ISO 13643-6:2013

Ships and marine technology — Manoeuvring of ships — Part 6: Model test specials

ISO 13643-6:2013 defines symbols and terms and provides guidelines for the conduct of tests to determine the hydrodynamic forces and moments due to prescribed motions under a planar-motion, a circular-motion, or an oblique towing or flow system for models of surface ships and submarines. It also defines symbols and terms and provides guidelines for the conduct of tests in a wind tunnel. It is intended to be read in conjunction with ISO 13643-1.

Navires et technologie maritime — Manoeuvres des navires — Partie 6: Spécificités des essais sur modéle

General Information

• Status: Withdrawn
• Publication Date: 18-Jun-2013
• Withdrawal Date: 18-Jun-2013
• ICS: 47.020.70 - Navigation and control equipment
• Technical Committee: ISO/TC 8/SC 6 - Navigation and ship operations
• Drafting Committee: ISO/TC 8/SC 6 - Navigation and ship operations
• Current Stage: 9599 - Withdrawal of International Standard
• Completion Date: 09-Feb-2017

Relations

• Revised: ISO 13643-6:2017 - Ships and marine technology — Manoeuvring of ships — Part 6: Model test specials
• Effective Date: 28-May-2016

Standards Content (Sample)

INTERNATIONAL ISO
STANDARD 13643-6
First edition
2013-07-01
Ships and marine technology —
Manoeuvring of ships —
Part 6:
Model test specials
Navires et technologie maritime — Manoeuvres des navires —
Partie 6: Spécificités des essais sur modéle
Reference number
ISO 13643-6:2013(E)
©
ISO 2013

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ISO 13643-6:2013(E)

COPYRIGHT PROTECTED DOCUMENT
© ISO 2013
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ii © ISO 2013 – All rights reserved

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ISO 13643-6:2013(E)

Contents Page
Foreword .iv
1 Scope . 1
2 Normative references . 1
3 Terms and definitions . 1
4 Test-related physical quantities . 2
5 General test conditions .16
6 Test 6.1 — Planar motion test .16
6.1 General .16
6.2 Description .18
6.3 Analysis and presentation of results of a planar motion test .19
6.4 Designation of a planar motion test .29
7 Test 6.2 — Circular motion test .29
7.1 General .29
7.2 Description .30
7.3 Analysis and presentation of results of a circular motion test .30
7.4 Designation of a circular motion test.31
8 Test 6.3 — Oblique towing or flow test .32
8.1 General .32
8.2 Description .33
8.3 Analysis and presentation of results of an oblique towing or flow test.33
8.4 Designation of an oblique towing or flow test .34
9 Test 6.4 — Wind tunnel test .36
9.1 General .36
9.2 Description of the test .37
9.3 Analysis and presentation of test results .37
9.4 Designation of a wind tunnel test .37
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ISO 13643-6:2013(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.
The procedures used to develop this document and those intended for its further maintenance are
described in the ISO/IEC Directives, Part 1. In particular the different approval criteria needed for the
different types of ISO documents should be noted. This document was drafted in accordance with the
editorial rules of the ISO/IEC Directives, Part 2. www.iso.org/directives
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. Details of any
patent rights identified during the development of the document will be in the Introduction and/or on
the ISO list of patent declarations received. www.iso.org/patents
Any trade name used in this document is information given for the convenience of users and does not
constitute an endorsement.
The committee responsible for this document is ISO/TC 8, Ships and marine technology, Subcommittee
SC 6, Navigation and ship operations.
ISO 13643 consists of the following parts, under the general title Ships and marine technology —
Manoeuvring of ships:
— Part 1: General concepts, quantities and test conditions
— Part 2: Turning and yaw checking
— Part 3: Yaw stability and steering
— Part 4: Stopping, acceleration, traversing
— Part 5: Submarine specials
— Part 6: Model test specials
iv © ISO 2013 – All rights reserved

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INTERNATIONAL STANDARD ISO 13643-6:2013(E)
Ships and marine technology — Manoeuvring of ships —
Part 6:
Model test specials
1 Scope
This part of ISO 13643 defines symbols and terms and provides guidelines for the conduct of tests to
determine the hydrodynamic forces and moments due to prescribed motions under a planar-motion,
a circular-motion, or an oblique towing or flow system for models of surface ships and submarines. It
also defines symbols and terms and provides guidelines for the conduct of tests in a wind tunnel. It is
intended to be read in conjunction with ISO 13643-1.
2 Normative references
The following documents, in whole or in part, are normatively referenced in this document and are
indispensable for its application. For dated references, only the edition cited applies. For undated
references, the latest edition of the referenced document (including any amendments) applies.
ISO 13643-1, Ships and marine technology — Manoeuvring of ships — Part 1: General concepts, quantities
and test conditions
3 Terms and definitions
For the purposes of this document, the following terms and definitions apply.
3.1
planar motion test
manoeuvring test to determine the hydrodynamic forces and moments as functions of lateral velocity
and acceleration as well as of angular velocity and acceleration about the z-axis or the y-axis, respectively
3.2
circular motion test
manoeuvring test to determine the hydrodynamic forces and moments as a function of the angular
velocity for surface ships primarily about the z-axis, for submarines primarily about the z-axis as well
as the y-axis
3.3
oblique towing or flow test
manoeuvring test to determine the forces and moments as a function of the drift angle and of the
manoeuvring device angle and, in the case of submarines, the angle of attack and hydroplane deflections,
in a towing tank, a circulating water tunnel, or a wind tunnel
3.4
wind tunnel test
test to determine the aerodynamic forces and moments acting upon the above-water portion of the ship
as a function of the relative wind
Note 1 to entry: A wind tunnel may also be used for the underwater hull.
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ISO 13643-6:2013(E)

3.5
manoeuvring device
rudder, azimuthing thruster, hydroplane, cycloidal propeller, or equivalent system used to
manoeuvre a vessel
4 Test-related physical quantities
Test-related physical quantities are according to Table 1. General quantities and concepts are according
to ISO 13643-1.
Table 1 — Test-related physical quantities
Concept
Symbol CC-code SI-unit
Term Definition or explanation
2
A ALV m Lateral area above waterline (See ISO 13643-1.)
LV
Transverse projected area of ship Projected cross section area above DWL, gen-
2
A AXV m
XV
above waterline erally without rigging, railings, etc.
AP AP — After perpendicular (See ISO 13643-1.)
Displacement amplitude of the model
a A0PMM m —
0
movement
C CWI N Cross force Force perpendicular to relative wind direction
2
C CC 1 Cross force coefficient 2C/(ϱ V A )
C A
WRALV
2
C CD 1 Drag coefficient 2D/(ϱ V A )
D A
WRALV
2
C CDAX 1 Drag coefficient 2D/(ϱ V A ), relative to cross section
DAX A
WRAXV
2
C CK 1 Roll-moment coefficient 2K /(ϱ V A L )
K A
WRALV OA
2
C CN 1 Coefficient of moment about z-axis 2N/(ϱ V AL )
N A
WRALVOA
2
C CX 1 Longitudinal-force coefficient 2X/(ϱ V A )
X A
WRALV
2
C CXAX 1 Longitudinal-force coefficient 2X/(ϱ V A ), relative to cross section
XAX A
WRAXV
2
C CY 1 Lateral-force coefficient 2Y/(ϱ V A )
Y A
WRALV
D DWI N Drag Force in direction in which relative wind blows
DWL DWL — Design waterline (See ISO 13643-1.)
FP FP — Fore perpendicular (See ISO 13643-1.)
22 22
F FTWI N Resultant force
T
CD+
XY+
and , respectively
F FN 1 Froude number (See ISO 13643-1.)
n
F FN0 1 (Reference) Froude number VL/g
n0
0
GM GM m Metacentric height (See ISO 13643-1.)
Mean height of lateral area above
H HLM m A /L
LM LV OA
design waterline
Moment of inertia of the model about
2
l IXX kg m (See ISO 13643-1.)
xx
x-axis
Moment of inertia of the model about
2
l IYY kg m (See ISO 13643-1.)
yy
y-axis
a
For angles, the unit ° (degree) may be used.
b
The unit kn, common in navigation, may be used.
2 © ISO 2013 – All rights reserved

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ISO 13643-6:2013(E)

Table 1 (continued)
Concept
Symbol CC-code SI-unit
Term Definition or explanation
2
l IZX kg m Product of inertia of the model (See ISO 13643-1.)
zx
Moment of inertia of the model about
2
l IZZ kg m (See ISO 13643-1.)
zz
z-axis
Moment about x-axis
K MX N m Roll moment
Relative to ship-fixed axis system
∂K
–1a
K DKDPST N m rad —
ϕstat
∂φ
V=0
from static test or calculation
Especially for submarines:
K
ρ
3 2
LV
2
q
where K (u, v, w, p, q, r, v , ẇ, ṗ, , ṙ, ϕ, θ)
K’ MXS 1 Non-dimensional roll moment
For surface ships only:
K
ρ
3 2
LV
0
2
where K (V , Δu, v, w, p, q, r, , ẇ, ṗ, , ṙ, ϕ, θ)
 
0 v q
tn+ T
2
In-phase part of non-dimensional roll
′
K′ Kt()sinωttd
MXINS 1
in
∫
moment
nT
t
tn+ T
2
Quadrature part of non-dimensional
′ Kt′ cosωttd
K MXOUTS 1 ()
out
∫
roll moment
nT
t
′
∂K
′
K
DKDPS 1 —
p
′
∂p
ˆ
′ ′
KK=
0
∂K′
′
K
 DKDPTS 1 —
p
∂p′
ˆ
KK′= ′
0
′
∂K
K′
DKDP3TS 1 —
p
′
∂p
ˆ
′ ′
KK=
0
∂K′
K′
DKDRS 1 Slope through zero of K’ versus r’
r
∂r′
ˆ
KK′= ′
0
′
∂K
′
K DKDRTS 1 —

r
′
∂r
ˆ
′ ′
KK=
0
∂K′
K′
DKDVS 1 Slope through zero of K’ versus v’
v
∂v′
ˆ
KK′= ′
0
′
∂K
′
K DKDVTS 1 —

v
′
∂v
ˆ
′ ′
KK=
0
Non-dimensional coefficient used in
ˆ
K′
MXPQS 1 —
pq
representing K’ as a function of p’ q’
a
For angles, the unit ° (degree) may be used.
b
The unit kn, common in navigation, may be used.
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ISO 13643-6:2013(E)

Table 1 (continued)
Concept
Symbol CC-code SI-unit
Term Definition or explanation
Non-dimensional coefficient used in
ˆ
′
K MXRS 1 (for surface ships only)
r
representing K’ as a function of F r’
n0
Non-dimensional coefficient used in
ˆ
K′ MXURS 1 (especially for submarines)
ur
representing K’ as a function of u’ r’
Non-dimensional coefficient used in
ˆ
′
K MXUUS 1 (especially for submarines)
uu 2
representing K’ as a function of u’
Non-dimensional coefficient used in
ˆ
K MXUUDRS 1 (especially for submarines)
uuδ R 2
representing K’ as a function of u’ δ
R
Non-dimensional coefficient used in
ˆ representing K’ as a function of
K
MXUUDR3S 1 (especially for submarines)
uuδδδ R
23
′
u δ
R
Non-dimensional coefficient used in
ˆ
′
K MXUVS 1 (especially for submarines)
uv
representing K’ as a function of u’ v’
Non-dimensional coefficient used
ˆ
K
MXUVDRS 1 in representing K’ as a function of (especially for submarines)
uvδ R
u’ v’ δ
R
Non-dimensional coefficient used in
ˆ
′
K MXVS 1 (for surface ships only)
v
representing K’ as a function of F v’
n0
Non-dimensional coefficient used in
representing K’ as a function of
ˆ
K′ MXV3S 1 (for surface ships only)
vvv
22
′′ ′ ′
vv vw+ F
n0
Non-dimensional coefficient used in
representing K’ as a function of
ˆ
′
K
MXVVAS 1 —
vv
22
′′ ′
vv +w
Non-dimensional coefficient used
ˆ
K ’
MXVDRS 1 in representing K’ as a function of (for surface ships only)
vδ R
F v’ δ
n0 R
Non-dimensional coefficient used in
ˆ
K′
MXWPS 1 —
wp
representing K’ as a function of w’ p’
Non-dimensional coefficient used in
ˆ
′
K MXWRS 1 —
wr
representing K’ as a function of w’ r’
Non-dimensional coefficient used in
ˆ
K′ MXDUS 1 (for surface ships only)
Δu
representing K’ as a function of Δu’
Non-dimensional coefficient used in
ˆ
′
K MXDUVS 1 (for surface ships only)
Δuv
representing K’ as a function of Δu’ v’
Non-dimensional coefficient used in
ˆ
K′ MXDU2S 1 (for surface ships only)
ΔΔu 2
representing K’ as a function of (Δu’)
Non-dimensional coefficient used
ˆ
K′
MXDRS 1 in representing K’ as a function of (for surface ships only)
δ R
2
F δ
n0 R
Non-dimensional coefficient used in
ˆ representing K’ as a function of
K′
MXDR3S 1 (for surface ships only)
δδδ R
23
F δ
nR0
Non-dimensional coefficient used in
representing K’ when angle of attack
ˆ
K′ MX0S 1 —
0
α, drift angle β, manoeuvring device,
and plane angles are zero
Non-dimensional oscillatory

′
K MXOPHS 1 —
φ
roll coefficient
a
For angles, the unit ° (degree) may be used.
b
The unit kn, common in navigation, may be used.
4 © ISO 2013 – All rights reserved

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ISO 13643-6:2013(E)

Table 1 (continued)
Concept
Symbol CC-code SI-unit
Term Definition or explanation
L L m Model length Reference length (see ISO 13643-1)
Length between the most aft and most
L LOA m Length overall forward points of the ship, permanent outfit
OA
included, measured parallel to DWL
M MY N m Moment about y-axis Relative to ship-fixed axis system
MA MAX — Main axis (See ISO 13643-1.)
∂M
–1 a
M DMDTST N m rad —
θstat
∂θ
V=0
from static test or calculation
Especially for submarines
M
,
ρ
32
LV
2
where M (u, v, w, p, q, r, , ẇ, ṗ, , ṙ, ϕ, θ)
 q
v
Non-dimensional moment about
M’ MYS 1
y-axis
For surface ships only:
M
,
ρ
3 2
LV
0
2
where M (V Δu, v, w, p, q, r,  , ẇ, ṗ,  , ṙ, ϕ, θ)
0, v q
tn+ T
2
In-phase part of non-dimensional
′ Mt′ sinωttd
M MYINS 1 ()
in
∫
moment about y-axis
nT
t
tn+ T
2
Quadrature part of non-dimensional
′
M′ Mt cosωttd
MYOUTS 1 ()
out ∫
moment about y-axis
nT
t
∂M′
′
M
DMDQS 1 Slope through zero of M’ versus q’
q
′
∂q
ˆ
MM′ ′
=
0
′
∂M
M′
DMDQTS 1 —

q

∂q′
ˆ
MM′= ′
0
∂M′
′
M
DMDQ3TS 1 —
q
′
∂q
ˆ
′ ′
MM=
0
′
∂M
′
M DMDWS 1 Slope through zero of M’ versus w’
w
∂w′
ˆ
MM′= ′
0
∂M′
M′
DMDWTS 1 —

w
′
∂w
ˆ
′ ′
MM=
0
′
∂M
′ –1a
M DMDTHS rad —
θ
∂θ
ˆ
MM′= ′
0
ˆ Non-dimensional coefficient used in
M′
MYPPS 1 —
pp
2
representing M′ as a function of p′
Non-dimensional coefficient used in
ˆ
′
M
MYPRS 1 —
pr
representing M’ as a function of p′ r′
a
For angles, the unit ° (degree) may be used.
b
The unit kn, common in navigation, may be used.
© ISO 2013 – All rights reserved 5

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ISO 13643-6:2013(E)

Table 1 (continued)
Concept
Symbol CC-code SI-unit
Term Definition or explanation
Non-dimensional coefficient used in
ˆ
′
M
MYQS 1 —
q
representing M’ as a function of u’ q′
ˆ Non-dimensional coefficient used in
M′
MYQQAS 1 —
qq||
representing M’ as a function of q′ |q′|
Non-dimensional coefficient used
ˆ
′
M
MYQADSS 1 in representing M′ as a function of —
qδ S
u′ |q′| δ
S
Non-dimensional coefficient used in
ˆ
′
M
MYRRS 1 —
rr
2
representing M′ as a function of r′
Non-dimensional coefficient used in
ˆ
M′
MYUUS 1 —
uu
2
representing M′ as a function of u′
Non-dimensional coefficient used in
ˆ
′
M
MYVPS 1 —
vp
representing M′ as a function of v′ p′
Non-dimensional coefficient used in
ˆ
M′
MYVRS 1 —
vr
representing M′ as a function of v′ r′
Non-dimensional coefficient used in
ˆ
′
M
MYWS 1 —
w
representing M’ as a function of u’ w’
Non-dimensional coefficient used in
representing M’ as a function of |w′|
ˆ
′
M
MYWWS 1 —
ww
''22
vw+
Non-dimensional coefficient used in
ˆ representing M′ as a function of w′
′
M
MYWWAS 1 —
ww
''22
vw+
Non-dimensional coefficient used
ˆ
M′
w MYWAS 1 in representing M’ as a function of —
u′ |w’|
Non-dimensional coefficient used in
ˆ
representing M’ as a function of q′
M′
MYWAQS 1 —
wq
''22
vw+
ˆ Non-dimensional coefficient used in
′
M
MYDBS 1 —
δ B
2
representing M’ as a function of u′ δ
B
ˆ
Non-dimensional coefficient used in
M′
δ S MYDSS 1 —
2
representing M’ as a function of u′ δ
s
Non-dimensional coefficient used in
representing M’ when angle of attack
ˆ
′
M MY0S 1 —
0
α, drift angle β, manoeuvring device,
and plane angles are zero
Non-dimensional oscillatory coef-

′
M MYOTHS 1 —
θ
ficient about y-axis
m MA kg Model mass —
N MZ N m Moment about z-axis Relative to ship-fixed axis system
N
φ stat
∂N′
−
–1a
N DNDPDYS rad —
ϕdyn
∂φρ
32
ˆ
NN′= ′
LV
0
2
∂N
–1a
N DNDPST N m rad —
ϕstat ∂φ
V=0
from static test or calculation
a
For angles, the unit ° (degree) may be used.
b
The unit kn, common in navigation, may be used.
6 © ISO 2013 – All rights reserved

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ISO 13643-6:2013(E)

Table 1 (continued)
Concept
Symbol CC-code SI-unit
Term Definition or explanation
Especially for submarines:
N
,
ρ
32
LV
2
 q
v
where N (u, v, w, p, q, r, , ẇ, ṗ, , ṙ, ϕ, θ)
Non-dimensional moment about
N’ MZS 1
z-axis
For surface ships only:
N

, where N (V , Δu, v, w, p, q, r, v , ẇ, ṗ,
ρ 0
3 2
LV
0
2

                      q , ṙ, ϕ, θ)
tn+ T
2
In-phase part of non-dimensional
′ Nt′ sinωttd
N MZINS 1 ()
in
∫
moment about z-axis
nT
t
tn+ T
2
Quadrature part of non-dimensional
′ ′
N Nt cosωttd
MZOUTS 1 ()
out
∫
moment about z-axis
nT
t
∂N′
′
N
DNDPS 1 —
p
′
∂p
ˆ
NN′= ′
0
′
∂N
N′
DNDPTS 1 —

p

∂p′
ˆ
NN′= ′
0
∂N′
N′
 DNDP3TS 1 —
p

∂p
ˆ
NN′= ′
0
′
∂N
′
N DNDRS 1 Slope through zero of N’ versus r’
r
∂r′
ˆ
NN′= ′
0
∂N′
N′
DNDRTS 1 —

r
′
∂r
ˆ
NN′= ′
0
′
∂N
′
N DNDVS 1 Slope through zero of N’ versus v’
v
∂v′
ˆ
NN′= ′
0
∂N′
N′
DNDVTS 1 —

v
′
∂v
ˆ
NN′= ′
0
Non-dimensional coefficient used in
ˆ
′
N MZPQS 1 —
pq
representing N’ as a function of p’ q’
Non-dimensional coefficient used in
ˆ
N′
MZQRS 1 —
qr
representing N’ as a function of q’ r’
Non-dimensional coefficient used in
ˆ
′
N MZRS 1 (for surface ships only)
r
representing N’ as a function of F r’
n0
ˆ Non-dimensional coefficient used in
N′
MZRRAS 1 —
rr
representing N′ as a function of r′ |r′|
Non-dimensional coefficient used in
representing N’ as a function of F
ˆ n0
′
N MZRDDS 1 (for surface ships only)
rδδ R
2
′
r δ
R
a
For angles, the unit ° (degree) may be used.
b
The unit kn, common in navigation, may be used.
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ISO 13643-6:2013(E)

Table 1 (continued)
Concept
Symbol CC-code SI-unit
Term Definition or explanation
Non-dimensional coefficient used in
ˆ representing N’ as a function of F
n0
N′
MZRADS 1 (for surface ships only)
r δ R
′
r δ
R
Non-dimensional coefficient used in
ˆ
′
N MZURS 1 (especially for submarines)
ur
representing N’ as a function of u’ r’
Non-dimensional coefficient used in
representing N’ as a function of
ˆ
N′
MZURDDS 1 (especially for submarines)
urδδR
2
ur′′δ
R
Non-dimensional coefficient used in
representing N’ as a function of
ˆ
′
N MZURADS 1 (especially for submarines)
ur||δ R
ur′′δ
R
Non-dimensional coefficient used in
ˆ
′
N
MZUUS 1 (especially for submarines)
uu
2
representing N’ as a function of u’
Non-dimensional coefficient used in
ˆ
N′
MZUUDS 1 (especially for submarines)
uuδ R
2
representing N’ as a function of u’ δ
R
Non-dimensional coefficient used in
2
ˆ
representing N’ as a function of u’
N′
uuδδδ R MZUUD3S 1 (especially for submarines)
3
δ
R
Non-dimensional coefficient used in
ˆ
′
N
MZUVS 1 (especially for submarines)
uv
representing N’ as a function of u’ v’
Non-dimensional coefficient used in
ˆ
N′
MZVS 1 (for surface ships only)
v
representing N’ as a function of v’
Non-dimensional coefficient used in
ˆ
′
N
MZVQS 1 —
vq
representing N’ as a function of v’ q’
Non-dimensional coefficient used
ˆ
N′
MZVRRS 1 in representing N’ as a function of (for surface ships only)
vrr
2
F v’ r’
n0
Non-dimensional coefficient used
ˆ
N′
MZVVRS 1 in representing N’ as a function of (for surface ships only)
vvr
2
F v’ r’
n0
Non-dimensional coefficient used in
representing N’ as a function of
ˆ
N′
MZV3S 1 (for surface ships only)
vvv
22 2
vv′′ +wF′
n0
Non-dimensional coefficient used in
representing N’ as a function of
ˆ
′
N
MZVVAS 1 —
vv
22
vv′′ +w′
Non-dimensional coefficient used in
representing N’ as a function of
ˆ
′
N
MZVARS 1 —
vr
22
rv′′ +w′
Non-dimensional coefficient used in
ˆ
′
N
MZWPS 1 —
wp
representing N’ as a function of w’ p’
Non-dimensional coefficient used in
ˆ
N′
MZWRS 1 —
wr
representing N’ as a function of w’ r’
Non-dimensional coefficient used in
ˆ
′
N
MZDUS 1 (for surface ships only)
Δu
representing N’ as a function of Δu’
Non-dimensional coefficient used in
ˆ
N′
MZDUVS 1 (for surface ships only)
Δuv
representing N’ as a function of Δu’ v’
Non-dimensional coefficient used in
ˆ
′
N
MZDU2S 1 (for surface ships only)
ΔΔu
2
representing N’ as a function of (Δu’)
a
For angles, the unit ° (degree) may be used.
b
The unit kn, common in navigation, may be used.
8 © ISO 2013 – All rights reserved

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ISO 13643-6:2013(E)

Table 1 (continued)
Concept
Symbol CC-code SI-unit
Term Definition or explanation
Non-dimensional coefficient used
ˆ
′
N
MZDRS 1 in representing N’ as a function of (for surface ships only)
δ R
2
F δ
n0 R
Non-dimensional coefficient used in
representing N’ as a function of
ˆ
′
N
MZDR3S 1 (for surface ships only)
δδδ R
23
F δ
n0 R
Non-dimensional coefficient used in
representing N’ when angle of attack
ˆ
N′
MZ0S 1 —
0
α, drift angle β, manoeuvring device,
and plane angles are zero
Non-dimensional oscillatory coef-

′
N
MZOPHS 1 —
φ
ficient about z-axis
N 1 — Number of periods used in Fourier integral
n
NWI 1 Exponent —
− V/R sinθ
S
–1 a
p OMX rad s Roll velocity
Angular velocity about x-axis
p’ OXS 1 Non-dimensional roll velocity p L/V
0
 –2 a
p OXRT rad s Roll acceleration Angular acceleration about x-axis
' 22
 
p OXRTS 1 Non-dimensional roll acceleration pL /V
0
 –4 a
p OXR3T rad s 3rd derivative of roll velocity —
' Non-dimensional 3rd derivative of 4 4
 
p OXR3TS 1 pL V
0
roll velocity
V/R sin ϕ cos θ
S S
–1 a
q OMY rad s Angular velocity about y-axis
Relative to ship-fixed axis system
Non-dimensional angular velocity
q’ OYS 1 q L/V
0
about y-axis
 –2 a
q
OYRT rad s Angular acceleration about y-axis Relative to ship-fixed axis system
Non-dimensional angular accelera-
2 2

q′ 
OYRTS 1 qL V
0
tion about y-axis
3rd derivative of angular velocity
 –4 a
q
OYR3T rad s —
about y-axis
Non-dimensional 3rd derivative of
4 4

q′ 
OYR3TS 1 qL V
0
angular velocity about y-axis
R RCM m Circular motion radius —
R RNA 1 Reynolds number V L /ν
nA WRA OA A
R RN0 1 (Reference) Reynolds number V L/ν
n0 0
V/R cos ϕ cos θ
S S
–1 a
r OMZ rad s Angular velocity about z-axis
Relative to ship-fixed axis system
Non-dimensional angular velocity
r’ OZS 1 r L/V
0
about z-axis
–2 a
 OZRT rad s Angular acceleration about z-axis Relative to ship-fixed axis system
r
Non-dimensional angular accelera-
2 2
OZRTS 1 rL V
r′
0
tion about z-axis
T TIP s Period of oscillation —
V cos θ cos β
S
–1 b
u VX m s Longitudinal velocity
Relative to ship-fixed axis system
a
For angles, the unit ° (degree) may be used.
b
The unit kn, common in navigation, may be used.
© ISO 2013 – All rights reserved 9

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ISO 13643-6:2013(E)

Table 1 (continued)
Concept
Symbol CC-code SI-unit
Term Definition or explanation
–1
u VX0 m s Longitudinal reference velocity —
0
Non-dimensional velocity in direc-
u’ VXS 1 u/V
0
tion of x-axis
–1 b 22 2
V V m s Model speed
uv++w
–1 b
V VWREL m s Relative wind velocity (See ISO 13643-1.)
WR
Reference velocity:
–1 b
V VWRELA m s Relative wind velocity at reference Usually 10 m above water surface, for full scale
WRA
height z
0A
–1 b
V VWABS m s True wind velocity (See ISO 13643-1.)
WT
Reference velocity:
–1 b
V VWABSA m s True wind velocity at reference Usually 10 m above water surface, for full scale
WTA
height z
0A
22 2
–1 b
V V0 m s Reference speed
0 uv++w
0
–1 b
V’ VS m s Non-dimensional speed V/V
0
V (sin ϕ cos β sin θ – sin β cos ϕ )
S S S
–1 b
v VY m s Lateral velocity
Velocity in direction of y-axis
v’ VYS 1 Non-dimensional lateral velocity v/V
0
–2

v VYRT m s Lateral acceleration Relative to ship-fixed axis system
2
′ VYRTS 1 Non-dimensional lateral acceleration vL V
v
0
WL WL — Waterline (See ISO 13643-1.)
V (sin ϕ sin β + cos ϕ cos β sin θ )
S S S
–1 b
w VZ m s Normal velocity
Velocity in direction of z-axis
w’ VZS 1 Non-dimensional normal velocity w/V
0
–2

w VZRT m s Normal acceleration Acceleration in direction of z-axis
Non-dimensional normal accelera- 2

′ VZRTS 1 wL V
w
0
tion
X FX N Longitudinal force (See ISO 13643-1.)
X
ρ
X’ FXS 1 Non-dimensional longitudinal force
2 2
LV
0
2
Non-dimensional coefficient used in
ˆ
′
X
FXQQS 1 —
qq
2
representing X’ as a function of q’
ˆ
Non-dimensional coefficient used in
X′
FXQQAS 1 —
qq
representing X’ as a function of q’ |q’|
Non-dimensional coefficient used in
ˆ
′
X
FXRRS 1 —
rr
2
representing X’ as a function of r’
Non-dimensional coefficient used in
ˆ
X′
FXUUS 1 (especially for submarines)
uu
2
representing X’ as a function of u’
Non-dimensional coefficient used in
representing X’ as a function of
ˆ
′
X
FXUUDDS 1 (especially for submarines)
uuδδ R
2 2
u′ δ
R
Non-dimensional coefficient used in
ˆ
′
X
FXVRS 1 —
vr
representing X’ as a function of v’ r’
a
For angles, the unit ° (degree) may be used.
b
The unit kn, common in navigation, may be used.
10 © ISO 2013 – All rights reserved

---------------------- Page: 14 ----------------------
ISO 13643-6:2013(E)

Table 1 (continued)
Concept
Symbol CC-code SI-unit
Term Definition or explanation
Non-dimensional coefficient used in
ˆ
′
X
FXVVS 1 —
vv
2
representing X’ as a function of v’
ˆ Non-dimensional coefficient used in
X′
FXWQS 1 —
wq
representing X’ as a function of w’ q’
Non-dimensional coefficient used in
ˆ
′
X
FXWWS 1 —
ww
2
representing X’ as a function of w’
Non-dimensional coefficient used in
ˆ
X′
FXDUS 1 (for surface ships only)
Δu
representing X’ as a function of Δu’
Non-dimensional coefficient used in
ˆ
′
X
FXDU2S 1 (for surface ships only)
ΔΔu
2
represent
...