ISO 13643-6:2017

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

ISO 13643-6:2017 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 modèle

General Information

• Status: Published
• Publication Date: 08-Feb-2017
• 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: 9093 - International Standard confirmed
• Completion Date: 06-Oct-2022

Relations

• Revises: ISO 13643-6:2013 - 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
Second edition
2017-02
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 modèle
Reference number
ISO 13643-6:2017(E)
©
ISO 2017

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ISO 13643-6:2017(E)

COPYRIGHT PROTECTED DOCUMENT
© ISO 2017, Published in Switzerland
All rights reserved. Unless otherwise specified, no part of this publication may be reproduced or utilized otherwise in any form
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written permission. Permission can be requested from either ISO at the address below or ISO’s member body in the country of
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ii © ISO 2017 – All rights reserved

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ISO 13643-6:2017(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 .19
6 Test 6.1 — Planar motion test .19
6.1 General .19
6.2 Description .21
6.3 Analysis and presentation of results of a planar motion test .22
6.3.1 Tests in the horizontal plane of motion .22
6.3.2 Tests in the vertical plane of motion (for submarines only) .28
6.3.3 Tests for angular motion about x-axis (roll) .31
6.4 Designation of a planar motion test .32
6.4.1 Designation of a planar motion test in the horizontal plane (H) .32
6.4.2 Designation of a planar motion test in the vertical plane (V) .33
6.4.3 Designation of a planar motion test for roll motion (R) .33
7 Test 6.2 — Circular motion test .33
7.1 General .33
7.2 Description .34
7.3 Analysis and presentation of results of a circular motion test .34
7.4 Designation of a circular motion test.34
8 Test 6.3 — Oblique towing or flow test .36
8.1 General .36
8.2 Description .37
8.3 Analysis and presentation of results of an oblique towing or flow test.37
8.4 Designation of an oblique towing or flow test .37
9 Test 6.4 — Wind tunnel test .40
9.1 General .40
9.2 Description .40
9.3 Analysis and presentation of results of a wind tunnel test .40
9.4 Designation of a wind tunnel test .41
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ISO 13643-6:2017(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 (see 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 (see 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.
For an explanation on the meaning of ISO specific terms and expressions related to conformity assessment,
as well as information about ISO’s adherence to the World Trade Organization (WTO) principles in the
Technical Barriers to Trade (TBT) see the following URL: www . i so .org/ iso/ foreword .html.
The committee responsible for this document is ISO/TC 8, Ships and marine technology, Subcommittee
SC 6, Navigation and ship operations.
This second edition cancels and replaces the first edition (ISO 13643-6:2013), of which it constitutes a
minor revision with the following changes:
— in 3.6 xyψ-carriage was inserted;
— in Table 1 “DNDPDYS” row, the symbol was changed from “N ” to “N′ ”;
ϕdyn ϕdyn
— in Table 1 “DYDVTS” row, the SI-unit was changed from “—” to “1”;
— in Equation (20) “ρ ” was changed to “ρ”;
w
— in 7.3 paragraph 3, “moments” was changed to “motions”.
A list of all parts in the ISO 13643 series can be found on the ISO website.
iv © ISO 2017 – All rights reserved

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INTERNATIONAL STANDARD ISO 13643-6:2017(E)
Ships and marine technology — Manoeuvring of ships —
Part 6:
Model test specials
1 Scope
This document 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 are referred to in the text in such a way that some or all of their content
constitutes requirements 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 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.
ISO and IEC maintain terminological databases for use in standardization at the following addresses:
— IEC Electropedia: available at http:// www .electropedia .org/
— ISO Online browsing platform: available at http:// www .iso .org/ obp
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
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ISO 13643-6:2017(E)

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.
3.5
manoeuvring device
rudder, azimuthing thruster, hydroplane, cycloidal propeller or equivalent system used to manoeuvre
a vessel
3.6
xyψ-carriage
sub carriage (secondary towing system) to the towing carriage that allows a differential longitudinal, a
transverse and a rotational motion of the model in the horizontal plane
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, gener-
2
A AXV m
XV
above waterline ally 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
C
2CV/( A )
A WRALV
2
C CD 1 Drag coefficient
D
2DV/( A )
A WRALV
2
C CDAX 1 Drag coefficient
DAX
2DV/( A ) , relative to cross section
A WRAXV
2
C CK 1 Roll-moment coefficient
K
2KV/(ρ AL )
A WRALVOA
2
C CN 1 Coefficient of moment about z-axis
N
2NV/( AL )
A WRALVOA
C CX 1 Longitudinal-force coefficient 2
X
2XV/( A )
A WRALV
C CXAX 1 Longitudinal-force coefficient 2
XAX
2XV/( A ) , relative to cross section
A WRAXV
C CY 1 Lateral-force coefficient 2
Y
2YV/( A )
A WRALV
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ISO 13643-6:2017(E)

Table 1 (continued)
Concept
Symbol CC-code SI-unit
Term Definition or explanation
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+ and XY+ , respectively
F FN 1 Froude number (see ISO 13643-1)
n
F FN0 1 (Reference) Froude number
n0
Vg/ L
0
GM m Metacentric height (see ISO 13643-1)
GM
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
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
|
V=0
–1 a
K DKDPST N m rad —
ϕstat
∂φ
from static test or calculation
Especially for submarines:
K

ρ
32
LV
K′ MXS 1
2
    
where K (u, v, w, p, q, r, v , w , p , q , r , ϕ, θ)
Non-dimensional roll moment
For surface ships only:
K

ρ
3 2
LV
0
2
    
where K (V , Δu, v, w, p, q, r, v , w , p , q , r , ϕ, θ)
0
tn+ T
2
In-phase part of non-dimensional
′ MXINS 1
Kt′ sinωtdt
()
K roll moment
∫
in nT
t
tn+ T
Quadrature part of non-dimensional 2
′ MXOUTS 1 Kt′ cosωtdt
()
K roll moment
∫
out nT
t
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ISO 13643-6:2017(E)

Table 1 (continued)
Concept
Symbol CC-code SI-unit
Term Definition or explanation
∂K′
′
DKDPS 1 —
K |
ˆ′
p
KK′=
∂p′
0
∂K′
′
DKDPTS 1 —
|
K
 ′
ˆ
p
KK′=

∂p′
0
'
′ ∂K
DKDP3TS 1 —
K
|

p ˆ′
 KK′=
∂p ′
0
∂K′
′ DKDRS 1 Slope through zero of K′ versus r′
|
′
K ˆ
KK′=
r ∂r′
0
∂K′
′ DKDRTS 1 —
|
ˆ
K
KK′′=


r ∂r′ 0
∂K′
′ DKDVS 1 Slope through zero of K′ versus v′
|
′
K ˆ
KK′=
v ∂v′
0
∂K′
′ DKDVTS 1 —
|
K ˆ′
  KK′=
v ∂v′
0
Non-dimensional coefficient used in
′
ˆ
MXPQS 1 —
K
representing K′ as a function of p′ q′
pq
Non-dimensional coefficient used in
′
MXRS 1 (for surface ships only)
ˆ
K representing K′ as a function of F r′
n0
r
Non-dimensional coefficient used in
′ MXURS 1 (especially for submarines)
ˆ
K representing K′ as a function of u′ r′
ur
Non-dimensional coefficient used in
′ MXUUS 1 (especially for submarines)
ˆ
2
K representing K′ as a function of u′
uu
Non-dimensional coefficient used
MXUUDRS 1 in representing K′ as a function of (especially for submarines)
ˆ
K
uuδ R 2
u′ δ
R
Non-dimensional coefficient used in
representing K′ as a function of
MXUUDR3S 1 (especially for submarines)
ˆ
K
uuδδδ R 23
′
u δ
R
Non-dimensional coefficient used in
MXUVS 1 (especially for submarines)
ˆ
′
K
representing K′ as a function of u′ v′
uv
Non-dimensional coefficient used
ˆ
MXUVDRS 1 in representing K′ as a function of (especially for submarines)
K
uvδ R
u′ v′ δ
R
Non-dimensional coefficient used in
ˆ
MXVS 1 (for surface ships only)
K ′
representing K′ as a function of F v′
v n0
Non-dimensional coefficient used in
representing K′ as a function of
ˆ
MXV3S 1 (for surface ships only)
K ′
′′22
vvv
vv′′|| vw+ F
n0
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ISO 13643-6:2017(E)

Table 1 (continued)
Concept
Symbol CC-code SI-unit
Term Definition or explanation
Non-dimensional coefficient used in
representing K′ as a function of
′
ˆ
MXVVAS 1 —
K
vv ′′22
vv′ +w
Non-dimensional coefficient used
′
ˆ MXVDRS 1 in representing K′ as a function of (for surface ships only)
K
vδ R
F v′ δ
n0 R
Non-dimensional coefficient used in
′
ˆ
MXWPS 1 —
K
representing K′ as a function of w′ p′
wp
Non-dimensional coefficient used in
′
ˆ MXWRS 1 —
K
representing K′ as a function of w′ r′
wr
Non-dimensional coefficient used in
′
ˆ MXDUS 1 (for surface ships only)
K
representing K′ as a function of Δu′
Du
Non-dimensional coefficient used in
′
ˆ
MXDUVS 1 (for surface ships only)
K
representing K′ as a function of Δu′ v′
Duv
Non-dimensional coefficient used
′
ˆ MXDU2S 1 in representing K′ as a function of (for surface ships only)
K
DDu 2
(Δu′)
Non-dimensional coefficient used
′
ˆ MXDRS 1 in representing K′ as a function of (for surface ships only)
K
δ R 2
F δ
n0 R
Non-dimensional coefficient used in
representing K′ as a function of
′
ˆ MXDR3S 1 (for surface ships only)
K
23
δδδ R
F δ
nR0
Non-dimensional coefficient used in
representing K′ when angle of attack
′
ˆ MX0S 1 —
K
α, drift angle β, manoeuvring device,
0
and plane angles are zero
Non-dimensional oscillatory roll co-
′
ˆ
MXOPHS 1 —
K
efficient
φ
L L m Model length Reference length (see ISO 13643-1)
Length between the most aft and most forward
L LOA m Length overall points of the ship, permanent outfit included,
OA
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
|
V=0
–1 a
M DMDTST N m rad —
θstat
∂θ
from static test or calculation
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ISO 13643-6:2017(E)

Table 1 (continued)
Concept
Symbol CC-code SI-unit
Term Definition or explanation
Especially for submarines
M
ρ
32
LV
2
    
where M (u, v, w, p, q, r, v , w , p , q , r , ϕ, θ)
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, v , w , p , q , r , ϕ, θ)
0,
tn+ T
In-phase part of non-dimensional 2
′
MYINS 1
M Mt′() sinωtdt
moment about y-axis
in
∫
nT
t
tn+ T
2
Quadrature part of non-dimensional
'
′
MYOUTS 1
Mt cosωtdt
M ()
moment about y-axis
out ∫
nT
t
∂M′
′
DMDQS 1 Slope through zero of M′ versus q′
M |
′
q ˆ
MM′=
∂q′
0
∂M′
′
DMDQTS 1 —
M |
 ′
q
ˆ
MM′=

∂q′
0
∂M′
′
DMDQ3TS 1 —
|
M
′
 ˆ
q
 MM′=
∂q′
0
∂M′
′
DMDWS 1 Slope through zero of M′ versus w′
|
M
′
w ˆ
MM′=
∂w′
0
∂M′
′
DMDWTS 1 —
M |
 ′
w ˆ
 MM′=
∂w′
0
∂M′
′
–1 a
DMDTHS rad —
|
M
′
θ ˆ
MM′=
∂θ
0
Non-dimensional coefficient used in
′
ˆ MYPPS 1 —
M
2
representing M′ as a function of p′
pp
Non-dimensional coefficient used in
′
ˆ
MYPRS 1 —
M
representing M′ as a function of p′ r′
pr
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ISO 13643-6:2017(E)

Table 1 (continued)
Concept
Symbol CC-code SI-unit
Term Definition or explanation
Non-dimensional coefficient used in
′
ˆ
MYQS 1 —
M
representing M′ as a function of u′ q′
q
’ Non-dimensional coefficient used in
ˆ
MYQQAS 1 —
M
representing M′ as a function of q′|q′|
qq
Non-dimensional coefficient used
′
ˆ
MYQADSS 1 in representing M′ as a function of —
M
q δ S
u′|q′|δ
S
Non-dimensional coefficient used in
′
ˆ MYRRS 1 —
M 2
representing M′ as a function of r′
rr
Non-dimensional coefficient used in
′
ˆ MYUUS 1 —
M 2
representing M′ as a function of u′
uu
Non-dimensional coefficient used in
′
ˆ
MYVPS 1 —
M
representing M′ as a function of v′ p′
vp
Non-dimensional coefficient used in
′
ˆ MYVRS 1 —
M
representing M′ as a function of v′ r′
vr
Non-dimensional coefficient used in
′
ˆ MYWS 1 —
M
representing M′ as a function of u′ w′
w
Non-dimensional coefficient used in
representing M′ as a function of
′
ˆ MYWWS 1 —
M
ww
''22
|'wv| + w
Non-dimensional coefficient used in
representing M′ as a function of
′
ˆ
MYWWAS 1 —
M
ww
′22′
wv' + w
Non-dimensional coefficient used
′
ˆ
MYWAS 1 in representing M′ as a function of —
M
w
u′|w′|
Non-dimensional coefficient used in
representing M′ as a function of
′
ˆ
MYWAQS 1 —
M
wq
′22′
qv' + w
Non-dimensional coefficient used
′
ˆ MYDBS 1 in representing M′ as a function of —
M
δ B 2
u′ δ
B
Non-dimensional coefficient used
′
ˆ MYDSS 1 in representing M′ as a function of —
M
δ S 2
u′ δ
S
Non-dimensional coefficient used in
representing M′ when angle of attack
α, drift angle β, manoeuvring device,
′
ˆ MY0S 1 —
and plane angles are zero
M
0
Non-dimensional oscillatory coeffi-
′
 MYOTHS 1 —
M
cient about y-axis
θ
m MA kg Model mass —
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ISO 13643-6:2017(E)

Table 1 (continued)
Concept
Symbol CC-code SI-unit
Term Definition or explanation
N MZ N m Moment about z-axis Relative to ship-fixed axis system
N
′
φ stat
∂N
′ | −
–1 a
DNDPDYS rad — ′
N ˆ
NN′=
φdyn ∂φρ
0 32
LV
2
∂N
|
V=0
–1 a
N DNDPST N m rad —
ϕstat
∂φ
from static test or calculation
Especially for submarines:
N
ρ
32
LV
2
    
where N (u, v, w, p, q, r, v , w , p , q , r , ϕ, θ)
Non-dimensional moment about
N′ MZS 1
z-axis
For surface ships only:
N
ρ
3 2
LV
0
2
    
where N (V , Δu, v, w, p, q, r, v , w , p , q , r , ϕ, θ)
0
tn+ T
2
In-phase part of non-dimensional
′
MZINS 1
N Nt′ sinωtdt
()
moment about z-axis
in ∫
nT
t
tn+ T
2
Quadrature part of non-dimensional
′
MZOUTS 1
Nt′ cosωtdt
N ()
moment about z-axis
out ∫
nT
t
∂′N
′
DNDPS 1 —
N |
′
p ˆ
NN′=
∂′p
0
∂′N
′
DNDPTS 1 —
N |

′
p ˆ
NN′=

∂ ′
p
0
∂′N
′
DNDP3TS 1 —
N |
 ′
p ˆ
NN′=

∂p
0
∂′N
′
DNDRS 1 Slope through zero of N′ versus r′
|
N
′
r ˆ
NN′=
∂′r
0
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ISO 13643-6:2017(E)

Table 1 (continued)
Concept
Symbol CC-code SI-unit
Term Definition or explanation
∂′N
′
DNDRTS 1 —
N |
 ′
ˆ
r
NN′=

∂′r
0
∂′N
′
DNDVS 1 Slope through zero of N′ versus v′
|
N
′
v ˆ
NN′=
∂′v
0
∂′N
′
DNDVTS 1 —
N |
 ′
ˆ
v
NN′=

∂′v
0
Non-dimensional coefficient used in
′
ˆ MZPQS 1 —
N
representing N′ as a function of p′ q′
pq
Non-dimensional coefficient used in
′
ˆ MZQRS 1 —
N
representing N′ as a function of q′ r′
qr
Non-dimensional coefficient used in
′
ˆ
MZRS 1 (for surface ships only)
N
representing N′ as a function of F r′
n0
r
′ Non-dimensional coefficient used in
ˆ
MZRRAS 1 —
N
representing N′ as a function of r′|r′|
rr
Non-dimensional coefficient used in
representing N′ as a function of
′
ˆ MZRDDS 1 (for surface ships only)
N
2
rδδ R
Fr′δ
n0 R
Non-dimensional coefficient used in
representing N′ as a function of
′
ˆ
MZRADS 1 (for surface ships only)
N
r δ R
Fr||′ δ
n0 R
Non-dimensional coefficient used in
′
ˆ MZURS 1 (especially for submarines)
N
representing N′ as a function of u′ r′
ur
Non-dimensional coefficient used in
representing N′ as a function of
′
ˆ
MZURDDS 1 (especially for submarines)
N
2
urδδ R
ur′′δ
R
Non-dimensional coefficient used in
representing N′ as a function of
′
ˆ
MZURADS 1 (especially for submarines)
N
ur δ R
ur′′|| δ
R
Non-dimensional coefficient used in
′
ˆ MZUUS 1 (especially for submarines)
N 2
representing N′ as a function of u′
uu
Non-dimensional coefficient used
′
ˆ MZUUDS 1 in representing N′ as a function of (especially for submarines)
N
uuδ R 2
u′ δ
R
Non-dimensional coeffi cient used in
representing N′ as a function of
′
ˆ MZUUD3S 1 (especially for submarines)
N
23
uuδδδ R
u′ δ
R
Non-dimensional coefficient used in
′
ˆ MZUVS 1 (especially for submarines)
N
representing N′ as a function of u′ v′
uv
© ISO 2017 – All rights reserved 9

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ISO 13643-6:2017(E)

Table 1 (continued)
Concept
Symbol CC-code SI-unit
Term Definition or explanation
Non-dimensional coefficient used in
′
ˆ MZVS 1 (for surface ships only)
N
representing N′ as a function of v′
v
Non-dimensional coefficient used in
′
ˆ
MZVQS 1 —
N
representing N′ as a function of v′ q′
vq
Non-dimensional coefficient used
′
ˆ MZVRRS 1 in representing N′ as a function of (for surface ships only)
N
vrr 2
F v′ r′
n0
Non-dimensional coefficient used
′
ˆ MZVVRS 1 in representing N′ as a function of (for surface ships only)
N
vvr 2
F v′ r′
n0
Non-dimensional coefficient used in
representing N′ as a function of
′
ˆ MZV3S 1 (for surface ships only)
N
′′22 ′2
vvv
vv +wF
n0
Non-dimensional coefficient used in
representing N′ as a function of
′
ˆ
MZVVAS 1 —
N
vv ′′22
vv′ +w
Non-dimensional coefficient used in
representing N′ as a function of
′
ˆ
MZVARS 1 —
N
vr ′′22
rv′ +w
Non-dimensional coefficient used in
′
ˆ
MZWPS 1 —
N
representing N′ as a function of w′ p′
wp
Non-dimensional coefficient used in
′
ˆ MZWRS 1 —
N
representing N′ as a function of w′ r′
wr
Non-dimensional coefficient used in
′
MZDUS 1 (for surface ships only)
ˆ
N
representing N′ as a function of Δu′
Du
Non-dimensional coefficient used in
′
ˆ MZDUVS 1 (for surface ships only)
N
representing N′ as a function of Δu′ v′
Duv
Non-dimensional coefficient used
′
ˆ MZDU2S 1 in representing N′ as a function of (for surface ships only)
N
DDu
2
(Δu′)
Non-dimensional coefficient used
′
ˆ MZDRS 1 in representing N′ as a function of (for surface ships only)
N
δ R 2
F δ
n0 R
Non-dimensional coefficient used in
representing N′ as a function of
′
ˆ MZDR3S 1 (for surface ships only)
N
23
δδδ R
F δ
n0 R
Non-dimensional coefficient used in
representing N′ when angle of attack
′
ˆ MZ0S 1 —
N
α, drift angle β, manoeuvring device,
0
and plane angles are zero
10 © ISO 2017 – All rights reserved

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ISO 13643-6:2017(E)

Table 1 (continued)
Concept
Symbol CC-code SI-unit
Term Definition or explanation
Non-dimensional oscillatory coeffi-
′
ˆ
MZOPHS 1 —
N
cient about z-axis
φ
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
Non-dimensional roll
p′ OXS 1 p L/V
0
velocity
–2 a
 OXRT rad s Roll acceleration Angular acceleration about x-axis
p
Non-dimensional roll
2 2
 OXRTS 1

p′
pL / V
acceleration
0
3rd derivative of roll
–4 a
OXR3T rad s —

p
velocity
Non-dimensional 3rd
4 4
′ OXR3TS 1

pL / V

derivative of roll velocity
p
0
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
 OYRT rad s Angular acceleration about y-axis Relative to ship-fixed axis system
q
Non-dimensional angular accelera-
2 2
 OYRTS 1
q′ 
qL / V
tion about y-axis
0
3rd derivative of angular velocity
–4 a
 OYR3T rad s —
q
about y-axis
Non-dimensional 3rd
4 4
 OYR3TS 1 derivative of angular velocity about
q ′ 
qL / V
0
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
r ′ 
rL / V
tion about z-axis
0
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
–1
u VX0 m s Longitudinal reference velocity —
0
Non-dimensional velocity in direc-
u′ VXS 1 u/V
0
tion of x-axis
© ISO 2017 – All rights reserved 11

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ISO 13643-6:2017(E)

Table 1 (continued)
Concept
Symbol CC-code SI-unit
Term Definition or explanation
–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
 VYRT m s Lateral acceleration Relative to ship-fixed axis system
v
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
 VZRT m s Normal acceleration Acceleration in direction of z-axis
w
Non-dimensional normal acceler-
2
 VZRTS 1
w ′ 
wL / V
ation
0
X FX N Longitudinal force (see ISO 13643-1)
X
Non-dimensional
X′ FXS 1
ρ
longitudinal force
2 2
LV
0
2
Non-dimensional coefficient used in
′
...