ISO 12215-8 was prepared by Technical Committee ISO/TC 188, Small craft.
ISO 12215 consists of the following parts, under the general title Small craft — Hull construction and
scantlings:
⎯ Part 1: Materials: Thermosetting resins, glass-fibre reinforcement, reference laminate
⎯ Part 2: Materials: Core materials for sandwich construction, embedded materials
⎯ Part 3: Materials: Steel, aluminium alloys, wood, other materials
⎯ Part 4: Workshop and manufacturing
⎯ Part 5: Design pressures for monohulls, design stresses, scantlings determination
⎯ Part 6: Structural arrangements and details
⎯ Part 8: Rudders
ISO 12215-8:2009(E)
Introduction
The reason underlying the preparation of this part of ISO 12215 is that standards and recommended practices
for loads on the hull and the dimensioning of small craft differ considerably, thus limiting the general worldwide
acceptability of craft. This part of ISO 12215 has been set towards the lower boundary range of common
practice.
The objective of this part of ISO 12215 is to achieve an overall structural strength that ensures the watertight
and weathertight integrity of the craft.
The working group considers this part of ISO 12215 to have been developed applying present practice and
sound engineering principles. The design loads and criteria of this part of ISO 12215 may be used with the
scantling determination equations of this part of ISO 12215 or using equivalent engineering methods such as
continuous beam theory, matrix-displacement method and classical lamination theory, as indicated within.
Considering future development in technology and craft types, and small craft presently outside the scope of
this part of ISO 12215, provided that methods supported by appropriate technology exist, consideration may
be given to their use as long as equivalent strength to this part of ISO 12215 is achieved.
The dimensioning according to this part of ISO 12215 is regarded as reflecting current practice, provided the
craft is correctly handled in the sense of good seamanship and equipped and operated at a speed appropriate
to the prevailing sea state.
vi © ISO 2009 – All rights reserved

INTERNATIONAL STANDARD ISO 12215-8:2009(E)

Small craft — Hull construction and scantlings —
Part 8:
Rudders
1 Scope
This part of ISO 12215 gives requirements on the scantlings of rudders fitted to small craft with a length of hull,
L , of up to 24 m, measured according to ISO 8666. It applies only to monohulls.
H
This part of ISO 12215 does not give requirements on rudder characteristics required for proper steering
capabilities.
This part of ISO 12215 only considers pressure loads on the rudder due to craft manoeuvring. Loads on the
rudder or its skeg, where fitted, induced by grounding or docking, where relevant, are out of scope and need
to be considered separately.
NOTE Scantlings derived from this part of ISO 12215 are primarily intended to apply to recreational craft including
charter craft.
2 Normative references
The following referenced documents are indispensable for the application of this document. For dated
references, only the edition cited applies. For undated references, the latest edition of the referenced
document (including any amendments) applies.
ISO 8666, Small craft — Principal data
ISO 12215-5:2008, Small craft — Hull construction and scantlings — Part 5: Design pressures for monohulls,
design stresses, scantlings determination
3 Terms and definitions
For the purposes of this document, the following terms and definitions apply.
3.1
design categories
sea and wind conditions for which a craft is assessed by this part of ISO 12215 to be suitable, provided the
craft is correctly handled in the sense of good seamanship and operated at a speed appropriate to the
prevailing sea state
3.1.1
design category A (“ocean”)
category of craft considered suitable to operate in seas with significant wave heights above 4 m and wind
speeds in excess of Beaufort Force 8, but excluding abnormal conditions such as hurricanes
ISO 12215-8:2009(E)
3.1.2
design category B (“offshore”)
category of craft considered suitable to operate in seas with significant wave heights up to 4 m and winds of
Beaufort Force 8 or less
3.1.3
design category C (“inshore”)
category of craft considered suitable to operate in seas with significant wave heights up to 2 m and a typical
steady wind force of Beaufort Force 6 or less
3.1.4
design category D (“sheltered waters”)
category of craft considered suitable to operate in waters with significant wave heights up to and including
0,3 m with occasional waves of 0,5 m height, for example from passing vessels, and a typical steady wind
force of Beaufort Force 4 or less
3.2
loaded displacement mass
m
LDC
mass of the craft, including all appendages, when in the fully loaded ready-for-use condition as defined in
ISO 8666
3.3
sailing craft
2/3
craft for which the primary means of propulsion is wind power, having A > 0,07(m ) where A is the total
S LDC S
profile area of all sails that may be set at one time when sailing closed hauled, as defined in ISO 8666 and
expressed in square metres
NOTE 1 For the headsails, A is the area of the fore triangle.
S
NOTE 2 In the rest of this part of ISO 12215, non-sailing craft are called motor craft.
4 Symbols
For the purposes of this document, unless specifically otherwise defined, the symbols given in Table 1 apply.
NOTE The symbols used in the annexes are not listed in Table 1.
2 © ISO 2009 – All rights reserved

ISO 12215-8:2009(E)
Table 1 — Symbols, coefficients, parameters
(Sub)clause/table
Symbol Unit Designation/meaning of symbol
concerned
A m Total area of the moving part of the rudder 6.2.1, 6.2.3
A m Rudder effective area (Types II to IV) 6.2.3
A m Rudder blade area (Types II to IV) or top blade area (Type V) 6.2.3
A m Bottom rudder blade area (Type V) 6.2.3
A m Rudder skeg area [only used to determine type (see Figure 3)] 6.2.3
c m Rudder chord length at centre of area level 6.2.1, 6.2.2
c m Length of the top chord (Type I) 6.2.1
c m Length of the bottom chord (Type I) 6.2.1
co m Compensation at top chord (distance from LE to rotation axis) (Type I) 6.2.2
co m Compensation at bottom chord (distance from LE to stock CL) (Type I) 6.2.2
d mm Required solid stock diameter 10.4
d mm Inner diameter of tubular stock 10.6
i
d mm Outer diameter of tubular stock 10.6
o
F N Final side force on rudder 7.1
F N Side force on rudder in design category sea state 7.2
F N Side force on rudder during a turn at speed in slight sea 7.3
h m Height between rudder top and centre of hull bearing 6.2.1
b
h m Height between rudder top and centre of area 6.2.1
c
h m Height between rudder top and centre of skeg bearing (Type V) 6.2.3
d
h m Height between rudder bottom and centre of skeg bearing (Type V) 6.2.3
e
h m Height between centre of upper bearing and a point inside the hull (Type I) 6.2.1
in
h m Height between bottom of spade and a point outside the hull (Type I) 6.2.1
ou
h m Average height of rudder blade (see Figure 1) 6.2.1
r
h m Height of skeg from hull attachment to skeg bearing (Types II to V) 6.2.3
s
h m Height between centres of hull (lower) bearing and upper bearing 6.2.1
u
k 1 Rudder bending coefficient 6.2.1
b
k 1 Coefficient lowering force for flat or wedge rudder blade shape 7.3
FLAT
k 1 Coefficient lowering force due to gap hull/rudder top 7.2
GAP
k 1 Length displacement coefficient 7.2
LD
k 1 Coefficient for skeg deflection 8.3.4
S
k 1 Coefficient considering extra load due to sea in design categories A and B 7.2
SEA
k 1 Coefficient considering lower required service in design categories C and
SERV
7.3
D
k 1 Coefficient lowering design stress for F 7.3
SIG 2
k 1 Coefficient considering lower usage of craft with damage survey 7.2
USE
k 1 Fibre type factor 13.3.1.2
L m Effective length of the skeg 8.3.4
S
ISO 12215-8:2009(E)
Table 1 (continued)
(Sub)clause/table
Symbol Unit Designation/meaning of symbol
concerned
L m Length at waterline, according to ISO 8666 in m conditions 7.2
WL LDC
M Nm Bending moments on the rudder stock or skeg 8
M , M Nm Bending moments at skeg or hull 8.3.4
S H
m kg Loaded displacement mass 3.2, 7.2
LDC
r m Horizontal distance from rudder force to stock axis 6.2.1
r m Minimum value of r 9
min
R , R , R N Reaction force at upper bearing, hull bearing, skeg bearing, respectively 8
U H S
t mm Skin thickness of tubular or hollowed closed section Table 6
T Nm Torque (twisting moment) on the rudder stock 9
u m Longitudinal distance from leading edge to stock axis at centroid chord 6.2.1
V knots Maximum speed of craft in calm water, m conditions 7.3
MAX LDC
w kg/m Minimum fibre mass per area of rudder blade 13.3.1.2
z m Effective bending moment lever z = k ⋅ h + h 8.2.1
b b b r c
z m Equivalent bending moment lever 10.4
eq
α 1 Tip chord to root chord ratio (c /c) 6.2.2
2 1
Λ 1 Geometric aspect ratio of the rudder 6.2.1, 6.2.3
σ N/mm Direct stress (ultimate, yield, design) 5
τ N/mm Shear stress (ultimate, yield, design) 5
χ 1 Ratio between reaction at skeg and rudder force 8.3.2

5 Design stresses
5.1 Rudder material
Values of design stresses shall be taken from Table 2
Table 2 — Values of design stresses
Stresses in newtons per square millimetre
Direct stresses
Combined
Material
Tensile/compressive Shear Bearing
stresses
σ τ σ
d d db
a
min σ ; 0,5 σ 0,58 τ 1,8 σ
()
Metals yu σ + 3τσu
d d
d
Wood and fibre-reinforced ⎛⎞ ⎛ ⎞
στ
0,5 × σ 0,5 τ 1,8 σ
+< 0,25
u u d ⎜⎟ ⎜ ⎟
plastics (FRP) ⎜⎟ ⎜ ⎟
στ
⎝⎠uu⎝ ⎠
a
Steel, stainless steel, aluminium alloys, titanium alloys, copper alloys (see Annex A). In welded condition for welded metals.

4 © ISO 2009 – All rights reserved

ISO 12215-8:2009(E)
In Table 2,
⎯ σ is the design tensile, compressive, or flexural strength (as relevant);
d
⎯ σ is the ultimate tensile, compressive, or flexural strength (as relevant);
u
⎯ σ is the yield tensile, compressive, or flexural strength (as relevant);
y
⎯ σ is the design bearing strength;
db
⎯ τ is the design shear strength;
d
⎯ τ is the ultimate shear strength.
u
Additional requirements are given in Annex A (metals) and Annex B (composites)
For wood and composites, the strength values of the relevant annexes of ISO 12215-5 shall be used.
6 Rudder and steering arrangement, rudder types
6.1 General
6.1.1 General definition
The rudder and steering arrangement comprises all components necessary for manoeuvring the craft, from
the rudder and the rudder operating gear to the steering position.
Rudder and steering equipment shall be arranged so as to permit inspection.
NOTE It is good practice that the rudder keeps the steering effect after grounding (for example, a spade rudder with
the stock not going down to the bottom enables the rudder blade to break without bending the stock).
6.1.2 Multi-rudder arrangement
If the craft has several rudders, the following requirements apply to each one of the rudders.
NOTE On sailing craft, twin rudders, frequently canted outwards, are not usually protected from contact with floating
objects by the keel, a skeg, the hull canoe body at centreline, etc. This is particularly the case for the windward rudder,
close to the waterline, that can also be hit by breaking waves and can therefore support a part of the craft's weight. It is
therefore current practice to have twin rudders installed on sailing craft that are significantly stronger than required in this
part of ISO 12215, which only considers loads from normal lift forces. This enhanced strength is not quantified here.
6.1.3 Vertical support
The rudder stock or blade shall be supported vertically with limited axial upwards movement.
6.1.4 Hard over stops
Rudder stocks that are, or can be, actuated by a remote steering system (i.e. not directly by the tiller) shall be
fitted with hard over stops, angled at 30° to 45° from zero lift position (usually at centreline). This also applies
to rudders only actuated by a tiller of design category A and B.
Hard over stops can act on the rudder, the tiller, the quadrant, or any device directly connected to the rudder.
NOTE The need for stops is both to avoid excessive angle of attack and lift when running backwards and to avoid
excessive range of movement of the steering system.
ISO 12215-8:2009(E)
6.1.5 Actuating system of the rudder
The following devices shall be able to transmit the rudder torque, T, defined in Clause 9, without exceeding
their design stress, as defined in Clause 5:
⎯ the actuating device that turns the rudder including the tiller, rudder arm and quadrant;
⎯ the connection between the rudder stock and the actuating device (cone, square, key, etc.);
⎯ the stops provided at either end of the tiller, rudder arm or quadrant stroke.
The connection between the rudder stock and the actuating device shall be designed to ensure alignment
between the rudder blade and the tiller, actuating arm, etc. and allow a visual instant checking of this
alignment.
6.1.6 Emergency tiller
Any component of the emergency tiller, where fitted, shall be able to transmit a rudder torque of 0,5 T, where T
is defined in Clause 9, without exceeding its design stress defined in Clause 5.
6.2 Rudder types
This part of ISO 12215 is applicable to five types of rudder configuration: Type I to Type V, as shown in
Figures 2 and 3. In all cases except case I c, the rudder blade is taken as rectangular or trapezoidal.
6.2.1 Type I (spade) rudders (see Figures 1 and 2)
The main variables are as follows:
⎯ A is the rudder (spade) area;
h
r
⎯ Λ = is the rudder geometric aspect ratio (1)
A
where h is the average height of the rudder;
r
⎯ h is the height between rudder top and centre of hull bearing;
b
⎯ c and c are, respectively, the top and bottom chords or their natural extension;
1 2
⎯ co and co are the top and bottom compensation, respectively, i.e. the distance, measured from fore to
1 2
aft, between the leading edge and the rotation axis;
⎯ c is the chord length at the height of the centroid of rudder area;
⎯ h is the height between rudder top and centroid of rudder area (this is the position where the rudder force
c
is considered to act);
⎯ h and h are, respectively, any local height outside and inside the centre of hull bearing to be used in
ou in
Figure 5;
⎯ k is the rudder bending coefficient with k = h /h ;
b b c r
⎯ r is the horizontal distance between the position of the resultant of the rudder force (taken at rudder
centroid) and the rudder's rotational axis, as defined in Table 6, and shall not be taken less than r ;
min
6 © ISO 2009 – All rights reserved

ISO 12215-8:2009(E)
⎯ u is, for Type I (spade) rudders, the horizontal distance from fore to aft, from the leading edge to the
rudder rotational axis at the height of centroid of rudder area (i.e. the geometric centre of the profile area);
u is positive if the leading edge is forward of the axis (see Figure 2 Types I a, I b, or I c) or negative in the
opposite case (see Type I d).
6.2.2 Rudder spade with trapezoidal shape
For spade rudders with a trapezoidal (or close to) shape some values are easily calculated as follows:
cc+
Ah= is the area of a trapezoidal spade; (2)
r
h 12+ α
c
k== for a trapezoidal spade; (3)
b
h 3(1+ α)
r
c
where α = is the taper coefficient.
c
See Table 3.
Table 3 — Calculated values of k for a trapezoidal spade as a function of c /c
b 2 1
c /c = α
1,00 0,90 0,80 0,70 0,60 0,50 0,40 0,30 0,20
2 1
k
0,50 0,49 0,48 0,47 0,46 0,44 0,43 0,41 0,39
b
hk=×h (4)
cb r
cc=−k()c−c for a trapezoidal spade (5)
1b 1 2
u=−co k()co− co for a trapezoidal spade (6)
1b 1 2
The value of h can also be determined graphically, as shown in Figure 1.
c
Figure 1 — Graphical determination of centroid, CS, of a trapeze
ISO 12215-8:2009(E)
Type I a: Typical fast motor craft spade rudder with low aspect ratio and cut out top aft to avoid ventilation
Type I b: Near-rectangular shape
Type I c: Semi-elliptical shape typical on performance sailing craft
Type I d: Transom-hung spade rudder
NOTE The marking with a shaded circle shows the geometric centre of surface. The rudder force is located at the
same height, but at a distance 0,3 c aft of the chord's leading edge.
Figure 2 — Spade rudders: Type I
8 © ISO 2009 – All rights reserved

ISO 12215-8:2009(E)
6.2.3 Rudder types II to V (see Figure 3)
The dimensions are the same as for spade rudders, except that:
⎯ A is the total area of the moving part of the rudder, divided into A and A in Type V;
1 2
⎯ A is the skeg area (only used to determine the type in Figure 3);
⎯ h is the average height of the rudder;
r
h
r
⎯ Λ = is the effective rudder geometric aspect ratio (7)
A
where A is the rudder effective area (moving part plus effective part of the skeg, see Table 4);
⎯ c = A /h is the mean chord;
0 r
⎯ h is the height of the skeg/horn between hull and mid-skeg bearing for Type V and the lower bearing for
s
Types III and IV.
Table 4 gives values of A and A according to rudder type.
Table 4 — Rudder types and effective areas
Value
Type
A A
II A
III A A + A
1 1 3
IV A A
1 1
V A + A A + A + A
1 2 1 2 3
For Type V, h and h are the portions of h above and below the skeg bearing, respectively.
d e r
For Types II to V:
⎯ u is, for rudder Types II and IV, the horizontal distance, fore to aft, from the leading edge of the rudder to
the stock vertical axis at the height of centroid of rudder area. For rudder Types III and V, u is measured
aft of the leading edge of the partial or full narrow skeg (see Figure 3);
⎯ r is the horizontal distance between the position of the centroid of rudder area and the rudder's rotational
axis, as defined in Table 6, and shall not be taken less than r .
min
The rudders of Types II to V are considered to be held by three bearings (two bearings inside the hull and one
skeg bearing, see 8.3.1)
ISO 12215-8:2009(E)
Type II Supported by skeg (solepiece) and skeg bearing Type III Narrow full skeg
Type IV Wide full skeg Type V Partial skeg
Figure 3 — Other rudder types: Types II to V
7 Design rudder force calculation
7.1 General
The design rudder force, F, shall be taken as follows:
⎯ for motor craft, the greater of F and F , defined in 7.2 and 7.3, respectively;
1 2
⎯ for sailing craft, the force F , defined in 7.2.
10 © ISO 2009 – All rights reserved

ISO 12215-8:2009(E)
7.2 Force F and corresponding load case
This case corresponds to loads associated with boat handling in the design category sea state.
F=×23Lk× ×k ×k ×k ×A (8)
1 WL SEA LD GAP USE
where
k =
SEA
⎯ 1,4 for sailing craft of design categories A and B and motor craft of design category A,
⎯ 1,2 for motor craft of design category B,
⎯ 1,0 for craft of design categories C and D;
NOTE 1 k recognizes that in higher design categories the sea and related waves can induce higher lateral loads
SEA
than in smooth water.
k = 6,15 for motor craft of all design categories and sailing craft of design categories C and D;
LD
for sailing craft of design categories A and B,
L
WL
k = (9)
LD
1/ 3
⎛⎞m
LDC
⎜⎟
⎝⎠
but shall not be taken less than 6,15;
NOTE 2 k recognizes that slender sailing craft can experience additional speeds due to surfing. It is derived from
LD
an established yacht rudder scantling guide that has been in use for many years.
k =
GAP
⎯ 1,0 for rudders where the root gap (average clearance between the hull and the rudder root
plane) is less than 5 % of the mean rudder chord. This gap shall not be exceeded at any rudder
angle,
⎯ 0,85 for rudders which are surface piercing (e.g. transom held) or exceed the gap limitation or
can otherwise exhibit significant 3-D flow over the root;
NOTE 3 k recognizes that in general, 3-D flow over the root reduces rudder forces. Where there is doubt
GAP
regarding the configuration under consideration, the conservative approach is to use k = 1.
GAP
k = 1 for all craft but may be taken as 0,9 for category C and D sailing craft which are essentially used
USE
for close inshore racing with suitable safety procedures in place and for which the rudder can be easily
inspected on a regular basis. If k is taken as 0,9, a warning requiring regular inspection of rudder(s)
USE
should be included in the owner's manual.
NOTE 4 Rudder aspect ratio does not feature in the above formula since experimental evidence suggests that
maximal rudder force is fairly insensitive to aspect ratio. The lift slope increases with increasing aspect ratio but the
angle of maximal force reduces to maintain a sensibly constant rudder force coefficient.
ISO 12215-8:2009(E)
7.3 Force F and corresponding load case
This case corresponds to loads connected with motor craft handling during a turn at speed in slight seas. It is
therefore only applicable to motor craft.
0,43 1,3
F=×370 Λ ×Vk× ×k ×k ×k ×A (10)
2 MAX GAP SERV FLAT SIG
where
Λ is the geometric aspect ratio defined in Equation (1) or (7);
V is the craft maximum speed in calm water and m conditions;
MAX LDC
k is as given in 7.2;
GAP
k =
SERV
⎯ 1,0 for design category A and B craft,
⎯ 0,8 for design category C and D craft (may also be taken as 1);
NOTE 1 k recognizes that design category C and D craft generally operate in circumstances where the
SERV
consequences of rudder problems are less severe than for ocean-going craft (i.e. proximity of other craft, shallow
water and ability to anchor). The use of this factor is optional.
If k = 0,8 is used, a note to this effect should be placed in the owner's manual.
SERV
kV=−1,08 0,008× with 0,75≤ FLAT MAX FLAT
NOTE 2 k considers that a flat plate or wedge generates less lift at the same angle of attack than a typical
FLAT
NACA section used to develop the above equations.
NOTE 3 Aspect ratio is included in Equation (11) since the rudder dimensioning force is based on a rudder angle
that is lower than the stall angle. The dimensioning speed is lower than V since high speed craft cannot execute
MAX
practical manoeuvres at this speed. The dimensioning speed and practical rudder angle are derived by realistically
achievable steady turning radius to craft length ratio values based on craft test data.
A note should be entered into the user's manual to the effect that owners are expected to execute
responsible craft handling and helm actuation rates (degrees/second) should reflect the prevailing craft
speed.
k = 1,25
SIG
NOTE 4 The coefficient of 370 in Equation (10) corresponds to the expected force when executing a reasonably
tight high-speed turn. As it is not an extreme load case, it is necessary to use a lower design stress than is used for
F to cover the expected large number of times that F will be experienced during the life of the boat. The enhanced
1 2
design stress factor is k = 1,25.
SIG
12 © ISO 2009 – All rights reserved

ISO 12215-8:2009(E)
8 Rudder bending moment and reactions at bearings
8.1 General
Knowledge of the bending moment, reaction at bearings and torque is necessary to calculate the resistant part
of the rudder blade, whether the rudder stock, the blade fin, or a combination of both.
The analysis of the bending moment and the reaction at bearings varies with rudder type:
⎯ 8.2 analyses spade rudders;
⎯ 8.3 analyses skeg rudders.
8.2 Analysis of spade rudder (Type I)
8.2.1 Values of k , bending moment M and reactions at bearings for spade rudders (Type I)
b
M =×Fz (12)
Hb
is the design rudder bending moment (at hull bearing) for spade rudders, where
⎯ F is determined according to 7.1;
⎯ z is the bending moment lever for spade rudders (see 6.2.1):
b
z=×()kh +h=h+h (13)
bb r b c b
where k is the rudder bending coefficient, determined according to rudder type, as follows.
b
To calculate z , one shall first determine the value of h :
b c
⎯ for a trapezoidal or near trapezoidal shape, either
a) use the value of k given by Equation (3) or Table 3, or
b
b) apply the graphical method shown in Figure 1;
⎯ for other shapes, find h =k × h by any geometrical method
c b r
and then calculate z =h + h .
b c b
The reactions at bearings for spade rudders are as follows:
z
b
RF= (14)
U
h
u
is the reaction at the upper bearing (at deck or intermediate level), where h is the vertical distance between
u
the centres of the upper and lower bearings (see Figure 2);
R=+RF (15)
HU
is the reaction at the hull bearing.
ISO 12215-8:2009(E)
8.3 Analysis of skeg rudders (Types II to V)
8.3.1 General
Rudders supported by a skeg or horn are considered to be held, from bottom to top, by three bearings
(see Figure 3):
⎯ a skeg bearing, with reaction R ;
S
⎯ a hull bearing located close to the hull bottom a
...