ITTC Symbols and Terminology List Version 2014 Supersedes all … · 2016. 7. 7. · ITTC Symbols 1 General 1.1 Fundamental Concepts Version 2014 1.1.1 Uncertainty 5 ITTC Symbol Computer

ITTC Symbols and Terminology List

Version 2014

September 2014

Supersedes all previous versions

Please go to next page for hypertext table of contents

Updated by the 27th ITTC Quality Systems Group

ITTC Symbols and Terminology List Version 2014

Table of Contents

all lines have hypertext link to symbols pages

ITTC SYMBOLS AND TERMINOLOGY

LIST VERSION 2014 2

TABLE OF CONTENTS 2

1 GENERAL 4

11 Fundamental Concepts 4

111 Uncertainty 4

112 Coordinates and Space Related

Quantities 10

1121 Basic Quantities 13

113 Time and Frequency Domain

Quantities 15

1132 Complex Transforms 16

1133 Complex Quantities 16

114 Random Quantities and Stochastic

Processes 18

1141 Random Quantities 18

1142 Stochastic Processes 19

1143 Probability Operators

(Superscripts) 20

115 Balances and System Related

Concepts 21

12 Solid Body Mechanics 22

121 Inertial and Hydrodynamic

Properties 22

122 Loads 24

1221 External Loads 24

1222 Sectional Loads 25

123 Rigid Body Motions 26

1231 Motions 26

1232 Attitudes 27

13 Fluid Mechanics 28

131 Flow Parameters 28

1311 Fluid Properties 28

1312 Flow parameters 28

1313 Boundary conditions 29

132 Flow Fields 30

1321 Velocities etc 30

1322 Circulation etc 30

133 Lifting Surfaces 32

1331 Geometry 32

1332 Flow angles etc 33

1333 Forces 34

1334 Sectional coefficients 34

134 Boundary Layers 35

1341 Two-dimensional Boundary Layers

135 Cavitation 37

1352 Flow fields 37

1353 Pumps 38

14 Environmental Mechanics 39

141 Waves 39

1411 Periodic waves 39

1412 Irregular waves 40

1413 Time Domain Analysis 41

1414 Frequency Domain Analysis 42

1415 Directional Waves 43

142 Wind 44

143 Ice Mechanics 45

15 Noise 46

151 Underwater Noise 46

2 SHIPS IN GENERAL 47

22 Geometry and Hydrostatics 50

221 Hull Geometry 50

2212 Derived Quantities 53

2213 Symbols for Attributes and

Subscripts 54

222 Propulsor Geometry 56

2221 Screw Propellers 56

2222 Ducts60

2223 Waterjets (see also section 135) 60

2224 Pods 61

2225 Operators and identifiers 61

223 Appendage Geometry 62

2232 Identifiers for Appendages

(Subscripts) 63

224 Hydrostatics and Stability 64

2241 Points and Centres (Still under

construction) 64

2242 Static Stability levers 65

3 2243 Derived Quantities 67

2244 Intact and Damage (Flooded)

Stability 68

Subscripts (under construction) 69

23 Resistance and Propulsion 70

231 Hull Resistance (see also Section

141 on Waves) 70

Subscripts 73

232 Ship Performance 74

2323 Efficiencies etc 76

233 Propulsor Performance 77

2333 Induced Velocities etc 80

234 Unsteady Propeller Forces 81

235 Water Jets 83

24 Manoeuvrability and Sea Keeping 87

241 Manoeuvrability 87

2411 Geometrical Quantities 87

2412 Motions and Attitudes 87

2413 Flow Angles etc 89

2414 Forces and Derivatives 89

2415 Linear Models 91

2416 Turning Circles 91

2417 Zig-Zag Manoeuvres 92

2418 Stopping Manoeuvres 93

242 Sea Keeping 94

243 Large Amplitude Motions

Capsizing 96

Subscripts 104

3 SPECIAL CRAFT 106

31 Planing and Semi-Displacement

Vessels 106

312 Geometry and Levers Underway

3121 Geometry Underway 107

3122 Levers Underway 108

32 Multi-Hull Vessels (Add trimaran

symbols) 112

3221 Resistance Components 114

33 Hydrofoil Boats 115

34 ACV and SES 120

35 Ice Going Vessels 124

36 Sailing Vessels 126

4 BACKGROUND AND REFERENCES

41 Symbols and Terminology Group 130

42 Description of the List of Symbols 130

421 Classification 130

422 Structure of the Lists 130

423 Organization of the matrix

structured list 130

5 PRINCIPLES OF NOTATION 132

51 Excerpts of ISO 31 133

52 Computer Symbols 145

53 Documentation 146

531 ITTC Documents 146

532 Translations 146

533 Other References 146

ITTC Symbols 1 General

11 Fundamental Concepts

Version 2014 111 Uncertainty 4

Symbol

Computer

Symbol

Definition or

Explanation

1 GENERAL

111 Uncertainty

(The following table follows ISOIEC Guide 98-32008 ndash Annex J)

a Half-width of a rectangular

distribution

Half-width of a rectangular

distribution of possible val-

ues of input quantity Xi

a = (a+ndash a_) 2

a+ Upper bound Upper bound or upper limit

of input quantity Xi

a_ Lower bound Lower bound or lower limit

b+ Upper bound of the deviation Upper bound or upper limit

of the deviation of input

quantity Xi from its estimate

xi b+ = a+ - xi

b_ Lower bound of the deviation Lower bound or lower limit

xi b_ = xi ndash a_

ci Sensitivity coefficient ii xfc 1

f Function Functional relationship be-

tween measurand Y and in-

put quantities Xi on which Y

depends and between output

estimate y and input esti-

mates xi on which y depends

ixf Partial derivative Partial derivative of f with

respect to input quantity xi

k Coverage factor For calculation of expanded

uncertainty U = kuc(y)

kp Coverage factor for probabil-

For calculation of expanded

uncertainty Up = kpuc(y)

n Number of repeated observa-

Symbol

Computer

Symbol

Definition or

Explanation

N Number of input quantities Number of input quantities

Xi on which the measurand Y

depends

p Probability Level of confidence 0 p

q Random quantity 1

q Arithmetic mean or average 1

qk kth observation of q kth independent repeated ob-

servation of randomly vary-

ing quantity q

r(xixj) Estimated correlation coeffi-

r(xi xj) = u(xi xj)(u(xi) u(xj)) 1

ps Pooled estimate of variance 1

sp Pooled experimental standard

deviation Positive square root of 2

)(2 qs Experimental variance of the

mean nqsqs k )()( 22 estimated

variance obtained from a

Type A evaluation

)(qs Experimental standard devia-

tion of the mean

Positive square root of

)(2 qs

kqs Experimental variance from

repeated observations

)( kqs Experimental standard devia-

tion of repeated observations

iXs Experimental variance of in-

put mean From mean iX determined

from n independent repeated

observations Xik estimated

Type A evaluation

)( iXs Standard deviation of input

)( 12 Xs

)( rqs Estimate of covariance of

)( ji XXs Estimate of covariance of in-

put means

Symbol

Computer

Symbol

Definition or

Explanation

tp(v) Inverse Student t Student t-distribution for v

degrees of freedom corre-

sponding to a given proba-

bility p

tp(veff) Inverse Student t for effec-

tive degrees of freedom

Student t-distribution for veff

bility p in calculation of ex-

panded uncertainty Up

u2(xi) Estimated variance Associated with input esti-

mate xi that estimates input

quantity Xi

u(xi) Standard deviation Positive square root of u2(xi) 1

u(xixj) Estimated covariance 1

c yu Combined variance Combined variance associ-

ated with output estimate y

uc(y) Combined standard uncer-

tainty

ucA(y) Combined standard uncer-

tainty from Type A

From Type A evaluations

ucB(y) Combined standard uncer-

tainty from Type B

From Type B evaluations

uc(yi) Combined standard uncer-

tainty

Combined standard uncer-

tainty of output estimate yi

when two or more measur-

ands or output quantities are

determined in the same

measurement

1)(2 yui Component of combined var-

22 )]([)( iii xucyu 1

1ui(y) Component of combined

standard uncertainty )()( iii xucyu 1

u(xi)|xi| Relative standard uncertainty

of output estimate x

uc(y)|y| Relative combined standard

uncertainty of output esti-

mate y

Symbol

Computer

Symbol

Definition or

Explanation

[u(xi)|xi|]2 Estimated relative variance Estimated relative variance

associated with input esti-

mate xi

[uc(y)|y|]2 Relative combined variance Relative combined variance

associated with output esti-

mate y

u(xi xj))|xi xj| Estimated relative covariance Estimated relative covari-

ance associated with input

estimates xi and xj

U Expanded uncertainty Expanded uncertainty of out-

put estimate y that defines an

interval Y = y plusmnU having a

high level of confidence

equal to coverage factor k

times the combined standard

uncertainty uc(y) of y

U = k uc(y)

Up Expanded uncertainty associ-

ated to confidence level p

Expanded uncertainty of out-

interval Y = y plusmnUp having a

high level of confidence p

equal to coverage factor kp

Up = kp uc(y)

xi Estimate of input quantity Xi Estimate of input quantity Xi

NOTE when xi is deter-

mined from the arithmetic

mean or average of n inde-

pendent repeated observa-

tion i ix X

Xi ith input quantity

ith input quantity on which

measurand Y depends

NOTE Xi may be the phys-

ical quantity or the random

variable

Symbol

Computer

Symbol

Definition or

Explanation

Estimate of the value of input

quantity Xi

Estimate of the value of in-

put quantity Xi equal to the

arithmetic mean or average

of n independent repeated

observation Xik of Xi

Xik kth independent repeated ob-

servation of Xi

y Estimated of measurand Y or

Result of a measurement or

Output estimate

yi Estimate of measurand Yi Estimate of measurand Yi

ands are determined in the

same measurement

Y A measurand

Estimated relative uncer-

tainty of standard uncertainty

u(xi) of inputs estimate xi

microp Expectation or mean of the

probability distribution

Expectation or mean of the

probability distribution of

random-varying quantity q

ν Degrees of freedom (general)

νi Degrees of freedom Degrees of freedom or ef-

fective degrees of freedom

of standard uncertainty u(xi)

of input estimate xi

νeff Effective degrees of freedom Effective degrees of freedom

of uc(y) used to obtain tp(νeff)

for calculating expanded un-

certainty Up

2 Variance of a probability Variance of a probability

distribution of (for example)

a randomly-variing quantity

q estimated by s2(qk)

Standard deviation of a prob-

ability distribution

Standard deviation of a

equal to the positive square

root of 2

Symbol

Computer

Symbol

Definition or

Explanation

Variance of Variance of equal to 2

n estimated by

Standard deviation of Standard deviation of

equal to the positive root of

Variance of experimental

standard deviation of

Standard deviation of experi-

mental standard deviation

of equal to the posi-

tive square root of

Version 2014 112 Coordinates and Space related Quantities 10

112 Coordinates and Space Related Quan-

tities

Orientation of coordinates

A problem of general interest the orientation

of the axes of coordinate systems has been

treated extensively in the Report of the 17th

ITTC Information Committee The present QS

Group recommends that the orientations of the

coordinate systems chosen for convenience

should be stated explicitly in any case The co-

ordinate system orientation should not be in-

ferred from the symbols andor names of the

concepts or from national or professional tradi-

tions All sign conventions of related Quantities

should be consistent with the orientation chosen

For ready reference the recommendation of

the 17th ITTC Information Committee is quoted

in the following

In order to adapt ITTC nomenclature to

common practice a proposal for a standard coor-

dinate system was published in the newsletter

No 7 March 1983 to generate discussion The

response was quite diverse On the one hand it

was suggested that instead of the two orthogonal

right handed systems with the positive x-axis

forward and the positive z-axis either up- or

downward as proposed only one system should

be selected in particular the one with the posi-

tive z-axis upwards On the other hand the atten-

tion of the Information Committee was drawn to

the fact that in ship flow calculations neither of

the two systems proposed is customary Nor-

mally the x-axis is directed in the main flow di-

rection ie backwards the y-axis is taken posi-

tive to starboard and the z-axis is positive up-

wards The origin of the co-ordinates in this case

is usually in the undisturbed free surface half

way between fore and aft perpendicular

In view of this state of affairs the Infor-

mation Committee (now Quality System Group

- QSG) may offer the following recommenda-

tion if any

Axes coordinates

Preferably orthogonal right handed systems

of Cartesian co-ordinates should be used orien-

tation and origin in any particular case should be

chosen for convenience

Body axes (xyz)

Coordinate systems fixed in bodies ocean

platforms or ships

For the definition of hull forms and ocean

wave properties and the analysis of structural

deflections it is customary to take the x-axis pos-

itive forward and parallel to the reference or

base line used to describe the bodys shape the

y-axis positive to port and the z-axis positive

upwards

For seakeeping and manoeuvrability prob-

lems the coordinate system is defined as follows

usually the x-axis as before the y-axis positive

to starboard and the z-axis positive downwards

the origin customarily at the centre of mass of

the vehicle or at a geometrically defined posi-

For ship flow calculations usually the x-axis

positive in the main flow direction ie back-

wards the y-axis positive to starboard and the

z-axis positive upwards the origin customarily

at the intersection of the plane of the undisturbed

free-surface the centre plane and the midship

section

Fixed or space axes (x0y0z0)

Coordinate systems fixed in relation to the

earth or the water For further references see ISO

Standard 11511 6 Terms and symbols for

flight dynamics

There may be other coordinate systems in

use and there is no possibility for the adoption

of a single system for all purposes Any problem

requires an adequate coordinate system and

transformations between systems are simple

provided that orientations and origins are com-

pletely and correctly documented for any partic-

ular case

Origins of coordinates

In sea keeping and manoeuvrability prob-

lems customarily the centre of mass of the vehi-

cle is chosen as the origin of the coordinates

This is in most cases not necessarily advanta-

geous as all the hydrodynamic properties enter-

ing the problems are related rather to the geom-

etries of the bodies under investigation So any

geometrically defined point may be more ade-

quate for the purposes at hand

ISO Standard 31-11 makes the following suggestions

Item No Coordinates Position vector and its

differential

Name of coordi-

nate system

Remarks

11-121

x y z r = xex + yey + zez

dr = dx ex + dy ey + dz ez

cartesian

coordinates

ex ey and ez form an

orthonormal right-handed

system See Figure 1

11-122

ρ φ z r= ρeρ + zez

dr = dρ eρ + dφ eφ + dz ez

cylindrical

coordinates

eρ(φ) eφ(φ) and ez form an

system See Figures 3 and

4 If z = 0 then ρ and φ are

the polar coordinates

11-123

(-) r φ r=rer

dr = dr er + r d e +

r sin dφ eφ

spherical

coordinates er(9 gyp) e ( φ) and

eφ(φ) form an orthonormal

right-handed system See

Figures 3 and 5

NOTE 1 If exceptionally a left-handed system (see figure 2) is used for certain purposes this shall be

clearly stated to avoid the risk of sign errors

Symbol

Computer

Symbol

Definition or

Explanation

1121 Basic Quantities

s S Any scalar quantity distrib-

uted maybe singularly in

S0ij SM0(IJ) Zeroth order moment of a

scalar quantity δijds =δijS

S1ij SM1(IJ) First order moment of a sca-

lar quantity

formerly static moments of a

scalar distribution

εikjxkds

S2ij SM2(IJ) Second moment of a scalar

quantity formerly moments

of inertia of a scalar distribu-

εklixlεjkm xmds

Suv S(UV) Generalized moment of a

scalar quantity distributed in

Sij = S0ij

Si 3+j = S1ij

S3+i j = S1ij

S3+i 3+j = S2ij

Tij T(IJ) Tensor in space referred to

an orthogonal system of Car-

tesian coordinates

fixed in the body

Tijs + Tij

TijA TAS(IJ) Anti-symmetric part of a

tensor

( Tij - Tji ) 2

TijS TSY(IJ) Symmetric part of a tensor ( Tij + Tji ) 2

TijT TTR(IJ) Transposed tensor Tji

Tij vj Tensor product Tij vj

ui vi U(I) V(I) Any vector quantities

ui vi UVPS Scalar product uivi

ui vj UVPD(IJ) Diadic product uivj

uv UVPV(I) Vector product εijkujvk

Symbol

Computer

Symbol

Definition or

Explanation

V0i Vi V0(I)V(I) Zeroth order moments of a

vector quantity distributed in

space referred to an orthog-

onal system of Cartesian co-

ordinates fixed in the body

V1i V1(I) First order moments of a

vector distribution εijkxjdvk

Vu V(U) Generalized vector Vi = V0i

V3+i = V1i

X X(1)

Y X(2)

Z X(3)

Body axes and correspond-

ing Cartesian coordinates

Right-hand orthogonal sys-

tem of coordinates fixed in

the body

x0 x01

y0 x02

z0 x03

X0 X0(1)

Y0 X0(2)

Z0 X0(3)

Space axes and correspond-

relation to the space

xF xF1

yF xF2

zF xF3

XF XF(1)

YF XF(2)

ZF XF(3)

Flow axes and correspond-

relation to the flow

εijk EPS(IJK) Epsilon operator +1 ijk = 123 231 312

1 ijk = 321 213 132

0 if otherwise

δij DEL(IJ) Delta operator +1 ij = 11 22 33

0 if otherwise

ITTC Symbols 1 Mechanics in General

Version 2014 113 Time and Frequency Domain Quantities 15

Symbol

Computer

Symbol

Definition or

Explanation

Unit 113 Time and Frequency Domain Quantities

a ADMP Damping sr in Laplace variable 1s

f FR Frequency Hz

fC FC Basic frequency in repeating

functions

1 TC Hz

fS FS Frequency of sampling 1 TS

period in repeating spectra

i I Imaginary unit sqrt(-1) 1

I IM Imaginary variable 1

j J Integer values - + 1

R R Complex variable exp(s TS)

Laurent transform

s S Complex variable a + 2πif

Laplace transform

t TI Time - + s

tj TI(J) Sample time instances j TS

TC TC Period of cycle 1 fC duration of cycles in

periodic repeating processes

TS TS Period of sampling Duration between samples s

x x Values of real quantities x(t)

X Real valued function

xj X(J) Variables for samples values

of real quantities x(tj) = x(t)δ(t - tj)dt

z Z Complex variable

Symbol

Computer

Symbol

Definition or

Explanation

1132 Complex Transforms

xA XA Analytic function XA(t) = X(t) + iXH(t)

xDF XDF Fourier transform of sam-

pled function

XDF(f) = xjexp(-i2πfjTS)

ie periodically repeating

= X(0)2 + fSXF(f + jfS)

sample theorem aliasing

xDL XDL Laurent transform of

sampled function XDL(s) = xjexp(-sjTS)

xF XFT Fourier transform XF(f) = X(t)exp(-i2πft)dt

inverse form

= XF(f)exp(-i2πft)dt

if X(t) = 0 and a = 0 then

XF(f)=XL(f)

xFj XFT(J) Fourier transform of

periodic function 1TCX(t)exp(-i2πjtTC)dt

t = 0 TC

XF = xFjδ(f - jTC)

inverse form

X(t) = xFjexp(-i2πfjTC)

xH XHT Hilbert transform XH(t) = 1π X(τ)(t - τ)dτ

xHF XHF Fourier transform of

Hilbert transform

XHF(f) = XF(f)(-i sgn f)

(1t)F = -i sgn f

xL XLT Laplace transform XL(s) = X(t)exp(-st)dt

if X(tlt0) = 0 then

= (X(t)exp(-at))F

xR XRT Laurent transform XR(r) = xjr-j=XDL

xS XS Single-sided complex spec-

XS(f) = XF(f)(1 + sgn f)

ie = 0 for f lt 0

xSj XS(J) Single-sided complex Fou-

rier series

XFj(1 + sgn j)

line spectra

1133 Complex Quantities

za ZAM Amplitude mod(z) = sqrt(zr2+zi2)

zc ZRE Real or cosine component zc = real(z) = zacos(zp)

Symbol

Computer

Symbol

Definition or

Explanation

zi ZIM Imaginary or sine

component

imag(z) = zasin(zp) = zs

zj ZCJ Conjugate zr - izi

zl ZLG (Phase) Lag

zp ZPH Phase arc(z) = arctg(zi zr)

zr ZRE Real or cosine component real(z) = zacos(zp) = zc

zs ZIM Imaginary or sine

component

zs = imag(z) = zasin(zp)

Version 2014 114 Stochastic Processes 18

Symbol

Computer

Symbol

Definition or

Explanation

114 Random Quantities and Stochastic Processes

1141 Random Quantities

gE gM gMR

Expected value of a function

of a random quantity

E(g) = g(x)fx(x)dx

Random quantities

x(ζ) y(ζ)

X(I) Y(I)

Samples of random quanti-

i = 1 n

n sample size

m-th moment of a random

quantity

xD xDR σx

Standard deviation of a ran-

dom quantity

xVR frac12

xDS sx

Sample deviation of a ran-

dom quantity

xVS 12

unbiased random estimate of

the standard deviation

xxR xxMR Rxx

Auto-correlation of a ran-

dom quantity

xyR xyMR Rxy

Cross-correlation of two ran-

dom quantities

xE xM xMR

Expectation or population

mean of a random quantity

xA xMS mx

Average or sample mean of

a random quantity

1n xi i = 1n

the expectation with

xAE = xE

xVSE = xV n

xPD fx

Probability density of a ran-

dom quantity

d Fx dx

xyPD fxy

Joint probability density of

two random quantities

2 Fxy (x y)

xPF Fx

Probability function (distri-

bution) of a random quantity

xyPF Fxy

Joint probability function

(distribution) function of two

random quantities

Symbol

Computer

Symbol

Definition or

Explanation

xV xVR xxVR

XVR XXVR

Variance of a random quan-

x2 E - xE 2

xVS xxVS

XVS XXVS

Sample variance of a ran-

dom quantity

1 (n - 1) (xi - x

i = 1n

the variance xVSE = xV

xyV xyVR

Variance of two random

quantities

x yE - xE yE

Outcome of a random ex-

periment

1142 Stochastic Processes

Mean of a function of a ran-

dom quantity

M(g(t)) = lim(1T g(t)dt)

t =-T2 +T2

T =- +

a function of a random quan-

A(g(t)) = 1T g(t)dt

t =0 +T

Stationary stochastic process

x(ζt) y(ζt)

xxC xxCR Cxx

Auto-covariance of a station-

ary stochastic process

(x(t) - xE)(x(t + τ) - xE)E

xyC xyCR Cxy

Cross-covariance of two sta-

tionary stochastic processes

(x(t) - xE)(y(t + τ) - yE)E

xxR xxRR Rxx

Auto-correlation of a station-

x(t)x(t + τ)E = Rxx(τ)

Rxx(τ) = Rxx(-τ)

if x is ergodic Rxx(τ)

= x(t)x(t + τ)MR

Rxx(τ) = Sxx(ω)cos(ωτ)dτ

τ = 0

xyR Rxy

Cross-correlation of two sta-

x(t)y(t + τ)E = Rxy(τ)

Ryx(τ) = Rxy(-τ)

if x y are ergodic

Rxy(τ) = x(t)y(t + τ)MR

Symbol

Computer

Symbol

Definition or

Explanation

xxS Sxx

Power spectrum or autospec-

tral power density of a sto-

chastic process

xxRRSR

xyS Sxy

XYSR Cross-power spectrum of

two stationary stochastic

processes

xyRRSR

Covariance or correlation

periment

1143 Probability Operators (Superscripts)

Average sample mean

Population covariance

Sample covariance

Population deviation

Sample deviation

E M MR

Expectation population

Probability density

Probability function

(Power) Spectrum

Sample spectrum

Population correlation

Sample correlation

Population variance

Sample variance

Version 2014 115 Balances and System Related Concepts 21

Symbol

Computer

Symbol

Definition or

Explanation

115 Balances and System Related Concepts

q QQ Quantity of the quality under

consideration stored in a

control volume

Q Quality under consideration QUs

QC QCF Convective flux QUs

QD QDF Diffusive flux QUs

QF QFL Total flux across the

surface of the control vol-

Inward positive QUs

QM Molecular diffusion QUs

QP QPN Production of sources in the

control volume

QS QRT Storage in the control vol-

ume rate of change of the

quantity stored

dq dt QUs

QT QDT Turbulent diffusion QUs

12 Solid Body Mechanics

Version 2014 121 Inertial and Hydrodynamic Properties 22

Symbol

Computer

Symbol

Definition or

Explanation

121 Inertial and Hydrodynamic Properties

AM(IJ)

Added mass coefficient in

ith mode due to jth motion

DA(IJ)

Damping coefficient in ith

mode due to jth motion

RF(IJ)

Restoring force coefficient

in ith mode due to jth motion

uv DH(UV)

Generalized hydrodynamic

damping

u FH(U)

uv IH(UV)

inertia

Longitudinal second mo-

ment of water-plane area

About transverse axis

through centre of floatation

Transverse second moment

of water-plane area

About longitudinal axis

Iy Iyy

IY IYY

M2(22)

MA(55)

Pitch moment of inertia

around the principal axis y

Iz Izz

IZ IZZ

M2(33)

MA(66)

Yaw moment of inertia

around the principal axis z

Ixy I12

Iyz I23

Izx I31

IXY I2(12)

IYZ I2(23)

IZX I2(31)

Real products of inertia in

case of non-principal axes

kx kxx

Roll radius of gyration

around the principal axis x

(Ixxm)12

Symbol

Computer

Symbol

Definition or

Explanation

ky kyy

Pitch radius of gyration

(Iyym)12

kz kzz

Yaw radius of gyration

(Izzm)12

M0(IJ)

MA(IJ)

Zero-th moments of mass

ie inertia distribution mass

tensor

mij = m δij

ij M1(IJ)

First moments of mass ie

inertia distribution

Alias static moments of

M2(IJ)

IN(IJ)

Second moments of mass

ie inertia distribution

Alias mass moments of iner-

MA(UV)

Generalized mass i e gen-

eralized inertia tensor

of a (rigid) body referred

to a body fixed coordinate

system

Mij = M0

Mi 3+j = M1Tij

M3+i j = M1ij

M3+i 3+j = M2ij

Version 2014 122 Loads 24

Symbol

Computer

Symbol

Definition or

Explanation

122 Loads

1221 External Loads

Force generalized load

in body coordinates

u = MMu

Fi = F0i

F3+i = F1i

Gravity field strength gener-

alized in body coordinates

gi = g1

g3+i = 0

Gravity field strength

in body coordinates

F11 F4

K M(1)

F1(1) F(4)

Moment around body axis x

F12 F5

M M(2)

F1(2) F(5)

Moment around body axis y

FN13 F6

N M(3)

F1(3) F(6)

Moment around body axis z

F01 F1

F0(1) F(1)

Force in direction of body

axis x

F02 F2

F0(2) F(2)

axis y

F03 F3

F0(3) F(3)

axis z

Gravity or weight force gen-

eralized in body co-ordi-

Gu = muv gv

G0i Gi

Gravity or weight force

in body coordinates

Gi = G0

i = m0ij gj

i G1(I)

Gravity or weight moment

in body coordinates

G3+i = G1

i = εikj xk G0

= m1ij gj

Load per unit length

Weight per unit length

dW dx1

Symbol

Computer

Symbol

Definition or

Explanation

1222 Sectional Loads

FSu FS(U) Force or load acting at a

given planar cross-section of

the body generalized in

section coordinates

FSi = FS0

FS3+i = FS1

i = MBi

FSi FS(I) Shearing force FS0

Tensioning or normal force FS01 N

MBi MB(I) Bending moment FS1

Twisting or torsional mo-

FS11 Nm

Version 2014 123 Rigid Body Motions 26

Symbol

Computer

Symbol

Definition or

Explanation

123 Rigid Body Motions

1231 Motions

v01 v4

V0(1) V(4)

Rotational velocity around

body axis x

v02 v5

V0(2) V(5)

body axis y

v03 v6

V0(3) V(6)

body axis z

v11 v1

V1(1) V(1)

Translatory velocity in the

direction of body axis x

v12 v2

V1(2) V(2)

direction of body axis y

v13 v3

V1(3) V(3)

direction of body axis z

Components of generalized

velocity or motion relative to

body axes

vi = v1

v3+i = v0i

Rates of change of compo-

nents of rotational velocity

relative to body axes

nents of linear velocity rela-

tive to body axes

Angular acceleration

Symbol

Computer

Symbol

Definition or

Explanation

1232 Attitudes

Angle of attack

The angle of the longitudinal

body axis from the projec-

tion into the principal plane

of symmetry of the velocity

of the origin of the body

axes relative to the fluid

positive in the positive sense

of rotation about the y-axis

Angle of drift or side-slip

The angle to the principal

plane of symmetry from the

velocity vector of the origin

of the body axes relative to

the fluid positive in the pos-

itive sense of rotation about

the z-axis

Projected angle of roll or

The angular displacement

about the xo axis of the prin-

cipal plane of symmetry

from the vertical positive in

the positive sense of rotation

about the xo axis

X(4) RO

Angle of roll heel or list

Positive in the positive sense

of rotation about the x-axis

X(5) TR

Angle of pitch or trim

X(6) YA

Angle of yaw heading or

course

of rotation about the z-axis

13 Fluid Mechanics

Version 2014 131 Flow Parameters 28

Symbol

Computer

Symbol

Definition or

Explanation

13 Fluid Mechanics

131 Flow Parameters

1311 Fluid Properties

Velocity of sound

(E ρ)12

Modulus of elasticity

Weight density

ρg (See 111)

Kinematic capillarity

Viscosity

Kinematic viscosity

DN RHO

Mass density

Capillarity

Surface tension per unit

length

1312 Flow parameters

Boussinesq number

V (g RH)12

Cauchy number

V (E ρ)12

Froude number

V (g L)12

Froude depth number

V (g h)12

Froude displacement number

V (g 13)12

Mach number

Reynolds number

Strouhal number

Thoma number

Cavitation number

(pA ndash pV)q

Weber number

V2 L κ

07R Ac V nDRe

13 Fluid Mechanics

Symbol

Computer

Symbol

Definition or

Explanation

1313 Boundary conditions

Roughness height or magni-

Roughness height usually in

terms of some average

Sand roughness

Mean diameter of the equiv-

alent sand grains covering a

surface

Hydraulic radius

Area of section divided by

wetted perimeter

13 Fluid Mechanics

Version 2014 132 Flow Fields 30

Symbol

Computer

Symbol

Definition or

Explanation

132 Flow Fields

1321 Velocities etc

Density of total flow

energy

ρ V2 2 + p + ρ g h

Mass specific force

Strength of force fields usu-

ally only gravity field gi

Static pressure head

z0-axis positive vertical up

Total head

e w = h +pw +qw

Pressure density of static

flow energy

Ambient pressure in undis-

turbed flow

Dynamic pressure density

of kinetic flow energy

ρ V2 2

Rate of flow

Volume passing across a

control surface in time unit

Total head loss

ij SR(IJ)

Turbulent or Reynolds stress

ρ vivj

Pa sij

ST(IJ)

Total stress tensor

Density of total diffusive

momentum flux due to mo-

lecular and turbulent ex-

change

ij SV(IJ)

Viscous stress

u vx v1

v vy v2

w vz v3

Velocity component in di-

rection of x y z axes

Velocity

V = vivi

Velocity of undisturbed flow

Wall shear stress

μ (U y)y=0

1322 Circulation etc

13 Fluid Mechanics

Symbol

Computer

Symbol

Definition or

Explanation

Γn CN Normalized circulation Γ (π D V)

π is frequently omitted

Induction factor

Ratio between velocities in-

duced by helicoidal and by

straight line vortices

Vortex density

Strength per length or per

area of vortex distribution

Circulation

intV ds

along a closed line

Potential function

Stream function

ψ = const

is the equation of a stream

surface

13 Fluid Mechanics

Version 2014 133 Lifting Surfaces 32

Symbol

Computer

Symbol

Definition or

Explanation

133 Lifting Surfaces

1331 Geometry

Projected area

Wing or foil span

Flap span

Mean chord length

Tip chord length

Root chord length

Camber of lower side (gen-

Camber of upper side

Sweep angle

Slat deflection angle

Thickness ratio of foil sec-

tion (general)

Thickness ratio of trailing

edge of struts

Camber ratio of mean line

(general)

Angle of flap deflection

Camber ratio of lower side

of foil

Thickness ratio of strut

Theoretical thickness ratio of

section

tS cSTH

Camber ratio of upper side

Taper ratio

Aspect ratio

13 Fluid Mechanics

Symbol

Computer

Symbol

Definition or

Explanation

1332 Flow angles etc

Induced velocity

Resultant velocity of

flow approaching a hydrofoil

Taking vortex induced ve-

locities into account

Angle of attack or incidence

Angle between the direction

of undisturbed relative flow

and the chord line

Effective angle of attack

or incidence

The angle of attack relative

to the chord line including

the effect of induced veloci-

Geometric angle of

attack or incidence

to the chord line neglecting

Hydrodynamic angle

of attack

In relation to the position at

zero lift

Ideal angle of attack

For thin airfoil or hydrofoil

angle of attack for which the

streamlines are tangent to

the mean line at the leading

edge This condition is usu-

ally referred to as shock-

free entry or smooth

Angle of zero lift

at zero lift

13 Fluid Mechanics

Symbol

Computer

Symbol

Definition or

Explanation

1333 Forces

Foil drag

Force in the direction of mo-

tion of an immersed foil

DRIND Induced drag

For finite span foil the com-

ponent of lift in the direction

of motion

Interference drag

Due to mutual interaction of

the boundary layers of inter-

secting foil

Section or profile drag at

zero lift

Streamline drag

Lift force on foil

CL AFT q

Lift force for angle of attack

of zero

CL0 AFT q

1334 Sectional coefficients

CDSE Section drag coefficient

Section induced drag coeffi-

CLSE Section lift coefficient

Section moment coefficient

Lift-Drag ratio

13 Fluid Mechanics

Version 2014 134 Boundary Layers 35

Symbol

Computer

Symbol

Definition or

Explanation

134 Boundary Layers

Skin friction coefficient

τ (ρ Ue

Entrainment factor

1 (Ue dQ dx)

Boundary layer shape pa-

rameter

Entrainment shape parame-

(δ - δ) Θ

Static pressure

Total pressure

Entrainment

Reynolds number based

on displacement thickness

U δ v or Ue δ

RTHETA

on momentum thickness

U Θ v or Ue Θ v

Velocity fluctuations in

boundary layer

Root mean square value

of velocity fluctuations

Non-dimensional distance

from surface

Shear (friction) velocity

(τ ρ)12

Time mean of velocity in

boundary layer

Instantaneous velocity

Free-stream velocity far

from the surface

UE Velocity at the edge of the

boundary layer at y=δ995

Velocity defect in boundary

(Ue- U) uτ

13 Fluid Mechanics

Symbol

Computer

Symbol

Definition or

Explanation

from the wall

y uτ v

Equilibrium parameter

δ (τw dp dx)

Thickness of a boundary

layer at U=0995Ue

δ δ1

Displacement thickness of

boundary layer

(Ue- U) Ue dy

von Karman constant

Pressure gradient parameter

δ995 (v dUe dx)

Energy thickness

(U Ue) (1 - U2 Ue

Momentum thickness

(U Ue) (1 - U Ue)dy

Local skin friction

μ (U y)y=0

13 Fluid Mechanics

Version 2014 135 Cavitation 37

Symbol

Computer

Symbol

Definition or

Explanation

135 Cavitation

Gas content ratio

α αS

Gas content

Actual amount of solved and

undissolved gas in a liquid

Gas content of saturated liq-

Maximum amount of gas

solved in a liquid at a given

temperature

Cavitation number

(pA - pC) q

Inception cavitation number

Vapour cavitation number

(pA - pV) q

1352 Flow fields

Cavity drag

Cavity length

Stream wise dimension of a

fully-developed cavitating

region

Ambient pressure

PACO Collapse pressure

Absolute ambient pressure at

which cavities collapse

Critical pressure

which cavitation inception

takes place

Cavity pressure

Pressure within a steady or

quasi-steady cavity

Initial cavity pressure

Pressure may be negative

ie tensile strength neces-

sary to create a cavity

Vapour pressure of water

At a given temperature

Critical velocity

Free stream velocity at

takes place

Volume loss

13 Fluid Mechanics

Symbol

Computer

Symbol

Definition or

Explanation

WL WTLS

Weight loss

Weight of material eroded

from a specimen during a

specified time

Cavity height or thickness

Maximum height of a fully-

developed cavity normal to

the surface and the stream-

wise direction of the cavity

1353 Pumps

Net useful head of turbo-en-

Total head upstream of

turbo-engines

Thoma number

(HU - pV w) HN

14 Environmental Mechanics

Version 2014 141 Waves 39

Symbol

Computer

Symbol

Definition or

Explanation

141 Waves

This section is related to Sections 312 Time and Frequency Domain Quantities and 313 Random

Quantities and Stochastic Processes

1411 Periodic waves

cW VP Wave phase velocity or ce-

lerity LW TW =

2WgL in

deep water

cWi VP(I) Wave phase velocity of har-

monic components of a peri-

odic wave

const = cW

for periodic waves in deep

cG VG Wave group velocity or ce-

lerity

The average rate of ad-

vance of the energy in a

finite train of gravity

fW FW Basic wave frequency 1 TW Hz

fWi FW(I) Frequencies of harmonic

components of a periodic

i fW Hz

HW HW Wave height The vertical distance from

wave crest to wave

trough or twice the wave

amplitude of a harmonic

wave ηC - ηT

k κ WN Wave number 2 π LW = ω2g 1m

LW λW LW Wave length The horizontal distance

between adjacent wave

crests in the direction of

advance

TW TW Basic wave period Time between the passage

of two successive wave

crests past a fixed point

micro WD Wave direction The angle between the di-

rection of a component

wave and the x0 axis

Symbol

Computer

Symbol

Definition or

Explanation

η EW Instantaneous wave elevation

at a given location

z-axis positive vertical up

zero at mean water level

ηαi EWAM(I) Amplitudes of harmonic

ηFSα m

ηpi εi EWPH(I) Phases of harmonic compo-

nents of a periodic wave

ηFSp rad

ηC EC Wave crest elevation m

ηT ET Wave trough depression Negative values m

ζ DW Instantaneous wave depres-

z-axis positive vertical

down zero at mean water

ζA WAMP Wave amplitude Radius of orbital motion

of a surface wave particle

ωW σ FC Circular wave frequency 2 π fW = 2 π TW rads

1412 Irregular waves

Hd HD Wave height by zero down-

crossing

The vertical distance be-

tween a successive crest and

trough

Hu HU Wave height by zero up-

crossing

tween a successive trough

and crest

Significant wave height

Average of the highest one

third zero down-crossing

wave heights

Significant wave period

Wave periods by zero down-

crossing

By downcrossing analysis

By upcrossing analysis

Time elapsing between two

successive downward cross-

ings of zero in a record

Tu TU Wave periods by zero up-

crossing

successive upward crossings

of zero in a record

ηC EC Maximum of elevations of

wave crests in a record

Symbol

Computer

Symbol

Definition or

Explanation

ηT ET Elevations of wave troughs

in a record

Negative values m

λd LD Wave length by zero down-

crossing

The horizontal distance be-

tween adjacent down cross-

ing in the direction of ad-

λu LU Wave length by zero up-

crossing

tween adjacent up crossing

in the direction of advance

1413 Time Domain Analysis

HWV HWV Wave height estimated from

visual observation

H13d H13D Zero down-crossing signifi-

cant wave height

wave heights

H13u H13U Zero up-crossing significant

wave height

third zero up-crossing wave

heights

Hσ HWDS Estimate of significant wave

height from sample devia-

tion of wave elevation rec-

Wave length estimated by

visual observation

Measured in the direction of

wave propagation

Trt TRT Return period The average interval in years

between times that a given

design wave is exceeded

TR TR Duration of record 1 fR s

TS TS Sample interval 1 fS

time between two successive

samples

TWV TWV Wave period estimated from

visual observation

Symbol

Computer

Symbol

Definition or

Explanation

1414 Frequency Domain Analysis

b B Bandwidth of spectral reso-

lution

Sampling frequency divided

by the number of transform

points

Cr CRA Average reflection coeffi-

Cr(f) CRF Reflection coefficient ampli-

tude function

fP FRPK Spectral peak in frequency Frequency at which the

spectrum has its maximum

fR FRRC Frequency resolution 1 TR Hz

fS FRSA Sample frequency 1 TS Hz

Hmo HMO Significant wave height

based on zeroth moment for

narrow banded spectrum

4 (m0)12 m

mn MN n-th moment of wave

power spectral density

fn S(f)df m2 sn

Si(ω)

Incident wave power spec-

tral density

Sr(ω)

Reflected wave power spec-

tral density

Sη(f)

Sη(ω)

Wave power spectral density m2Hz

TP TP Period with maximum en-

2πfP s

T01 T1 Average period from zeroth

and first moment

m0m1 s

and second moment

(m0m2)12 s

Symbol

Computer

Symbol

Definition or

Explanation

1415 Directional Waves

DX(fθ)

DX(ωμ)

SIGMAOX

Directional spreading func-

S(fθ)=S(f)DX(fθ) where

f FR Frequency 2πω=1T Hz

Sζ (ωμ)

Sθ (ωμ)

Two dimensional spectral

density

Sρ(fθ)

Sζ(ωμ)

STHETA Directional spectral density

θ μ CWD Component wave direction rad

θm MWD

THETAMOX

Mean or dominant wave di-

rection

Version 2014 142 Wind 44

Symbol

Computer

Symbol

Definition or

Explanation

142 Wind

Surface drag coefficient

(008 + 0065U10)10-3

Fetch length

Distance over water the

wind blows

DURATN

Wind duration

Return period

The average interval in

years between times that a

given wind speed is ex-

ceeded

uz uzi

UFLUCT

Turbulent wind fluctua-

USHEAR

Wind shear velocity

12 U10 or 071U10123

Reference mean wind

speed at elevation 10 me-

ters above sea surface

U10 = (10z)17 Uz

Average wind speed at ele-

vation z above the sea sur-

(Uz + uzi)

UzA = (z10)17 U10 or

UzA = U10 + UA ln(z10)

Apparent wind velocity

see section 141

True wind velocity

see section 141

Dimensionless Fetch

Height above the sea sur-

face in meters

Apparent wind angle (rela-

tive to vessel course)

see section 26

True wind angle

(relative to vessel course)

see section 26

Wind direction

Version 2014 143 Ice Mechanics 45

Symbol

Computer

Symbol

Definition or

Explanation

143 Ice Mechanics

EI MEI Modulus of elasticity of ice Pa

SI SAIC Salinity of ice Weight of salt per unit

weight of ice

SW SAWA Salinity of water Weight of dissolved salt per

unit weight of saline water

tA TEAI Temperature of air C

tI TEIC Local temperature of ice C

tW TEWA Temperature of water C

δI ELIC Deflection of ice sheet Vertical elevation of ice sur-

εI STIC Ice strain Elongation per unit length 1

I STRTIC Ice strain rate ε τ 1s

μI POIIC Poissons ratio of ice 1

vA POAI Relative volume of air Volume of gas pores per unit

volume of ice

vB POBR Relative volume of brine Volume of liquid phase per

unit volume of ice

v0 POIC Total porosity of ice v0 = vA + vB 1

ρI DNIC Mass density of ice Mass of ice per unit volume kgm3

ρSN DNSN Mass density of snow Mass of snow per unit vol-

ρW DNWA Mass density of water kgm3

ρΔ DNWI Density difference ρΔ = ρW - ρI kgm3

σCI SCIC Compressive strength of ice Pa

σFI SFIC Flexural strength of ice Pa

σTI SNIC Tensile strength of ice Pa

τSI STIC Shear strength of ice Pa

15 Noise

Version 2014 151 Underwater noise 46

Symbol

Computer

Symbol

Definition or

Explanation

15 Noise

151 Underwater Noise

119889 DIDR Distance hydrophone to

acoustic centre

119871119901 SPL Sound pressure level 119871119901

= 10 log10

(119903119898119904

1199011199031198901198912 ) dB 119901119903119890119891

119871s SRNL Underwater sound radiated

noise level at a reference dis-

tance of 1m

119871s

= 119871p

+ 20 log10 [119889

119889119903119890119891] dB 119889119903119890119891

p SPRE Sound pressure Pa

ITTC Symbols 2 Ships in General

Version 2014 21 Basic Quantities 47

Symbol

Computer

Symbol

Definition or

Explanation

2 SHIPS IN GENERAL

21 Basic Quantities

a a1 AC A1 Linear or translatory acceler-

dv dt ms2

A A AR

Area in general m2

B B BR Breadth m

C FF2 FF(2) Cross force Force normal to lift and drag

(forces)

Cc CC Cross force coefficient C

D FF1 FF(1) Resistance Drag (force) Force opposing translatory ve-

locity generally for a com-

pletely immersed body

d D D DI Diameter m

E E EN Energy J

f FR Frequency 1 T Hz

F F0 F F0 Force N

g G GR Acceleration of gravity Weight force mass strength

of the earth gravity field

h DE Depth m

H H HT Height m

I I IN Moment of inertia Second order moment of a

mass distribution

L L LE Length m

L FF3 FF(3) Lift (force) Force perpendicular to transla-

tory velocity

m M MA

Mass kg

Symbol

Computer

Symbol

Definition or

Explanation

M F1 M1 F1 Moment of forces First order moment of a force

distribution

M MO Momentum Ns

n N FR N Frequency or rate of revolu-

Alias RPS (RPM in some pro-

pulsor applications)

P P PO Power W

r R RD Radius m

R FF1 R RE FF(1) Resistance (force) Force opposing translatory ve-

locity

s SP Distance along path m

t TI Time s

t TE Temperature K

T TC Period Duration of a cycle of a repeat-

ing or periodic not necessarily

harmonic process

U U UN Undisturbed velocity of a

v V1 V V1 Linear or translatory velocity

of a body

ds dt ms

V VO Volume m3

w WD Weight density formerly

specific weight

dW dV = ρg Nm3

W WT Weight (force) gravity force

acting on a body

γ MR Relative mass or weight in

English speaking countries

called specific gravity

Mass density of a substance di-

vided by mass density of dis-

tilled water at 4C

η EF ETA Efficiency Ratio of powers

ρ DN RHO Mass density dm dV kgm3

τ ST TAU Tangential stress Pa

λ SC Scale ratio Ship dimension divided by cor-

responding model dimension

σ SN SIGS Normal stress Pa

ω FC OMF Circular frequency 2 π f 1s

Symbol

Computer

Symbol

Definition or

Explanation

ω V0 V0 OMN Rotational velocity 2 π n rads

22 Geometry and Hydrostatics

Version 2014 221 Hull Geometry 50

Symbol

Computer

Symbol

Definition or

Explanation

221 Hull Geometry

ABL ABL Area of bulbous bow in lon-

gitudinal plane

The area of the ram pro-

jected on the middle line

plane forward of the fore

perpendicular

ABT ABT Area of transverse cross-sec-

tion of a bulbous bow (full

area port and star-board)

The cross sectional area at

the fore perpendicular

Where the water lines are

rounded so as to terminate

on the forward perpendicular

ABT is measured by continu-

ing the area curve forward to

the perpendicular ignoring

the final rounding

AM AM Area of midship section Midway between fore and

aft perpendiculars

AT ATR Area of transom (full area

port and starboard)

Cross-sectional area of tran-

som stern below the load

waterline

AV AV Area exposed to wind Area of portion of ship

above waterline projected

normally to the direction of

relative wind

AW AW Area of water-plane m2

AWA AWA Area of water-plane aft of

midship

AWF AWF Area of water-plane forward

of midship

AX AX Area of maximum transverse

section

B B Beam or breadth moulded

of ships hull

BM BM Breadth moulded of mid-

ship section at design water

Symbol

Computer

Symbol

Definition or

Explanation

BT BTR Breadth moulded of tran-

som at design water line

BWL BWL Maximum moulded breadth

at design water line

BX BX Breadth moulded of maxi-

mum section area at design

water line

d T T Draught moulded of ship

dKL KDROP Design drop of the keel line TAD - TFD alias ldquokeel dragrdquo

or ldquoslope of keelrdquo

D DEP Depth moulded of a ship

f FREB Freeboard From the freeboard markings

to the freeboard deck ac-

cording to official rules

iE ANEN Angle of entrance half Angle of waterline at the

bow with reference to centre

plane neglecting local shape

at stem

iR ANRU Angle of run half Angle of waterline at the

stern with reference to the

centre-plane neglecting lo-

cal shape of stern frame

L L Length of ship Reference length of ship

(generally length between

the perpendiculars)

LE LEN Length of entrance From the forward perpendic-

ular to the forward end of

parallel middle body or

maximum section

LOA LOA Length overall m

LOS LOS Length overall submerged m

LP LP Length of parallel middle

Length of constant trans-

verse section

LPP LPP Length between perpendicu-

Symbol

Computer

Symbol

Definition or

Explanation

LR LRU Length of run From section of maximum

area or after end of parallel

middle body to waterline ter-

mination or other designated

point of the stern

LWL LWL Length of waterline m

LFS LFS Frame spacing used for structures m

LSS LSS Station spacing m

S S AWS Area of wetted surface m2

t TT Taylor tangent of the area

The intercept of the tangent

to the sectional area curve at

the bow on the midship ordi-

T d T Draught moulded of ship

TA dA TA TAP Draught at aft perpendicular m

TAD TAD TAPD Design draught at aft per-

pendicular

TF dF TF TFP Draught at forward perpen-

dicular

TFD TFD TFPD Design draught at forward

perpendicular

TH THUL Draught of the hull Maximum draught of the

hull without keel or skeg

TM dM TM TMS Draught at midship (TA + TF) 2 for rigid bodies

with straight keel

TMD TMD TMSD Design draught at midship (TAD + TFD) 2 for rigid bod-

TT TTR Immersion of transom Vertical depth of trailing

edge of boat at keel below

water surface level

V DISPVOL Displacement volume Δ (ρ g) = BH + AP m3

BH DISPVBH Displacement volume of

bare hull

ΔBH (ρ g) m3

APP DISPVAP Displacement volume of ap-

pendages

ΔAP (ρ g) m3

Symbol

Computer

Symbol

Definition or

Explanation

Δ DISPF Displacement force (buoy-

ancy) g ρ N

ΔBH DISPFBH Displacement force (buoy-

ancy) of bare hull g ρ BH N

ΔAPP DISPFAP Displacement force (buoy-

ancy) of appendages g ρ AP N

Δm DISPM Displacement mass ρ kg

λ SC Linear scale of ship model λ = LS LM = BS BM

= TS TM

2212 Derived Quantities

BC CIRCB RE Froudes breadth coeffi-

cient B 13 1

CB CB Block coefficient (L B T) 1

CGM CGM Dimensionless GM coeffi-

GM 13 1

CGZ CGZ Dimensionless GZ coeffi-

GZ 13 1

CKG CKG Dimensionless KG coeffi-

cient KG T

CIL CWIL Coefficient of inertia of wa-

ter plane longitudinal

12 IL ( B L3) 1

CIT CWIT Coefficient of inertia of wa-

ter plane transverse

12 IT (B3 L) 1

CM CMS Midship section coefficient

(midway between forward

and aft perpendiculars)

AM (B T) 1

CP CPL Longitudinal prismatic coef-

ficient (AX L) or (AM L) 1

CPA CPA Prismatic coefficient after

body A (AX L 2) or

A (AM L 2)

CPE CPE Prismatic coefficient en-

trance E (AX LE) or

E (AM LE)

CPF CPF Prismatic coefficient fore

body F (AX L 2) or

F (AM L 2)

Symbol

Computer

Symbol

Definition or

Explanation

CPR CPR Prismatic coefficient run R (AX LR) or

R (AM LR)

CS CS Wetted surface coefficient S (V L)12 1

CVP CVP Prismatic coefficient vertical (AW T) 1

CWA CWA Water plane area coefficient

AWA (B L 2) 1

CWF CWF Water plane area coefficient

forward

AWF (B L 2) 1

CWP CW Water plane area coefficient AW (L B) 1

CX CX Maximum transverse section

coefficient

AX (B T) where B and T are

measured at the position of

maximum area

C CVOL Volumetric coefficient L3 1

fBL CABL Area coefficient for bulbous

ABL (L T) 1

fBT CABL Taylor sectional area coeffi-

cient for bulbous bow

ABT AX 1

fT ATR Sectional area coefficient for

transom stern

AT AX 1

MC CIRCM RE Froudes length coeffi-

cient or length-displacement

L 13 1

SC CIRCS RE Froudes wetted surface

area coefficient S 23 1

TC CIRCT RE Froudes draught coeffi-

cient T 13 1

2213 Symbols for Attributes and Subscripts

A AB After body

AP AP After perpendicular

APP APP Appendages

B BH Bare hull

DW Design waterline

E EN Entry

Symbol

Computer

Symbol

Definition or

Explanation

F FB Fore body

FP FP Fore perpendicular

FS Frame spacing

H HE Hull

LR Reference Line

LP LP Based on LPP

LW LW Based on LWL

M MS Midships

PB Parallel body

R RU Run

SS Station spacing

W WP Water plane

S WS Wetted surface

Version 2014 222 Propulsor Geometry 56

Symbol

Computer

Symbol

Definition or

Explanation

222 Propulsor Geometry

2221 Screw Propellers

AD AD Developed blade area Developed blade area of a

screw propeller outside the

boss or hub

AE AE Expanded blade area Expanded blade area of a

boss or hub

A0 AO Propeller Disc Area π D2 4 m2

AP AP Projected blade area Projected blade area of a

boss or hub

aD ADR Developed blade area ratio AD A0 1

aE ADE Expanded blade area ratio AE A0 1

aP ADP Projected blade area ratio AP A0 1

c LCH Chord length m

c07 C07 Chord length Chord length at rR=07 m

cLE CHLE Chord leading part The part of the Chord delim-

ited by the Leading Edge

and the intersection between

the Generator Line and the

pitch helix at the considered

radius

cM CHME Mean chord length The expanded or developed

area of a propeller blade di-

vided by the span from the

hub to the tip

cS CS Skew displacement The displacement between

middle of chord and the

blade reference line Positive

when middle chord is at the

trailing side regarding the

blade reference line

Symbol

Computer

Symbol

Definition or

Explanation

cTE CHTE Chord trailing part The part of the Chord delim-

ited by the Trailing Edge and

the intersection between the

Generator Line and the pitch

helix at the considered ra-

dh DH Boss or hub diameter 2 rh m

dha DHA Hub diameter aft Aft diameter of the hub not

considering any shoulder

dhf DHF Hub diameter fore Fore diameter of the hub not

D DP Propeller diameter m

f FBP Camber of a foil section m

GZ GAP Gap between the propeller

blades

2 π r sin (φ) z m

h0 HO Immersion The depth of submergence

of the propeller measured

vertically from the propeller

centre to the free surface

HTC HTC Hull tip clearance Distance between the propel-

ler sweep circle and the hull

iG Rk(ISO) RAKG Rake The displacement from the

propeller plane to the gener-

ator line in the direction of

the shaft axis Aft displace-

ment is positive rake

iS RAKS Rake skew-induced The axial displacement of a

blade section which occurs

when the propeller is

skewed Aft displacement is

positive rake

iT RAKT Rake total The axial displacement of

the blade reference line from

the propeller plane

iG + iS = cS sinφ

Positive direction is aft

lh LH Hub length The length of the hub in-

cluding any fore and aft

shoulder

Symbol

Computer

Symbol

Definition or

Explanation

lha LHA Hub length aft Length of the hub taken

from the propeller plane to

the aft end of the hub includ-

ing aft shoulder

lhf LHF Hub length fore Length of the hub taken

the fore end of the hub in-

cluding fore shoulder

NP NPR Number of propellers 1

p PDR Pitch ratio P D 1

Ρ PITCH Propeller pitch in general m

r LR Blade section radius m

rh RH Hub radius m

R RDP Propeller radius m

t TM Blade section thickness m

t0 TO Thickness on axis of propel-

ler blade

Thickness of propeller blade

as extended down to propel-

ler axis

xB XBDR Boss to diameter ratio dh D

xP XP Longitudinal propeller posi-

Distance of propeller centre

forward of the after perpen-

dicular

yP YP Lateral propeller position Transverse distance of wing

propeller centre from middle

Z z NPB Number of propeller blades 1

zP ZP Vertical propeller position Height of propeller centre

above base line

ε ψbP PSIBP Propeller axis angle meas-

ured to body fixed coordi-

Angle between reference

line and propeller shaft axis

Symbol

Computer

Symbol

Definition or

Explanation

θs TETS Skew angle The angular displacement

about the shaft axis of the

reference point of any blade

section relative to the gener-

ator line measured in the

plane of rotation It is posi-

tive when opposite to the di-

rection of ahead rotation

θ RAKA Angle of rake rad

θEXT TEMX Skew angle extent The difference between

maximum and minimum lo-

cal skew angle

φ PHIP Pitch angle of screw propel-

arctg (P (2 π R)) 1

φF PHIF Pitch angle of screw propel-

ler measured to the face line

ψaP PSIAP Propeller axis angle meas-

ured to space fixed coordi-

Angle between horizontal

plane and propeller shaft

τB Blade thickness ratio t0 D 1

Symbol

Computer

Symbol

Definition or

Explanation

2222 Ducts

ADEN ADEN Duct entry area m2

ADEX ADEX Duct exit area m2

dD CLEARD Propeller tip clearance Clearance between propeller

tip and inner surface of duct

fD FD Camber of duct profile m

LD LD Duct length m

LDEN LDEN Duct entry part length Axial distance between lead-

ing edge of duct and propel-

ler plane

LDEX LDEX Duct exit length Axial distance between pro-

peller plane and trailing edge

of duct

tD TD Thickness of duct profile m

αD AD Duct profile-shaft axis angle Angle between nose-tail line

of duct profile and propeller

βD BD Diffuser angle of duct Angle between inner duct

tail line and propeller shaft

2223 Waterjets (see also section 135)

6nA A Nozzle discharge area m2

Cross sectional area at sta-

tion s

D Impeller diameter (maxi-

Nozzle discharge diameter m

Head between station i and j m

Jet System Head m

maximum height of cross

sectional area of stream tube

at station 1A

Symbol

Computer

Symbol

Definition or

Explanation

Head coefficient 2 5

2224 Pods

APB APB Wetted Surface Area of Pod

Main Body

APBF APBF Wetted Surface Area of Bot-

tom Fin

APS APS Wetted Surface Area of Strut m2

CBFTC CBFTC Thickness Cord Ratio of

Bottom Fin

CSTC CSTC Thickness Cord Ratio of

DPB DPB Maximum Diameter of Pod

LPB LPB Length of Pod Main Body m

LPBF LPBF Length of Bottom Fin Code length of bottom fin

under pod main body

LPS LPS Length of Upper Strut Code length of strut between

forward edge and aft edge

TPBS TPBS Bottom Thickness of Strut m

2225 Operators and identifiers

a absolute (space) reference (superscript)

b body axis reference (superscript)

P propeller shaft axis (subscript)

D Duct (subscript)

Version 2014 223 Appendage Geometry 62

Symbol

Computer

Symbol

Definition or

Explanation

223 Appendage Geometry

Related information may be found in Section 333 on Lifting Surfaces

AC AC Area under cut-up m2

AFB AFB Area of bow fins m2

AFR AFR Frontal area Projected frontal area of an

appendage

ARF AF Projected flap area m2

AR ARU Lateral rudder area Area of the rudder including

ARX ARX Lateral area of the fixed part

of rudder

ARP ARP Lateral area of rudder in the

propeller race

ART ART Total lateral rudder area ARX + ARmov m2

AFS AFS Projected area of stern fins m2

ASK ASK Projected skeg area m2

SWBK SWBK Wetted surface area of bilge

c CH Chord length of foil section m

cM CHME Mean chord length ART S m

cR CHRT Chord length at the root m

cT CHTP Chord length at the tip m

f FM Camber of an aerofoil or a

hydrofoil

Maximum separation of me-

dian and nose-tail line

LF LF Length of flap or wedge Measured in direction paral-

lel to keel

t TMX Maximum thickness of an

aerofoil or a hydrofoil

Measured normal to mean

αFB ANFB Bow fin angle rad

αFS ANFS Stern fin angle rad

δF DELFS Flap angle (general) Angle between the planing

surface of a flap and the bot-

tom before the leading edge

Symbol

Computer

Symbol

Definition or

Explanation

δW DELWG Wedge angle Angle between the planing

surface of a wedge and the

bottom before the leading

δFR ANFR Flanking rudder angle rad

δFRin ANFRIN Assembly angle of flanking

rudders

Initial angle set up during

the assembly as zero angle

of flanking rudders

δR ANRU Rudder angle rad

δRF ANRF Rudder-flap angle rad

λR TARU Rudder taper cT cR 1

λFR TAFR Flanking rudder taper 1

ΛR ASRU Rudder aspect ratio bR2 ART 1

ΛFR ASRF Flanking rudder aspect ratio

2232 Identifiers for Appendages (Subscripts)

BK Bilge keel

BS Bossing

FB Bow foil

FR Flanking rudder

FS Stern foil

KL Keel

RU Rudder

RF Rudder flap

SA Stabilizer

SH Shafting

SK Skeg

ST Strut

TH Thruster

WG Wedge

Version 2014 224 Hydrostatics and Stability 64

Symbol

Computer

Symbol

Definition or

Explanation

224 Hydrostatics and Stability

2241 Points and Centres (Still under construction)

Assumed centre of gravity

above keel used for cross

curves of stability

Centre of flotation of added

buoyant layer or centre of

lost buoyancy of the flooded

volume

Centre of buoyancy

Centroid of the underwater

volume

Centre of flotation of the wa-

ter plane

Centre of gravity of an

added or removed weight

(mass)

Centre of gravity of a vessel

Keel reference

Metacentre of a vessel

See subscripts for qualifica-

XCB LCB

Longitudinal centre of buoy-

ancy (LCB)

Longitudinal distance from

reference point to the centre

of buoyancy B such as XMCF

from Midships

XCF LCF

Longitudinal centre of flota-

tion (LCF)

of flotation F such as XMCF

from Midships

xCb XACB Longitudinal centre of buoy-

ancy of added buoyant layer

of buoyancy of the added

buoyant layer b such as xMCb

from Midships

Symbol

Computer

Symbol

Definition or

Explanation

xCf XACF Longitudinal centre of flota-

tion of added buoyant layer

of flotation of the added

buoyant layer f such as xMCf

from Midships

Longitudinal centre of grav-

ity of added weight (mass)

reference to the centre of

gravity g of an added or re-

moved weight (mass) such

as xMCg from Midships

XCG LCG

ity (LCG)

Longitudinal distance from a

of gravity G such as XMCG

from Midships

Lateral displacement of cen-

tre of gravity (YCG)

Lateral distance from a ref-

erence point to the centre of

gravity G

Intersection of righting arm

with line of action of the

centre of buoyancy

2242 Static Stability levers

XAB Longitudinal centre of buoy-

ancy from aft perpendicular

Distance of centre of buoy-

XAF Distance of centre of flota-

tion from aft perpendicular

L XAG Longitudinal centre of grav-

ity from aft perpendicular

Distance of centre of gravity

from aft perpendicular

T YAG Transverse distance from as-

sumed centre of gravity A

to actual centre of gravity G

V ZAG Vertical distance from as-

YAZ Righting arm based on hori-

zontal distance from as-

Generally tabulated in cross

curves of stability

Symbol

Computer

Symbol

Definition or

Explanation

ZBM Transverse metacentre above

centre of buoyancy

Distance from the centre of

buoyancy B to the transverse

metacentre M

L ZBML Longitudinal metacentre

above centre of buoyancy L -

XFB Longitudinal centre of buoy-

ancy LCB from forward per-

pendicular

ancy from forward perpen-

dicular

XFF Longitudinal centre of float-

ation LCF from forward per-

pendicular

Distance of centre of flota-

tion from forward perpendic-

XFG Longitudinal centre of grav-

ity from forward perpendicu-

from forward perpendicular

HGG GGH Horizontal stability lever

caused by a weight shift or

weight addition

LGG GGL Longitudinal stability lever

weight addition

1GG VGG GG1 GGV Vertical stability lever

weight addition

101 GGKGKG m

GM Transverse metacentric

height

to the metacentre

EFFGM GMEFF Effective transverse meta-

centric height corrected for free sur-

face andor free communica-

tion effects

LGM GML Longitudinal centre of meta-

centric height

gravity G to the longitudinal

metacentre ML

KGKMGM LL

GZ Righting arm or lever sinVAGAZGZ ndash

TAG cosφ

KB-KM =I =BM T

BM KM KB

Symbol

Computer

Symbol

Definition or

Explanation

MAXGZ GZMAX Maximum righting arm or

ZKA Assumed centre of gravity

above moulded base or keel

Distance from the assumed

centre of gravity A to the

moulded base or keel K

ZKB Centre of buoyancy above

moulded base or keel

buoyancy B to the moulded

base or keel K

ZKG Centre of gravity above

Distance from centre of

gravity G to the moulded

base or keel K

ZKAG Vertical centre of gravity of

gravity g to the moulded

base or keel K

ZKM Transverse metacentre above

Distance from the transverse

metacentre M to the

ZKML Longitudinal metacentre

Distance from the longitudi-

nal metacentre ML to the

l XTA Longitudinal trimming arm xCG - xCB m

t YHA Equivalent transverse heel-

ing arm

Heeling moment Δ m

GM 13 1

GZ 13 1

cient KG T

CMTL CMTL Longitudinal trimming coef-

ficient

Trimming moment divided

by change in trim which ap-

proximately equals

Symbol

Computer

Symbol

Definition or

Explanation

2244 Intact and Damage (Flooded) Stability

ficient

trimming moment divided

proximately equals

ASI IAS ASI Attained subdivision index (to be clarified) 1

MS MS Moment of ship stability in

general Other moments such

as those of capsizing heel-

ing etc will be represented

by MS with additional sub-

scripts as appropriate

m SHIPMA Ship mass W g kg

MTC MTC Moment to change trim by

one centimetre

MTM MTM Moment to change trim by

one meter

ΔCMTL Nmm

RSI RSI Required subdivision index 1

ts tKL TRIM Static trim TA - TF - dKL m

W SHIPWT Ship weight m g N

zSF ZSF Static sinkage at FP Caused by loading m

zSA ZSA Static sinkage at AP Caused by loading m

zS ZS Mean static sinkage (zSF + zSA) 2 m

δ D Finite increment in Prefix to other symbol 1

δtKL DTR Change in static trim m

Δ DISPF Displacement (buoyant)

force g ρ N

DISPVOL Displacement volume Δ (ρg) m3

fw DISVOLFW Displacement volume of

flooded water

Δfw (ρg) m3

θS TRIMS Static trim angle tan-1((zSF - zSA) L) rad

Symbol

Computer

Symbol

Definition or

Explanation

μ PMVO Volumetric permeability The ratio of the volume of

flooding water in a compart-

ment to the total volume of

the compartment

HEELANG Heel angle rad

F HEELANGF Heel angle at flooding rad

VS HEELANGV Heel angle for vanishing sta-

bility

2245 Symbols for Attributes and Subscripts (under construction)

a apparent

A att attained

d dyn dynamic

e EFF effective

f false

KL keel line

L longitudinal

MAX maximum

MTL longitudinal trimming moment

R req required (to be clarified)

s Static

S sqt Sinkage squat

TC Trim in cm

TM Trim in m

T transverse

V vertical

0 Initial

at heel angle

θ at trim angle θ

23 Resistance and Propulsion

Version 2014 231 Hull Resistance 70

Symbol

Computer

Symbol

Definition or

Explanation

231 Hull Resistance

(see also Section 141 on Waves)

m BLCK Blockage parameter Maximum transverse area of

model ship divided by tank

cross section area

RA RA Model-ship correlation al-

lowance

Incremental resistance to be

added to the smooth ship re-

sistance to complete the

model-ship prediction

RAA RAA Air or wind resistance N

RAPP RAP Appendage resistance N

RAR RAR Roughness resistance N

RC RC Resistance corrected for dif-

ference in temperature be-

tween resistance and self-

propulsion tests

RTM[(1 + k) CFMC + CR]

[(1 + k) CFM + CR]

where CFMC is the frictional

coefficient at the temperature

of the self-propulsion test

RF RF Frictional resistance of a

Due to fluid friction on the

surface of the body

RF0 RF0 Frictional resistance of a flat

RP RP Pressure resistance Due to the normal stresses

over the surface of a body

RPV RPV Viscous pressure resistance Due to normal stress related

to viscosity and turbulence

RR RR Residuary resistance RT - RF or RT - RF0 N

RRBH RRBH Residuary resistance of the

bare hull

RS RS Spray resistance Due to generation of spray N

RT RT Total resistance Total towed resistance N

RTBH RTBH Total resistance of bare hull N

RV RV Total viscous resistance RF + RPV N

RW RW Wave making resistance Due to formation of surface

RWB RWB Wave breaking resistance Associated with the break

down of the bow wave

RWP RWP Wave pattern resistance N

S S Wetted surface area under-

SBH + SAPP m2

S0 S0 Wetted surface area at rest SBH0 + SAPP0 m2

Symbol

Computer

Symbol

Definition or

Explanation

SAPP SAP Appendage wetted surface

area underway

SAPP0 SAP0 Appendage wetted surface

area at rest

SBH SBH Bare Hull wetted surface

area underway

SBH0 SBH0 Bare Hull wetted surface

area at rest

ΔCF DELCF Roughness allowance 1

V V Speed of the model or the

VKN VKN Speed in knots

VWR VWR Wind velocity relative ms

zVF ZVF Running sinkage at FP m

zVA ZVA Running sinkage at AP m

zVM ZVM Mean running sinkage (zVF + zVA) 2 m

η EW Wave Elevation see 341 m

θV θD TRIMV Running (dynamic) trim an-

tan-1((zVF - zVA) L) 1

τW LSF TAUW Local skin friction see 334 N m2

CA CA Incremental resistance coef-

ficient for model ship corre-

lation

RA (S q) 1

CAA CAA Air or wind resistance coef-

ficient

RAA (AV qR) 1

CAPP CAPP Appendage resistance coeffi-

RAPP (S q) 1

CD CD Drag coefficient D (S q) 1

CF CF Frictional resistance coeffi-

cient of a body

RF (S q) 1

CF0 CF0 Frictional resistance coeffi-

cient of a corresponding

RF0 (S q) 1

Cp CP Local pressure coefficient 1

CPR CPR Pressure resistance coeffi-

cient including wave effect

RP (S q) 1

CPV CPV Viscous pressure resistance

coefficient

RPV (S q) 1

Symbol

Computer

Symbol

Definition or

Explanation

CR CR Residuary resistance coeffi-

RR (S q) 1

CS CSR Spray resistance coefficient RS (S q) 1

CT CT Total resistance coefficient RT (S q) 1

CTL CTLT Telfers resistance coeffi-

g R L (ΔV2) 1

CTQ CTQ Qualified resistance coeffi-

cient CT (ηH ηR) 1

CT CTVOL Resistance displacement RT (23 q) 1

CV CV Total viscous resistance co-

efficient

RV (S q) 1

CW CW Wave making resistance co-

efficient

RW (S q) 1

CWP CWP Wave pattern resistance co-

efficient by wave analysis

CC CIRCC RE Froudes resistance co-

efficient

1000 R (Δ(KC)2)

FC CIRCF RE Froudes frictional re-

sistance coefficient

1000 RF (Δ(KC)2) 1

f FC Friction coefficient Ratio of tangential force to

normal force between two

sliding bodies

k K Three dimensional form fac-

tor on flat plate friction

(CV - CF0) CF0 1

k(θ) WDC Wind direction coefficient CAA CAA0 1

KC CIRCK RE Froudes speed dis-

placement coefficient (4 π)12 Fr or

(4πg)12VK16

KR KR Resistance coefficient corre-

sponding to KQ KT

R (ρ D4 n2) 1

q PD EK Dynamic pressure density

ρ V2 2

see 332

qR PDWR

Dynamic pressure based on

apparent wind

ρ VWR2 2

see 342

SC CIRCS R E Froudersquos wetted sur-

face coefficient S 23 1

Symbol

Computer

Symbol

Definition or

Explanation

ε EPSG Resistance-displacement ra-

tio in general

R Δ 1

εR EPSR Residuary resistance-dis-

placement ratio

RR Δ 1

FW Fresh water

MF Faired model data

MR Raw model data

OW Open water

SF Faired full scale data

SR Raw full scale data

SW Salt water

Version 2014 232 Ship Performance 74

Symbol

Computer

Symbol

Definition or

Explanation

232 Ship Performance

FD SFC Friction deduction force in

self propulsion test

Towing force applied to a

model to correct the model

resistance for different Re

between model and full

Force pulling or towing a

Pull during bollard test

Frequency commonly rate

of revolution

Brake power

Power delivered by prime

Delivered power

propeller power

Effective power

resistance power

Indicated power

Determined from pressure

measured by indicator

Shaft power

Power measured on the shaft

Thrust power

Torque

Running trim

Ship speed

Propeller advance speed

Equivalent propeller open

water speed based on thrust

or torque identity

Running sinkage of model or

Rotational shaft velocity

2 π n

Symbol

Computer

Symbol

Definition or

Explanation

Resistance augment fraction

(T - RT) RT

Admiralty coefficient

Δ23 V3 PS

Power-displacement coeffi-

PD (ρ V3 23 2)

Trial correction for propeller

rate of revolution at speed

identity

rate of revolution at power

identity

PDT PDS

Trial correction for delivered

Ship model correlation fac-

tor for propulsive efficiency

ηDS ηDM

tor for propeller rate revolu-

Appendage correction

factor

Scale effect correction factor

for model appendage drag

applied at the towing force

in a self-propulsion test

Sinkage dynamic

Change of draught fore and

aft divided by length

Trim dynamic

Change of the trim due to

dynamic condition divided

by length

Thrust deduction fraction

(T - RT) T

Taylor wake fraction in gen-

(V - VA) V

Froude wake fraction

(V - VA) VA

Torque wake fraction

Propeller speed VA deter-

mined from torque identity

Thrust wake fraction

mined from thrust identity

Symbol

Computer

Symbol

Definition or

Explanation

Ship-model correlation fac-

tor for wake fraction

wTM - wTS

tor with respect to wTS

method formula of ITTC

1978 method

Load fraction in power pre-

diction

ηD PD PE - 1

Appendage scale effect fac-

Ship appendage resistance

divided by model appendage

resistance

2323 Efficiencies etc

Appendage efficiency

PEw0APP PEwAPP RTBH RT

Propeller efficiency behind

PT PD = T VA (Q ω)

Quasi-propulsive efficiency

coefficient

PE PD = PR PP

Gearing efficiency

Hull efficiency

PE PT = PR PT

= (1 - t) (1 - w)

Mechanical efficiency of

transmission between engine

and propeller

Propeller efficiency in open

PT PD = T VA (Q ω) all

quantities measured in open

water tests

Propulsive efficiency coeffi-

Relative rotative efficiency

ηB ηO

Shafting efficiency

PD PS = PP PS

Version 2014 233 Propulsor Performance 77

Symbol

Computer

Symbol

Definition or

Explanation

233 Propulsor Performance

A0 AO Propeller disc area π D2 4 m2

n FR Propeller frequency of revo-

lution

κS KS Roughness height of propel-

ler blade surface

qA QA Dynamic pressure based on

advance speed

ρ VA2 2

qS QS Dynamic pressure based on

section advance speed

ρ VS2 2 Pa

QS QSP Spindle torque About spindle axis of con-

trollable pitch propeller

QS=QSC+ QSH

positive if it increases pitch

QSC QSPC Centrifugal spindle torque Nm

QSH QSPH Hydrodynamic spindle

torque

T TH Propeller thrust N

TD THDU Duct thrust N

TDP THDP Ducted propeller thrust N

TDT THDT Total thrust of a ducted pro-

peller unit

TxP TXP Propeller Thrust along shaft

TyP TYP Propeller normal force in y

direction in propeller axis

TzP TZP Propeller normal force in z

VA VA Advance speed of propeller ms

VP VP Mean axial velocity at pro-

peller plane of ducted pro-

peller

Symbol

Computer

Symbol

Definition or

Explanation

VS VS Section advance speed

at 07 R

(VA2+ (07 R ω)2)12

ρP DNP Propeller mass density kgm3

ω V0P Propeller rotational velocity 2 π n 1s

BP BP Taylors propeller coefficient

based on delivered horse-

n PDfrac12 VA

with n in revsmin

PD in horsepower and

VA in kn (obsolete)

BU BU Taylors propeller coefficient

based on thrust horsepower

n PTfrac12 VA

with n in revsmin

PT in horsepower and

VA in kn (obsolete)

CP CPD Power loading coefficient PD (AP qA VA) 1

CQ CQS Torque index Q (AP qS D) 1

CTh CTH Thrust loading coefficient

energy loading coefficient

T (AP qA)

= (TP AP) qA

CT CTHS Thrust index T (AP qS) 1

J JEI Propeller advance ratio VA (D n) 1

JA JH JA JH Apparent or hull advance ra-

V (D n) = VH (D n) 1

JP JP Propeller advance ratio for

ducted propeller

VP (D n)

JT JPT JT JPT Advance ratio of propeller

determined from thrust iden-

JQ JPQ JQ JPQ Advance ratio of propeller

determined from torque

identity

KP KP Delivered power coefficient PD (ρ n3 D5) = 2 π KQ 1

KQ KQ Torque coefficient Q (ρ n2 D5) 1

KSC KSC Centrifugal spindle torque

coefficient

QSC (ρ n2 D5) 1

Symbol

Computer

Symbol

Definition or

Explanation

KSH KSH Hydrodynamic spindle

torque coefficient

QSH (ρ n2 D5) 1

KT KT Thrust coefficient T (ρ n2 D4) 1

KTD KTD Duct thrust coefficient TD (ρ n2 D4) 1

KTP KTP Ducted propeller thrust coef-

ficient

TP (ρ n2 D4) 1

KTT KTT Total thrust coefficient for a

ducted propeller unit

KTP+ KTD 1

KQ0 KQ0 Torque coefficient of propel-

ler converted from behind to

open water condition

KQηR 1

KQT KQT Torque coefficient of propel-

ler determined from thrust

coefficient identity

PJ PJ Propeller jet power ηTJ T VA

SA SRA Apparent slip ratio 1 - V (n P) 1

SR SRR Real slip ratio 1 - VA (n P) 1

δ ADCT Taylors advance coefficient n D VA

with n in revsmin D in

feet VA in kn

ηJP EFJP Propeller pump or hydraulic

efficiency

PJ PD = PJ PP 1

ηJP0 ZET0

Propeller pump efficiency at

zero advance speed

alias static thrust coefficient

T (ρ π 2)13 (PD D)23 1

ηI EFID Ideal propeller efficiency Efficiency in non-viscous

ηTJ EFTJ Propeller jet efficiency 2 (1 + (1 + CTh)12) 1

η0 ηTP0 ETA0

water tests

λ ADR Advance ratio of a propeller VA (n D) π = J π 1

τ TMR Ratio between propeller

thrust and total thrust of

ducted propeller

TP TT 1

Symbol

Computer

Symbol

Definition or

Explanation

2333 Induced Velocities etc

Axial velocity induced by

propeller

duct of ducted propeller

Radial velocity induced by

propeller of ducted propeller

propeller

Tangential velocity induced

by duct of ducted propeller

by propeller of ducted pro-

peller

by propeller

Advance angle of a propeller

blade section

arctg (VA r ω)

Hydrodynamic flow angle of

a propeller blade section

Flow angle taking into ac-

count induced velocity

Effective advance angle

arctg (VA (07 R ω))

Version 2014 234 Unsteady Propeller Forces 81

Symbol

Computer

Symbol

Definition or

Explanation

234 Unsteady Propeller Forces

Cuv SI(UV) Generalized stiffness

Duv DA(UV) Generalized damping

Fu FG(I) Generalized vibratory

u = 1 6

u = 1 2 3 force

u = 4 5 6 moment

Fi F(I) Vibratory force i = 1 2 3 N

KFu KF(U) Generalized vibratory force

coefficients

According to definitions of

KFi and KMi

KFi KF(I) Vibratory force coefficients Fi (ρ n2 D4) 1

KMi KM(I) Vibratory moment coeffi-

cients

Mi (ρ n2 D5) 1

Kp KPR Pressure coefficient p (ρ n2 D2) 1

Mi M(I) Vibratory moment i = 1 2 3 Nm

Muv MA(UV) Generalized mass

p PR Pressure Pa

Ru R(U) Generalized vibratory bear-

ing reaction

u = 1 6

u = 1 2 3 force

u = 4 5 6 moment

Vi V(I) Velocity field of the wake i = 1 2 3 ms

Cartesian coordinates Origin O coinciding with the

centre of the propeller The

longitudinal x-axis coincides

with the shaft axis positive

forward the trans-verse y-

axis positive to port the

third z-axis positive upward

Cylindrical coordinates Cylindrical system with

origin O and longitudinal x-

axis as defined before angu-

lar a-(attitude)-coordinate

zero at 12 oclock position

positive clockwise looking

forward r distance measured

from the x-axis

Symbol

Computer

Symbol

Definition or

Explanation

u DP(U) Generalized vibratory dis-

placement

u = 1 6

u = 1 2 3 linear

u = 4 5 6 angular

DPVL(U) Generalized vibratory veloc-

u = 1 6

u = 1 2 3 linear

u = 4 5 6 angular

DPAC(U) Generalized vibratory accel-

eration

u = 1 6

u = 1 2 3 linear

u = 4 5 6 angular

Version 2014 235 Water Jets 83

Symbol

Computer

Symbol

Definition or

Explanation

235 Water Jets

Cp CP Local pressure coefficient (p-p0)(ρ Vsup22) 1

Thrust loading coefficient net

210 n2

Energy velocity coefficient

at station s

Momentum velocity coeffi-

cient at station s

Dp Pressure differential of flow

rate transducer

Ej EJ Energy flux at station j

Ej = (ρ2)VEj2dQj

Total energy flux at station s

(kinetic + potential + pres-

j j i i

pg x u n dA

sE Total axial (in direction)

energy flux at station s

j j i i

pu g x u n dA

Skin friction correction in a

self propulsion test carried

out at the ship self-propul-

sion point

H1 HT1 Local total head at station 1 m

H35 H35 Mean increase of total head

across pump and stator or

several pump stages

IVR IVR Intake velocity ratio VIV 1

JVR JVR Jet velocity ratio VJV 1

Impeller torque coefficient 2 5

Flow rate coefficient J

siM Momentum flux at station s

in i direction

u u n dA

NVR Nozzle velocity ratio 6

Symbol

Computer

Symbol

Definition or

Explanation

Tjx TJX Jet thrust (can be measured

directly in bollard pull con-

dition)

n Impeller rotation rate

Unit normal vector in i direc-

Delivered Power to pump

impeller

Effective power TBH 0R U

Effective Jet System Power J 1A7Q H

Pump effective power J 35Q H

ETP Effective thrust power W

p0 PR0 Ambient pressure in undis-

turbed flow

Local static pressure at sta-

tion s

Q Impeller torque Nm

Qbl Volume flow rate inside

boundary layer

msup3s

Volume flow rate through

water jet system

msup3s

Total resistance of bare hull N

jet xT

Jet thrust (can be measured

dition)

Net thrust exerted by the jet

system on the hull

t Thrust deduction fraction TBH

Free stream velocity

e siu Mean energy velocity in i di-

rection at station s

Symbol

Computer

Symbol

Definition or

Explanation

esu Mean (total) energy velocity

at station s

Velocity component in i-di-

su Velocity at station s

u7φ UJFI Local tangential velocity at

station 7

Geometric intake width at

station 1

Width of capture area meas-

ured over hull surface at sta-

tion 1A

Vertical distance of nozzle

centre relative to undisturbed

surface

ΔM DMF Change of momentum flux N

xM Change in Momentum Flux

in x direction

D Overall propulsive effi-

ciency E

Ducting efficiency JSE

Energy interaction effi-

ciency JSE0

I Ideal efficiency equivalent

to jet efficiency in free

stream conditions

Installation efficiency to ac-

count for the distorted flow

delivered by the jet intake to

the pump

Total interaction efficiency eI

Momentum or jet efficiency TE

Symbol

Computer

Symbol

Definition or

Explanation

Jet system efficiency JSE

Momentum interaction effi-

ciency

P ETAP Pump efficiency PE

Pump efficiency from a

pump loop test

0 Free stream efficiency

P duct I

n Jet angle relative to the hori-

zontal at the nozzle (station

Mass density of fluid kgmsup3

Energy loss coefficient be-

tween station i and j

ZETA13 Inlet duct loss coefficient 3 1

ZETA57 Nozzle duct loss coefficient 7 5

24 Manoeuvrability and Sea Keeping

Version 2014 241 Manoeuvrability 87

Symbol

Computer

Symbol

Definition or

Explanation

241 Manoeuvrability

2411 Geometrical Quantities

See also Section 221 on Hull Geometry

Area of jib or genoa

Lateral area of keel

Total lateral area of yacht

Area of mainsail

Normalized sail area

Area of spinnaker

Sail area in general

(P E + I J) 2

Beam overall

Center of pressure for Ai

Mainsail base

Fore triangle height

Fore triangle base

Mainsail height

Effective length for Reyn-

olds Number

Wetted surface area of ca-

noe body

Wetted surface area of keel

Wetted surface area of rud-

Draught of canoe body

Effective draught

FH (ρVB

Height of centre of effort of

sails above waterline in ver-

tical centre plane

Displaced volume of canoe

Displaced volume of keel

36 Sailing Vessels

Symbol

Computer

Symbol

Definition or

Explanation

Displaced volume of rudder

Displacement force

(weight) of canoe body

Displacement force

(weight) of keel

Displacement force

(weight) of rudder

36 Sailing Vessels

Symbol

Computer

Symbol

Definition or

Explanation

362 Resistance and Propulsion CFU

Frictional resistance coeffi-

cient (upright)

RFU (S q)

Residuary resistance coeffi-

cient (upright)

RRU (S q)

Total resistance

coefficient (upright)

RTU (S q)

Wave resistance coefficient

(upright)

Total resistance coefficient

with heel and leeway

RTφ (S q)

Induced resistance coeffi-

Cx Cy Cz

Force coefficients

Heeling force of sails

Driving force of sails

Vertical force of sails

Side force

Hydrodynamic lift force

Added Resistance in waves

Friction resistance (upright)

Residuary resistance (up-

right)

Resistance increase due to

side (induced resistance)

Total resistance (upright)

Total resistance when heeled

RTU + Rφ

Rφ RH

heel (with zero side force)

Components of resultant

force along designated axis

Vessel velocity

36 Sailing Vessels

Symbol

Computer

Symbol

Definition or

Explanation

True wind velocity

Velocity made good on

course

Velocity made good to wind-

ward (contrary to wind direc-

leaway angle

apparent wind angle (relative

to boat course)

true wind angle (relative to

boat course)

ITTC Symbols 4 Background and references

Version 2014 130

4 BACKGROUND AND

REFERENCES

41 Symbols and Terminology Group

The tasks of the former Symbols and Termi-

nology Group (SaT) have been handed over to

the Quality Systems Group in 2002

42 Description of the List of Symbols

421 Classification

The prime concern of the QS Group was to

revise and try to complement the list of ITTC

Standard Symbols sticking to the system for the

classification of concepts

With this regard the following design re-

quirements and goals have been maintained

1 a coherent document meeting the pre-

sent and possibly the future require-

ments of the ITTC community in gen-

eral and particular user groups

2 an open ended matrix structure that can

be easily expanded as requirements

arise without the need of restructuring

and repetition or too many explicit

cross-references

3 minimized departures from the well es-

tablished and widely accepted previous

list of symbols

On the other hand to facilitate the practical

use of the list a second version in which the

symbols are arranged in alphabetic order was

prepared Symbols which have been listed sev-

eral times in the matrix structured document

have been maintained and for each symbol the

field in which it is used is given in italic letters

prior to the meaning of the symbol

422 Structure of the Lists

The concepts related to a given subject area

or model are designated by the ITTC Symbol

and called by their Name Their meaning can in

principle only be concluded from the context of

the model The logically consistent so called

implicit definition is derived from a definitely

defined statement of the model ideally a gener-

ally accepted system or an equivalent eg a

drawing

The problem is that traditionally in lists of

symbols as in dictionaries these explicit mod-

els are missing for various reasons One reason

is that many subject areas under discussion are

far from being developed and understood to the

extent necessary A consequence of this situa-

tion is that the symbols proposed are not always

as coherent as would be necessary for advanced

and systematic work for which explicit models

and adequate notations are essential

The problem under discussion is of course

the same in national and international standards

However there is an accepted international

standard which deals with the general principles

concerning physical quantities equations quan-

tity and unit symbols and coherent unit systems

for general use within the various fields of sci-

ence and technology (ISO 31

423 Organization of the matrix structured

As has been emphasized the development of

symbols is a continuing process and as the sub-

ject develops further amendments and additions

as approved by the Conference will be included

in future editions of the list

In order to avoid any extra problems the

symbols are arranged in alphabetical order in

each subject area as in previous lists Continu-

ous page numbering was discarded in earlier

Version 2014 131 versions The idea was to establish a loose leaf

organization as the most appropriate in view of

new draughts to be incorporated

In view of the tremendous effort which ex-

plicit mathematical models explanations and

sketches take for their preparation the present

QS Group can only follow the former SaT

Group and state that the Technical Committees

and other interested parties are urged to provide

further material for review by the QS Group and

future inclusion into the list

It has been noted that some users dislike the

disruption of the list of symbols by lengthy ex-

planations The present QS Group feels that the

subject and the sensible use of the symbols re-

quire such explanations also as the fundamen-

tals of the theory of science and terminology of-

ten are not taught to students of naval architec-

ture and marine engineering However the ar-

rangement has been changed so that these expla-

nations can be visited by using hyperlinks and

the list is not disrupted any more

ITTC Symbols 5 Principles of notation

Version 2014 132 5 PRINCIPLES OF NOTATION

In Fig 1 the principles of notation in accord-

ing to ISO 31 are shown

Symbols representing physical quantities

normally are one Latin or Greek letter with Sub-

scripts for further identification They are writ-

ten in italic style letters

Numbers are normally written in roman

style letters For more details look at the list be-

low or in the Excerpts of ISO 31 below or in

standard itself

Superscripts signify operators eg

exponentiation

the various aspects of complex quantities

the various aspects of spectra and

the various aspects of random quantities

and stochastic processes eg probability

operators

Subscripts signify identifiers

matrix components

identifiers tested eg ship S or model M

appendages (App)or the various bodies

in a multi-body problem

identifiers of coordinate systems and of

the reference points quantities( LPP)

Symbols for physical units italic one letter except dimensionless

quantities

A ( eg Area in

msup2)

Symbols for characteristic num-

2 letters italic Re Fr

Numbers roman generally 103

Symbols representing numbers italic xij

Units roman lower case unless derived from

Prefix of units roman microm

Symbols for chemical elements roman H2O

Symbols for universal constants italic g = 980665 mssup2

ITTC Symbols 5 Principles of Notation

51 Excerpt of ISO 31

Version 2011 133

Superscripts signify Operators

Numbers in roman

(power of n)

Symbols representing numbers

(n = 1 2 3 etc) in italic

SYMBOLS

in italic

NUMBERS

in roman

Subscripts signify Identifiers

Symbol for physical quantity in italic

(T = Thrust)

Other symbols in roman

(M = Model) Fig 1

51 Excerpts of ISO 31

1 Scope

This part of ISO 31 gives general infor-

mation about principles concerning physical

quantities equations quantity and unit symbols

and coherent unit systems especially the Inter-

national System of Units SI

The principles laid down in this part of ISO

31 are intended for general use within the vari-

ous fields of science and technology and as a

general introduction to the other parts of ISO 31

2 Quantities and units

21 Physical quantity unit and numerical

In ISO 31 only physical quantities used for

the quantitative description of physical phenom-

ena are treated Conventional scales such as the

Beaufort scale Richter scale and colour inten-

sity scales and quantities expressed as the re-

sults of conventional tests eg corrosion re-

sistance are not treated here neither are curren-

cies nor information contents

Physical quantities may be grouped together

into categories of quantities which are mutually

comparable Lengths diameters distances

heights wavelengths and so on would constitute

such a category Mutually comparable quantities

are called quantities of the same kind

If a particular example of a quantity from

such a category is chosen as a reference quan-

tity called the unit then any other quantity from

this category can be expressed in terms of this

unit as a product of this unit and a number This

number is called the numerical value of the

TK 102

Version 2014 134 quantity expressed in this unit

In formal treatments of quantities and units

this relation may be expressed in the form

A=A-[A]

where A is the symbol for the physical quantity

[A] the symbol for the unit and A symbolizes

the numerical value of the quantity A expressed

in the unit [A] For vectors and tensors the com-

ponents are quantities which may be expressed

as described above

If a quantity is expressed in another unit

which is k times the first unit then the new nu-

merical value becomes 1k times the first numer-

ical value the physical quantity which is the

product of the numerical value and the unit is

thus independent of the unit

REMARK ON NOTATION FOR

NUMERICAL VALUES

It is essential to distinguish between the

quantity itself and the numerical value of the

quantity expressed in a particular unit The nu-

merical value of a quantity expressed in a par-

ticular unit could be indicated by placing braces

(curly brackets) around the quantity symbol and

using the unit as a subscript It is however pref-

erable to indicate the numerical value explicitly

as the ratio of the quantity to the unit

22 Quantities and equations

221 Mathematical operations with quanti-

Two or more physical quantities cannot be

added or subtracted unless they belong to the

same category of mutually comparable quanti-

Physical quantities are multiplied or divided

by one another according to the rules of algebra

the product or the quotient of two quantities A

and B satisfies the relations

AB = A B - [A] [B]

Thus the product A B is the numerical

value AB of the quantity AB and the product

[A] [B] is the unit [AB] of the quantity AB Sim-

ilarly the quotient AB) is the numerical

value AB of the quantity AB and the quo-

tient [A][B] is the unit [AB] of the quantity

222 Equations between quantities and equa-

tions between numerical values

Two types of equation are used in science and

technology equations between quantities

in which a letter symbol denotes the physical

quantity (ie numerical value times unit) and equa-

tions between numerical values Equations

between numerical values depend on the choice

of units whereas equations between quantities

have the advantage of being independent of this

choice Therefore the use of equations between

quantities should normally be preferred

223 Empirical constants

An empirical relation is often expressed in the

form of an equation between the numerical val-

ues of certain physical quantities Such a relation

depends on the units in which the various physi-

cal quantities are expressed

An empirical relation between numerical val-

ues can be transformed into an equation between

physical quantities containing one or more em-

pirical constants Such an equation between

physical quantities has the advantage that the

form of the equation is independent of the choice

of the units The numerical values of the empiri-

cal constants occurring in such an equation de-

pend however on the units in which they are ex-

pressed as is the case with other physical quanti-

224 Numerical factors in quantity equations

Version 2014 135

Equations between quantities sometimes con-

tain numerical factors These numerical factors

depend on the definitions chosen for the quanti-

ties occurring in the equations

EXAMPLE

Ek = 2

1mvsup2

225 Systems of quantities and equations

between quantities base quantities and de-

rived quantities

Physical quantities are related to one another

through equations that express laws of nature or

define new quantities

For the purpose of defining unit systems and

introducing the concept of dimensions it is con-

venient to consider some quantities as mutually

independent ie to regard these as base quanti-

ties in terms of which the other quantities can be

defined or expressed by means of equations the

latter quantities are called derived quantities

It is a matter of choice how many and which

quantities are considered to be base quantities

The whole set of physical quantities included

in ISO 31 is considered as being founded on

seven base quantities length L mass M time T

electric current I thermodynamic tempera-

ture Θ amount of substance N and luminous

intensity J

In the field of mechanics a system of quanti-

ties and equations founded on three base quanti-

ties is generally used In ISO 31-3 the base quan-

tities used are length mass and time

In the field of electricity and magnetism a

system of quantities and equations founded on

four base quantities is generally used In ISO 31-

5 the base quantities used are length mass time

and electric current

In the same field however systems founded

on only three base quantities length mass and

time in particular the Gaussian or symmetric

system have been widely used (See ISO 31-

51992 annex A)

226 Dimension of a quantity

Any quantity Q can be expressed in terms of

other quantities by means of an equation The ex-

pression may consist of a sum of terms Each of

these terms can be expressed as a product of pow-

ers of base quantities A B C from a chosen

set sometimes multiplied by a numerical factor

ξ ie ξAαBβCγ where the set of exponents (α

β γ ) is the same for each term

The dimension of the quantity Q is then ex-

pressed by the dimensional product

dim Q = AαBβCγ

where A B C denote the dimensions of the

base quantities A B C and where α β γ

are called the dimensional exponents

A quantity all of whose dimensional expo-

nents are equal to zero is often called a dimen-

sionless quantity Its dimensional product or di-

mension is A0 B0 C0 = 1 Such a quantity of di-

mension one is expressed as a number

In the system founded on the seven base

quantities length mass time electric current

thermodynamic temperature amount of sub-

stance and luminous intensity the base dimen-

sions may be denoted by L M T I O N and J

respectively and the dimension of a quantity Q

becomes in general

dim Q = LαMβTγIδΘεNζJη

EXAMPLES

Quantity Dimension

velocity LT-1

angular velocity T-1

force LMT-2

energy L2MT-2

relative density 1

Version 2014 136

23 Units

231 Coherent unit systems

Units might be chosen arbitrarily but making

an independent choice of a unit for each quantity

would lead to the appearance of additional nu-

merical factors in the equations between the nu-

merical values

It is possible however and in practice more

convenient to choose a system of units in such a

way that the equations between numerical values

have exactly the same form (including the nu-

merical factors) as the corresponding equations

between the quantities A unit system defined in

this way is called coherent with respect to the

system of quantities and equations in question

The SI is such a system The corresponding sys-

tem of quantities is given in ISO 31-1 to ISO 31-

10 and in ISO 31-12 and ISO 31-13

For a particular system of quantities and

equations a coherent system of units is obtained

by first defining units for the base quantities the

base units Then for each derived quantity the

definition of the corresponding derived unit in

terms of the base units is given by an algebraic

expression obtained from the dimensional prod-

uct (see 226) by replacing the symbols for the

base dimensions by those of the base units In

particular a quantity of dimension one acquires

the unit 1 In such a coherent unit system no nu-

merical factor other than the number 1 ever oc-

curs in the expressions for the derived units in

terms of the base units

232 SI units and their decimal multi-

ples and sub-multiples

The name International System of Units

(Systegraveme International dUniteacutes) with the inter-

national abbreviation SI was adopted by the 11th

General Conference on Weights and

Measures (Confeacuterence Geacuteneacuterale des Poids et

Mesures CGPM) in 1960

This system includes

- base units

- derived units including supplementary units

which together form the coherent system of SI

2321 Base units

The seven base units are listed in Table 1

Table 1 - SI base units

Base quantity SI base unit

Name Symbol

length metre m

mass kilogram kg

time second s

electric current ampere A

thermodynamic tem-

perature kelvin K

amount of substance mole mol

luminous intensity candela cd

2322 Derived units including supplemen-

tary units

The expressions for the coherent derived

units in terms of the base units can be obtained

from the dimensional products by using the fol-

lowing formal substitutions

L rarr m I rarr A

M rarr kg Θ rarr K

T rarr s N rarrmol

J rarr cd

In 1960 the CGPM classified the SI units ra-

dian rad and steradian sr for plane angle and

solid angle respectively as supplementary

In 1980 the International Committee for

Weights and Measures (Comiteacute International des

Poids et Mesures CIPM) decided to interpret the

Version 2014 137 class of supplementary units in the SI as a class

of dimensionless derived units for which the

CGPM allows the freedom of using or not using

them in expressions for SI derived units

Although as a consequence of this interpre-

tation the coherent unit for plane angle and for

solid angle is the number 1 it is convenient to use

the special names radian rad and steradian sr

instead of the number 1 in many practical cases

Table 2 - SI derived units with special names including SI supplementary units

Derived quantity

SI derived unit

Special name Symbol Expressed in terms of SI base

units and SI derived units

plane angle radian rad 1 rad = 1 mm = 1

solid angle steradian sr 1 sr = 1 m2 m2 = 1

frequency hertz Hz 1 Hz = 1 s-

force newton N 1 N = 1 kg ms2

pressure pascal Pa 1 Pa = 1 Nm2

stress energy joule J 1 J = 1 N - m

work quantity of heat power watt W 1 W = 1 Js radiant flux electric charge coulomb C 1 C = 1 A - s

quantity of electricity

electric potential volt V 1 V = 1 WA

potential difference tension electromotive force

capacitance farad F 1 F = 1 CV

electric resistance ohm S2 1Ω = 1 VA

electric conductance siemens S 1 S = 1 Ω-

magnetic flux weber Wb 1 Wb = 1 V s

magnetic flux density tesla T 1 T = 1 Wbm2

inductance henry H 1 H = 1 WbA

Celsius temperature degree degC 1 degC = 1 K

Celsius) luminous flux lumen Im 1 lm = 1 cd sr

illuminance lux Ix 1 lx = 1 lmm2

1) Degree Celsius is a special name for the unit kelvin for use in stating values of Celsius

temperature (See also ISO 31-41992 items 4-1a and 4-2a)

EXAMPLES

Version 2014 138

Quantity Symbol for SI unit

expressed in terms

of the seven base

units (and the sup-

plementary units in

some cases)

velocity ms

angular velocity rads or s-

force kg ms2

energy kg m2s2

relative density 1

For some of the SI derived units special

names and symbols exist those approved by the

CGPM are listed in tables 2 (and 3)

It is often of advantage to use special names and

symbols in compound expressions for units

2323 SI prefixes

In order to avoid large or small numerical

values decimal multiples and sub-multiples of

the SI units are added to the coherent system

within the framework of the SI They are formed

by means of the prefixes listed in Table 4

Table 4 - Sl prefixes

Factor Prefix

Name Symbol

1024 yotta Y

1021 zetta z

1018 exa E

1015 peta P

1012 tera T

109 giga G

106 mega M

103 kilo k

102 hecto h

10 deca da

10-1 deci d

10-2 centi c

10-3 milli m

10-6 micro micro

10-9 nano n

10-12 pico p

10-15 femto f

10-18 atto a

10-21 zepto z

10-24 yocto y

For information about the use of the pre-

fixes see 324

The SI units and their decimal multiples and

submultiples formed by use of the prefixes are

specially recommended

233 The unit one

The coherent SI unit for any quantity of di-

mension one is the unit one symbol 1 It is gen-

erally not written out explicitly when such a

quantity is expressed numerically

EXAMPLE

Refractive index n = 153 times 1 = 153

In the case of certain such quantities how-

ever the unit 1 has special names that could be

used or not depending on the context

EXAMPLES

Plane angle α = 05

rad = 05

Solid angle Ω = 23 sr

Decimal multiples and sub-multiples of the

unit one are expressed by powers of 10 They

shall not be expressed by combining the symbol

1 with a prefix

In some cases the symbol (per cent) is used

for the number 001

3 In some countries the symbol o (per mill or

per thousand) is used for the number 0001 This

symbol should be avoided

Version 2014 139 4 Since per cent and per mill are num-

bers it is in principle meaningless to speak about

percentage by mass or percentage by volume

Additional information such as (mm) or

(VV) should not therefore be attached to the unit

symbol The preferred way of expressing a mass

fraction is the mass fraction is 067 or the

mass fraction is 67 and the preferred way of

expressing a volume fraction is the volume

fraction is 075 or the volume fraction is 75

Mass and volume fractions can also be expressed

in the form 5 microgg or 42 mlm3

Abbreviations such as ppm pphm and ppb

shall not be used

234 Other unit systems and miscella-

neous units

The CGS system of mechanical units is a co-

herent system the base units of which are centi-

metre gram and second for the three base quan-

tities length mass and time

In practice this system was enlarged by add-

ing the kelvin the candela and the mole as base

units for the base quantities thermodynamic tem-

perature luminous intensity and amount of sub-

stance

Units used in electricity and magnetism have

been defined in the CGS system in several ways

depending on the system of quantities and equa-

tions chosen The Gaussian or symmetric CGS

system coherent with the Gaussian or symmet-

ric system of quantities and equations founded on

three base quantities has been widely used For

further information on this system see ISO 31-

51992 Annex A

The special names and symbols for derived

CGS units such as dyne erg poise stokes gauss

oersted and maxwell shall not be used together

with the Sl

Table 5 - Units used with the SI

Quantity Unit

Name Sym-

bol Definition

time minute

1 min= 60s

1 h = 60 min

1 d = 24 h

plane an-

degree

minute

second

1 deg =

(π180)rad =

(nl80) rad

1 = (160)deg

1 = (160)

volume litre I L 1) 1l = 1 dm3

= 1 dm

mass tonne2) t 1 t = 103 kg 1) The two symbols for litre are on an equal

footing The CIPM will however make a sur-

vey on the development of the use of the two

symbols in order to see if one of the two may

be suppressed 2) Also called the metric ton in the English lan-

Table 6 - Units used with the SI whose values in

SI units are obtained experimentally

Name Sym-

bol Definition

energy electronvolt eV The electronvolt is

the kinetic energy

acquired by an elec-

tron in passing

through a potential

difference of 1 volt

in vacuum 1 eV

1602 177 times10-19 J

mass unified

atomic

mass unit

u The unified atomic

mass unit is equal to

(1 12) of the mass

of an atom of the

nuclide 12C 1u

1660 540 times10-27kg

In other parts of ISO 31 the special names for

Version 2014 140 the derived CGS units are given in informative

annexes which are not integral parts of the stand-

There are certain units outside the SI which

are recognized by the CIPM as having to be re-

tained for use together with the SI eg minute

hour and electronvolt These units are given in

Tables 5 and 6

Other coherent systems of units have been de-

fined eg a system based on the units foot pound

and second and a system based on the units me-

tre kilogram-force and second

Apart from these other units have been de-

fined which do not belong to any coherent sys-

tem eg the atmosphere the nautical mile and

the curie

3 Recommendations for printing symbols

and numbers

31 Symbols for quantities

311 Symbols

The symbols for physical quantities are gen-

erally single letters of the Latin or Greek alpha-

bet sometimes with subscripts or other modify-

ing signs These symbols are printed in italic

(sloping) type (irrespective of the type used in

the rest of the text)

The symbol is not followed by a full stop ex-

cept for normal punctuation eg at the end of a

sentence

5 Symbols for quantities are given in ISO 31-1

to ISO 31-10 and in ISO 31-12 and ISO 31-13

6 Notations for vectorial and other non-scalar

quantities are given in ISO 31-11 on mathemat-

ical signs and symbols

7 Exceptionally symbols made up of two let-

ters are sometimes used for combinations of di-

mension one of quantities (eg Reynolds num-

ber Re) If such a two-letter symbol appears as

a factor in a product it is recommended that it

be separated from the other symbols

312 Rules for the printing of subscripts

When in a given context different quanti-

ties have the same letter symbol or when for one

quantity different applications or different val-

ues are of interest a distinction can be made by

use of subscripts

The following principles for the printing of

subscripts are recommended

A subscript that represents a symbol for a

physical quantity is printed in italic (sloping)

Other subscripts are printed in roman (up-

right) type

EXAMPLES

Upright sub-

scripts Sloping subscripts

Cg (g gas) Cp (p pressure)

gn (n normal) sumnanδn (n running

number)

micror (r relative) sumxaxbx (x running

number)

Ek (k kinetic) gik (i k running

numbers)

χe (e electric) px (xx-coordi-

T12 (12 half) lλ (λ wavelength)

Version 2014 141 8 Numbers as subscripts should be printed in ro-

man (upright type However letter symbols rep-

resenting numbers are generally printed in italic

(sloping) type

313 Combination of symbols for quantities

elementary Operations with quantities

When symbols for quantities are combined

in a product this process of combination may be

indicated in one of the following ways

ab a b abull b atimesb

10 In some fields eg in vector analysis distinc-

tion is made between abull b and a times b

11 For multiplication of numbers see 333

12 In systems with limited character sets a dot

on the line may be used instead of a half-high

Division of one quantity by another may be

a ab or by writing the product of a and b-1

eg a∙ b-1

32 Names and symbols for units

321 International symbols for units

When international symbols for units exist

they and no other shall be used They shall be

printed in roman (upright) type (irrespective of

the type used in the rest of the text) shall remain

unaltered in the plural shall be written without a

final full stop (period) except for normal punc-

tuation eg at the end of a sentence

Any attachment to a unit symbol as a means

of giving information about the special nature of

the quantity or context of measurement under

consideration is incorrect

EXAMPLE

Umax = 500 V (not U = 500 Vmax)

The unit symbols shall in general be printed

in lower case letters except that the first letter is

printed in upper case when the name of the unit

is derived from a proper name

EXAMPLES

m metre

s second

A ampere

Wb weber

322 Combination of symbols for units

When a compound unit is formed by multi-

plication of two or more units this should be in-

dicated in one of the following ways

N∙m N m

NOTES 13 In systems with limited character sets a dot

on the line may be used instead of a half high

14 The latter form may also be written without

a space provided that special care is taken when

the symbol for one of the units is the same as the

symbol for a prefix

EXAMPLE

mN means millinewton not metre newton

When a compound unit is formed by divid-

ing one unit by another this should be indicated

in one of the following ways

Version 2014 142

m ms m∙s-1

A solidus () shall not be followed by a mul-

tiplication sign or a division sign an the same

line unless parentheses are inserted to avoid any

ambiguity In complicated cases negative pow-

ers or parentheses shall be used

323 Printing of symbols for units

No recommendation is made or implied

about the font of upright type in which symbols

for units are to be printed

NOTE 15 In this series of publications the font

used in such cases is generally that of the asso-

ciated text but this does not constitute a recom-

mendation

324 Printing and use of prefixes

Symbols for prefixes should be printed in ro-

man (upright) type without a space between the

symbol for the prefix and the symbol for the

Compound prefixes shall not be used

EXAMPLE

Write nm (nanometre) for 10-9 m not mμm

The symbol of a prefix is considered to be

combined with the single unit symbol to which

it is directly attached forming with it a new

symbol (for a decimal multiple or sub-multiple)

which can be raised to a positive or negative

power and which can be combined with other

unit symbols to form symbols for compound

units (see 322)

EXAMPLES

1cm3 = (10-2m)3=10-6 m3

1 μs-1= (10-6 s)-1 = 106 s-1

1 kAm = (103A)m = 103 Am

NOTE 16 For historical reasons the name of the

base unit or mass the kilogram contains the

name of the SI prefix kilo Names of the dec-

imal multiples and sub-multiples of the unit of

mass are formed by adding the prefixes to the

word gramldquo eg milligram (mg) instead of mi-

crokilogram (μkg)

33 Numbers

331 Printing of numbers

Numbers should generally be printed in ro-

man (upright) type

To facilitate the reading of numbers with

many digits these may be separated into suita-

ble groups preferably of three counting from

the decimal sign towards the left and the right

the groups should be separated by a small space

and never by a comma or a point or by any other

332Decimal sign

The decimal sign is a comma on the line

If the magnitude of the number is less than

unity the decimal sign should be preceded by a

NOTE 17 In documents in the English lan-

guage a dot is often used instead of a comma If

a dot is used it should be on the line In accord-

ance with an ISO Council decision the decimal

sign is a comma in ISO documents

333 Multiplication of numbers

The sign for multiplication of numbers is a

cross (times) or a dot half-high (middot)

18 If a dot half-high is used as the multiplication

sign a comma should be used as the decimal

Version 2014 143 sign If a dot is used as the decimal sign a cross

should be used as the multiplication sign

19 In ISO documents the dot is not used di-

rectly between numbers to indicate multiplica-

34 Expressions for quantities

The symbol of the unit shall be placed after

the numerical value in the expression for a quan-

tity leaving a space between the numerical

value and the unit symbol It should be noted

that in accordance with this rule the symbol degC

for degree Celsius shall be preceded by a space

when expressing a Celsius temperature

The only exceptions to this rule are for the

units degree minute and second for plane angle

in which case there shall be no space between

the numerical value and the unit symbol

If the quantity to be expressed is a sum or a

difference of quantities then either parentheses

shall be used to combine the numerical values

placing the common unit symbol after the com-

plete numerical value or the expression shall be

written as the sum or difference of expressions

for the quantities

EXAMPLES

l = 12 m - 7 m= (12 - 7) m = 5m

t = 284 degC plusmn 02 degC = (284 plusmn 02) degC

(not 284 plusmn 02 degC)

λ=220 times (1 plusmn 002) W(m∙K)

35 Symbols for chemical elements and nu-

clides

Symbols for chemical elements shall be

written in roman (upright) type (irrespective of

the type used in the rest of the text) The symbol

is not followed by a full stop except for normal

punctuation eg at the end of a sentence

EXAMPLES

H He C Ca

A complete list of the symbols for the chem-

ical elements is given in ISO 31-81992 annex

A and 150 31-91992 annex A

The attached subscripts or superscripts spec-

ifying a nuclide or molecule shall have the fol-

lowing meanings and positions

The nucleon number (mass number) of a nu-

clide is shown in the left superscript position

The number of atoms of a nuclide in a mole-

cule is shown in the right subscript position eg

The proton number (atomic number) may be

indicated in the left subscript position eg

If necessary a state of ionization or an ex-

cited state may be indicated in the right super-

script position

EXAMPLES State of ionization Na+

4O or (PO4)3-

Electronic excited state Hebull N0bull

Nuclear excited state 110Agbull 110Agm

36 Mathematical signs and symbols

Mathematical signs and symbols recom-

mended for use in the physical sciences and

technology are given in 1S031-11

Version 2014 144 37 Greek alphabet (upright and sloping

types)

alpha Α a Α a

beta Β β Β β

gamma Γ γ Γ γ

delta Δ δ Δ δ

epsilon Ε ε Ε ε

zeta Ζ ζ Ζ ζ

eta Η η Η η

theta Θ θ Θ θ

iota Ι ι Ι ι

kappa Κ κ Κ κ

lambda Λ λ Λ λ

mu Μ μ Μ μ

nu Ν ν Ν ν

xi Ξ ξ Ξ ξ

omicron Ο ο Ο ο

pi Π π Π π

rho P ρ Ρ ρ

sigma Σ σ Σ σ

tau Τ τ Τ τ

upsilon Υ υ Υ υ

phi Φ φ Φ φ

chi Χ χ Χ χ

psi Ψ ψ Ψ ψ

omega Ω ω Ω ω

52 Computer symbols

Version 2014 145

52 Computer Symbols

Wherever possible the symbols in the second

column of the tables have been chosen so that

their meaning is readily apparent They have

been constructed from the CCITT International

Telegraph Alphabet restricted character set

They are therefore suitable for use in a wide

range of situations e g Telex messages letters

computer printouts etc

To ensure that the symbols can be used in a

wide range of programming languages they cur-

rently have been kept to less than six characters

long The symbols should be used as defined

and in accordance with modern programming

practice should have their type explicitly de-

clared before use The following rules were ap-

plied in the derivation of the symbols

1 Only upper case letter A - Z and digits 0

- 9 have been used

2 Formerly Greek letters have been

spelled out if necessary in abbreviated

form or with changed spelling This

practice is considered obsolete

3 The Froude circular symbols are de-

fined by the prefix CIRC

4 All symbols start with a letter

5 Qualifiers and operators preferably two

characters are currently suffixed to the

main symbol line without spacing

6 No one computer compatible symbol

should be used for different concepts in

a given context This goal has not been

completely achieved for the whole list

Ad hoc solutions have been attempted

but discarded as unsatisfactory

7 Since the computer compatible symbols

have been proposed as the basis of attribute

names for data exchanges the above rules

will probably be further developed in the

near future

A final remark on the Computer Symbols in

the computer the letter O and figure 0 (zero)

have fundamentally different meanings but ow-

ing to their resemblance they can be easily con-

fused Thus it is necessary to distinguish rigor-

ously between them As a matter of fact there are

contradictory conventions being widely used

53 Documentation

Version 2014 146

53 Documentation

531 ITTC Documents

1 International Towing Tank Conference

Standard Symbols 1971 BSRA Technical

Memorandum No400 August 1971

Standard Symbols 1976 BSRA TM

No500 1976

3 ITTC Dictionary of Ship Hydrodynamics

RINA Maritime Technology Monograph

No6 1978

4 Translation of Overall Index of Titles of Dic-

tionary of Ship Hydrodynamics Vol 1

CETENA Genova 1984

Vol 2 University of Tokyo 1984

5 Bibliography and Proposed Symbols on Hy-

drodynamic Technology as Related Model

Tests of High Speed Marine Vehicles

Prep by 17th ITTC High-Speed Marine Ve-

hicle Committee SPPA Maritime Research

and Consulting Rep No101 1984

532 Translations

A number of translations of the List of ITTC

Standard Symbols into languages other than

English have been made including French Ger-

man Italian Japanese Russian Spanish and

Chinese For obvious reasons these translations

are no longer up-to-date as the present accepted

list in English and the Russian one

1 French Translation of ITTC Standard Sym-

bols 1971 Association Francaise de Nor-

malisation (AFNOR)

2 International vereinbarte Buchstabensymbole

und Bezeichnungen auf dem Gebiet der

Schiffshydrodynamik Collatz G

Schiff und Hafen 27 (1975) No10

3 Italian Translation of ITTC Standard Symbols

1971 Luise E Appendix II Report of

Presentation Committee

Proceedings 14th ITTC Vol 4 Ottawa 1975

4 Japanese Translation of ITTC Standard Sym-

bols Transactions of the Society of Naval

Architects of Japan No538 April 1974

5 Russian Translation of ITTC Standard Sym-

bols 1971 Brodarski Institute Publication

No28 Zagreb 1974

6 Simbolos Internacionales en Arquitectura Na-

val Asociacion de Investigacion de la Cons-

truccion Naval

Publication 775 Juli 1975 Madrid

7 Report of Information Committee Proc 17th

ITTC Goumlteborg 1984

8 Chinese Translation of ITTC Standard Sym-

bols China Ship Scientific Research Centre

533 Other References

Apart from the organizations represented on

the ITTC these symbols have been recom-

mended for use in technical writing on naval ar-

chitecture by a number of organizations con-

cerned with marine matters including The Royal

Institution of Naval Architects the American

Society of Naval Architects and Marine Engi-

neers and the American British Canadian Aus-

tralian and Italian Navies Where possible the

symbols for Section 341 Waves are consistent

with the IAHRPIANC List of Sea State Param-

eters Supplement to Bulletin No 52 January

53 Documentation

Version 2014 147

In 1985 the Draught International Standard

ISODIS 7463 Shipbuilding - Symbols for Com-

puter Applications - has been published The

symbols are based on the list approved by the

ITTC in Ottawa 1975 and a related list produced

by the ISSC in 1974 inconsistencies having

been removed The ISOTC8SC15 has been no-

tified that major changes of the ITTC Symbols

are under discussion Subsequently processing

of ISODIS 7463 has not been postponed but

the standard has been published as ISO 7463 in

Table of Contents

1 General


111 Uncertainty

112 Coordinates and Space Related Quantities


113 Time and Frequency Domain Quantities












122 Loads

1221 External Loads



1231 Motions

1232 Attitudes

13 Fluid Mechanics

131 Flow Parameters




132 Flow Fields

1321 Velocities etc



1331 Geometry


1333 Forces


134 Boundary Layers


135 Cavitation


1352 Flow fields

1353 Pumps


141 Waves

1411 Periodic waves





142 Wind


143 Ice Mechanics


15 Noise


2 Ships in General

21 Basic Quantities


221 Hull Geometry






2222 Ducts


2224 Pods












231 Hull Resistance (see also Section 141 on Waves)














235 Water Jets


241 Manoeuvrability





2415 Linear Models




242 Sea Keeping




3 Special Craft











33 Hydrofoil Boats






34 ACV and SES





36 Sailing Vessels



4 Background and References



421 Classification


423 Organization of the matrix structured list

5 Principles of Notation


52 Computer Symbols

53 Documentation

531 ITTC Documents

532 Translations


Table of Contents

all lines have hypertext link to symbols pages

ITTC SYMBOLS AND TERMINOLOGY

LIST VERSION 2014 2

TABLE OF CONTENTS 2

1 GENERAL 4

11 Fundamental Concepts 4

111 Uncertainty 4

112 Coordinates and Space Related

Quantities 10

113 Time and Frequency Domain

Quantities 15

1132 Complex Transforms 16

1133 Complex Quantities 16

114 Random Quantities and Stochastic

Processes 18

1141 Random Quantities 18

1142 Stochastic Processes 19

1143 Probability Operators

(Superscripts) 20

115 Balances and System Related

Concepts 21

12 Solid Body Mechanics 22

121 Inertial and Hydrodynamic

Properties 22

122 Loads 24

1221 External Loads 24

1222 Sectional Loads 25

123 Rigid Body Motions 26

1231 Motions 26

1232 Attitudes 27

13 Fluid Mechanics 28

131 Flow Parameters 28

1311 Fluid Properties 28

1313 Boundary conditions 29

132 Flow Fields 30

1321 Velocities etc 30

1322 Circulation etc 30

133 Lifting Surfaces 32

1331 Geometry 32

1332 Flow angles etc 33

1333 Forces 34

1334 Sectional coefficients 34

134 Boundary Layers 35

135 Cavitation 37

1352 Flow fields 37

1353 Pumps 38

14 Environmental Mechanics 39

141 Waves 39

1411 Periodic waves 39

1412 Irregular waves 40

1413 Time Domain Analysis 41

1414 Frequency Domain Analysis 42

1415 Directional Waves 43

142 Wind 44

143 Ice Mechanics 45

15 Noise 46

151 Underwater Noise 46

2 SHIPS IN GENERAL 47

221 Hull Geometry 50

Subscripts 54

222 Propulsor Geometry 56

2221 Screw Propellers 56

2222 Ducts60

2223 Waterjets (see also section 135) 60

2224 Pods 61

2225 Operators and identifiers 61

223 Appendage Geometry 62

2232 Identifiers for Appendages

(Subscripts) 63

224 Hydrostatics and Stability 64

2241 Points and Centres (Still under

construction) 64

2242 Static Stability levers 65

Stability 68

141 on Waves) 70

Subscripts 73

235 Water Jets 83

242 Sea Keeping 94

Capsizing 96

Subscripts 104

3 SPECIAL CRAFT 106

Vessels 106

symbols) 112

34 ACV and SES 120

structured list 130

Symbol

Computer

Symbol

Definition or

Explanation

1 GENERAL

111 Uncertainty

distribution

a = (a+ndash a_) 2

xi b+ = a+ - xi

xi b_ = xi ndash a_

Symbol

Computer

Symbol

Definition or

Explanation

depends

q Random quantity 1

ing quantity q

Type A evaluation

tion of the mean

)(2 qs

Type A evaluation

)( 12 Xs

put means

Symbol

Computer

Symbol

Definition or

Explanation

bility p

quantity Xi

tainty

tainty from Type A

tainty from Type B

tainty

measurement

22 )]([)( iii xucyu 1

mate y

Symbol

Computer

Symbol

Definition or

Explanation

mate xi

mate y

estimates xi and xj

U = k uc(y)

Up = kp uc(y)

tion i ix X

measurand Y depends

variable

Symbol

Computer

Symbol

Definition or

Explanation

quantity Xi

servation of Xi

Output estimate

same measurement

Y A measurand

certainty Up

root of 2

Symbol

Computer

Symbol

Definition or

Explanation

n estimated by

tive square root of

tities

in the following

tion if any

Axes coordinates

Body axes (xyz)

platforms or ships

upwards

section

flight dynamics

ular case

differential

Name of coordi-

nate system

Remarks

11-121

cartesian

coordinates

system See Figure 1

11-122

cylindrical

coordinates

11-123

(-) r φ r=rer

r sin dφ eφ

spherical

Figures 3 and 5

Symbol

Computer

Symbol

Definition or

Explanation

lar quantity

scalar distribution

εikjxkds

εklixlεjkm xmds

Sij = S0ij

Si 3+j = S1ij

S3+i j = S1ij

S3+i 3+j = S2ij

tesian coordinates

fixed in the body

Tijs + Tij

tensor

( Tij - Tji ) 2

Symbol

Computer

Symbol

Definition or

Explanation

V3+i = V1i

X X(1)

Y X(2)

Z X(3)

the body

x0 x01

y0 x02

z0 x03

X0 X0(1)

Y0 X0(2)

Z0 X0(3)

xF xF1

yF xF2

zF xF3

XF XF(1)

YF XF(2)

ZF XF(3)

1 ijk = 321 213 132

0 if otherwise

Symbol

Computer

Symbol

Definition or

Explanation

f FR Frequency Hz

functions

1 TC Hz

Laurent transform

Laplace transform

t TI Time - + s

Symbol

Computer

Symbol

Definition or

Explanation

pled function

= X(0)2 + fSXF(f + jfS)

inverse form

XF(f)=XL(f)

t = 0 TC

XF = xFjδ(f - jTC)

inverse form

Hilbert transform

(1t)F = -i sgn f

if X(tlt0) = 0 then

= (X(t)exp(-at))F

ie = 0 for f lt 0

rier series

XFj(1 + sgn j)

line spectra

Symbol

Computer

Symbol

Definition or

Explanation

component

zl ZLG (Phase) Lag

component

Symbol

Computer

Symbol

Definition or

Explanation

gE gM gMR

E(g) = g(x)fx(x)dx

Random quantities

x(ζ) y(ζ)

X(I) Y(I)

i = 1 n

n sample size

quantity

xD xDR σx

dom quantity

xVR frac12

xDS sx

dom quantity

xVS 12

xxR xxMR Rxx

dom quantity

xyR xyMR Rxy

dom quantities

xE xM xMR

xA xMS mx

a random quantity

1n xi i = 1n

xAE = xE

xVSE = xV n

xPD fx

dom quantity

d Fx dx

xyPD fxy

2 Fxy (x y)

xPF Fx

xyPF Fxy

random quantities

Symbol

Computer

Symbol

Definition or

Explanation

xV xVR xxVR

XVR XXVR

x2 E - xE 2

xVS xxVS

XVS XXVS

dom quantity

1 (n - 1) (xi - x

i = 1n

xyV xyVR

quantities

x yE - xE yE

periment

dom quantity

t =-T2 +T2

T =- +

A(g(t)) = 1T g(t)dt

t =0 +T

x(ζt) y(ζt)

xxC xxCR Cxx

(x(t) - xE)(x(t + τ) - xE)E

xyC xyCR Cxy

(x(t) - xE)(y(t + τ) - yE)E

xxR xxRR Rxx

Rxx(τ) = Rxx(-τ)

= x(t)x(t + τ)MR

τ = 0

xyR Rxy

Ryx(τ) = Rxy(-τ)

if x y are ergodic

Symbol

Computer

Symbol

Definition or

Explanation

xxS Sxx

chastic process

xxRRSR

xyS Sxy

processes

xyRRSR

periment

Average sample mean

Sample covariance

Sample deviation

E M MR

Probability density

(Power) Spectrum

Sample spectrum

Sample correlation

Population variance

Sample variance

Symbol

Computer

Symbol

Definition or

Explanation

control volume

Inward positive QUs

control volume

quantity stored

dq dt QUs

Symbol

Computer

Symbol

Definition or

Explanation

AM(IJ)

DA(IJ)

RF(IJ)

uv DH(UV)

damping

u FH(U)

uv IH(UV)

inertia

of water-plane area

Iy Iyy

IY IYY

M2(22)

MA(55)

Iz Izz

IZ IZZ

M2(33)

MA(66)

Ixy I12

Iyz I23

Izx I31

IXY I2(12)

IYZ I2(23)

IZX I2(31)

kx kxx

(Ixxm)12

Symbol

Computer

Symbol

Definition or

Explanation

ky kyy

(Iyym)12

kz kzz

(Izzm)12

M0(IJ)

MA(IJ)

tensor

mij = m δij

ij M1(IJ)

M2(IJ)

IN(IJ)

MA(UV)

system

Mij = M0

Mi 3+j = M1Tij

M3+i j = M1ij

M3+i 3+j = M2ij

Symbol

Computer

Symbol

Definition or

Explanation

122 Loads

1221 External Loads

in body coordinates

u = MMu

Fi = F0i

F3+i = F1i

gi = g1

g3+i = 0

in body coordinates

F11 F4

K M(1)

F1(1) F(4)

F12 F5

M M(2)

F1(2) F(5)

FN13 F6

N M(3)

F1(3) F(6)

F01 F1

F0(1) F(1)

axis x

F02 F2

F0(2) F(2)

axis y

F03 F3

F0(3) F(3)

axis z

Gu = muv gv

G0i Gi

in body coordinates

Gi = G0

i = m0ij gj

i G1(I)

in body coordinates

G3+i = G1

i = εikj xk G0

= m1ij gj

dW dx1

Symbol

Computer

Symbol

Definition or

Explanation

section coordinates

FSi = FS0

FS3+i = FS1

i = MBi

FS11 Nm

Symbol

Computer

Symbol

Definition or

Explanation

1231 Motions

v01 v4

V0(1) V(4)

body axis x

v02 v5

V0(2) V(5)

body axis y

v03 v6

V0(3) V(6)

body axis z

v11 v1

V1(1) V(1)

v12 v2

V1(2) V(2)

v13 v3

V1(3) V(3)

body axes

vi = v1

v3+i = v0i

tive to body axes

Symbol

Computer

Symbol

Definition or

Explanation

1232 Attitudes

Angle of attack

the z-axis

about the xo axis

X(4) RO

X(5) TR

X(6) YA

course

13 Fluid Mechanics

Symbol

Computer

Symbol

Definition or

Explanation

13 Fluid Mechanics

131 Flow Parameters

Velocity of sound

(E ρ)12

Weight density

ρg (See 111)

Viscosity

Kinematic viscosity

DN RHO

Mass density

Capillarity

length

Boussinesq number

V (g RH)12

Cauchy number

V (E ρ)12

Froude number

V (g L)12

Froude depth number

V (g h)12

V (g 13)12

Mach number

Reynolds number

Strouhal number

Thoma number

Cavitation number

(pA ndash pV)q

Weber number

V2 L κ

07R Ac V nDRe

13 Fluid Mechanics

Symbol

Computer

Symbol

Definition or

Explanation

Sand roughness

surface

Hydraulic radius

wetted perimeter

13 Fluid Mechanics

Symbol

Computer

Symbol

Definition or

Explanation

132 Flow Fields

1321 Velocities etc

energy

ρ V2 2 + p + ρ g h

Mass specific force

Total head

e w = h +pw +qw

flow energy

turbed flow

ρ V2 2

Rate of flow

Total head loss

ij SR(IJ)

ρ vivj

Pa sij

ST(IJ)

Total stress tensor

change

ij SV(IJ)

Viscous stress

u vx v1

v vy v2

w vz v3

Velocity

V = vivi

Wall shear stress

μ (U y)y=0

13 Fluid Mechanics

Symbol

Computer

Symbol

Definition or

Explanation

Induction factor

Vortex density

Circulation

intV ds

along a closed line

Potential function

Stream function

ψ = const

surface

13 Fluid Mechanics

Symbol

Computer

Symbol

Definition or

Explanation

1331 Geometry

Projected area

Wing or foil span

Flap span

Mean chord length

Tip chord length

Root chord length

Sweep angle

tion (general)

edge of struts

(general)

of foil

section

tS cSTH

Taper ratio

Aspect ratio

13 Fluid Mechanics

Symbol

Computer

Symbol

Definition or

Explanation

Induced velocity

and the chord line

or incidence

Geometric angle of

attack or incidence

Hydrodynamic angle

of attack

zero lift

Angle of zero lift

at zero lift

13 Fluid Mechanics

Symbol

Computer

Symbol

Definition or

Explanation

1333 Forces

Foil drag

DRIND Induced drag

of motion

Interference drag

secting foil

zero lift

Streamline drag

Lift force on foil

CL AFT q

of zero

CL0 AFT q

Lift-Drag ratio

13 Fluid Mechanics

Symbol

Computer

Symbol

Definition or

Explanation

134 Boundary Layers

τ (ρ Ue

Entrainment factor

1 (Ue dQ dx)

rameter

(δ - δ) Θ

Static pressure

Total pressure

Entrainment

U δ v or Ue δ

RTHETA

U Θ v or Ue Θ v

boundary layer

from surface

(τ ρ)12

boundary layer

from the surface

(Ue- U) uτ

13 Fluid Mechanics

Symbol

Computer

Symbol

Definition or

Explanation

from the wall

y uτ v

δ (τw dp dx)

layer at U=0995Ue

δ δ1

boundary layer

(Ue- U) Ue dy

von Karman constant

δ995 (v dUe dx)

Energy thickness

(U Ue) (1 - U2 Ue

Momentum thickness

(U Ue) (1 - U Ue)dy

Local skin friction

μ (U y)y=0

13 Fluid Mechanics

Symbol

Computer

Symbol

Definition or

Explanation

135 Cavitation

Gas content ratio

α αS

Gas content

temperature

Cavitation number

(pA - pC) q

(pA - pV) q

1352 Flow fields

Cavity drag

Cavity length

region

Ambient pressure

Critical pressure

takes place

Cavity pressure

quasi-steady cavity

Critical velocity

takes place

Volume loss

13 Fluid Mechanics

Symbol

Computer

Symbol

Definition or

Explanation

WL WTLS

Weight loss

specified time

1353 Pumps

turbo-engines

Thoma number

(HU - pV w) HN

Symbol

Computer

Symbol

Definition or

Explanation

141 Waves

1411 Periodic waves

lerity LW TW =

2WgL in

deep water

odic wave

const = cW

lerity

i fW Hz

wave crest to wave

wave ηC - ηT

advance

Symbol

Computer

Symbol

Definition or

Explanation

at a given location

ηFSα m

ηFSp rad

crossing

trough

crossing

and crest

wave heights

crossing

of zero in a record

Symbol

Computer

Symbol

Definition or

Explanation

in a record

Negative values m

crossing

visual observation

cant wave height

wave heights

wave height

heights

visual observation

wave propagation

samples

visual observation

Symbol

Computer

Symbol

Definition or

Explanation

lution

points

tude function

4 (m0)12 m

fn S(f)df m2 sn

Si(ω)

tral density

Sr(ω)

tral density

Sη(f)

Sη(ω)

2πfP s

and first moment

m0m1 s

and second moment

(m0m2)12 s

Symbol

Computer

Symbol

Definition or

Explanation

DX(fθ)

DX(ωμ)

SIGMAOX

Sζ (ωμ)

Sθ (ωμ)

density

Sρ(fθ)

Sζ(ωμ)

θm MWD

THETAMOX

rection

Symbol

Computer

Symbol

Definition or

Explanation

142 Wind

(008 + 0065U10)10-3

Fetch length

wind blows

DURATN

Wind duration

Return period

ceeded

uz uzi

UFLUCT

USHEAR

Wind shear velocity

12 U10 or 071U10123

Reference mean wind

U10 = (10z)17 Uz

(Uz + uzi)

UzA = (z10)17 U10 or

see section 141

True wind velocity

see section 141

Dimensionless Fetch

face in meters

see section 26

True wind angle

see section 26

Wind direction

Symbol

Computer

Symbol

Definition or

Explanation

143 Ice Mechanics

weight of ice

volume of ice

unit volume of ice

15 Noise

Symbol

Computer

Symbol

Definition or

Explanation

15 Noise

acoustic centre

= 10 log10

(119903119898119904

1199011199031198901198912 ) dB 119901119903119890119891

tance of 1m

119871s

= 119871p

+ 20 log10 [119889

119889119903119890119891] dB 119889119903119890119891

Symbol

Computer

Symbol

Definition or

Explanation

2 SHIPS IN GENERAL

21 Basic Quantities

dv dt ms2

A A AR

Area in general m2

B B BR Breadth m

(forces)

d D D DI Diameter m

E E EN Energy J

F F0 F F0 Force N

h DE Depth m

H H HT Height m

mass distribution

L L LE Length m

tory velocity

m M MA

Mass kg

Symbol

Computer

Symbol

Definition or

Explanation

distribution

M MO Momentum Ns

P P PO Power W

r R RD Radius m

locity

t TI Time s

t TE Temperature K

harmonic process

of a body

ds dt ms

V VO Volume m3

specific weight

dW dV = ρg Nm3

acting on a body

tilled water at 4C

Symbol

Computer

Symbol

Definition or

Explanation

Symbol

Computer

Symbol

Definition or

Explanation

221 Hull Geometry

gitudinal plane

perpendicular

the final rounding

aft perpendiculars

port and starboard)

waterline

relative wind

midship

of midship

section

of ships hull

Symbol

Computer

Symbol

Definition or

Explanation

water line

at stem

the perpendiculars)

maximum section

verse section

Symbol

Computer

Symbol

Definition or

Explanation

point of the stern

pendicular

dicular

perpendicular

with straight keel

water surface level

bare hull

ΔBH (ρ g) m3

pendages

ΔAP (ρ g) m3

Symbol

Computer

Symbol

Definition or

Explanation

ancy) g ρ N

= TS TM

cient B 13 1

GM 13 1

GZ 13 1

cient KG T

12 IL ( B L3) 1

12 IT (B3 L) 1

AM (B T) 1

body A (AX L 2) or

A (AM L 2)

trance E (AX LE) or

E (AM LE)

body F (AX L 2) or

F (AM L 2)

Symbol

Computer

Symbol

Definition or

Explanation

R (AM LR)

AWA (B L 2) 1

forward

AWF (B L 2) 1

coefficient

maximum area

ABL (L T) 1

ABT AX 1

transom stern

AT AX 1

L 13 1

cient T 13 1

A AB After body

APP APP Appendages

B BH Bare hull

DW Design waterline

E EN Entry

Symbol

Computer

Symbol

Definition or

Explanation

F FB Fore body

FS Frame spacing

H HE Hull

LR Reference Line

LP LP Based on LPP

LW LW Based on LWL

M MS Midships

PB Parallel body

R RU Run

SS Station spacing

W WP Water plane

S WS Wetted surface

Symbol

Computer

Symbol

Definition or

Explanation

boss or hub

radius

hub to the tip

Symbol

Computer

Symbol

Definition or

Explanation

blades

2 π r sin (φ) z m

positive rake

the propeller plane

iG + iS = cS sinφ

shoulder

Symbol

Computer

Symbol

Definition or

Explanation

ing aft shoulder

rh RH Hub radius m

ler blade

ler axis

dicular

above base line

Symbol

Computer

Symbol

Definition or

Explanation

cal skew angle

Symbol

Computer

Symbol

Definition or

Explanation

2222 Ducts

LD LD Duct length m

ler plane

of duct

tion s

Jet System Head m

at station 1A

Symbol

Computer

Symbol

Definition or

Explanation

2224 Pods

Main Body

tom Fin

Bottom Fin

under pod main body

D Duct (subscript)

Symbol

Computer

Symbol

Definition or

Explanation

appendage

of rudder

propeller race

hydrofoil

lel to keel

Symbol

Computer

Symbol

Definition or

Explanation

rudders

of flanking rudders

BK Bilge keel

BS Bossing

FB Bow foil

FR Flanking rudder

FS Stern foil

KL Keel

RU Rudder

RF Rudder flap

SA Stabilizer

SH Shafting

SK Skeg

ST Strut

TH Thruster

WG Wedge

Symbol

Computer

Symbol

Definition or

Explanation

curves of stability

volume

Centre of buoyancy

volume

ter plane

(mass)

Keel reference

XCB LCB

ancy (LCB)

from Midships

XCF LCF

tion (LCF)

from Midships

Symbol

Computer

Symbol

Definition or

Explanation

from Midships

XCG LCG

ity (LCG)

from Midships

gravity G

centre of buoyancy

curves of stability

Symbol

Computer

Symbol

Definition or

Explanation

centre of buoyancy

metacentre M

pendicular

dicular

pendicular

weight addition

101 GGKGKG m

height

to the metacentre

tion effects

centric height

metacentre ML

KGKMGM LL

TAG cosφ

KB-KM =I =BM T

BM KM KB

Symbol

Computer

Symbol

Definition or

Explanation

base or keel K

metacentre M to the

ing arm

Heeling moment Δ m

GM 13 1

GZ 13 1

cient KG T

ficient

proximately equals

Symbol

Computer

Symbol

Definition or

Explanation

ficient

proximately equals

one centimetre

one meter

ΔCMTL Nmm

force g ρ N

flooded water

Δfw (ρg) m3

Symbol

Computer

Symbol

Definition or

Explanation

the compartment

bility

a apparent

A att attained

d dyn dynamic

e EFF effective

f false

KL keel line

L longitudinal

MAX maximum

s Static

S sqt Sinkage squat

TC Trim in cm

TM Trim in m

T transverse

V vertical

0 Initial

at heel angle

θ at trim angle θ

Symbol

Computer

Symbol

Definition or

Explanation

231 Hull Resistance

cross section area

lowance

propulsion tests

[(1 + k) CFM + CR]

surface of the body

bare hull

SBH + SAPP m2

Symbol

Computer

Symbol

Definition or

Explanation

area underway

area at rest

area underway

area at rest

lation

RA (S q) 1

ficient

RAA (AV qR) 1

RAPP (S q) 1

cient of a body

RF (S q) 1

RF0 (S q) 1

RP (S q) 1

coefficient

RPV (S q) 1

Symbol

Computer

Symbol

Definition or

Explanation

RR (S q) 1

g R L (ΔV2) 1

efficient

RV (S q) 1

efficient

RW (S q) 1

efficient

1000 R (Δ(KC)2)

1000 RF (Δ(KC)2) 1

sliding bodies

(CV - CF0) CF0 1

(4πg)12VK16

sponding to KQ KT

R (ρ D4 n2) 1

ρ V2 2

see 332

qR PDWR

apparent wind

ρ VWR2 2

see 342

Symbol

Computer

Symbol

Definition or

Explanation

tio in general

R Δ 1

placement ratio

RR Δ 1

FW Fresh water

MR Raw model data

OW Open water

SW Salt water

Symbol

Computer

Symbol

Definition or

Explanation

of revolution

Brake power

Delivered power

propeller power

Effective power

resistance power

Indicated power

Shaft power

Thrust power

Torque

Running trim

Ship speed

or torque identity

2 π n

Symbol

Computer

Symbol

Definition or

Explanation

(T - RT) RT

Δ23 V3 PS

PD (ρ V3 23 2)

identity

PDT PDS

ηDS ηDM

factor

Sinkage dynamic

Trim dynamic

by length

(T - RT) T

(V - VA) V

(V - VA) VA

Symbol

Computer

Symbol

Definition or

Explanation

wTM - wTS

1978 method

diction

ηD PD PE - 1

resistance

PT PD = T VA (Q ω)

coefficient

PE PD = PR PP

Gearing efficiency

Hull efficiency

PE PT = PR PT

= (1 - t) (1 - w)

and propeller

water tests

ηB ηO

Shafting efficiency

PD PS = PP PS

Symbol

Computer

Symbol

Definition or

Explanation

lution

ler blade surface

advance speed

ρ VA2 2

ρ VS2 2 Pa

QS=QSC+ QSH

torque

peller unit

peller

Symbol

Computer

Symbol

Definition or

Explanation

at 07 R

(VA2+ (07 R ω)2)12

n PDfrac12 VA

with n in revsmin

VA in kn (obsolete)

n PTfrac12 VA

with n in revsmin

VA in kn (obsolete)

T (AP qA)

= (TP AP) qA

V (D n) = VH (D n) 1

ducted propeller

VP (D n)

identity

coefficient

QSC (ρ n2 D5) 1

Symbol

Computer

Symbol

Definition or

Explanation

torque coefficient

QSH (ρ n2 D5) 1

ficient

TP (ρ n2 D4) 1

KTP+ KTD 1

KQηR 1

feet VA in kn

efficiency

PJ PD = PJ PP 1

ηJP0 ZET0

zero advance speed

T (ρ π 2)13 (PD D)23 1

η0 ηTP0 ETA0

water tests

ducted propeller

TP TT 1

Symbol

Computer

Symbol

Definition or

Explanation

propeller

peller

by propeller

blade section

arctg (VA r ω)

Symbol

Computer

Symbol

Definition or

Explanation

u = 1 6

u = 1 2 3 force

u = 4 5 6 moment

coefficients

KFi and KMi

cients

Mi (ρ n2 D5) 1

p PR Pressure Pa

ing reaction

u = 1 6

u = 1 2 3 force

u = 4 5 6 moment

from the x-axis

Symbol

Computer

Symbol

Definition or

Explanation

placement

u = 1 6

u = 1 2 3 linear

u = 4 5 6 angular

u = 1 6

u = 1 2 3 linear

u = 4 5 6 angular

eration

u = 1 6

u = 1 2 3 linear

u = 4 5 6 angular

Symbol

Computer

Symbol

Definition or

Explanation

235 Water Jets

210 n2

at station s

cient at station s

rate transducer

Ej = (ρ2)VEj2dQj

j j i i

pg x u n dA

j j i i

pu g x u n dA

sion point

several pump stages

in i direction

u u n dA

Symbol

Computer

Symbol

Definition or

Explanation

dition)

impeller

turbed flow

tion s

boundary layer

msup3s

water jet system

msup3s

jet xT

dition)

system on the hull

Symbol

Computer

Symbol

Definition or

Explanation

at station s

station 7

station 1

tion 1A

surface

in x direction

ciency E

ciency JSE0

stream conditions

the pump

Symbol

Computer

Symbol

Definition or

Explanation

ciency

pump loop test

P duct I

Symbol

Computer

Symbol

Definition or

Explanation

241 Manoeuvrability

of rudder

(AR + ARmov) 2 m2

root to tip

AHL (L T) 1

h DE Water depth m

der axis

Symbol

Computer

Symbol

Definition or

Explanation

dp dt 1s2

dq dt 1s2

dr dt 1s2

du dt ms2

dv dt ms2

dw dt ms2

body axes

χ YX Yaw angle rad

Symbol

Computer

Symbol

Definition or

Explanation

RO Roll angle rad

Pitch angle

the hull

Drift angle

the hull

ANWIRL

ANRUEF

Bow fin angle

Stern fin angle

Rudder angle

ANRUOR

COWIAB

COWIRL

Symbol

Computer

Symbol

Definition or

Explanation

N r Nms2

N v Nms2

along body x-axis

X u Nsm

eration

X u Ns2m

tion of body axis y

Y r Ns2

Symbol

Computer

Symbol

Definition or

Explanation

Y v Ns2m

along body z-axis

2415 Linear Models

ship length

turning diameter

DC LPP 1

ameter δR = δ0

D0 LPP 1

unstable ship

Symbol

Computer

Symbol

Definition or

Explanation

unstable ship

turning rate

change of heading

heading

(starboard)

(port)

tr TIR Reach time s

Symbol

Computer

Symbol

Definition or

Explanation

track reach

Symbol

Computer

Symbol

Definition or

Explanation

242 Sea Keeping

system

spectively

Frequency

Alias horizontal

Alias vertical

moment

Alias horizontal

ing moment

Alias vertical

lution in waves

Symbol

Computer

Symbol

Definition or

Explanation

Sη(f) Sηη(f)

Sη(ω) Sηη(ω)

density

roll pitch yaw

rad TAW

Wave period

Yz(ω)

Azζ(ω)

tory motions

za(ω) ζa(ω) or

za(ω) ηa(ω)

Yθζ(ω)

Aθζ(ω)

motions

Θa(ω) ζa(ω) or

Tuning factor

w w wL L L

w w w= = =

q fL L L= = =

(short crested)

Symbol

Computer

Symbol

Definition or

Explanation

I991241

- I991242

lever curve

cording to ISO 8666

IMOIS IMOHSC2000

acter sets

Symbol

Computer

Symbol

Definition or

Explanation

curves of stability

volume

centre of buoyancy

metacentre M

volume

needed for crew

sons on board

ficient - I991243

proximately equals

hull - I99121

Symbol

Computer

Symbol

Definition or

Explanation

merged test weights

ter plane

pendicular

dicular

pendicular

(mass)

weight addition

101 GGKGKG m

weight addition

101 GGKGKG m

Symbol

Computer

Symbol

Definition or

Explanation

height

to the metacentre

KGKMGM

face effect)

tion effects

height

metacentre ML

KGKMGM LL

TAG cos φ

IMOtable

profile

K Keel reference

base of keel or K

Symbol

Computer

Symbol

Definition or

Explanation

base of keel or K

metacentre M to the

condition - IMOIS

IMOtable

ment due to crew

is taken of rolling

Symbol

Computer

Symbol

Definition or

Explanation

inclination

centimetre

meter CMTL Nmm

due to wind

above waterline

PV Wind pressure Pa

s Wave steepness 1

according to hellip

value see hellip

Symbol

Computer

Symbol

Definition or

Explanation

TL Turning lever m

IMOHSC2000

ancy (LCB)

of buoyancy B

tion (LCF)

of flotation F

ity (LCG)

of gravity G

gravity G

Symbol

Computer

Symbol

Definition or

Explanation

centre of buoyancy

force g N

gle during hellip

Symbol

Computer

Symbol

Definition or

Explanation

according to hellip

gle seehellip

bility

the compartment

stability curve

Symbol

Computer

Symbol

Definition or

Explanation

E Entrance

F Fore

Z Heave

θ Pitch

φ Roll

Symbol

Computer

Symbol

Definition or

Explanation

3 SPECIAL CRAFT

Planing bottom area

strips

gravity

Beam over chines

Transom breadth

spray strips

chines

spray strips

bossings

bottom

section

Shaft angle

inclined downwards)

Symbol

Computer

Symbol

Definition or

Explanation

derway

water surface level

(flange mounting)

forces underway

ing surface

(LK + LC) 2

planing hull

water line

SWS SS

spray edge

Symbol

Computer

Symbol

Definition or

Explanation

ALFBAR

Barrel flow angle

LM LWL

TRIMDWL

design waterline

(positive bow up)

θS θ0

Static trim angle

θV θD

LM (BLCG)

TAUDWL

reference line

Spray angle

plane of bottom)

tal friction area

normally to NA)

normally to NB)

Symbol

Computer

Symbol

Definition or

Explanation

force NPN

ler pressure forces

normally to NPP)

suction forces NPS

normal to NPS)

pressure forces NRP

normal to NRP)

normal to RAA)

normal to RAP)

normal to RF)

sistance RK

normal to RK)

drag ΔRRP

normal to ΔRRP)

thrust

normal to RT)

Symbol

Computer

Symbol

Definition or

Explanation

deadrise

Δ (BCG

surface

Δ (BCG

breadth

V (BCG g)12

Load coefficient

Δ (BCG

3 ρ g )

1 LVHD

drodynamic lift

Hydrostatic lift

Due to buoyancy

reference line

ence line

reference line

Symbol

Computer

Symbol

Definition or

Explanation

reference line

Keel drag

Induced drag

g ρ tg τ

Parasitic drag

openings

Total resistance

spray drag

CF SWS qS

of the hull

Spray velocity

the spray

Symbol

Computer

Symbol

Definition or

Explanation

Box beam

Beam of main deck

Hull spacing

Tunnel width

Hull diameter

submerged hulls

dinal position X

Deck clearance

ANENIN

nel (inner) side

of demihull

ANENOU

outer side

of demihull

Box length

Length of main deck

Symbol

Computer

Symbol

Definition or

Explanation

to trailing edge

Symbol

Computer

Symbol

Definition or

Explanation

hull vessel

ence correction

RFMH - Σ RF

tion of multi-hull

RTMH - RFMH

ence correction

RRMH - Σ RR

vessel

correction

RTMH - Σ RT

33 Hydrofoil Boats

Symbol

Computer

Symbol

Definition or

Explanation

33 Hydrofoil Boats

cluding foils

Span of struts

tance of struts

Mean chord length

section with foil

Weight of foil

Dihedral angle

Submerged foil area

take-off speed

33 Hydrofoil Boats

Symbol

Computer

Symbol

Definition or

Explanation

Foil span wetted

distance

V (g LF)12

chord length

V (g cM)12

foilborne

Flight height

at rest

Keel clearance

centre of gravity

and rear foils

lF + lR

centre of gravity

Foil immersion

ALFIND

with twist

33 Hydrofoil Boats

Symbol

Computer

Symbol

Definition or

Explanation

33 Hydrofoil Boats

Symbol

Computer

Symbol

Definition or

Explanation

Foil drag

CDF AFR q

CDF AFF q

DRIND Induced drag

of motion

Interference drag

secting foil

Streamline drag

Spray drag

Strut drag

Wave drag

Ventilation drag

Lift force on foil

CL AFT q

CL AFF q

CL AFR q

attack of zero

CL0 AFT q

CLTO AFT q

33 Hydrofoil Boats

Symbol

Computer

Symbol

Definition or

Explanation

DP (AFS q) 1

L0 (AFS q) 1

condition

LTO (AFS q) 1

34 ACV and SES

Symbol

Computer

Symbol

Definition or

Explanation

34 ACV and SES

Cushion area

Cushion beam

At the water line

neath craft

Bow seal height

Skirt depth

Stern seal height

Cushion length

at rest off cushion

to structure

needs clarification

34 ACV and SES

Symbol

Computer

Symbol

Definition or

Explanation

structure

needs clarification

to structure

needs clarification

to water contact

SSHC SSH0

cushion periphery

of air

the skirt

34 ACV and SES

Symbol

Computer

Symbol

Definition or

Explanation

coefficient

R0 (ρA VR2 AC 2) 1

PCU LC Pam

in general

ρA QT VA N

of cushion

ρA QCU VA N

of skirt

ρA QTS VA N

34 ACV and SES

Symbol

Computer

Symbol

Definition or

Explanation

Symbol

Computer

Symbol

Definition or

Explanation

sistance

RI (ρI g h2 B)

of ice

RIW (S qIW)

normal

rection of motion

thickness

V (g hI)

ice force

ice (dynamic)

ice (static)

condition)

Thickness of ice

KQICMS

in ice

QIA (ρW nIA

KTICMS

in ice

TIA (ρW nIA

FRICMS

revolution in ice

Symbol

Computer

Symbol

Definition or

Explanation

in ice

2 π QIA nIA

Net ice resistance

RIT - RIW

in presence of ice

in ice

ciency in ice

ηID ηD

36 Sailing Vessels

Symbol

Computer

Symbol

Definition or

Explanation

36 Sailing Vessels

Area of mainsail

Area of spinnaker

(P E + I J) 2

Beam overall

Mainsail base

Fore triangle base

Mainsail height

olds Number

noe body

Effective draught

FH (ρVB

tical centre plane

36 Sailing Vessels

Symbol

Computer

Symbol

Definition or

Explanation

Displacement force

(weight) of keel

Displacement force

(weight) of rudder

36 Sailing Vessels

Symbol

Computer

Symbol

Definition or

Explanation

cient (upright)

RFU (S q)

cient (upright)

RRU (S q)

Total resistance

RTU (S q)

(upright)

RTφ (S q)

Cx Cy Cz

Force coefficients

Side force

right)

RTU + Rφ

Rφ RH

Vessel velocity

36 Sailing Vessels

Symbol

Computer

Symbol

Definition or

Explanation

True wind velocity

course

leaway angle

to boat course)

boat course)

Version 2014 130

4 BACKGROUND AND

REFERENCES

421 Classification

cross-references

list of symbols

drawing

standard itself

exponentiation

operators

matrix components

quantities

A ( eg Area in

msup2)

Version 2011 133

Numbers in roman

(power of n)

SYMBOLS

in italic

NUMBERS

in roman

(T = Thrust)

(M = Model) Fig 1

1 Scope

TK 102

A=A-[A]

as described above

NUMERICAL VALUES

AB = A B - [A] [B]

Version 2014 135

EXAMPLE

Ek = 2

1mvsup2

rived quantities

intensity J

51992 annex A)

dim Q = AαBβCγ

becomes in general

EXAMPLES

Quantity Dimension

velocity LT-1

force LMT-2

energy L2MT-2

relative density 1

Version 2014 136

23 Units

merical values

- base units

2321 Base units

Name Symbol

length metre m

mass kilogram kg

time second s

thermodynamic tem-

perature kelvin K

tary units

L rarr m I rarr A

M rarr kg Θ rarr K

T rarr s N rarrmol

J rarr cd

Derived quantity

SI derived unit

EXAMPLES

Version 2014 138

expressed in terms

of the seven base

units (and the sup-

plementary units in

some cases)

velocity ms

force kg ms2

energy kg m2s2

relative density 1

2323 SI prefixes

Factor Prefix

Name Symbol

1024 yotta Y

1021 zetta z

1018 exa E

1015 peta P

1012 tera T

109 giga G

106 mega M

103 kilo k

102 hecto h

10 deca da

10-1 deci d

10-2 centi c

10-3 milli m

10-6 micro micro

10-9 nano n

10-12 pico p

10-15 femto f

10-18 atto a

10-21 zepto z

10-24 yocto y

fixes see 324

233 The unit one

EXAMPLE

EXAMPLES

Plane angle α = 05

rad = 05

1 with a prefix

for the number 001

shall not be used

neous units

stance

51992 Annex A

with the Sl

Quantity Unit

Name Sym-

bol Definition

time minute

1 min= 60s

1 h = 60 min

1 d = 24 h

plane an-

degree

minute

second

1 deg =

(π180)rad =

(nl80) rad

1 = (160)deg

1 = (160)

= 1 dm

Name Sym-

bol Definition

the kinetic energy

tron in passing

through a potential

in vacuum 1 eV

1602 177 times10-19 J

mass unified

atomic

mass unit

(1 12) of the mass

of an atom of the

nuclide 12C 1u

1660 540 times10-27kg

Tables 5 and 6

the curie

and numbers

311 Symbols

sentence

use of subscripts

right) type

EXAMPLES

Upright sub-

number)

numbers)

(sloping) type

eg a∙ b-1

EXAMPLE

EXAMPLES

m metre

s second

A ampere

Wb weber

N∙m N m

symbol for a prefix

EXAMPLE

Version 2014 142

m ms m∙s-1

mendation

EXAMPLE

units (see 322)

EXAMPLES

1cm3 = (10-2m)3=10-6 m3

1 μs-1= (10-6 s)-1 = 106 s-1

1 kAm = (103A)m = 103 Am

crokilogram (μkg)

33 Numbers

man (upright) type

332Decimal sign

for the quantities

EXAMPLES

l = 12 m - 7 m= (12 - 7) m = 5m

clides

EXAMPLES

H He C Ca

A and 150 31-91992 annex A

script position

4O or (PO4)3-

types)

alpha Α a Α a

beta Β β Β β

gamma Γ γ Γ γ

delta Δ δ Δ δ

epsilon Ε ε Ε ε

zeta Ζ ζ Ζ ζ

eta Η η Η η

theta Θ θ Θ θ

iota Ι ι Ι ι

kappa Κ κ Κ κ

lambda Λ λ Λ λ

mu Μ μ Μ μ

nu Ν ν Ν ν

xi Ξ ξ Ξ ξ

omicron Ο ο Ο ο

pi Π π Π π

rho P ρ Ρ ρ

sigma Σ σ Σ σ

tau Τ τ Τ τ

upsilon Υ υ Υ υ

phi Φ φ Φ φ

chi Χ χ Χ χ

psi Ψ ψ Ψ ψ

omega Ω ω Ω ω

52 Computer symbols

Version 2014 145

52 Computer Symbols

- 9 have been used

near future

53 Documentation

Version 2014 146

53 Documentation

531 ITTC Documents

No500 1976

No6 1978

CETENA Genova 1984

532 Translations

malisation (AFNOR)

No28 Zagreb 1974

truccion Naval

53 Documentation

Version 2014 147

Table of Contents

1 General


111 Uncertainty















122 Loads

1221 External Loads



1231 Motions

1232 Attitudes

13 Fluid Mechanics

131 Flow Parameters




132 Flow Fields

1321 Velocities etc



1331 Geometry


1333 Forces


134 Boundary Layers


135 Cavitation


1352 Flow fields

1353 Pumps


141 Waves

1411 Periodic waves





142 Wind


143 Ice Mechanics


15 Noise


2 Ships in General

21 Basic Quantities


221 Hull Geometry






2222 Ducts


2224 Pods


























235 Water Jets


241 Manoeuvrability





2415 Linear Models




242 Sea Keeping




3 Special Craft











33 Hydrofoil Boats






34 ACV and SES





36 Sailing Vessels






421 Classification





52 Computer Symbols

53 Documentation

531 ITTC Documents

532 Translations


Stability 68

141 on Waves) 70

Subscripts 73

235 Water Jets 83

242 Sea Keeping 94

Capsizing 96

Subscripts 104

3 SPECIAL CRAFT 106

Vessels 106

symbols) 112

34 ACV and SES 120

structured list 130

Symbol

Computer

Symbol

Definition or

Explanation

1 GENERAL

111 Uncertainty

distribution

a = (a+ndash a_) 2

xi b+ = a+ - xi

xi b_ = xi ndash a_

Symbol

Computer

Symbol

Definition or

Explanation

depends

q Random quantity 1

ing quantity q

Type A evaluation

tion of the mean

)(2 qs

Type A evaluation

)( 12 Xs

put means

Symbol

Computer

Symbol

Definition or

Explanation

bility p

quantity Xi

tainty

tainty from Type A

tainty from Type B

tainty

measurement

22 )]([)( iii xucyu 1

mate y

Symbol

Computer

Symbol

Definition or

Explanation

mate xi

mate y

estimates xi and xj

U = k uc(y)

Up = kp uc(y)

tion i ix X

measurand Y depends

variable

Symbol

Computer

Symbol

Definition or

Explanation

quantity Xi

servation of Xi

Output estimate

same measurement

Y A measurand

certainty Up

root of 2

Symbol

Computer

Symbol

Definition or

Explanation

n estimated by

tive square root of

tities

in the following

tion if any

Axes coordinates

Body axes (xyz)

platforms or ships

upwards

section

flight dynamics

ular case

differential

Name of coordi-

nate system

Remarks

11-121

cartesian

coordinates

system See Figure 1

11-122

cylindrical

coordinates

11-123

(-) r φ r=rer

r sin dφ eφ

spherical

Figures 3 and 5

Symbol

Computer

Symbol

Definition or

Explanation

lar quantity

scalar distribution

εikjxkds

εklixlεjkm xmds

Sij = S0ij

Si 3+j = S1ij

S3+i j = S1ij

S3+i 3+j = S2ij

tesian coordinates

fixed in the body

Tijs + Tij

tensor

( Tij - Tji ) 2

Symbol

Computer

Symbol

Definition or

Explanation

V3+i = V1i

X X(1)

Y X(2)

Z X(3)

the body

x0 x01

y0 x02

z0 x03

X0 X0(1)

Y0 X0(2)

Z0 X0(3)

xF xF1

yF xF2

zF xF3

XF XF(1)

YF XF(2)

ZF XF(3)

1 ijk = 321 213 132

0 if otherwise

Symbol

Computer

Symbol

Definition or

Explanation

f FR Frequency Hz

functions

1 TC Hz

Laurent transform

Laplace transform

t TI Time - + s

Symbol

Computer

Symbol

Definition or

Explanation

pled function

= X(0)2 + fSXF(f + jfS)

inverse form

XF(f)=XL(f)

t = 0 TC

XF = xFjδ(f - jTC)

inverse form

Hilbert transform

(1t)F = -i sgn f

if X(tlt0) = 0 then

= (X(t)exp(-at))F

ie = 0 for f lt 0

rier series

XFj(1 + sgn j)

line spectra

Symbol

Computer

Symbol

Definition or

Explanation

component

zl ZLG (Phase) Lag

component

Symbol

Computer

Symbol

Definition or

Explanation

gE gM gMR

E(g) = g(x)fx(x)dx

Random quantities

x(ζ) y(ζ)

X(I) Y(I)

i = 1 n

n sample size

quantity

xD xDR σx

dom quantity

xVR frac12

xDS sx

dom quantity

xVS 12

xxR xxMR Rxx

dom quantity

xyR xyMR Rxy

dom quantities

xE xM xMR

xA xMS mx

a random quantity

1n xi i = 1n

xAE = xE

xVSE = xV n

xPD fx

dom quantity

d Fx dx

xyPD fxy

2 Fxy (x y)

xPF Fx

xyPF Fxy

random quantities

Symbol

Computer

Symbol

Definition or

Explanation

xV xVR xxVR

XVR XXVR

x2 E - xE 2

xVS xxVS

XVS XXVS

dom quantity

1 (n - 1) (xi - x

i = 1n

xyV xyVR

quantities

x yE - xE yE

periment

dom quantity

t =-T2 +T2

T =- +

A(g(t)) = 1T g(t)dt

t =0 +T

x(ζt) y(ζt)

xxC xxCR Cxx

(x(t) - xE)(x(t + τ) - xE)E

xyC xyCR Cxy

(x(t) - xE)(y(t + τ) - yE)E

xxR xxRR Rxx

Rxx(τ) = Rxx(-τ)

= x(t)x(t + τ)MR

τ = 0

xyR Rxy

Ryx(τ) = Rxy(-τ)

if x y are ergodic

Symbol

Computer

Symbol

Definition or

Explanation

xxS Sxx

chastic process

xxRRSR

xyS Sxy

processes

xyRRSR

periment

Average sample mean

Sample covariance

Sample deviation

E M MR

Probability density

(Power) Spectrum

Sample spectrum

Sample correlation

Population variance

Sample variance

Symbol

Computer

Symbol

Definition or

Explanation

control volume

Inward positive QUs

control volume

quantity stored

dq dt QUs

Symbol

Computer

Symbol

Definition or

Explanation

AM(IJ)

DA(IJ)

RF(IJ)

uv DH(UV)

damping

u FH(U)

uv IH(UV)

inertia

of water-plane area

Iy Iyy

IY IYY

M2(22)

MA(55)

Iz Izz

IZ IZZ

M2(33)

MA(66)

Ixy I12

Iyz I23

Izx I31

IXY I2(12)

IYZ I2(23)

IZX I2(31)

kx kxx

(Ixxm)12

Symbol

Computer

Symbol

Definition or

Explanation

ky kyy

(Iyym)12

kz kzz

(Izzm)12

M0(IJ)

MA(IJ)

tensor

mij = m δij

ij M1(IJ)

M2(IJ)

IN(IJ)

MA(UV)

system

Mij = M0

Mi 3+j = M1Tij

M3+i j = M1ij

M3+i 3+j = M2ij

Symbol

Computer

Symbol

Definition or

Explanation

122 Loads

1221 External Loads

in body coordinates

u = MMu

Fi = F0i

F3+i = F1i

gi = g1

g3+i = 0

in body coordinates

F11 F4

K M(1)

F1(1) F(4)

F12 F5

M M(2)

F1(2) F(5)

FN13 F6

N M(3)

F1(3) F(6)

F01 F1

F0(1) F(1)

axis x

F02 F2

F0(2) F(2)

axis y

F03 F3

F0(3) F(3)

axis z

Gu = muv gv

G0i Gi

in body coordinates

Gi = G0

i = m0ij gj

i G1(I)

in body coordinates

G3+i = G1

i = εikj xk G0

= m1ij gj

dW dx1

Symbol

Computer

Symbol

Definition or

Explanation

section coordinates

FSi = FS0

FS3+i = FS1

i = MBi

FS11 Nm

Symbol

Computer

Symbol

Definition or

Explanation

1231 Motions

v01 v4

V0(1) V(4)

body axis x

v02 v5

V0(2) V(5)

body axis y

v03 v6

V0(3) V(6)

body axis z

v11 v1

V1(1) V(1)

v12 v2

V1(2) V(2)

v13 v3

V1(3) V(3)

body axes

vi = v1

v3+i = v0i

tive to body axes

Symbol

Computer

Symbol

Definition or

Explanation

1232 Attitudes

Angle of attack

the z-axis

about the xo axis

X(4) RO

X(5) TR

X(6) YA

course

13 Fluid Mechanics

Symbol

Computer

Symbol

Definition or

Explanation

13 Fluid Mechanics

131 Flow Parameters

Velocity of sound

(E ρ)12

Weight density

ρg (See 111)

Viscosity

Kinematic viscosity

DN RHO

Mass density

Capillarity

length

Boussinesq number

V (g RH)12

Cauchy number

V (E ρ)12

Froude number

V (g L)12

Froude depth number

V (g h)12

V (g 13)12

Mach number

Reynolds number

Strouhal number

Thoma number

Cavitation number

(pA ndash pV)q

Weber number

V2 L κ

07R Ac V nDRe

13 Fluid Mechanics

Symbol

Computer

Symbol

Definition or

Explanation

Sand roughness

surface

Hydraulic radius

wetted perimeter

13 Fluid Mechanics

Symbol

Computer

Symbol

Definition or

Explanation

132 Flow Fields

1321 Velocities etc

energy

ρ V2 2 + p + ρ g h

Mass specific force

Total head

e w = h +pw +qw

flow energy

turbed flow

ρ V2 2

Rate of flow

Total head loss

ij SR(IJ)

ρ vivj

Pa sij

ST(IJ)

Total stress tensor

change

ij SV(IJ)

Viscous stress

u vx v1

v vy v2

w vz v3

Velocity

V = vivi

Wall shear stress

μ (U y)y=0

13 Fluid Mechanics

Symbol

Computer

Symbol

Definition or

Explanation

Induction factor

Vortex density

Circulation

intV ds

along a closed line

Potential function

Stream function

ψ = const

surface

13 Fluid Mechanics

Symbol

Computer

Symbol

Definition or

Explanation

1331 Geometry

Projected area

Wing or foil span

Flap span

Mean chord length

Tip chord length

Root chord length

Sweep angle

tion (general)

edge of struts

(general)

of foil

section

tS cSTH

Taper ratio

Aspect ratio

13 Fluid Mechanics

Symbol

Computer

Symbol

Definition or

Explanation

Induced velocity

and the chord line

or incidence

Geometric angle of

attack or incidence

Hydrodynamic angle

of attack

zero lift

Angle of zero lift

at zero lift

13 Fluid Mechanics

Symbol

Computer

Symbol

Definition or

Explanation

1333 Forces

Foil drag

DRIND Induced drag

of motion

Interference drag

secting foil

zero lift

Streamline drag

Lift force on foil

CL AFT q

of zero

CL0 AFT q

Lift-Drag ratio

13 Fluid Mechanics

Symbol

Computer

Symbol

Definition or

Explanation

134 Boundary Layers

τ (ρ Ue

Entrainment factor

1 (Ue dQ dx)

rameter

(δ - δ) Θ

Static pressure

Total pressure

Entrainment

U δ v or Ue δ

RTHETA

U Θ v or Ue Θ v

boundary layer

from surface

(τ ρ)12

boundary layer

from the surface

(Ue- U) uτ

13 Fluid Mechanics

Symbol

Computer

Symbol

Definition or

Explanation

from the wall

y uτ v

δ (τw dp dx)

layer at U=0995Ue

δ δ1

boundary layer

(Ue- U) Ue dy

von Karman constant

δ995 (v dUe dx)

Energy thickness

(U Ue) (1 - U2 Ue

Momentum thickness

(U Ue) (1 - U Ue)dy

Local skin friction

μ (U y)y=0

13 Fluid Mechanics

Symbol

Computer

Symbol

Definition or

Explanation

135 Cavitation

Gas content ratio

α αS

Gas content

temperature

Cavitation number

(pA - pC) q

(pA - pV) q

1352 Flow fields

Cavity drag

Cavity length

region

Ambient pressure

Critical pressure

takes place

Cavity pressure

quasi-steady cavity

Critical velocity

takes place

Volume loss

13 Fluid Mechanics

Symbol

Computer

Symbol

Definition or

Explanation

WL WTLS

Weight loss

specified time

1353 Pumps

turbo-engines

Thoma number

(HU - pV w) HN

Symbol

Computer

Symbol

Definition or

Explanation

141 Waves

1411 Periodic waves

lerity LW TW =

2WgL in

deep water

odic wave

const = cW

lerity

i fW Hz

wave crest to wave

wave ηC - ηT

advance

Symbol

Computer

Symbol

Definition or

Explanation

at a given location

ηFSα m

ηFSp rad

crossing

trough

crossing

and crest

wave heights

crossing

of zero in a record

Symbol

Computer

Symbol

Definition or

Explanation

in a record

Negative values m

crossing

visual observation

cant wave height

wave heights

wave height

heights

visual observation

wave propagation

samples

visual observation

Symbol

Computer

Symbol

Definition or

Explanation

lution

points

tude function

4 (m0)12 m

fn S(f)df m2 sn

Si(ω)

tral density

Sr(ω)

tral density

Sη(f)

Sη(ω)

2πfP s

and first moment

m0m1 s

and second moment

(m0m2)12 s

Symbol

Computer

Symbol

Definition or

Explanation

DX(fθ)

DX(ωμ)

SIGMAOX

Sζ (ωμ)

Sθ (ωμ)

density

Sρ(fθ)

Sζ(ωμ)

θm MWD

THETAMOX

rection

Symbol

Computer

Symbol

Definition or

Explanation

142 Wind

(008 + 0065U10)10-3

Fetch length

wind blows

DURATN

Wind duration

Return period

ceeded

uz uzi

UFLUCT

USHEAR

Wind shear velocity

12 U10 or 071U10123

Reference mean wind

U10 = (10z)17 Uz

(Uz + uzi)

UzA = (z10)17 U10 or

see section 141

True wind velocity

see section 141

Dimensionless Fetch

face in meters

see section 26

True wind angle

see section 26

Wind direction

Symbol

Computer

Symbol

Definition or

Explanation

143 Ice Mechanics

weight of ice

volume of ice

unit volume of ice

15 Noise

Symbol

Computer

Symbol

Definition or

Explanation

15 Noise

acoustic centre

= 10 log10

(119903119898119904

1199011199031198901198912 ) dB 119901119903119890119891

tance of 1m

119871s

= 119871p

+ 20 log10 [119889

119889119903119890119891] dB 119889119903119890119891

Symbol

Computer

Symbol

Definition or

Explanation

2 SHIPS IN GENERAL

21 Basic Quantities

dv dt ms2

A A AR

Area in general m2

B B BR Breadth m

(forces)

d D D DI Diameter m

E E EN Energy J

F F0 F F0 Force N

h DE Depth m

H H HT Height m

mass distribution

L L LE Length m

tory velocity

m M MA

Mass kg

Symbol

Computer

Symbol

Definition or

Explanation

distribution

M MO Momentum Ns

P P PO Power W

r R RD Radius m

locity

t TI Time s

t TE Temperature K

harmonic process

of a body

ds dt ms

V VO Volume m3

specific weight

dW dV = ρg Nm3

acting on a body

tilled water at 4C

Symbol

Computer

Symbol

Definition or

Explanation

Symbol

Computer

Symbol

Definition or

Explanation

221 Hull Geometry

gitudinal plane

perpendicular

the final rounding

aft perpendiculars

port and starboard)

waterline

relative wind

midship

of midship

section

of ships hull

Symbol

Computer

Symbol

Definition or

Explanation

water line

at stem

the perpendiculars)

maximum section

verse section

Symbol

Computer

Symbol

Definition or

Explanation

point of the stern

pendicular

dicular

perpendicular

with straight keel

water surface level

bare hull

ΔBH (ρ g) m3

pendages

ΔAP (ρ g) m3

Symbol

Computer

Symbol

Definition or

Explanation

ancy) g ρ N

= TS TM

cient B 13 1

GM 13 1

GZ 13 1

cient KG T

12 IL ( B L3) 1

12 IT (B3 L) 1

AM (B T) 1

body A (AX L 2) or

A (AM L 2)

trance E (AX LE) or

E (AM LE)

body F (AX L 2) or

F (AM L 2)

Symbol

Computer

Symbol

Definition or

Explanation

R (AM LR)

AWA (B L 2) 1

forward

AWF (B L 2) 1

coefficient

maximum area

ABL (L T) 1

ABT AX 1

transom stern

AT AX 1

L 13 1

cient T 13 1

A AB After body

APP APP Appendages

B BH Bare hull

DW Design waterline

E EN Entry

Symbol

Computer

Symbol

Definition or

Explanation

F FB Fore body

FS Frame spacing

H HE Hull

LR Reference Line

LP LP Based on LPP

LW LW Based on LWL

M MS Midships

PB Parallel body

R RU Run

SS Station spacing

W WP Water plane

S WS Wetted surface

Symbol

Computer

Symbol

Definition or

Explanation

boss or hub

radius

hub to the tip

Symbol

Computer

Symbol

Definition or

Explanation

blades

2 π r sin (φ) z m

positive rake

the propeller plane

iG + iS = cS sinφ

shoulder

Symbol

Computer

Symbol

Definition or

Explanation

ing aft shoulder

rh RH Hub radius m

ler blade

ler axis

dicular

above base line

Symbol

Computer

Symbol

Definition or

Explanation

cal skew angle

Symbol

Computer

Symbol

Definition or

Explanation

2222 Ducts

LD LD Duct length m

ler plane

of duct

tion s

Jet System Head m

at station 1A

Symbol

Computer

Symbol

Definition or

Explanation

2224 Pods

Main Body

tom Fin

Bottom Fin

under pod main body

D Duct (subscript)

Symbol

Computer

Symbol

Definition or

Explanation

appendage

of rudder

propeller race

hydrofoil

lel to keel

Symbol

Computer

Symbol

Definition or

Explanation

rudders

of flanking rudders

BK Bilge keel

BS Bossing

FB Bow foil

FR Flanking rudder

FS Stern foil

KL Keel

RU Rudder

RF Rudder flap

SA Stabilizer

SH Shafting

SK Skeg

ST Strut

TH Thruster

WG Wedge

Symbol

Computer

Symbol

Definition or

Explanation

curves of stability

volume

Centre of buoyancy

volume

ter plane

(mass)

Keel reference

XCB LCB

ancy (LCB)

from Midships

XCF LCF

tion (LCF)

from Midships

Symbol

Computer

Symbol

Definition or

Explanation

from Midships

XCG LCG

ity (LCG)

from Midships

gravity G

centre of buoyancy

curves of stability

Symbol

Computer

Symbol

Definition or

Explanation

centre of buoyancy

metacentre M

pendicular

dicular

pendicular

weight addition

101 GGKGKG m

height

to the metacentre

tion effects

centric height

metacentre ML

KGKMGM LL

TAG cosφ

KB-KM =I =BM T

BM KM KB

Symbol

Computer

Symbol

Definition or

Explanation

base or keel K

metacentre M to the

ing arm

Heeling moment Δ m

GM 13 1

GZ 13 1

cient KG T

ficient

proximately equals

Symbol

Computer

Symbol

Definition or

Explanation

ficient

proximately equals

one centimetre

one meter

ΔCMTL Nmm

force g ρ N

flooded water

Δfw (ρg) m3

Symbol

Computer

Symbol

Definition or

Explanation

the compartment

bility

a apparent

A att attained

d dyn dynamic

e EFF effective

f false

KL keel line

L longitudinal

MAX maximum

s Static

S sqt Sinkage squat

TC Trim in cm

TM Trim in m

T transverse

V vertical

0 Initial

at heel angle

θ at trim angle θ

Symbol

Computer

Symbol

Definition or

Explanation

231 Hull Resistance

cross section area

lowance

propulsion tests

[(1 + k) CFM + CR]

surface of the body

bare hull

SBH + SAPP m2

Symbol

Computer

Symbol

Definition or

Explanation

area underway

area at rest

area underway

area at rest

lation

RA (S q) 1

ficient

RAA (AV qR) 1

RAPP (S q) 1

cient of a body

RF (S q) 1

RF0 (S q) 1

RP (S q) 1

coefficient

RPV (S q) 1

Symbol

Computer

Symbol

Definition or

Explanation

RR (S q) 1

g R L (ΔV2) 1

efficient

RV (S q) 1

efficient

RW (S q) 1

efficient

1000 R (Δ(KC)2)

1000 RF (Δ(KC)2) 1

sliding bodies

(CV - CF0) CF0 1

(4πg)12VK16

sponding to KQ KT

R (ρ D4 n2) 1

ρ V2 2

see 332

qR PDWR

apparent wind

ρ VWR2 2

see 342

Symbol

Computer

Symbol

Definition or

Explanation

tio in general

R Δ 1

placement ratio

RR Δ 1

FW Fresh water

MR Raw model data

OW Open water

SW Salt water

Symbol

Computer

Symbol

Definition or

Explanation

of revolution

Brake power

Delivered power

propeller power

Effective power

resistance power

Indicated power

Shaft power

Thrust power

Torque

Running trim

Ship speed

or torque identity

2 π n

Symbol

Computer

Symbol

Definition or

Explanation

(T - RT) RT

Δ23 V3 PS

PD (ρ V3 23 2)

identity

PDT PDS

ηDS ηDM

factor

Sinkage dynamic

Trim dynamic

by length

(T - RT) T

(V - VA) V

(V - VA) VA

Symbol

Computer

Symbol

Definition or

Explanation

wTM - wTS

1978 method

diction

ηD PD PE - 1

resistance

PT PD = T VA (Q ω)

coefficient

PE PD = PR PP

Gearing efficiency

Hull efficiency

PE PT = PR PT

= (1 - t) (1 - w)

and propeller

water tests

ηB ηO

Shafting efficiency

PD PS = PP PS

Symbol

Computer

Symbol

Definition or

Explanation

lution

ler blade surface

advance speed

ρ VA2 2

ρ VS2 2 Pa

QS=QSC+ QSH

torque

peller unit

peller

Symbol

Computer

Symbol

Definition or

Explanation

at 07 R

(VA2+ (07 R ω)2)12

n PDfrac12 VA

with n in revsmin

VA in kn (obsolete)

n PTfrac12 VA

with n in revsmin

VA in kn (obsolete)

T (AP qA)

= (TP AP) qA

V (D n) = VH (D n) 1

ducted propeller

VP (D n)

identity

coefficient

QSC (ρ n2 D5) 1

Symbol

Computer

Symbol

Definition or

Explanation

torque coefficient

QSH (ρ n2 D5) 1

ficient

TP (ρ n2 D4) 1

KTP+ KTD 1

KQηR 1

feet VA in kn

efficiency

PJ PD = PJ PP 1

ηJP0 ZET0

zero advance speed

T (ρ π 2)13 (PD D)23 1

η0 ηTP0 ETA0

water tests

ducted propeller

TP TT 1

Symbol

Computer

Symbol

Definition or

Explanation

propeller

peller

by propeller

blade section

arctg (VA r ω)

Symbol

Computer

Symbol

Definition or

Explanation

u = 1 6

u = 1 2 3 force

u = 4 5 6 moment

coefficients

KFi and KMi

cients

Mi (ρ n2 D5) 1

p PR Pressure Pa

ing reaction

u = 1 6

u = 1 2 3 force

u = 4 5 6 moment

from the x-axis

Symbol

Computer

Symbol

Definition or

Explanation

placement

u = 1 6

u = 1 2 3 linear

u = 4 5 6 angular

u = 1 6

u = 1 2 3 linear

u = 4 5 6 angular

eration

u = 1 6

u = 1 2 3 linear

u = 4 5 6 angular

Symbol

Computer

Symbol

Definition or

Explanation

235 Water Jets

210 n2

at station s

cient at station s

rate transducer

Ej = (ρ2)VEj2dQj

j j i i

pg x u n dA

j j i i

pu g x u n dA

sion point

several pump stages

in i direction

u u n dA

Symbol

Computer

Symbol

Definition or

Explanation

dition)

impeller

turbed flow

tion s

boundary layer

msup3s

water jet system

msup3s

jet xT

dition)

system on the hull

Symbol

Computer

Symbol

Definition or

Explanation

at station s

station 7

station 1

tion 1A

surface

in x direction

ciency E

ciency JSE0

stream conditions

the pump

Symbol

Computer

Symbol

Definition or

Explanation

ciency

pump loop test

P duct I

Symbol

Computer

Symbol

Definition or

Explanation

241 Manoeuvrability

of rudder

(AR + ARmov) 2 m2

root to tip

AHL (L T) 1

h DE Water depth m

der axis

Symbol

Computer

Symbol

Definition or

Explanation

dp dt 1s2

dq dt 1s2

dr dt 1s2

du dt ms2

dv dt ms2

dw dt ms2

body axes

χ YX Yaw angle rad

Symbol

Computer

Symbol

Definition or

Explanation

RO Roll angle rad

Pitch angle

the hull

Drift angle

the hull

ANWIRL

ANRUEF

Bow fin angle

Stern fin angle

Rudder angle

ANRUOR

COWIAB

COWIRL

Symbol

Computer

Symbol

Definition or

Explanation

N r Nms2

N v Nms2

along body x-axis

X u Nsm

eration

X u Ns2m

tion of body axis y

Y r Ns2

Symbol

Computer

Symbol

Definition or

Explanation

Y v Ns2m

along body z-axis

2415 Linear Models

ship length

turning diameter

DC LPP 1

ameter δR = δ0

D0 LPP 1

unstable ship

Symbol

Computer

Symbol

Definition or

Explanation

unstable ship

turning rate

change of heading

heading

(starboard)

(port)

tr TIR Reach time s

Symbol

Computer

Symbol

Definition or

Explanation

track reach

Symbol

Computer

Symbol

Definition or

Explanation

242 Sea Keeping

system

spectively

Frequency

Alias horizontal

Alias vertical

moment

Alias horizontal

ing moment

Alias vertical

lution in waves

Symbol

Computer

Symbol

Definition or

Explanation

Sη(f) Sηη(f)

Sη(ω) Sηη(ω)

density

roll pitch yaw

rad TAW

Wave period

Yz(ω)

Azζ(ω)

tory motions

za(ω) ζa(ω) or

za(ω) ηa(ω)

Yθζ(ω)

Aθζ(ω)

motions

Θa(ω) ζa(ω) or

Tuning factor

w w wL L L

w w w= = =

q fL L L= = =

(short crested)

Symbol

Computer

Symbol

Definition or

Explanation

I991241

- I991242

lever curve

cording to ISO 8666

IMOIS IMOHSC2000

acter sets

Symbol

Computer

Symbol

Definition or

Explanation

curves of stability

volume

centre of buoyancy

metacentre M

volume

needed for crew

sons on board

ficient - I991243

proximately equals

hull - I99121

Symbol

Computer

Symbol

Definition or

Explanation

merged test weights

ter plane

pendicular

dicular

pendicular

(mass)

weight addition

101 GGKGKG m

weight addition

101 GGKGKG m

Symbol

Computer

Symbol

Definition or

Explanation

height

to the metacentre

KGKMGM

face effect)

tion effects

height

metacentre ML

KGKMGM LL

TAG cos φ

IMOtable

profile

K Keel reference

base of keel or K

Symbol

Computer

Symbol

Definition or

Explanation

base of keel or K

metacentre M to the

condition - IMOIS

IMOtable

ment due to crew

is taken of rolling

Symbol

Computer

Symbol

Definition or

Explanation

inclination

centimetre

meter CMTL Nmm

due to wind

above waterline

PV Wind pressure Pa

s Wave steepness 1

according to hellip

value see hellip

Symbol

Computer

Symbol

Definition or

Explanation

TL Turning lever m

IMOHSC2000

ancy (LCB)

of buoyancy B

tion (LCF)

of flotation F

ity (LCG)

of gravity G

gravity G

Symbol

Computer

Symbol

Definition or

Explanation

centre of buoyancy

force g N

gle during hellip

Symbol

Computer

Symbol

Definition or

Explanation

according to hellip

gle seehellip

bility

the compartment

stability curve

Symbol

Computer

Symbol

Definition or

Explanation

E Entrance

F Fore

Z Heave

θ Pitch

φ Roll

Symbol

Computer

Symbol

Definition or

Explanation

3 SPECIAL CRAFT

Planing bottom area

strips

gravity

Beam over chines

Transom breadth

spray strips

chines

spray strips

bossings

bottom

section

Shaft angle

inclined downwards)

Symbol

Computer

Symbol

Definition or

Explanation

derway

water surface level

(flange mounting)

forces underway

ing surface

(LK + LC) 2

planing hull

water line

SWS SS

spray edge

Symbol

Computer

Symbol

Definition or

Explanation

ALFBAR

Barrel flow angle

LM LWL

TRIMDWL

design waterline

(positive bow up)

θS θ0

Static trim angle

θV θD

LM (BLCG)

TAUDWL

reference line

Spray angle

plane of bottom)

tal friction area

normally to NA)

normally to NB)

Symbol

Computer

Symbol

Definition or

Explanation

force NPN

ler pressure forces

normally to NPP)

suction forces NPS

normal to NPS)

pressure forces NRP

normal to NRP)

normal to RAA)

normal to RAP)

normal to RF)

sistance RK

normal to RK)

drag ΔRRP

normal to ΔRRP)

thrust

normal to RT)

Symbol

Computer

Symbol

Definition or

Explanation

deadrise

Δ (BCG

surface

Δ (BCG

breadth

V (BCG g)12

Load coefficient

Δ (BCG

3 ρ g )

1 LVHD

drodynamic lift

Hydrostatic lift

Due to buoyancy

reference line

ence line

reference line

Symbol

Computer

Symbol

Definition or

Explanation

reference line

Keel drag

Induced drag

g ρ tg τ

Parasitic drag

openings

Total resistance

spray drag

CF SWS qS

of the hull

Spray velocity

the spray

Symbol

Computer

Symbol

Definition or

Explanation

Box beam

Beam of main deck

Hull spacing

Tunnel width

Hull diameter

submerged hulls

dinal position X

Deck clearance

ANENIN

nel (inner) side

of demihull

ANENOU

outer side

of demihull

Box length

Length of main deck

Symbol

Computer

Symbol

Definition or

Explanation

to trailing edge

Symbol

Computer

Symbol

Definition or

Explanation

hull vessel

ence correction

RFMH - Σ RF

tion of multi-hull

RTMH - RFMH

ence correction

RRMH - Σ RR

vessel

correction

RTMH - Σ RT

33 Hydrofoil Boats

Symbol

Computer

Symbol

Definition or

Explanation

33 Hydrofoil Boats

cluding foils

Span of struts

tance of struts

Mean chord length

section with foil

Weight of foil

Dihedral angle

Submerged foil area

take-off speed

33 Hydrofoil Boats

Symbol

Computer

Symbol

Definition or

Explanation

Foil span wetted

distance

V (g LF)12

chord length

V (g cM)12

foilborne

Flight height

at rest

Keel clearance

centre of gravity

and rear foils

lF + lR

centre of gravity

Foil immersion

ALFIND

with twist

33 Hydrofoil Boats

Symbol

Computer

Symbol

Definition or

Explanation

33 Hydrofoil Boats

Symbol

Computer

Symbol

Definition or

Explanation

Foil drag

CDF AFR q

CDF AFF q

DRIND Induced drag

of motion

Interference drag

secting foil

Streamline drag

Spray drag

Strut drag

Wave drag

Ventilation drag

Lift force on foil

CL AFT q

CL AFF q

CL AFR q

attack of zero

CL0 AFT q

CLTO AFT q

33 Hydrofoil Boats

Symbol

Computer

Symbol

Definition or

Explanation

DP (AFS q) 1

L0 (AFS q) 1

condition

LTO (AFS q) 1

34 ACV and SES

Symbol

Computer

Symbol

Definition or

Explanation

34 ACV and SES

Cushion area

Cushion beam

At the water line

neath craft

Bow seal height

Skirt depth

Stern seal height

Cushion length

at rest off cushion

to structure

needs clarification

34 ACV and SES

Symbol

Computer

Symbol

Definition or

Explanation

structure

needs clarification

to structure

needs clarification

to water contact

SSHC SSH0

cushion periphery

of air

the skirt

34 ACV and SES

Symbol

Computer

Symbol

Definition or

Explanation

coefficient

R0 (ρA VR2 AC 2) 1

PCU LC Pam

in general

ρA QT VA N

of cushion

ρA QCU VA N

of skirt

ρA QTS VA N

34 ACV and SES

Symbol

Computer

Symbol

Definition or

Explanation

Symbol

Computer

Symbol

Definition or

Explanation

sistance

RI (ρI g h2 B)

of ice

RIW (S qIW)

normal

rection of motion

thickness

V (g hI)

ice force

ice (dynamic)

ice (static)

condition)

Thickness of ice

KQICMS

in ice

QIA (ρW nIA

KTICMS

in ice

TIA (ρW nIA

FRICMS

revolution in ice

Symbol

Computer

Symbol

Definition or

Explanation

in ice

2 π QIA nIA

Net ice resistance

RIT - RIW

in presence of ice

in ice

ciency in ice

ηID ηD

36 Sailing Vessels

Symbol

Computer

Symbol

Definition or

Explanation

36 Sailing Vessels

Area of mainsail

Area of spinnaker

(P E + I J) 2

Beam overall

Mainsail base

Fore triangle base

Mainsail height

olds Number

noe body

Effective draught

FH (ρVB

tical centre plane

36 Sailing Vessels

Symbol

Computer

Symbol

Definition or

Explanation

Displacement force

(weight) of keel

Displacement force

(weight) of rudder

36 Sailing Vessels

Symbol

Computer

Symbol

Definition or

Explanation

cient (upright)

RFU (S q)

cient (upright)

RRU (S q)

Total resistance

RTU (S q)

(upright)

RTφ (S q)

Cx Cy Cz

Force coefficients

Side force

right)

RTU + Rφ

Rφ RH

Vessel velocity

36 Sailing Vessels

Symbol

Computer

Symbol

Definition or

Explanation

True wind velocity

course

leaway angle

to boat course)

boat course)

Version 2014 130

4 BACKGROUND AND

REFERENCES

421 Classification

cross-references

list of symbols

drawing

standard itself

exponentiation

operators

matrix components

quantities

A ( eg Area in

msup2)

Version 2011 133

Numbers in roman

(power of n)

SYMBOLS

in italic

NUMBERS

in roman

(T = Thrust)

(M = Model) Fig 1

1 Scope

TK 102

A=A-[A]

as described above

NUMERICAL VALUES

AB = A B - [A] [B]

Version 2014 135

EXAMPLE

Ek = 2

1mvsup2

rived quantities

intensity J

51992 annex A)

dim Q = AαBβCγ

becomes in general

EXAMPLES

Quantity Dimension

velocity LT-1

force LMT-2

energy L2MT-2

relative density 1

Version 2014 136

23 Units

merical values

- base units

2321 Base units

Name Symbol

length metre m

mass kilogram kg

time second s

thermodynamic tem-

perature kelvin K

tary units

L rarr m I rarr A

M rarr kg Θ rarr K

T rarr s N rarrmol

J rarr cd

Derived quantity

SI derived unit

EXAMPLES

Version 2014 138

expressed in terms

of the seven base

units (and the sup-

plementary units in

some cases)

velocity ms

force kg ms2

energy kg m2s2

relative density 1

2323 SI prefixes

Factor Prefix

Name Symbol

1024 yotta Y

1021 zetta z

1018 exa E

1015 peta P

1012 tera T

109 giga G

106 mega M

103 kilo k

102 hecto h

10 deca da

10-1 deci d

10-2 centi c

10-3 milli m

10-6 micro micro

10-9 nano n

10-12 pico p

10-15 femto f

10-18 atto a

10-21 zepto z

10-24 yocto y

fixes see 324

233 The unit one

EXAMPLE

EXAMPLES

Plane angle α = 05

rad = 05

1 with a prefix

for the number 001

shall not be used

neous units

stance

51992 Annex A

with the Sl

Quantity Unit

Name Sym-

bol Definition

time minute

1 min= 60s

1 h = 60 min

1 d = 24 h

plane an-

degree

minute

second

1 deg =

(π180)rad =

(nl80) rad

1 = (160)deg

1 = (160)

= 1 dm

Name Sym-

bol Definition

the kinetic energy

tron in passing

through a potential

in vacuum 1 eV

1602 177 times10-19 J

mass unified

atomic

mass unit

(1 12) of the mass

of an atom of the

nuclide 12C 1u

1660 540 times10-27kg

Tables 5 and 6

the curie

and numbers

311 Symbols

sentence

use of subscripts

right) type

EXAMPLES

Upright sub-

number)

numbers)

(sloping) type

eg a∙ b-1

EXAMPLE

EXAMPLES

m metre

s second

A ampere

Wb weber

N∙m N m

symbol for a prefix

EXAMPLE

Version 2014 142

m ms m∙s-1

mendation

EXAMPLE

units (see 322)

EXAMPLES

1cm3 = (10-2m)3=10-6 m3

1 μs-1= (10-6 s)-1 = 106 s-1

1 kAm = (103A)m = 103 Am

crokilogram (μkg)

33 Numbers

man (upright) type

332Decimal sign

for the quantities

EXAMPLES

l = 12 m - 7 m= (12 - 7) m = 5m

clides

EXAMPLES

H He C Ca

A and 150 31-91992 annex A

script position

4O or (PO4)3-

types)

alpha Α a Α a

beta Β β Β β

gamma Γ γ Γ γ

delta Δ δ Δ δ

epsilon Ε ε Ε ε

zeta Ζ ζ Ζ ζ

eta Η η Η η

theta Θ θ Θ θ

iota Ι ι Ι ι

kappa Κ κ Κ κ

lambda Λ λ Λ λ

mu Μ μ Μ μ

nu Ν ν Ν ν

xi Ξ ξ Ξ ξ

omicron Ο ο Ο ο

pi Π π Π π

rho P ρ Ρ ρ

sigma Σ σ Σ σ

tau Τ τ Τ τ

upsilon Υ υ Υ υ

phi Φ φ Φ φ

chi Χ χ Χ χ

psi Ψ ψ Ψ ψ

omega Ω ω Ω ω

52 Computer symbols

Version 2014 145

52 Computer Symbols

- 9 have been used

near future

53 Documentation

Version 2014 146

53 Documentation

531 ITTC Documents

No500 1976

No6 1978

CETENA Genova 1984

532 Translations

malisation (AFNOR)

No28 Zagreb 1974

truccion Naval

53 Documentation

Version 2014 147

Table of Contents

1 General


111 Uncertainty















122 Loads

1221 External Loads



1231 Motions

1232 Attitudes

13 Fluid Mechanics

131 Flow Parameters




132 Flow Fields

1321 Velocities etc



1331 Geometry


1333 Forces


134 Boundary Layers


135 Cavitation


1352 Flow fields

1353 Pumps


141 Waves

1411 Periodic waves





142 Wind


143 Ice Mechanics


15 Noise


2 Ships in General

21 Basic Quantities


221 Hull Geometry






2222 Ducts


2224 Pods


























235 Water Jets


241 Manoeuvrability





2415 Linear Models




242 Sea Keeping




3 Special Craft











33 Hydrofoil Boats






34 ACV and SES





36 Sailing Vessels






421 Classification





52 Computer Symbols

53 Documentation

531 ITTC Documents

532 Translations


Symbol

Computer

Symbol

Definition or

Explanation

1 GENERAL

111 Uncertainty

distribution

a = (a+ndash a_) 2

xi b+ = a+ - xi

xi b_ = xi ndash a_

Symbol

Computer

Symbol

Definition or

Explanation

depends

q Random quantity 1

ing quantity q

Type A evaluation

tion of the mean

)(2 qs

Type A evaluation

)( 12 Xs

put means

Symbol

Computer

Symbol

Definition or

Explanation

bility p

quantity Xi

tainty

tainty from Type A

tainty from Type B

tainty

measurement

22 )]([)( iii xucyu 1

mate y

Symbol

Computer

Symbol

Definition or

Explanation

mate xi

mate y

estimates xi and xj

U = k uc(y)

Up = kp uc(y)

tion i ix X

measurand Y depends

variable

Symbol

Computer

Symbol

Definition or

Explanation

quantity Xi

servation of Xi

Output estimate

same measurement

Y A measurand

certainty Up

root of 2

Symbol

Computer

Symbol

Definition or

Explanation

n estimated by

tive square root of

tities

in the following

tion if any

Axes coordinates

Body axes (xyz)

platforms or ships

upwards

section

flight dynamics

ular case

differential

Name of coordi-

nate system

Remarks

11-121

cartesian

coordinates

system See Figure 1

11-122

cylindrical

coordinates

11-123

(-) r φ r=rer

r sin dφ eφ

spherical

Figures 3 and 5

Symbol

Computer

Symbol

Definition or

Explanation

lar quantity

scalar distribution

εikjxkds

εklixlεjkm xmds

Sij = S0ij

Si 3+j = S1ij

S3+i j = S1ij

S3+i 3+j = S2ij

tesian coordinates

fixed in the body

Tijs + Tij

tensor

( Tij - Tji ) 2

Symbol

Computer

Symbol

Definition or

Explanation

V3+i = V1i

X X(1)

Y X(2)

Z X(3)

the body

x0 x01

y0 x02

z0 x03

X0 X0(1)

Y0 X0(2)

Z0 X0(3)

xF xF1

yF xF2

zF xF3

XF XF(1)

YF XF(2)

ZF XF(3)

1 ijk = 321 213 132

0 if otherwise

Symbol

Computer

Symbol

Definition or

Explanation

f FR Frequency Hz

functions

1 TC Hz

Laurent transform

Laplace transform

t TI Time - + s

Symbol

Computer

Symbol

Definition or

Explanation

pled function

= X(0)2 + fSXF(f + jfS)

inverse form

XF(f)=XL(f)

t = 0 TC

XF = xFjδ(f - jTC)

inverse form

Hilbert transform

(1t)F = -i sgn f

if X(tlt0) = 0 then

= (X(t)exp(-at))F

ie = 0 for f lt 0

rier series

XFj(1 + sgn j)

line spectra

Symbol

Computer

Symbol

Definition or

Explanation

component

zl ZLG (Phase) Lag

component

Symbol

Computer

Symbol

Definition or

Explanation

gE gM gMR

E(g) = g(x)fx(x)dx

Random quantities

x(ζ) y(ζ)

X(I) Y(I)

i = 1 n

n sample size

quantity

xD xDR σx

dom quantity

xVR frac12

xDS sx

dom quantity

xVS 12

xxR xxMR Rxx

dom quantity

xyR xyMR Rxy

dom quantities

xE xM xMR

xA xMS mx

a random quantity

1n xi i = 1n

xAE = xE

xVSE = xV n

xPD fx

dom quantity

d Fx dx

xyPD fxy

2 Fxy (x y)

xPF Fx

xyPF Fxy

random quantities

Symbol

Computer

Symbol

Definition or

Explanation

xV xVR xxVR

XVR XXVR

x2 E - xE 2

xVS xxVS

XVS XXVS

dom quantity

1 (n - 1) (xi - x

i = 1n

xyV xyVR

quantities

x yE - xE yE

periment

dom quantity

t =-T2 +T2

T =- +

A(g(t)) = 1T g(t)dt

t =0 +T

x(ζt) y(ζt)

xxC xxCR Cxx

(x(t) - xE)(x(t + τ) - xE)E

xyC xyCR Cxy

(x(t) - xE)(y(t + τ) - yE)E

xxR xxRR Rxx

Rxx(τ) = Rxx(-τ)

= x(t)x(t + τ)MR

τ = 0

xyR Rxy

Ryx(τ) = Rxy(-τ)

if x y are ergodic

Symbol

Computer

Symbol

Definition or

Explanation

xxS Sxx

chastic process

xxRRSR

xyS Sxy

processes

xyRRSR

periment

Average sample mean

Sample covariance

Sample deviation

E M MR

Probability density

(Power) Spectrum

Sample spectrum

Sample correlation

Population variance

Sample variance

Symbol

Computer

Symbol

Definition or

Explanation

control volume

Inward positive QUs

control volume

quantity stored

dq dt QUs

Symbol

Computer

Symbol

Definition or

Explanation

AM(IJ)

DA(IJ)

RF(IJ)

uv DH(UV)

damping

u FH(U)

uv IH(UV)

inertia

of water-plane area

Iy Iyy

IY IYY

M2(22)

MA(55)

Iz Izz

IZ IZZ

M2(33)

MA(66)

Ixy I12

Iyz I23

Izx I31

IXY I2(12)

IYZ I2(23)

IZX I2(31)

kx kxx

(Ixxm)12

Symbol

Computer

Symbol

Definition or

Explanation

ky kyy

(Iyym)12

kz kzz

(Izzm)12

M0(IJ)

MA(IJ)

tensor

mij = m δij

ij M1(IJ)

M2(IJ)

IN(IJ)

MA(UV)

system

Mij = M0

Mi 3+j = M1Tij

M3+i j = M1ij

M3+i 3+j = M2ij

Symbol

Computer

Symbol

Definition or

Explanation

122 Loads

1221 External Loads

in body coordinates

u = MMu

Fi = F0i

F3+i = F1i

gi = g1

g3+i = 0

in body coordinates

F11 F4

K M(1)

F1(1) F(4)

F12 F5

M M(2)

F1(2) F(5)

FN13 F6

N M(3)

F1(3) F(6)

F01 F1

F0(1) F(1)

axis x

F02 F2

F0(2) F(2)

axis y

F03 F3

F0(3) F(3)

axis z

Gu = muv gv

G0i Gi

in body coordinates

Gi = G0

i = m0ij gj

i G1(I)

in body coordinates

G3+i = G1

i = εikj xk G0

= m1ij gj

dW dx1

Symbol

Computer

Symbol

Definition or

Explanation

section coordinates

FSi = FS0

FS3+i = FS1

i = MBi

FS11 Nm

Symbol

Computer

Symbol

Definition or

Explanation

1231 Motions

v01 v4

V0(1) V(4)

body axis x

v02 v5

V0(2) V(5)

body axis y

v03 v6

V0(3) V(6)

body axis z

v11 v1

V1(1) V(1)

v12 v2

V1(2) V(2)

v13 v3

V1(3) V(3)

body axes

vi = v1

v3+i = v0i

tive to body axes

Symbol

Computer

Symbol

Definition or

Explanation

1232 Attitudes

Angle of attack

the z-axis

about the xo axis

X(4) RO

X(5) TR

X(6) YA

course

13 Fluid Mechanics

Symbol

Computer

Symbol

Definition or

Explanation

13 Fluid Mechanics

131 Flow Parameters

Velocity of sound

(E ρ)12

Weight density

ρg (See 111)

Viscosity

Kinematic viscosity

DN RHO

Mass density

Capillarity

length

Boussinesq number

V (g RH)12

Cauchy number

V (E ρ)12

Froude number

V (g L)12

Froude depth number

V (g h)12

V (g 13)12

Mach number

Reynolds number

Strouhal number

Thoma number

Cavitation number

(pA ndash pV)q

Weber number

V2 L κ

07R Ac V nDRe

13 Fluid Mechanics

Symbol

Computer

Symbol

Definition or

Explanation

Sand roughness

surface

Hydraulic radius

wetted perimeter

13 Fluid Mechanics

Symbol

Computer

Symbol

Definition or

Explanation

132 Flow Fields

1321 Velocities etc

energy

ρ V2 2 + p + ρ g h

Mass specific force

Total head

e w = h +pw +qw

flow energy

turbed flow

ρ V2 2

Rate of flow

Total head loss

ij SR(IJ)

ρ vivj

Pa sij

ST(IJ)

Total stress tensor

change

ij SV(IJ)

Viscous stress

u vx v1

v vy v2

w vz v3

Velocity

V = vivi

Wall shear stress

μ (U y)y=0

13 Fluid Mechanics

Symbol

Computer

Symbol

Definition or

Explanation

Induction factor

Vortex density

Circulation

intV ds

along a closed line

Potential function

Stream function

ψ = const

surface

13 Fluid Mechanics

Symbol

Computer

Symbol

Definition or

Explanation

1331 Geometry

Projected area

Wing or foil span

Flap span

Mean chord length

Tip chord length

Root chord length

Sweep angle

tion (general)

edge of struts

(general)

of foil

section

tS cSTH

Taper ratio

Aspect ratio

13 Fluid Mechanics

Symbol

Computer

Symbol

Definition or

Explanation

Induced velocity

and the chord line

or incidence

Geometric angle of

attack or incidence

Hydrodynamic angle

of attack

zero lift

Angle of zero lift

at zero lift

13 Fluid Mechanics

Symbol

Computer

Symbol

Definition or

Explanation

1333 Forces

Foil drag

DRIND Induced drag

of motion

Interference drag

secting foil

zero lift

Streamline drag

Lift force on foil

CL AFT q

of zero

CL0 AFT q

Lift-Drag ratio

13 Fluid Mechanics

Symbol

Computer

Symbol

Definition or

Explanation

134 Boundary Layers

τ (ρ Ue

Entrainment factor

1 (Ue dQ dx)

rameter

(δ - δ) Θ

Static pressure

Total pressure

Entrainment

U δ v or Ue δ

RTHETA

U Θ v or Ue Θ v

boundary layer

from surface

(τ ρ)12

boundary layer

from the surface

(Ue- U) uτ

13 Fluid Mechanics

Symbol

Computer

Symbol

Definition or

Explanation

from the wall

y uτ v

δ (τw dp dx)

layer at U=0995Ue

δ δ1

boundary layer

(Ue- U) Ue dy

von Karman constant

δ995 (v dUe dx)

Energy thickness

(U Ue) (1 - U2 Ue

Momentum thickness

(U Ue) (1 - U Ue)dy

Local skin friction

μ (U y)y=0

13 Fluid Mechanics

Symbol

Computer

Symbol

Definition or

Explanation

135 Cavitation

Gas content ratio

α αS

Gas content

temperature

Cavitation number

(pA - pC) q

(pA - pV) q

1352 Flow fields

Cavity drag

Cavity length

region

Ambient pressure

Critical pressure

takes place

Cavity pressure

quasi-steady cavity

Critical velocity

takes place

Volume loss

13 Fluid Mechanics

Symbol

Computer

Symbol

Definition or

Explanation

WL WTLS

Weight loss

specified time

1353 Pumps

turbo-engines

Thoma number

(HU - pV w) HN

Symbol

Computer

Symbol

Definition or

Explanation

141 Waves

1411 Periodic waves

lerity LW TW =

2WgL in

deep water

odic wave

const = cW

lerity

i fW Hz

wave crest to wave

wave ηC - ηT

advance

Symbol

Computer

Symbol

Definition or

Explanation

at a given location

ηFSα m

ηFSp rad

crossing

trough

crossing

and crest

wave heights

crossing

of zero in a record

Symbol

Computer

Symbol

Definition or

Explanation

in a record

Negative values m

crossing

visual observation

cant wave height

wave heights

wave height

heights

visual observation

wave propagation

samples

visual observation

Symbol

Computer

Symbol

Definition or

Explanation

lution

points

tude function

4 (m0)12 m

fn S(f)df m2 sn

Si(ω)

tral density

Sr(ω)

tral density

Sη(f)

Sη(ω)

2πfP s

and first moment

m0m1 s

and second moment

(m0m2)12 s

Symbol

Computer

Symbol

Definition or

Explanation

DX(fθ)

DX(ωμ)

SIGMAOX

Sζ (ωμ)

Sθ (ωμ)

density

Sρ(fθ)

Sζ(ωμ)

θm MWD

THETAMOX

rection

Symbol

Computer

Symbol

Definition or

Explanation

142 Wind

(008 + 0065U10)10-3

Fetch length

wind blows

DURATN

Wind duration

Return period

ceeded

uz uzi

UFLUCT

USHEAR

Wind shear velocity

12 U10 or 071U10123

Reference mean wind

U10 = (10z)17 Uz

(Uz + uzi)

UzA = (z10)17 U10 or

see section 141

True wind velocity

see section 141

Dimensionless Fetch

face in meters

see section 26

True wind angle

see section 26

Wind direction

Symbol

Computer

Symbol

Definition or

Explanation

143 Ice Mechanics

weight of ice

volume of ice

unit volume of ice

15 Noise

Symbol

Computer

Symbol

Definition or

Explanation

15 Noise

acoustic centre

= 10 log10

(119903119898119904

1199011199031198901198912 ) dB 119901119903119890119891

tance of 1m

119871s

= 119871p

+ 20 log10 [119889

119889119903119890119891] dB 119889119903119890119891

Symbol

Computer

Symbol

Definition or

Explanation

2 SHIPS IN GENERAL

21 Basic Quantities

dv dt ms2

A A AR

Area in general m2

B B BR Breadth m

(forces)

d D D DI Diameter m

E E EN Energy J

F F0 F F0 Force N

h DE Depth m

H H HT Height m

mass distribution

L L LE Length m

tory velocity

m M MA

Mass kg

Symbol

Computer

Symbol

Definition or

Explanation

distribution

M MO Momentum Ns

P P PO Power W

r R RD Radius m

locity

t TI Time s

t TE Temperature K

harmonic process

of a body

ds dt ms

V VO Volume m3

specific weight

dW dV = ρg Nm3

acting on a body

tilled water at 4C

Symbol

Computer

Symbol

Definition or

Explanation

Symbol

Computer

Symbol

Definition or

Explanation

221 Hull Geometry

gitudinal plane

perpendicular

the final rounding

aft perpendiculars

port and starboard)

waterline

relative wind

midship

of midship

section

of ships hull

Symbol

Computer

Symbol

Definition or

Explanation

water line

at stem

the perpendiculars)

maximum section

verse section

Symbol

Computer

Symbol

Definition or

Explanation

point of the stern

pendicular

dicular

perpendicular

with straight keel

water surface level

bare hull

ΔBH (ρ g) m3

pendages

ΔAP (ρ g) m3

Symbol

Computer

Symbol

Definition or

Explanation

ancy) g ρ N

= TS TM

cient B 13 1

GM 13 1

GZ 13 1

cient KG T

12 IL ( B L3) 1

12 IT (B3 L) 1

AM (B T) 1

body A (AX L 2) or

A (AM L 2)

trance E (AX LE) or

E (AM LE)

body F (AX L 2) or

F (AM L 2)

Symbol

Computer

Symbol

Definition or

Explanation

R (AM LR)

AWA (B L 2) 1

forward

AWF (B L 2) 1

coefficient

maximum area

ABL (L T) 1

ABT AX 1

transom stern

AT AX 1

L 13 1

cient T 13 1

A AB After body

APP APP Appendages

B BH Bare hull

DW Design waterline

E EN Entry

Symbol

Computer

Symbol

Definition or

Explanation

F FB Fore body

FS Frame spacing

H HE Hull

LR Reference Line

LP LP Based on LPP

LW LW Based on LWL

M MS Midships

PB Parallel body

R RU Run

SS Station spacing

W WP Water plane

S WS Wetted surface

Symbol

Computer

Symbol

Definition or

Explanation

boss or hub

radius

hub to the tip

Symbol

Computer

Symbol

Definition or

Explanation

blades

2 π r sin (φ) z m

positive rake

the propeller plane

iG + iS = cS sinφ

shoulder

Symbol

Computer

Symbol

Definition or

Explanation

ing aft shoulder

rh RH Hub radius m

ler blade

ler axis

dicular

above base line

Symbol

Computer

Symbol

Definition or

Explanation

cal skew angle

Symbol

Computer

Symbol

Definition or

Explanation

2222 Ducts

LD LD Duct length m

ler plane

of duct

tion s

Jet System Head m

at station 1A

Symbol

Computer

Symbol

Definition or

Explanation

2224 Pods

Main Body

tom Fin

Bottom Fin

under pod main body

D Duct (subscript)

Symbol

Computer

Symbol

Definition or

Explanation

appendage

of rudder

propeller race

hydrofoil

lel to keel

Symbol

Computer

Symbol

Definition or

Explanation

rudders

of flanking rudders

BK Bilge keel

BS Bossing

FB Bow foil

FR Flanking rudder

FS Stern foil

KL Keel

RU Rudder

RF Rudder flap

SA Stabilizer

SH Shafting

SK Skeg

ST Strut

TH Thruster

WG Wedge

Symbol

Computer

Symbol

Definition or

Explanation

curves of stability

volume

Centre of buoyancy

volume

ter plane

(mass)

Keel reference

XCB LCB

ancy (LCB)

from Midships

XCF LCF

tion (LCF)

from Midships

Symbol

Computer

Symbol

Definition or

Explanation

from Midships

XCG LCG

ity (LCG)

from Midships

gravity G

centre of buoyancy

curves of stability

Symbol

Computer

Symbol

Definition or

Explanation

centre of buoyancy

metacentre M

pendicular

dicular

pendicular

weight addition

101 GGKGKG m

height

to the metacentre

tion effects

centric height

metacentre ML

KGKMGM LL

TAG cosφ

KB-KM =I =BM T

BM KM KB

Symbol

Computer

Symbol

Definition or

Explanation

base or keel K

metacentre M to the

ing arm

Heeling moment Δ m

GM 13 1

GZ 13 1

cient KG T

ficient

proximately equals

Symbol

Computer

Symbol

Definition or

Explanation

ficient

proximately equals

one centimetre

one meter

ΔCMTL Nmm

force g ρ N

flooded water

Δfw (ρg) m3

Symbol

Computer

Symbol

Definition or

Explanation

the compartment

bility

a apparent

A att attained

d dyn dynamic

e EFF effective

f false

KL keel line

L longitudinal

MAX maximum

s Static

S sqt Sinkage squat

TC Trim in cm

TM Trim in m

T transverse

V vertical

0 Initial

at heel angle

θ at trim angle θ

Symbol

Computer

Symbol

Definition or

Explanation

231 Hull Resistance

cross section area

lowance

propulsion tests

[(1 + k) CFM + CR]

surface of the body

bare hull

SBH + SAPP m2

Symbol

Computer

Symbol

Definition or

Explanation

area underway

area at rest

area underway

area at rest

lation

RA (S q) 1

ficient

RAA (AV qR) 1

RAPP (S q) 1

cient of a body

RF (S q) 1

RF0 (S q) 1

RP (S q) 1

coefficient

RPV (S q) 1

Symbol

Computer

Symbol

Definition or

Explanation

RR (S q) 1

g R L (ΔV2) 1

efficient

RV (S q) 1

efficient

RW (S q) 1

efficient

1000 R (Δ(KC)2)

1000 RF (Δ(KC)2) 1

sliding bodies

(CV - CF0) CF0 1

(4πg)12VK16

sponding to KQ KT

R (ρ D4 n2) 1

ρ V2 2

see 332

qR PDWR

apparent wind

ρ VWR2 2

see 342

Symbol

Computer

Symbol

Definition or

Explanation

tio in general

R Δ 1

placement ratio

RR Δ 1

FW Fresh water

MR Raw model data

OW Open water

SW Salt water

Symbol

Computer

Symbol

Definition or

Explanation

of revolution

Brake power

Delivered power

propeller power

Effective power

resistance power

Indicated power

Shaft power

Thrust power

Torque

Running trim

Ship speed

or torque identity

2 π n

Symbol

Computer

Symbol

Definition or

Explanation

(T - RT) RT

Δ23 V3 PS

PD (ρ V3 23 2)

identity

PDT PDS

ηDS ηDM

factor

Sinkage dynamic

Trim dynamic

by length

(T - RT) T

(V - VA) V

(V - VA) VA

Symbol

Computer

Symbol

Definition or

Explanation

wTM - wTS

1978 method

diction

ηD PD PE - 1

resistance

PT PD = T VA (Q ω)

coefficient

PE PD = PR PP

Gearing efficiency

Hull efficiency

PE PT = PR PT

= (1 - t) (1 - w)

and propeller

water tests

ηB ηO

Shafting efficiency

PD PS = PP PS

Symbol

Computer

Symbol

Definition or

Explanation

lution

ler blade surface

advance speed

ρ VA2 2

ρ VS2 2 Pa

QS=QSC+ QSH

torque

peller unit

peller

Symbol

Computer

Symbol

Definition or

Explanation

at 07 R

(VA2+ (07 R ω)2)12

n PDfrac12 VA

with n in revsmin

VA in kn (obsolete)

n PTfrac12 VA

with n in revsmin

VA in kn (obsolete)

T (AP qA)

= (TP AP) qA

V (D n) = VH (D n) 1

ducted propeller

VP (D n)

identity

coefficient

QSC (ρ n2 D5) 1

Symbol

Computer

Symbol

Definition or

Explanation

torque coefficient

QSH (ρ n2 D5) 1

ficient

TP (ρ n2 D4) 1

KTP+ KTD 1

KQηR 1

feet VA in kn

efficiency

PJ PD = PJ PP 1

ηJP0 ZET0

zero advance speed

T (ρ π 2)13 (PD D)23 1

η0 ηTP0 ETA0

water tests

ducted propeller

TP TT 1

Symbol

Computer

Symbol

Definition or

Explanation

propeller

peller

by propeller

blade section

arctg (VA r ω)

Symbol

Computer

Symbol

Definition or

Explanation

u = 1 6

u = 1 2 3 force

u = 4 5 6 moment

coefficients

KFi and KMi

cients

Mi (ρ n2 D5) 1

p PR Pressure Pa

ing reaction

u = 1 6

u = 1 2 3 force

u = 4 5 6 moment

from the x-axis

Symbol

Computer

Symbol

Definition or

Explanation

placement

u = 1 6

u = 1 2 3 linear

u = 4 5 6 angular

u = 1 6

u = 1 2 3 linear

u = 4 5 6 angular

eration

u = 1 6

u = 1 2 3 linear

u = 4 5 6 angular

Symbol

Computer

Symbol

Definition or

Explanation

235 Water Jets

210 n2

at station s

cient at station s

rate transducer

Ej = (ρ2)VEj2dQj

j j i i

pg x u n dA

j j i i

pu g x u n dA

sion point

several pump stages

in i direction

u u n dA

Symbol

Computer

Symbol

Definition or

Explanation

dition)

impeller

turbed flow

tion s

boundary layer

msup3s

water jet system

msup3s

jet xT

dition)

system on the hull

Symbol

Computer

Symbol

Definition or

Explanation

at station s

station 7

station 1

tion 1A

surface

in x direction

ciency E

ciency JSE0

stream conditions

the pump

Symbol

Computer

Symbol

Definition or

Explanation

ciency

pump loop test

P duct I

Symbol

Computer

Symbol

Definition or

Explanation

241 Manoeuvrability

of rudder

(AR + ARmov) 2 m2

root to tip

AHL (L T) 1

h DE Water depth m

der axis

Symbol

Computer

Symbol

Definition or

Explanation

dp dt 1s2

dq dt 1s2

dr dt 1s2

du dt ms2

dv dt ms2

dw dt ms2

body axes

χ YX Yaw angle rad

Symbol

Computer

Symbol

Definition or

Explanation

RO Roll angle rad

Pitch angle

the hull

Drift angle

the hull

ANWIRL

ANRUEF

Bow fin angle

Stern fin angle

Rudder angle

ANRUOR

COWIAB

COWIRL

Symbol

Computer

Symbol

Definition or

Explanation

N r Nms2

N v Nms2

along body x-axis

X u Nsm

eration

X u Ns2m

tion of body axis y

Y r Ns2

Symbol

Computer

Symbol

Definition or

Explanation

Y v Ns2m

along body z-axis

2415 Linear Models

ship length

turning diameter

DC LPP 1

ameter δR = δ0

D0 LPP 1

unstable ship

Symbol

Computer

Symbol

Definition or

Explanation

unstable ship

turning rate

change of heading

heading

(starboard)

(port)

tr TIR Reach time s

Symbol

Computer

Symbol

Definition or

Explanation

track reach

Symbol

Computer

Symbol

Definition or

Explanation

242 Sea Keeping

system

spectively

Frequency

Alias horizontal

Alias vertical

moment

Alias horizontal

ing moment

Alias vertical

lution in waves

Symbol

Computer

Symbol

Definition or

Explanation

Sη(f) Sηη(f)

Sη(ω) Sηη(ω)

density

roll pitch yaw

rad TAW

Wave period

Yz(ω)

Azζ(ω)

tory motions

za(ω) ζa(ω) or

za(ω) ηa(ω)

Yθζ(ω)

Aθζ(ω)

motions

Θa(ω) ζa(ω) or

Tuning factor

w w wL L L

w w w= = =

q fL L L= = =

(short crested)

Symbol

Computer

Symbol

Definition or

Explanation

I991241

- I991242

lever curve

cording to ISO 8666

IMOIS IMOHSC2000

acter sets

Symbol

Computer

Symbol

Definition or

Explanation

curves of stability

volume

centre of buoyancy

metacentre M

volume

needed for crew

sons on board

ficient - I991243

proximately equals

hull - I99121

Symbol

Computer

Symbol

Definition or

Explanation

merged test weights

ter plane

pendicular

dicular

pendicular

(mass)

weight addition

101 GGKGKG m

weight addition

101 GGKGKG m

Symbol

Computer

Symbol

Definition or

Explanation

height

to the metacentre

KGKMGM

face effect)

tion effects

height

metacentre ML

KGKMGM LL

TAG cos φ

IMOtable

profile

K Keel reference

base of keel or K

Symbol

Computer

Symbol

Definition or

Explanation

base of keel or K

metacentre M to the

condition - IMOIS

IMOtable

ment due to crew

is taken of rolling

Symbol

Computer

Symbol

Definition or

Explanation

inclination

centimetre

meter CMTL Nmm

due to wind

above waterline

PV Wind pressure Pa

s Wave steepness 1

according to hellip

value see hellip

Symbol

Computer

Symbol

Definition or

Explanation

TL Turning lever m

IMOHSC2000

ancy (LCB)

of buoyancy B

tion (LCF)

of flotation F

ity (LCG)

of gravity G

gravity G

Symbol

Computer

Symbol

Definition or

Explanation

centre of buoyancy

force g N

gle during hellip

Symbol

Computer

Symbol

Definition or

Explanation

according to hellip

gle seehellip

bility

the compartment

stability curve

Symbol

Computer

Symbol

Definition or

Explanation

E Entrance

F Fore

Z Heave

θ Pitch

φ Roll

Symbol

Computer

Symbol

Definition or

Explanation

3 SPECIAL CRAFT

Planing bottom area

strips

gravity

Beam over chines

Transom breadth

spray strips

chines

spray strips

bossings

bottom

section

Shaft angle

inclined downwards)

Symbol

Computer

Symbol

Definition or

Explanation

derway

water surface level

(flange mounting)

forces underway

ing surface

(LK + LC) 2

planing hull

water line

SWS SS

spray edge

Symbol

Computer

Symbol

Definition or

Explanation

ALFBAR

Barrel flow angle

LM LWL

TRIMDWL

design waterline

(positive bow up)

θS θ0

Static trim angle

θV θD

LM (BLCG)

TAUDWL

reference line

Spray angle

plane of bottom)

tal friction area

normally to NA)

normally to NB)

Symbol

Computer

Symbol

Definition or

Explanation

force NPN

ler pressure forces

normally to NPP)

suction forces NPS

normal to NPS)

pressure forces NRP

normal to NRP)

normal to RAA)

normal to RAP)

normal to RF)

sistance RK

normal to RK)

drag ΔRRP

normal to ΔRRP)

thrust

normal to RT)

Symbol

Computer

Symbol

Definition or

Explanation

deadrise

Δ (BCG

surface

Δ (BCG

breadth

V (BCG g)12

Load coefficient

Δ (BCG

3 ρ g )

1 LVHD

drodynamic lift

Hydrostatic lift

Due to buoyancy

reference line

ence line

reference line

Symbol

Computer

Symbol

Definition or

Explanation

reference line

Keel drag

Induced drag

g ρ tg τ

Parasitic drag

openings

Total resistance

spray drag

CF SWS qS

of the hull

Spray velocity

the spray

Symbol

Computer

Symbol

Definition or

Explanation

Box beam

Beam of main deck

Hull spacing

Tunnel width

Hull diameter

submerged hulls

dinal position X

Deck clearance

ANENIN

nel (inner) side

of demihull

ANENOU

outer side

of demihull

Box length

Length of main deck

Symbol

Computer

Symbol

Definition or

Explanation

to trailing edge

Symbol

Computer

Symbol

Definition or

Explanation

hull vessel

ence correction

RFMH - Σ RF

tion of multi-hull

RTMH - RFMH

ence correction

RRMH - Σ RR

vessel

correction

RTMH - Σ RT

33 Hydrofoil Boats

Symbol

Computer

Symbol

Definition or

Explanation

33 Hydrofoil Boats

cluding foils

Span of struts

tance of struts

Mean chord length

section with foil

Weight of foil

Dihedral angle

Submerged foil area

take-off speed

33 Hydrofoil Boats

Symbol

Computer

Symbol

Definition or

Explanation

Foil span wetted

distance

V (g LF)12

chord length

V (g cM)12

foilborne

Flight height

at rest

Keel clearance

centre of gravity

and rear foils

lF + lR

centre of gravity

Foil immersion

ALFIND

with twist

33 Hydrofoil Boats

Symbol

Computer

Symbol

Definition or

Explanation

33 Hydrofoil Boats

Symbol

Computer

Symbol

Definition or

Explanation

Foil drag

CDF AFR q

CDF AFF q

DRIND Induced drag

of motion

Interference drag

secting foil

Streamline drag

Spray drag

Strut drag

Wave drag

Ventilation drag

Lift force on foil

CL AFT q

CL AFF q

CL AFR q

attack of zero

CL0 AFT q

CLTO AFT q

33 Hydrofoil Boats

Symbol

Computer

Symbol

Definition or

Explanation

DP (AFS q) 1

L0 (AFS q) 1

condition

LTO (AFS q) 1

34 ACV and SES

Symbol

Computer

Symbol

Definition or

Explanation

34 ACV and SES

Cushion area

Cushion beam

At the water line

neath craft

Bow seal height

Skirt depth

Stern seal height

Cushion length

at rest off cushion

to structure

needs clarification

34 ACV and SES

Symbol

Computer

Symbol

Definition or

Explanation

structure

needs clarification

to structure

needs clarification

to water contact

SSHC SSH0

cushion periphery

of air

the skirt

34 ACV and SES

Symbol

Computer

Symbol

Definition or

Explanation

coefficient

R0 (ρA VR2 AC 2) 1

PCU LC Pam

in general

ρA QT VA N

of cushion

ρA QCU VA N

of skirt

ρA QTS VA N

34 ACV and SES

Symbol

Computer

Symbol

Definition or

Explanation

Symbol

Computer

Symbol

Definition or

Explanation

sistance

RI (ρI g h2 B)

of ice

RIW (S qIW)

normal

rection of motion

thickness

V (g hI)

ice force

ice (dynamic)

ice (static)

condition)

Thickness of ice

KQICMS

in ice

QIA (ρW nIA

KTICMS

in ice

TIA (ρW nIA

FRICMS

revolution in ice

Symbol

Computer

Symbol

Definition or

Explanation

in ice

2 π QIA nIA

Net ice resistance

RIT - RIW

in presence of ice

in ice

ciency in ice

ηID ηD

36 Sailing Vessels

Symbol

Computer

Symbol

Definition or

Explanation

36 Sailing Vessels

Area of mainsail

Area of spinnaker

(P E + I J) 2

Beam overall

Mainsail base

Fore triangle base

Mainsail height

olds Number

noe body

Effective draught

FH (ρVB

tical centre plane

36 Sailing Vessels

Symbol

Computer

Symbol

Definition or

Explanation

Displacement force

(weight) of keel

Displacement force

(weight) of rudder

36 Sailing Vessels

Symbol

Computer

Symbol

Definition or

Explanation

cient (upright)

RFU (S q)

cient (upright)

RRU (S q)

Total resistance

RTU (S q)

(upright)

RTφ (S q)

Cx Cy Cz

Force coefficients

Side force

right)

RTU + Rφ

Rφ RH

Vessel velocity

36 Sailing Vessels

Symbol

Computer

Symbol

Definition or

Explanation

True wind velocity

course

leaway angle

to boat course)

boat course)

Version 2014 130

4 BACKGROUND AND

REFERENCES

421 Classification

cross-references

list of symbols

drawing

standard itself

exponentiation

operators

matrix components

quantities

A ( eg Area in

msup2)

Version 2011 133

Numbers in roman

(power of n)

SYMBOLS

in italic

NUMBERS

in roman

(T = Thrust)

(M = Model) Fig 1

1 Scope

TK 102

A=A-[A]

as described above

NUMERICAL VALUES

AB = A B - [A] [B]

Version 2014 135

EXAMPLE

Ek = 2

1mvsup2

rived quantities

intensity J

51992 annex A)

dim Q = AαBβCγ

becomes in general

EXAMPLES

Quantity Dimension

velocity LT-1

force LMT-2

energy L2MT-2

relative density 1

Version 2014 136

23 Units

merical values

- base units

2321 Base units

Name Symbol

length metre m

mass kilogram kg

time second s

thermodynamic tem-

perature kelvin K

tary units

L rarr m I rarr A

M rarr kg Θ rarr K

T rarr s N rarrmol

J rarr cd

Derived quantity

SI derived unit

EXAMPLES

Version 2014 138

expressed in terms

of the seven base

units (and the sup-

plementary units in

some cases)

velocity ms

force kg ms2

energy kg m2s2

relative density 1

2323 SI prefixes

Factor Prefix

Name Symbol

1024 yotta Y

1021 zetta z

1018 exa E

1015 peta P

1012 tera T

109 giga G

106 mega M

103 kilo k

102 hecto h

10 deca da

10-1 deci d

10-2 centi c

10-3 milli m

10-6 micro micro

10-9 nano n

10-12 pico p

10-15 femto f

10-18 atto a

10-21 zepto z

10-24 yocto y

fixes see 324

233 The unit one

EXAMPLE

EXAMPLES

Plane angle α = 05

rad = 05

1 with a prefix

for the number 001

shall not be used

neous units

stance

51992 Annex A

with the Sl

Quantity Unit

Name Sym-

bol Definition

time minute

1 min= 60s

1 h = 60 min

1 d = 24 h

plane an-

degree

minute

second

1 deg =

(π180)rad =

(nl80) rad

1 = (160)deg

1 = (160)

= 1 dm

Name Sym-

bol Definition

the kinetic energy

tron in passing

through a potential

in vacuum 1 eV

1602 177 times10-19 J

mass unified

atomic

mass unit

(1 12) of the mass

of an atom of the

nuclide 12C 1u

1660 540 times10-27kg

Tables 5 and 6

the curie

and numbers

311 Symbols

sentence

use of subscripts

right) type

EXAMPLES

Upright sub-

number)

numbers)

(sloping) type

eg a∙ b-1

EXAMPLE

EXAMPLES

m metre

s second

A ampere

Wb weber

N∙m N m

symbol for a prefix

EXAMPLE

Version 2014 142

m ms m∙s-1

mendation

EXAMPLE

units (see 322)

EXAMPLES

1cm3 = (10-2m)3=10-6 m3

1 μs-1= (10-6 s)-1 = 106 s-1

1 kAm = (103A)m = 103 Am

crokilogram (μkg)

33 Numbers

man (upright) type

332Decimal sign

for the quantities

EXAMPLES

l = 12 m - 7 m= (12 - 7) m = 5m

clides

EXAMPLES

H He C Ca

A and 150 31-91992 annex A

script position

4O or (PO4)3-

types)

alpha Α a Α a

beta Β β Β β

gamma Γ γ Γ γ

delta Δ δ Δ δ

epsilon Ε ε Ε ε

zeta Ζ ζ Ζ ζ

eta Η η Η η

theta Θ θ Θ θ

iota Ι ι Ι ι

kappa Κ κ Κ κ

lambda Λ λ Λ λ

mu Μ μ Μ μ

nu Ν ν Ν ν

xi Ξ ξ Ξ ξ

omicron Ο ο Ο ο

pi Π π Π π

rho P ρ Ρ ρ

sigma Σ σ Σ σ

tau Τ τ Τ τ

upsilon Υ υ Υ υ

phi Φ φ Φ φ

chi Χ χ Χ χ

psi Ψ ψ Ψ ψ

omega Ω ω Ω ω

52 Computer symbols

Version 2014 145

52 Computer Symbols

- 9 have been used

near future

53 Documentation

Version 2014 146

53 Documentation

531 ITTC Documents

No500 1976

No6 1978

CETENA Genova 1984

532 Translations

malisation (AFNOR)

No28 Zagreb 1974

truccion Naval

53 Documentation

Version 2014 147

Table of Contents

1 General


111 Uncertainty















122 Loads

1221 External Loads



1231 Motions

1232 Attitudes

13 Fluid Mechanics

131 Flow Parameters




132 Flow Fields

1321 Velocities etc



1331 Geometry


1333 Forces


134 Boundary Layers


135 Cavitation


1352 Flow fields

1353 Pumps


141 Waves

1411 Periodic waves





142 Wind


143 Ice Mechanics


15 Noise


2 Ships in General

21 Basic Quantities


221 Hull Geometry






2222 Ducts


2224 Pods


























235 Water Jets


241 Manoeuvrability





2415 Linear Models




242 Sea Keeping




3 Special Craft











33 Hydrofoil Boats






34 ACV and SES





36 Sailing Vessels






421 Classification





52 Computer Symbols

53 Documentation

531 ITTC Documents

532 Translations


Symbol

Computer

Symbol

Definition or

Explanation

depends

q Random quantity 1

ing quantity q

Type A evaluation

tion of the mean

)(2 qs

Type A evaluation

)( 12 Xs

put means

Symbol

Computer

Symbol

Definition or

Explanation

bility p

quantity Xi

tainty

tainty from Type A

tainty from Type B

tainty

measurement

22 )]([)( iii xucyu 1

mate y

Symbol

Computer

Symbol

Definition or

Explanation

mate xi

mate y

estimates xi and xj

U = k uc(y)

Up = kp uc(y)

tion i ix X

measurand Y depends

variable

Symbol

Computer

Symbol

Definition or

Explanation

quantity Xi

servation of Xi

Output estimate

same measurement

Y A measurand

certainty Up

root of 2

Symbol

Computer

Symbol

Definition or

Explanation

n estimated by

tive square root of

tities

in the following

tion if any

Axes coordinates

Body axes (xyz)

platforms or ships

upwards

section

flight dynamics

ular case

differential

Name of coordi-

nate system

Remarks

11-121

cartesian

coordinates

system See Figure 1

11-122

cylindrical

coordinates

11-123

(-) r φ r=rer

r sin dφ eφ

spherical

Figures 3 and 5

Symbol

Computer

Symbol

Definition or

Explanation

lar quantity

scalar distribution

εikjxkds

εklixlεjkm xmds

Sij = S0ij

Si 3+j = S1ij

S3+i j = S1ij

S3+i 3+j = S2ij

tesian coordinates

fixed in the body

Tijs + Tij

tensor

( Tij - Tji ) 2

Symbol

Computer

Symbol

Definition or

Explanation

V3+i = V1i

X X(1)

Y X(2)

Z X(3)

the body

x0 x01

y0 x02

z0 x03

X0 X0(1)

Y0 X0(2)

Z0 X0(3)

xF xF1

yF xF2

zF xF3

XF XF(1)

YF XF(2)

ZF XF(3)

1 ijk = 321 213 132

0 if otherwise

Symbol

Computer

Symbol

Definition or

Explanation

f FR Frequency Hz

functions

1 TC Hz

Laurent transform

Laplace transform

t TI Time - + s

Symbol

Computer

Symbol

Definition or

Explanation

pled function

= X(0)2 + fSXF(f + jfS)

inverse form

XF(f)=XL(f)

t = 0 TC

XF = xFjδ(f - jTC)

inverse form

Hilbert transform

(1t)F = -i sgn f

if X(tlt0) = 0 then

= (X(t)exp(-at))F

ie = 0 for f lt 0

rier series

XFj(1 + sgn j)

line spectra

Symbol

Computer

Symbol

Definition or

Explanation

component

zl ZLG (Phase) Lag

component

Symbol

Computer

Symbol

Definition or

Explanation

gE gM gMR

E(g) = g(x)fx(x)dx

Random quantities

x(ζ) y(ζ)

X(I) Y(I)

i = 1 n

n sample size

quantity

xD xDR σx

dom quantity

xVR frac12

xDS sx

dom quantity

xVS 12

xxR xxMR Rxx

dom quantity

xyR xyMR Rxy

dom quantities

xE xM xMR

xA xMS mx

a random quantity

1n xi i = 1n

xAE = xE

xVSE = xV n

xPD fx

dom quantity

d Fx dx

xyPD fxy

2 Fxy (x y)

xPF Fx

xyPF Fxy

random quantities

Symbol

Computer

Symbol

Definition or

Explanation

xV xVR xxVR

XVR XXVR

x2 E - xE 2

xVS xxVS

XVS XXVS

dom quantity

1 (n - 1) (xi - x

i = 1n

xyV xyVR

quantities

x yE - xE yE

periment

dom quantity

t =-T2 +T2

T =- +

A(g(t)) = 1T g(t)dt

t =0 +T

x(ζt) y(ζt)

xxC xxCR Cxx

(x(t) - xE)(x(t + τ) - xE)E

xyC xyCR Cxy

(x(t) - xE)(y(t + τ) - yE)E

xxR xxRR Rxx

Rxx(τ) = Rxx(-τ)

= x(t)x(t + τ)MR

τ = 0

xyR Rxy

Ryx(τ) = Rxy(-τ)

if x y are ergodic

Symbol

Computer

Symbol

Definition or

Explanation

xxS Sxx

chastic process

xxRRSR

xyS Sxy

processes

xyRRSR

periment

Average sample mean

Sample covariance

Sample deviation

E M MR

Probability density

(Power) Spectrum

Sample spectrum

Sample correlation

Population variance

Sample variance

Symbol

Computer

Symbol

Definition or

Explanation

control volume

Inward positive QUs

control volume

quantity stored

dq dt QUs

Symbol

Computer

Symbol

Definition or

Explanation

AM(IJ)

DA(IJ)

RF(IJ)

uv DH(UV)

damping

u FH(U)

uv IH(UV)

inertia

of water-plane area

Iy Iyy

IY IYY

M2(22)

MA(55)

Iz Izz

IZ IZZ

M2(33)

MA(66)

Ixy I12

Iyz I23

Izx I31

IXY I2(12)

IYZ I2(23)

IZX I2(31)

kx kxx

(Ixxm)12

Symbol

Computer

Symbol

Definition or

Explanation

ky kyy

(Iyym)12

kz kzz

(Izzm)12

M0(IJ)

MA(IJ)

tensor

mij = m δij

ij M1(IJ)

M2(IJ)

IN(IJ)

MA(UV)

system

Mij = M0

Mi 3+j = M1Tij

M3+i j = M1ij

M3+i 3+j = M2ij

Symbol

Computer

Symbol

Definition or

Explanation

122 Loads

1221 External Loads

in body coordinates

u = MMu

Fi = F0i

F3+i = F1i

gi = g1

g3+i = 0

in body coordinates

F11 F4

K M(1)

F1(1) F(4)

F12 F5

M M(2)

F1(2) F(5)

FN13 F6

N M(3)

F1(3) F(6)

F01 F1

F0(1) F(1)

axis x

F02 F2

F0(2) F(2)

axis y

F03 F3

F0(3) F(3)

axis z

Gu = muv gv

G0i Gi

in body coordinates

Gi = G0

i = m0ij gj

i G1(I)

in body coordinates

G3+i = G1

i = εikj xk G0

= m1ij gj

dW dx1

Symbol

Computer

Symbol

Definition or

Explanation

section coordinates

FSi = FS0

FS3+i = FS1

i = MBi

FS11 Nm

Symbol

Computer

Symbol

Definition or

Explanation

1231 Motions

v01 v4

V0(1) V(4)

body axis x

v02 v5

V0(2) V(5)

body axis y

v03 v6

V0(3) V(6)

body axis z

v11 v1

V1(1) V(1)

v12 v2

V1(2) V(2)

v13 v3

V1(3) V(3)

body axes

vi = v1

v3+i = v0i

tive to body axes

Symbol

Computer

Symbol

Definition or

Explanation

1232 Attitudes

Angle of attack

the z-axis

about the xo axis

X(4) RO

X(5) TR

X(6) YA

course

13 Fluid Mechanics

Symbol

Computer

Symbol

Definition or

Explanation

13 Fluid Mechanics

131 Flow Parameters

Velocity of sound

(E ρ)12

Weight density

ρg (See 111)

Viscosity

Kinematic viscosity

DN RHO

Mass density

Capillarity

length

Boussinesq number

V (g RH)12

Cauchy number

V (E ρ)12

Froude number

V (g L)12

Froude depth number

V (g h)12

V (g 13)12

Mach number

Reynolds number

Strouhal number

Thoma number

Cavitation number

(pA ndash pV)q

Weber number

V2 L κ

07R Ac V nDRe

13 Fluid Mechanics

Symbol

Computer

Symbol

Definition or

Explanation

Sand roughness

surface

Hydraulic radius

wetted perimeter

13 Fluid Mechanics

Symbol

Computer

Symbol

Definition or

Explanation

132 Flow Fields

1321 Velocities etc

energy

ρ V2 2 + p + ρ g h

Mass specific force

Total head

e w = h +pw +qw

flow energy

turbed flow

ρ V2 2

Rate of flow

Total head loss

ij SR(IJ)

ρ vivj

Pa sij

ST(IJ)

Total stress tensor

change

ij SV(IJ)

Viscous stress

u vx v1

v vy v2

w vz v3

Velocity

V = vivi

Wall shear stress

μ (U y)y=0

13 Fluid Mechanics

Symbol

Computer

Symbol

Definition or

Explanation

Induction factor

Vortex density

Circulation

intV ds

along a closed line

Potential function

Stream function

ψ = const

surface

13 Fluid Mechanics

Symbol

Computer

Symbol

Definition or

Explanation

1331 Geometry

Projected area

Wing or foil span

Flap span

Mean chord length

Tip chord length

Root chord length

Sweep angle

tion (general)

edge of struts

(general)

of foil

section

tS cSTH

Taper ratio

Aspect ratio

13 Fluid Mechanics

Symbol

Computer

Symbol

Definition or

Explanation

Induced velocity

and the chord line

or incidence

Geometric angle of

attack or incidence

Hydrodynamic angle

of attack

zero lift

Angle of zero lift

at zero lift

13 Fluid Mechanics

Symbol

Computer

Symbol

Definition or

Explanation

1333 Forces

Foil drag

DRIND Induced drag

of motion

Interference drag

secting foil

zero lift

Streamline drag

Lift force on foil

CL AFT q

of zero

CL0 AFT q

Lift-Drag ratio

13 Fluid Mechanics

Symbol

Computer

Symbol

Definition or

Explanation

134 Boundary Layers

τ (ρ Ue

Entrainment factor

1 (Ue dQ dx)

rameter

(δ - δ) Θ

Static pressure

Total pressure

Entrainment

U δ v or Ue δ

RTHETA

U Θ v or Ue Θ v

boundary layer

from surface

(τ ρ)12

boundary layer

from the surface

(Ue- U) uτ

13 Fluid Mechanics

Symbol

Computer

Symbol

Definition or

Explanation

from the wall

y uτ v

δ (τw dp dx)

layer at U=0995Ue

δ δ1

boundary layer

(Ue- U) Ue dy

von Karman constant

δ995 (v dUe dx)

Energy thickness

(U Ue) (1 - U2 Ue

Momentum thickness

(U Ue) (1 - U Ue)dy

Local skin friction

μ (U y)y=0

13 Fluid Mechanics

Symbol

Computer

Symbol

Definition or

Explanation

135 Cavitation

Gas content ratio

α αS

Gas content

temperature

Cavitation number

(pA - pC) q

(pA - pV) q

1352 Flow fields

Cavity drag

Cavity length

region

Ambient pressure

Critical pressure

takes place

Cavity pressure

quasi-steady cavity

Critical velocity

takes place

Volume loss

13 Fluid Mechanics

Symbol

Computer

Symbol

Definition or

Explanation

WL WTLS

Weight loss

specified time

1353 Pumps

turbo-engines

Thoma number

(HU - pV w) HN

Symbol

Computer

Symbol

Definition or

Explanation

141 Waves

1411 Periodic waves

lerity LW TW =

2WgL in

deep water

odic wave

const = cW

lerity

i fW Hz

wave crest to wave

wave ηC - ηT

advance

Symbol

Computer

Symbol

Definition or

Explanation

at a given location

ηFSα m

ηFSp rad

crossing

trough

crossing

and crest

wave heights

crossing

of zero in a record

Symbol

Computer

Symbol

Definition or

Explanation

in a record

Negative values m

crossing

visual observation

cant wave height

wave heights

wave height

heights

visual observation

wave propagation

samples

visual observation

Symbol

Computer

Symbol

Definition or

Explanation

lution

points

tude function

4 (m0)12 m

fn S(f)df m2 sn

Si(ω)

tral density

Sr(ω)

tral density

Sη(f)

Sη(ω)

2πfP s

and first moment

m0m1 s

and second moment

(m0m2)12 s

Symbol

Computer

Symbol

Definition or

Explanation

DX(fθ)

DX(ωμ)

SIGMAOX

Sζ (ωμ)

Sθ (ωμ)

density

Sρ(fθ)

Sζ(ωμ)

θm MWD

THETAMOX

rection

Symbol

Computer

Symbol

Definition or

Explanation

142 Wind

(008 + 0065U10)10-3

Fetch length

wind blows

DURATN

Wind duration

Return period

ceeded

uz uzi

UFLUCT

USHEAR

Wind shear velocity

12 U10 or 071U10123

Reference mean wind

U10 = (10z)17 Uz

(Uz + uzi)

UzA = (z10)17 U10 or

see section 141

True wind velocity

see section 141

Dimensionless Fetch

face in meters

see section 26

True wind angle

see section 26

Wind direction

Symbol

Computer

Symbol

Definition or

Explanation

143 Ice Mechanics

weight of ice

volume of ice

unit volume of ice

15 Noise

Symbol

Computer

Symbol

Definition or

Explanation

15 Noise

acoustic centre

= 10 log10

(119903119898119904

1199011199031198901198912 ) dB 119901119903119890119891

tance of 1m

119871s

= 119871p

+ 20 log10 [119889

119889119903119890119891] dB 119889119903119890119891

Symbol

Computer

Symbol

Definition or

Explanation

2 SHIPS IN GENERAL

21 Basic Quantities

dv dt ms2

A A AR

Area in general m2

B B BR Breadth m

(forces)

d D D DI Diameter m

E E EN Energy J

F F0 F F0 Force N

h DE Depth m

H H HT Height m

mass distribution

L L LE Length m

tory velocity

m M MA

Mass kg

Symbol

Computer

Symbol

Definition or

Explanation

distribution

M MO Momentum Ns

P P PO Power W

r R RD Radius m

locity

t TI Time s

t TE Temperature K

harmonic process

of a body

ds dt ms

V VO Volume m3

specific weight

dW dV = ρg Nm3

acting on a body

tilled water at 4C

Symbol

Computer

Symbol

Definition or

Explanation

Symbol

Computer

Symbol

Definition or

Explanation

221 Hull Geometry

gitudinal plane

perpendicular

the final rounding

aft perpendiculars

port and starboard)

waterline

relative wind

midship

of midship

section

of ships hull

Symbol

Computer

Symbol

Definition or

Explanation

water line

at stem

the perpendiculars)

maximum section

verse section

Symbol

Computer

Symbol

Definition or

Explanation

point of the stern

pendicular

dicular

perpendicular

with straight keel

water surface level

bare hull

ΔBH (ρ g) m3

pendages

ΔAP (ρ g) m3

Symbol

Computer

Symbol

Definition or

Explanation

ancy) g ρ N

= TS TM

cient B 13 1

GM 13 1

GZ 13 1

cient KG T

12 IL ( B L3) 1

12 IT (B3 L) 1

AM (B T) 1

body A (AX L 2) or

A (AM L 2)

trance E (AX LE) or

E (AM LE)

body F (AX L 2) or

F (AM L 2)

Symbol

Computer

Symbol

Definition or

Explanation

R (AM LR)

AWA (B L 2) 1

forward

AWF (B L 2) 1

coefficient

maximum area

ABL (L T) 1

ABT AX 1

transom stern

AT AX 1

L 13 1

cient T 13 1

A AB After body

APP APP Appendages

B BH Bare hull

DW Design waterline

E EN Entry

Symbol

Computer

Symbol

Definition or

Explanation

F FB Fore body

FS Frame spacing

H HE Hull

LR Reference Line

LP LP Based on LPP

LW LW Based on LWL

M MS Midships

PB Parallel body

R RU Run

SS Station spacing

W WP Water plane

S WS Wetted surface

Symbol

Computer

Symbol

Definition or

Explanation

boss or hub

radius

hub to the tip

Symbol

Computer

Symbol

Definition or

Explanation

blades

2 π r sin (φ) z m

positive rake

the propeller plane

iG + iS = cS sinφ

shoulder

Symbol

Computer

Symbol

Definition or

Explanation

ing aft shoulder

rh RH Hub radius m

ler blade

ler axis

dicular

above base line

Symbol

Computer

Symbol

Definition or

Explanation

cal skew angle

Symbol

Computer

Symbol

Definition or

Explanation

2222 Ducts

LD LD Duct length m

ler plane

of duct

tion s

Jet System Head m

at station 1A

Symbol

Computer

Symbol

Definition or

Explanation

2224 Pods

Main Body

tom Fin

Bottom Fin

under pod main body

D Duct (subscript)

Symbol

Computer

Symbol

Definition or

Explanation

appendage

of rudder

propeller race

hydrofoil

lel to keel

Symbol

Computer

Symbol

Definition or

Explanation

rudders

of flanking rudders

BK Bilge keel

BS Bossing

FB Bow foil

FR Flanking rudder

FS Stern foil

KL Keel

RU Rudder

RF Rudder flap

SA Stabilizer

SH Shafting

SK Skeg

ST Strut

TH Thruster

WG Wedge

Symbol

Computer

Symbol

Definition or

Explanation

curves of stability

volume

Centre of buoyancy

volume

ter plane

(mass)

Keel reference

XCB LCB

ancy (LCB)

from Midships

XCF LCF

tion (LCF)

from Midships

Symbol

Computer

Symbol

Definition or

Explanation

from Midships

XCG LCG

ity (LCG)

from Midships

gravity G

centre of buoyancy

curves of stability

Symbol

Computer

Symbol

Definition or

Explanation

centre of buoyancy

metacentre M

pendicular

dicular

pendicular

weight addition

101 GGKGKG m

height

to the metacentre

tion effects

centric height

metacentre ML

KGKMGM LL

TAG cosφ

KB-KM =I =BM T

BM KM KB

Symbol

Computer

Symbol

Definition or

Explanation

base or keel K

metacentre M to the

ing arm

Heeling moment Δ m

GM 13 1

GZ 13 1

cient KG T

ficient

proximately equals

Symbol

Computer

Symbol

Definition or

Explanation

ficient

proximately equals

one centimetre

one meter

ΔCMTL Nmm

force g ρ N

flooded water

Δfw (ρg) m3

Symbol

Computer

Symbol

Definition or

Explanation

the compartment

bility

a apparent

A att attained

d dyn dynamic

e EFF effective

f false

KL keel line

L longitudinal

MAX maximum

s Static

S sqt Sinkage squat

TC Trim in cm

TM Trim in m

T transverse

V vertical

0 Initial

at heel angle

θ at trim angle θ

Symbol

Computer

Symbol

Definition or

Explanation

231 Hull Resistance

cross section area

lowance

propulsion tests

[(1 + k) CFM + CR]

surface of the body

bare hull

SBH + SAPP m2

Symbol

Computer

Symbol

Definition or

Explanation

area underway

area at rest

area underway

area at rest

lation

RA (S q) 1

ficient

RAA (AV qR) 1

RAPP (S q) 1

cient of a body

RF (S q) 1

RF0 (S q) 1

RP (S q) 1

coefficient

RPV (S q) 1

Symbol

Computer

Symbol

Definition or

Explanation

RR (S q) 1

g R L (ΔV2) 1

efficient

RV (S q) 1

efficient

RW (S q) 1

efficient

1000 R (Δ(KC)2)

1000 RF (Δ(KC)2) 1

sliding bodies

(CV - CF0) CF0 1

(4πg)12VK16

sponding to KQ KT

R (ρ D4 n2) 1

ρ V2 2

see 332

qR PDWR

apparent wind

ρ VWR2 2

see 342

Symbol

Computer

Symbol

Definition or

Explanation

tio in general

R Δ 1

placement ratio

RR Δ 1

FW Fresh water

MR Raw model data

OW Open water

SW Salt water

Symbol

Computer

Symbol

Definition or

Explanation

of revolution

Brake power

Delivered power

propeller power

Effective power

resistance power

Indicated power

Shaft power

Thrust power

Torque

Running trim

Ship speed

or torque identity

2 π n

Symbol

Computer

Symbol

Definition or

Explanation

(T - RT) RT

Δ23 V3 PS

PD (ρ V3 23 2)

identity

PDT PDS

ηDS ηDM

factor

Sinkage dynamic

Trim dynamic

by length

(T - RT) T

(V - VA) V

(V - VA) VA

Symbol

Computer

Symbol

Definition or

Explanation

wTM - wTS

1978 method

diction

ηD PD PE - 1

resistance

PT PD = T VA (Q ω)

coefficient

PE PD = PR PP

Gearing efficiency

Hull efficiency

PE PT = PR PT

= (1 - t) (1 - w)

and propeller

water tests

ηB ηO

Shafting efficiency

PD PS = PP PS

Symbol

Computer

Symbol

Definition or

Explanation

lution

ler blade surface

advance speed

ρ VA2 2

ρ VS2 2 Pa

QS=QSC+ QSH

torque

peller unit

peller

Symbol

Computer

Symbol

Definition or

Explanation

at 07 R

(VA2+ (07 R ω)2)12

n PDfrac12 VA

with n in revsmin

VA in kn (obsolete)

n PTfrac12 VA

with n in revsmin

VA in kn (obsolete)

T (AP qA)

= (TP AP) qA

V (D n) = VH (D n) 1

ducted propeller

VP (D n)

identity

coefficient

QSC (ρ n2 D5) 1

Symbol

Computer

Symbol

Definition or

Explanation

torque coefficient

QSH (ρ n2 D5) 1

ficient

TP (ρ n2 D4) 1

KTP+ KTD 1

KQηR 1

feet VA in kn

efficiency

PJ PD = PJ PP 1

ηJP0 ZET0

zero advance speed

T (ρ π 2)13 (PD D)23 1

η0 ηTP0 ETA0

water tests

ducted propeller

TP TT 1

Symbol

Computer

Symbol

Definition or

Explanation

propeller

peller

by propeller

blade section

arctg (VA r ω)

Symbol

Computer

Symbol

Definition or

Explanation

u = 1 6

u = 1 2 3 force

u = 4 5 6 moment

coefficients

KFi and KMi

cients

Mi (ρ n2 D5) 1

p PR Pressure Pa

ing reaction

u = 1 6

u = 1 2 3 force

u = 4 5 6 moment

from the x-axis

Symbol

Computer

Symbol

Definition or

Explanation

placement

u = 1 6

u = 1 2 3 linear

u = 4 5 6 angular

u = 1 6

u = 1 2 3 linear

u = 4 5 6 angular

eration

u = 1 6

u = 1 2 3 linear

u = 4 5 6 angular

Symbol

Computer

Symbol

Definition or

Explanation

235 Water Jets

210 n2

at station s

cient at station s

rate transducer

Ej = (ρ2)VEj2dQj

j j i i

pg x u n dA

j j i i

pu g x u n dA

sion point

several pump stages

in i direction

u u n dA

Symbol

Computer

Symbol

Definition or

Explanation

dition)

impeller

turbed flow

tion s

boundary layer

msup3s

water jet system

msup3s

jet xT

dition)

system on the hull

Symbol

Computer

Symbol

Definition or

Explanation

at station s

station 7

station 1

tion 1A

surface

in x direction

ciency E

ciency JSE0

stream conditions

the pump

Symbol

Computer

Symbol

Definition or

Explanation

ciency

pump loop test

P duct I

Symbol

Computer

Symbol

Definition or

Explanation

241 Manoeuvrability

of rudder

(AR + ARmov) 2 m2

root to tip

AHL (L T) 1

h DE Water depth m

der axis

Symbol

Computer

Symbol

Definition or

Explanation

dp dt 1s2

dq dt 1s2

dr dt 1s2

du dt ms2

dv dt ms2

dw dt ms2

body axes

χ YX Yaw angle rad

Symbol

Computer

Symbol

Definition or

Explanation

RO Roll angle rad

Pitch angle

the hull

Drift angle

the hull

ANWIRL

ANRUEF

Bow fin angle

Stern fin angle

Rudder angle

ANRUOR

COWIAB

COWIRL

Symbol

Computer

Symbol

Definition or

Explanation

N r Nms2

N v Nms2

along body x-axis

X u Nsm

eration

X u Ns2m

tion of body axis y

Y r Ns2

Symbol

Computer

Symbol

Definition or

Explanation

Y v Ns2m

along body z-axis

2415 Linear Models

ship length

turning diameter

DC LPP 1

ameter δR = δ0

D0 LPP 1

unstable ship

Symbol

Computer

Symbol

Definition or

Explanation

unstable ship

turning rate

change of heading

heading

(starboard)

(port)

tr TIR Reach time s

Symbol

Computer

Symbol

Definition or

Explanation

track reach

Symbol

Computer

Symbol

Definition or

Explanation

242 Sea Keeping

system

spectively

Frequency

Alias horizontal

Alias vertical

moment

Alias horizontal

ing moment

Alias vertical

lution in waves

Symbol

Computer

Symbol

Definition or

Explanation

Sη(f) Sηη(f)

Sη(ω) Sηη(ω)

density

roll pitch yaw

rad TAW

Wave period

Yz(ω)

Azζ(ω)

tory motions

za(ω) ζa(ω) or

za(ω) ηa(ω)

Yθζ(ω)

Aθζ(ω)

motions

Θa(ω) ζa(ω) or

Tuning factor

w w wL L L

w w w= = =

q fL L L= = =

(short crested)

Symbol

Computer

Symbol

Definition or

Explanation

I991241

- I991242

lever curve

cording to ISO 8666

IMOIS IMOHSC2000

acter sets

Symbol

Computer

Symbol

Definition or

Explanation

curves of stability

volume

centre of buoyancy

metacentre M

volume

needed for crew

sons on board

ficient - I991243

proximately equals

hull - I99121

Symbol

Computer

Symbol

Definition or

Explanation

merged test weights

ter plane

pendicular

dicular

pendicular

(mass)

weight addition

101 GGKGKG m

weight addition

101 GGKGKG m

Symbol

Computer

Symbol

Definition or

Explanation

height

to the metacentre

KGKMGM

face effect)

tion effects

height

metacentre ML

KGKMGM LL

TAG cos φ

IMOtable

profile

K Keel reference

base of keel or K

Symbol

Computer

Symbol

Definition or

Explanation

base of keel or K

metacentre M to the

condition - IMOIS

IMOtable

ment due to crew

is taken of rolling

Symbol

Computer

Symbol

Definition or

Explanation

inclination

centimetre

meter CMTL Nmm

due to wind

above waterline

PV Wind pressure Pa

s Wave steepness 1

according to hellip

value see hellip

Symbol

Computer

Symbol

Definition or

Explanation

TL Turning lever m

IMOHSC2000

ancy (LCB)

of buoyancy B

tion (LCF)

of flotation F

ity (LCG)

of gravity G

gravity G

Symbol

Computer

Symbol

Definition or

Explanation

centre of buoyancy

force g N

gle during hellip

Symbol

Computer

Symbol

Definition or

Explanation

according to hellip

gle seehellip

bility

the compartment

stability curve

Symbol

Computer

Symbol

Definition or

Explanation

E Entrance

F Fore

Z Heave

θ Pitch

φ Roll

Symbol

Computer

Symbol

Definition or

Explanation

3 SPECIAL CRAFT

Planing bottom area

strips

gravity

Beam over chines

Transom breadth

spray strips

chines

spray strips

bossings

bottom

section

Shaft angle

inclined downwards)

Symbol

Computer

Symbol

Definition or

Explanation

derway

water surface level

(flange mounting)

forces underway

ing surface

(LK + LC) 2

planing hull

water line

SWS SS

spray edge

Symbol

Computer

Symbol

Definition or

Explanation

ALFBAR

Barrel flow angle

LM LWL

TRIMDWL

design waterline

(positive bow up)

θS θ0

Static trim angle

θV θD

LM (BLCG)

TAUDWL

reference line

Spray angle

plane of bottom)

tal friction area

normally to NA)

normally to NB)

Symbol

Computer

Symbol

Definition or

Explanation

force NPN

ler pressure forces

normally to NPP)

suction forces NPS

normal to NPS)

pressure forces NRP

normal to NRP)

normal to RAA)

normal to RAP)

normal to RF)

sistance RK

normal to RK)

drag ΔRRP

normal to ΔRRP)

thrust

normal to RT)

Symbol

Computer

Symbol

Definition or

Explanation

deadrise

Δ (BCG

surface

Δ (BCG

breadth

V (BCG g)12

Load coefficient

Δ (BCG

3 ρ g )

1 LVHD

drodynamic lift

Hydrostatic lift

Due to buoyancy

reference line

ence line

reference line

Symbol

Computer

Symbol

Definition or

Explanation

reference line

Keel drag

Induced drag

g ρ tg τ

Parasitic drag

openings

Total resistance

spray drag

CF SWS qS

of the hull

Spray velocity

the spray

Symbol

Computer

Symbol

Definition or

Explanation

Box beam

Beam of main deck

Hull spacing

Tunnel width

Hull diameter

submerged hulls

dinal position X

Deck clearance

ANENIN

nel (inner) side

of demihull

ANENOU

outer side

of demihull

Box length

Length of main deck

Symbol

Computer

Symbol

Definition or

Explanation

to trailing edge

Symbol

Computer

Symbol

Definition or

Explanation

hull vessel

ence correction

RFMH - Σ RF

tion of multi-hull

RTMH - RFMH

ence correction

RRMH - Σ RR

vessel

correction

RTMH - Σ RT

33 Hydrofoil Boats

Symbol

Computer

Symbol

Definition or

Explanation

33 Hydrofoil Boats

cluding foils

Span of struts

tance of struts

Mean chord length

section with foil

Weight of foil

Dihedral angle

Submerged foil area

take-off speed

33 Hydrofoil Boats

Symbol

Computer

Symbol

Definition or

Explanation

Foil span wetted

distance

V (g LF)12

chord length

V (g cM)12

foilborne

Flight height

at rest

Keel clearance

centre of gravity

and rear foils

lF + lR

centre of gravity

Foil immersion

ALFIND

with twist

33 Hydrofoil Boats

Symbol

Computer

Symbol

Definition or

Explanation

33 Hydrofoil Boats

Symbol

Computer

Symbol

Definition or

Explanation

Foil drag

CDF AFR q

CDF AFF q

DRIND Induced drag

of motion

Interference drag

secting foil

Streamline drag

Spray drag

Strut drag

Wave drag

Ventilation drag

Lift force on foil

CL AFT q

CL AFF q

CL AFR q

attack of zero

CL0 AFT q

CLTO AFT q

33 Hydrofoil Boats

Symbol

Computer

Symbol

Definition or

Explanation

DP (AFS q) 1

L0 (AFS q) 1

condition

LTO (AFS q) 1

34 ACV and SES

Symbol

Computer

Symbol

Definition or

Explanation

34 ACV and SES

Cushion area

Cushion beam

At the water line

neath craft

Bow seal height

Skirt depth

Stern seal height

Cushion length

at rest off cushion

to structure

needs clarification

34 ACV and SES

Symbol

Computer

Symbol

Definition or

Explanation

structure

needs clarification

to structure

needs clarification

to water contact

SSHC SSH0

cushion periphery

of air

the skirt

34 ACV and SES

Symbol

Computer

Symbol

Definition or

Explanation

coefficient

R0 (ρA VR2 AC 2) 1

PCU LC Pam

in general

ρA QT VA N

of cushion

ρA QCU VA N

of skirt

ρA QTS VA N

34 ACV and SES

Symbol

Computer

Symbol

Definition or

Explanation

Symbol

Computer

Symbol

Definition or

Explanation

sistance

RI (ρI g h2 B)

of ice

RIW (S qIW)

normal

rection of motion

thickness

V (g hI)

ice force

ice (dynamic)

ice (static)

condition)

Thickness of ice

KQICMS

in ice

QIA (ρW nIA

KTICMS

in ice

TIA (ρW nIA

FRICMS

revolution in ice

Symbol

Computer

Symbol

Definition or

Explanation

in ice

2 π QIA nIA

Net ice resistance

RIT - RIW

in presence of ice

in ice

ciency in ice

ηID ηD

36 Sailing Vessels

Symbol

Computer

Symbol

Definition or

Explanation

36 Sailing Vessels

Area of mainsail

Area of spinnaker

(P E + I J) 2

Beam overall

Mainsail base

Fore triangle base

Mainsail height

olds Number

noe body

Effective draught

FH (ρVB

tical centre plane

36 Sailing Vessels

Symbol

Computer

Symbol

Definition or

Explanation

Displacement force

(weight) of keel

Displacement force

(weight) of rudder

36 Sailing Vessels

Symbol

Computer

Symbol

Definition or

Explanation

cient (upright)

RFU (S q)

cient (upright)

RRU (S q)

Total resistance

RTU (S q)

(upright)

RTφ (S q)

Cx Cy Cz

Force coefficients

Side force

right)

RTU + Rφ

Rφ RH

Vessel velocity

36 Sailing Vessels

Symbol

Computer

Symbol

Definition or

Explanation

True wind velocity

course

leaway angle

to boat course)

boat course)

Version 2014 130

4 BACKGROUND AND

REFERENCES

421 Classification

cross-references

list of symbols

drawing

standard itself

exponentiation

operators

matrix components

quantities

A ( eg Area in

msup2)

Version 2011 133

Numbers in roman

(power of n)

SYMBOLS

in italic

NUMBERS

in roman

(T = Thrust)

(M = Model) Fig 1

1 Scope

TK 102

A=A-[A]

as described above

NUMERICAL VALUES

AB = A B - [A] [B]

Version 2014 135

EXAMPLE

Ek = 2

1mvsup2

rived quantities

intensity J

51992 annex A)

dim Q = AαBβCγ

becomes in general

EXAMPLES

Quantity Dimension

velocity LT-1

force LMT-2

energy L2MT-2

relative density 1

Version 2014 136

23 Units

merical values

- base units

2321 Base units

Name Symbol

length metre m

mass kilogram kg

time second s

thermodynamic tem-

perature kelvin K

tary units

L rarr m I rarr A

M rarr kg Θ rarr K

T rarr s N rarrmol

J rarr cd

Derived quantity

SI derived unit

EXAMPLES

Version 2014 138

expressed in terms

of the seven base

units (and the sup-

plementary units in

some cases)

velocity ms

force kg ms2

energy kg m2s2

relative density 1

2323 SI prefixes

Factor Prefix

Name Symbol

1024 yotta Y

1021 zetta z

1018 exa E

1015 peta P

1012 tera T

109 giga G

106 mega M

103 kilo k

102 hecto h

10 deca da

10-1 deci d

10-2 centi c

10-3 milli m

10-6 micro micro

10-9 nano n

10-12 pico p

10-15 femto f

10-18 atto a

10-21 zepto z

10-24 yocto y

fixes see 324

233 The unit one

EXAMPLE

EXAMPLES

Plane angle α = 05

rad = 05

1 with a prefix

for the number 001

shall not be used

neous units

stance

51992 Annex A

with the Sl

Quantity Unit

Name Sym-

bol Definition

time minute

1 min= 60s

1 h = 60 min

1 d = 24 h

plane an-

degree

minute

second

1 deg =

(π180)rad =

(nl80) rad

1 = (160)deg

1 = (160)

= 1 dm

Name Sym-

bol Definition

the kinetic energy

tron in passing

through a potential

in vacuum 1 eV

1602 177 times10-19 J

mass unified

atomic

mass unit

(1 12) of the mass

of an atom of the

nuclide 12C 1u

1660 540 times10-27kg

Tables 5 and 6

the curie

and numbers

311 Symbols

sentence

use of subscripts

right) type

EXAMPLES

Upright sub-

number)

numbers)

(sloping) type

eg a∙ b-1

EXAMPLE

EXAMPLES

m metre

s second

A ampere

Wb weber

N∙m N m

symbol for a prefix

EXAMPLE

Version 2014 142

m ms m∙s-1

mendation

EXAMPLE

units (see 322)

EXAMPLES

1cm3 = (10-2m)3=10-6 m3

1 μs-1= (10-6 s)-1 = 106 s-1

1 kAm = (103A)m = 103 Am

crokilogram (μkg)

33 Numbers

man (upright) type

332Decimal sign

for the quantities

EXAMPLES

l = 12 m - 7 m= (12 - 7) m = 5m

clides

EXAMPLES

H He C Ca

A and 150 31-91992 annex A

script position

4O or (PO4)3-

types)

alpha Α a Α a

beta Β β Β β

gamma Γ γ Γ γ

delta Δ δ Δ δ

epsilon Ε ε Ε ε

zeta Ζ ζ Ζ ζ

eta Η η Η η

theta Θ θ Θ θ

iota Ι ι Ι ι

kappa Κ κ Κ κ

lambda Λ λ Λ λ

mu Μ μ Μ μ

nu Ν ν Ν ν

xi Ξ ξ Ξ ξ

omicron Ο ο Ο ο

pi Π π Π π

rho P ρ Ρ ρ

sigma Σ σ Σ σ

tau Τ τ Τ τ

upsilon Υ υ Υ υ

phi Φ φ Φ φ

chi Χ χ Χ χ

psi Ψ ψ Ψ ψ

omega Ω ω Ω ω

52 Computer symbols

Version 2014 145

52 Computer Symbols

- 9 have been used

near future

53 Documentation

Version 2014 146

53 Documentation

531 ITTC Documents

No500 1976

No6 1978

CETENA Genova 1984

532 Translations

malisation (AFNOR)

No28 Zagreb 1974

truccion Naval

53 Documentation

Version 2014 147

Table of Contents

1 General


111 Uncertainty















122 Loads

1221 External Loads



1231 Motions

1232 Attitudes

13 Fluid Mechanics

131 Flow Parameters




132 Flow Fields

1321 Velocities etc



1331 Geometry


1333 Forces


134 Boundary Layers


135 Cavitation


1352 Flow fields

1353 Pumps


141 Waves

1411 Periodic waves





142 Wind


143 Ice Mechanics


15 Noise


2 Ships in General

21 Basic Quantities


221 Hull Geometry






2222 Ducts


2224 Pods


























235 Water Jets


241 Manoeuvrability





2415 Linear Models




242 Sea Keeping




3 Special Craft











33 Hydrofoil Boats






34 ACV and SES





36 Sailing Vessels






421 Classification





52 Computer Symbols

53 Documentation

531 ITTC Documents

532 Translations


Symbol

Computer

Symbol

Definition or

Explanation

bility p

quantity Xi

tainty

tainty from Type A

tainty from Type B

tainty

measurement

22 )]([)( iii xucyu 1

mate y

Symbol

Computer

Symbol

Definition or

Explanation

mate xi

mate y

estimates xi and xj

U = k uc(y)

Up = kp uc(y)

tion i ix X

measurand Y depends

variable

Symbol

Computer

Symbol

Definition or

Explanation

quantity Xi

servation of Xi

Output estimate

same measurement

Y A measurand

certainty Up

root of 2

Symbol

Computer

Symbol

Definition or

Explanation

n estimated by

tive square root of

tities

in the following

tion if any

Axes coordinates

Body axes (xyz)

platforms or ships

upwards

section

flight dynamics

ular case

differential

Name of coordi-

nate system

Remarks

11-121

cartesian

coordinates

system See Figure 1

11-122

cylindrical

coordinates

11-123

(-) r φ r=rer

r sin dφ eφ

spherical

Figures 3 and 5

Symbol

Computer

Symbol

Definition or

Explanation

lar quantity

scalar distribution

εikjxkds

εklixlεjkm xmds

Sij = S0ij

Si 3+j = S1ij

S3+i j = S1ij

S3+i 3+j = S2ij

tesian coordinates

fixed in the body

Tijs + Tij

tensor

( Tij - Tji ) 2

Symbol

Computer

Symbol

Definition or

Explanation

V3+i = V1i

X X(1)

Y X(2)

Z X(3)

the body

x0 x01

y0 x02

z0 x03

X0 X0(1)

Y0 X0(2)

Z0 X0(3)

xF xF1

yF xF2

zF xF3

XF XF(1)

YF XF(2)

ZF XF(3)

1 ijk = 321 213 132

0 if otherwise

Symbol

Computer

Symbol

Definition or

Explanation

f FR Frequency Hz

functions

1 TC Hz

Laurent transform

Laplace transform

t TI Time - + s

Symbol

Computer

Symbol

Definition or

Explanation

pled function

= X(0)2 + fSXF(f + jfS)

inverse form

XF(f)=XL(f)

t = 0 TC

XF = xFjδ(f - jTC)

inverse form

Hilbert transform

(1t)F = -i sgn f

if X(tlt0) = 0 then

= (X(t)exp(-at))F

ie = 0 for f lt 0

rier series

XFj(1 + sgn j)

line spectra

Symbol

Computer

Symbol

Definition or

Explanation

component

zl ZLG (Phase) Lag

component

Symbol

Computer

Symbol

Definition or

Explanation

gE gM gMR

E(g) = g(x)fx(x)dx

Random quantities

x(ζ) y(ζ)

X(I) Y(I)

i = 1 n

n sample size

quantity

xD xDR σx

dom quantity

xVR frac12

xDS sx

dom quantity

xVS 12

xxR xxMR Rxx

dom quantity

xyR xyMR Rxy

dom quantities

xE xM xMR

xA xMS mx

a random quantity

1n xi i = 1n

xAE = xE

xVSE = xV n

xPD fx

dom quantity

d Fx dx

xyPD fxy

2 Fxy (x y)

xPF Fx

xyPF Fxy

random quantities

Symbol

Computer

Symbol

Definition or

Explanation

xV xVR xxVR

XVR XXVR

x2 E - xE 2

xVS xxVS

XVS XXVS

dom quantity

1 (n - 1) (xi - x

i = 1n

xyV xyVR

quantities

x yE - xE yE

periment

dom quantity

t =-T2 +T2

T =- +

A(g(t)) = 1T g(t)dt

t =0 +T

x(ζt) y(ζt)

xxC xxCR Cxx

(x(t) - xE)(x(t + τ) - xE)E

xyC xyCR Cxy

(x(t) - xE)(y(t + τ) - yE)E

xxR xxRR Rxx

Rxx(τ) = Rxx(-τ)

= x(t)x(t + τ)MR

τ = 0

xyR Rxy

Ryx(τ) = Rxy(-τ)

if x y are ergodic

Symbol

Computer

Symbol

Definition or

Explanation

xxS Sxx

chastic process

xxRRSR

xyS Sxy

processes

xyRRSR

periment

Average sample mean

Sample covariance

Sample deviation

E M MR

Probability density

(Power) Spectrum

Sample spectrum

Sample correlation

Population variance

Sample variance

Symbol

Computer

Symbol

Definition or

Explanation

control volume

Inward positive QUs

control volume

quantity stored

dq dt QUs

Symbol

Computer

Symbol

Definition or

Explanation

AM(IJ)

DA(IJ)

RF(IJ)

uv DH(UV)

damping

u FH(U)

uv IH(UV)

inertia

of water-plane area

Iy Iyy

IY IYY

M2(22)

MA(55)

Iz Izz

IZ IZZ

M2(33)

MA(66)

Ixy I12

Iyz I23

Izx I31

IXY I2(12)

IYZ I2(23)

IZX I2(31)

kx kxx

(Ixxm)12

Symbol

Computer

Symbol

Definition or

Explanation

ky kyy

(Iyym)12

kz kzz

(Izzm)12

M0(IJ)

MA(IJ)

tensor

mij = m δij

ij M1(IJ)

M2(IJ)

IN(IJ)

MA(UV)

system

Mij = M0

Mi 3+j = M1Tij

M3+i j = M1ij

M3+i 3+j = M2ij

Symbol

Computer

Symbol

Definition or

Explanation

122 Loads

1221 External Loads

in body coordinates

u = MMu

Fi = F0i

F3+i = F1i

gi = g1

g3+i = 0

in body coordinates

F11 F4

K M(1)

F1(1) F(4)

F12 F5

M M(2)

F1(2) F(5)

FN13 F6

N M(3)

F1(3) F(6)

F01 F1

F0(1) F(1)

axis x

F02 F2

F0(2) F(2)

axis y

F03 F3

F0(3) F(3)

axis z

Gu = muv gv

G0i Gi

in body coordinates

Gi = G0

i = m0ij gj

i G1(I)

in body coordinates

G3+i = G1

i = εikj xk G0

= m1ij gj

dW dx1

Symbol

Computer

Symbol

Definition or

Explanation

section coordinates

FSi = FS0

FS3+i = FS1

i = MBi

FS11 Nm

Symbol

Computer

Symbol

Definition or

Explanation

1231 Motions

v01 v4

V0(1) V(4)

body axis x

v02 v5

V0(2) V(5)

body axis y

v03 v6

V0(3) V(6)

body axis z

v11 v1

V1(1) V(1)

v12 v2

V1(2) V(2)

v13 v3

V1(3) V(3)

body axes

vi = v1

v3+i = v0i

tive to body axes

Symbol

Computer

Symbol

Definition or

Explanation

1232 Attitudes

Angle of attack

the z-axis

about the xo axis

X(4) RO

X(5) TR

X(6) YA

course

13 Fluid Mechanics

Symbol

Computer

Symbol

Definition or

Explanation

13 Fluid Mechanics

131 Flow Parameters

Velocity of sound

(E ρ)12

Weight density

ρg (See 111)

Viscosity

Kinematic viscosity

DN RHO

Mass density

Capillarity

length

Boussinesq number

V (g RH)12

Cauchy number

V (E ρ)12

Froude number

V (g L)12

Froude depth number

V (g h)12

V (g 13)12

Mach number

Reynolds number

Strouhal number

Thoma number

Cavitation number

(pA ndash pV)q

Weber number

V2 L κ

07R Ac V nDRe

13 Fluid Mechanics

Symbol

Computer

Symbol

Definition or

Explanation

Sand roughness

surface

Hydraulic radius

wetted perimeter

13 Fluid Mechanics

Symbol

Computer

Symbol

Definition or

Explanation

132 Flow Fields

1321 Velocities etc

energy

ρ V2 2 + p + ρ g h

Mass specific force

Total head

e w = h +pw +qw

flow energy

turbed flow

ρ V2 2

Rate of flow

Total head loss

ij SR(IJ)

ρ vivj

Pa sij

ST(IJ)

Total stress tensor

change

ij SV(IJ)

Viscous stress

u vx v1

v vy v2

w vz v3

Velocity

V = vivi

Wall shear stress

μ (U y)y=0

13 Fluid Mechanics

Symbol

Computer

Symbol

Definition or

Explanation

Induction factor

Vortex density

Circulation

intV ds

along a closed line

Potential function

Stream function

ψ = const

surface

13 Fluid Mechanics

Symbol

Computer

Symbol

Definition or

Explanation

1331 Geometry

Projected area

Wing or foil span

Flap span

Mean chord length

Tip chord length

Root chord length

Sweep angle

tion (general)

edge of struts

(general)

of foil

section

tS cSTH

Taper ratio

Aspect ratio

13 Fluid Mechanics

Symbol

Computer

Symbol

Definition or

Explanation

Induced velocity

and the chord line

or incidence

Geometric angle of

attack or incidence

Hydrodynamic angle

of attack

zero lift

Angle of zero lift

at zero lift

13 Fluid Mechanics

Symbol

Computer

Symbol

Definition or

Explanation

1333 Forces

Foil drag

DRIND Induced drag

of motion

Interference drag

secting foil

zero lift

Streamline drag

Lift force on foil

CL AFT q

of zero

CL0 AFT q

Lift-Drag ratio

13 Fluid Mechanics

Symbol

Computer

Symbol

Definition or

Explanation

134 Boundary Layers

τ (ρ Ue

Entrainment factor

1 (Ue dQ dx)

rameter

(δ - δ) Θ

Static pressure

Total pressure

Entrainment

U δ v or Ue δ

RTHETA

U Θ v or Ue Θ v

boundary layer

from surface

(τ ρ)12

boundary layer

from the surface

(Ue- U) uτ

13 Fluid Mechanics

Symbol

Computer

Symbol

Definition or

Explanation

from the wall

y uτ v

δ (τw dp dx)

layer at U=0995Ue

δ δ1

boundary layer

(Ue- U) Ue dy

von Karman constant

δ995 (v dUe dx)

Energy thickness

(U Ue) (1 - U2 Ue

Momentum thickness

(U Ue) (1 - U Ue)dy

Local skin friction

μ (U y)y=0

13 Fluid Mechanics

Symbol

Computer

Symbol

Definition or

Explanation

135 Cavitation

Gas content ratio

α αS

Gas content

temperature

Cavitation number

(pA - pC) q

(pA - pV) q

1352 Flow fields

Cavity drag

Cavity length

region

Ambient pressure

Critical pressure

takes place

Cavity pressure

quasi-steady cavity

Critical velocity

takes place

Volume loss

13 Fluid Mechanics

Symbol

Computer

Symbol

Definition or

Explanation

WL WTLS

Weight loss

specified time

1353 Pumps

turbo-engines

Thoma number

(HU - pV w) HN

Symbol

Computer

Symbol

Definition or

Explanation

141 Waves

1411 Periodic waves

lerity LW TW =

2WgL in

deep water

odic wave

const = cW

lerity

i fW Hz

wave crest to wave

wave ηC - ηT

advance

Symbol

Computer

Symbol

Definition or

Explanation

at a given location

ηFSα m

ηFSp rad

crossing

trough

crossing

and crest

wave heights

crossing

of zero in a record

Symbol

Computer

Symbol

Definition or

Explanation

in a record

Negative values m

crossing

visual observation

cant wave height

wave heights

wave height

heights

visual observation

wave propagation

samples

visual observation

Symbol

Computer

Symbol

Definition or

Explanation

lution

points

tude function

4 (m0)12 m

fn S(f)df m2 sn

Si(ω)

tral density

Sr(ω)

tral density

Sη(f)

Sη(ω)

2πfP s

and first moment

m0m1 s

and second moment

(m0m2)12 s

Symbol

Computer

Symbol

Definition or

Explanation

DX(fθ)

DX(ωμ)

SIGMAOX

Sζ (ωμ)

Sθ (ωμ)

density

Sρ(fθ)

Sζ(ωμ)

θm MWD

THETAMOX

rection

Symbol

Computer

Symbol

Definition or

Explanation

142 Wind

(008 + 0065U10)10-3

Fetch length

wind blows

DURATN

Wind duration

Return period

ceeded

uz uzi

UFLUCT

USHEAR

Wind shear velocity

12 U10 or 071U10123

Reference mean wind

U10 = (10z)17 Uz

(Uz + uzi)

UzA = (z10)17 U10 or

see section 141

True wind velocity

see section 141

Dimensionless Fetch

face in meters

see section 26

True wind angle

see section 26

Wind direction

Symbol

Computer

Symbol

Definition or

Explanation

143 Ice Mechanics

weight of ice

volume of ice

unit volume of ice

15 Noise

Symbol

Computer

Symbol

Definition or

Explanation

15 Noise

acoustic centre

= 10 log10

(119903119898119904

1199011199031198901198912 ) dB 119901119903119890119891

tance of 1m

119871s

= 119871p

+ 20 log10 [119889

119889119903119890119891] dB 119889119903119890119891

Symbol

Computer

Symbol

Definition or

Explanation

2 SHIPS IN GENERAL

21 Basic Quantities

dv dt ms2

A A AR

Area in general m2

B B BR Breadth m

(forces)

d D D DI Diameter m

E E EN Energy J

F F0 F F0 Force N

h DE Depth m

H H HT Height m

mass distribution

L L LE Length m

tory velocity

m M MA

Mass kg

Symbol

Computer

Symbol

Definition or

Explanation

distribution

M MO Momentum Ns

P P PO Power W

r R RD Radius m

locity

t TI Time s

t TE Temperature K

harmonic process

of a body

ds dt ms

V VO Volume m3

specific weight

dW dV = ρg Nm3

acting on a body

tilled water at 4C

Symbol

Computer

Symbol

Definition or

Explanation

Symbol

Computer

Symbol

Definition or

Explanation

221 Hull Geometry

gitudinal plane

perpendicular

the final rounding

aft perpendiculars

port and starboard)

waterline

relative wind

midship

of midship

section

of ships hull

Symbol

Computer

Symbol

Definition or

Explanation

water line

at stem

the perpendiculars)

maximum section

verse section

Symbol

Computer

Symbol

Definition or

Explanation

point of the stern

pendicular

dicular

perpendicular

with straight keel

water surface level

bare hull

ΔBH (ρ g) m3

pendages

ΔAP (ρ g) m3

Symbol

Computer

Symbol

Definition or

Explanation

ancy) g ρ N

= TS TM

cient B 13 1

GM 13 1

GZ 13 1

cient KG T

12 IL ( B L3) 1

12 IT (B3 L) 1

AM (B T) 1

body A (AX L 2) or

A (AM L 2)

trance E (AX LE) or

E (AM LE)

body F (AX L 2) or

F (AM L 2)

Symbol

Computer

Symbol

Definition or

Explanation

R (AM LR)

AWA (B L 2) 1

forward

AWF (B L 2) 1

coefficient

maximum area

ABL (L T) 1

ABT AX 1

transom stern

AT AX 1

L 13 1

cient T 13 1

A AB After body

APP APP Appendages

B BH Bare hull

DW Design waterline

E EN Entry

Symbol

Computer

Symbol

Definition or

Explanation

F FB Fore body

FS Frame spacing

H HE Hull

LR Reference Line

LP LP Based on LPP

LW LW Based on LWL

M MS Midships

PB Parallel body

R RU Run

SS Station spacing

W WP Water plane

S WS Wetted surface

Symbol

Computer

Symbol

Definition or

Explanation

boss or hub

radius

hub to the tip

Symbol

Computer

Symbol

Definition or

Explanation

blades

2 π r sin (φ) z m

positive rake

the propeller plane

iG + iS = cS sinφ

shoulder

Symbol

Computer

Symbol

Definition or

Explanation

ing aft shoulder

rh RH Hub radius m

ler blade

ler axis

dicular

above base line

Symbol

Computer

Symbol

Definition or

Explanation

cal skew angle

Symbol

Computer

Symbol

Definition or

Explanation

2222 Ducts

LD LD Duct length m

ler plane

of duct

tion s

Jet System Head m

at station 1A

Symbol

Computer

Symbol

Definition or

Explanation

2224 Pods

Main Body

tom Fin

Bottom Fin

under pod main body

D Duct (subscript)

Symbol

Computer

Symbol

Definition or

Explanation

appendage

of rudder

propeller race

hydrofoil

lel to keel

Symbol

Computer

Symbol

Definition or

Explanation

rudders

of flanking rudders

BK Bilge keel

BS Bossing

FB Bow foil

FR Flanking rudder

FS Stern foil

KL Keel

RU Rudder

RF Rudder flap

SA Stabilizer

SH Shafting

SK Skeg

ST Strut

TH Thruster

WG Wedge

Symbol

Computer

Symbol

Definition or

Explanation

curves of stability

volume

Centre of buoyancy

volume

ter plane

(mass)

Keel reference

XCB LCB

ancy (LCB)

from Midships

XCF LCF

tion (LCF)

from Midships

Symbol

Computer

Symbol

Definition or

Explanation

from Midships

XCG LCG

ity (LCG)

from Midships

gravity G

centre of buoyancy

curves of stability

Symbol

Computer

Symbol

Definition or

Explanation

centre of buoyancy

metacentre M

pendicular

dicular

pendicular

weight addition

101 GGKGKG m

height

to the metacentre

tion effects

centric height

metacentre ML

KGKMGM LL

TAG cosφ

KB-KM =I =BM T

BM KM KB

Symbol

Computer

Symbol

Definition or

Explanation

base or keel K

metacentre M to the

ing arm

Heeling moment Δ m

GM 13 1

GZ 13 1

cient KG T

ficient

proximately equals

Symbol

Computer

Symbol

Definition or

Explanation

ficient

proximately equals

one centimetre

one meter

ΔCMTL Nmm

force g ρ N

flooded water

Δfw (ρg) m3

Symbol

Computer

Symbol

Definition or

Explanation

the compartment

bility

a apparent

A att attained

d dyn dynamic

e EFF effective

f false

KL keel line

L longitudinal

MAX maximum

s Static

S sqt Sinkage squat

TC Trim in cm

TM Trim in m

T transverse

V vertical

0 Initial

at heel angle

θ at trim angle θ

Symbol

Computer

Symbol

Definition or

Explanation

231 Hull Resistance

cross section area

lowance

propulsion tests

[(1 + k) CFM + CR]

surface of the body

bare hull

SBH + SAPP m2

Symbol

Computer

Symbol

Definition or

Explanation

area underway

area at rest

area underway

area at rest

lation

RA (S q) 1

ficient

RAA (AV qR) 1

RAPP (S q) 1

cient of a body

RF (S q) 1

RF0 (S q) 1

RP (S q) 1

coefficient

RPV (S q) 1

Symbol

Computer

Symbol

Definition or

Explanation

RR (S q) 1

g R L (ΔV2) 1

efficient

RV (S q) 1

efficient

RW (S q) 1

efficient

1000 R (Δ(KC)2)

1000 RF (Δ(KC)2) 1

sliding bodies

(CV - CF0) CF0 1

(4πg)12VK16

sponding to KQ KT

R (ρ D4 n2) 1

ρ V2 2

see 332

qR PDWR

apparent wind

ρ VWR2 2

see 342

Symbol

Computer

Symbol

Definition or

Explanation

tio in general

R Δ 1

placement ratio

RR Δ 1

FW Fresh water

MR Raw model data

OW Open water

SW Salt water

Symbol

Computer

Symbol

Definition or

Explanation

of revolution

Brake power

Delivered power

propeller power

Effective power

resistance power

Indicated power

Shaft power

Thrust power

Torque

Running trim

Ship speed

or torque identity

2 π n

Symbol

Computer

Symbol

Definition or

Explanation

(T - RT) RT

Δ23 V3 PS

PD (ρ V3 23 2)

identity

PDT PDS

ηDS ηDM

factor

Sinkage dynamic

Trim dynamic

by length

(T - RT) T

(V - VA) V

(V - VA) VA

Symbol

Computer

Symbol

Definition or

Explanation

wTM - wTS

1978 method

diction

ηD PD PE - 1

resistance

PT PD = T VA (Q ω)

coefficient

PE PD = PR PP

Gearing efficiency

Hull efficiency

PE PT = PR PT

= (1 - t) (1 - w)

and propeller

water tests

ηB ηO

Shafting efficiency

PD PS = PP PS

Symbol

Computer

Symbol

Definition or

Explanation

lution

ler blade surface

advance speed

ρ VA2 2

ρ VS2 2 Pa

QS=QSC+ QSH

torque

peller unit

peller

Symbol

Computer

Symbol

Definition or

Explanation

at 07 R

(VA2+ (07 R ω)2)12

n PDfrac12 VA

with n in revsmin

VA in kn (obsolete)

n PTfrac12 VA

with n in revsmin

VA in kn (obsolete)

T (AP qA)

= (TP AP) qA

V (D n) = VH (D n) 1

ducted propeller

VP (D n)

identity

coefficient

QSC (ρ n2 D5) 1

Symbol

Computer

Symbol

Definition or

Explanation

torque coefficient

QSH (ρ n2 D5) 1

ficient

TP (ρ n2 D4) 1

KTP+ KTD 1

KQηR 1

feet VA in kn

efficiency

PJ PD = PJ PP 1

ηJP0 ZET0

zero advance speed

T (ρ π 2)13 (PD D)23 1

η0 ηTP0 ETA0

water tests

ducted propeller

TP TT 1

Symbol

Computer

Symbol

Definition or

Explanation

propeller

peller

by propeller

blade section

arctg (VA r ω)

Symbol

Computer

Symbol

Definition or

Explanation

u = 1 6

u = 1 2 3 force

u = 4 5 6 moment

coefficients

KFi and KMi

cients

Mi (ρ n2 D5) 1

p PR Pressure Pa

ing reaction

u = 1 6

u = 1 2 3 force

u = 4 5 6 moment

from the x-axis

Symbol

Computer

Symbol

Definition or

Explanation

placement

u = 1 6

u = 1 2 3 linear

u = 4 5 6 angular

u = 1 6

u = 1 2 3 linear

u = 4 5 6 angular

eration

u = 1 6

u = 1 2 3 linear

u = 4 5 6 angular

Symbol

Computer

Symbol

Definition or

Explanation

235 Water Jets

210 n2

at station s

cient at station s

rate transducer

Ej = (ρ2)VEj2dQj

j j i i

pg x u n dA

j j i i

pu g x u n dA

sion point

several pump stages

in i direction

u u n dA

Symbol

Computer

Symbol

Definition or

Explanation

dition)

impeller

turbed flow

tion s

boundary layer

msup3s

water jet system

msup3s

jet xT

dition)

system on the hull

Symbol

Computer

Symbol

Definition or

Explanation

at station s

station 7

station 1

tion 1A

surface

in x direction

ciency E

ciency JSE0

stream conditions

the pump

Symbol

Computer

Symbol

Definition or

Explanation

ciency

pump loop test

P duct I

Symbol

Computer

Symbol

Definition or

Explanation

241 Manoeuvrability

of rudder

(AR + ARmov) 2 m2

root to tip

AHL (L T) 1

h DE Water depth m

der axis

Symbol

Computer

Symbol

Definition or

Explanation

dp dt 1s2

dq dt 1s2

dr dt 1s2

du dt ms2

dv dt ms2

dw dt ms2

body axes

χ YX Yaw angle rad

Symbol

Computer

Symbol

Definition or

Explanation

RO Roll angle rad

Pitch angle

the hull

Drift angle

the hull

ANWIRL

ANRUEF

Bow fin angle

Stern fin angle

Rudder angle

ANRUOR

COWIAB

COWIRL

Symbol

Computer

Symbol

Definition or

Explanation

N r Nms2

N v Nms2

along body x-axis

X u Nsm

eration

X u Ns2m

tion of body axis y

Y r Ns2

Symbol

Computer

Symbol

Definition or

Explanation

Y v Ns2m

along body z-axis

2415 Linear Models

ship length

turning diameter

DC LPP 1

ameter δR = δ0

D0 LPP 1

unstable ship

Symbol

Computer

Symbol

Definition or

Explanation

unstable ship

turning rate

change of heading

heading

(starboard)

(port)

tr TIR Reach time s

Symbol

Computer

Symbol

Definition or

Explanation

track reach

Symbol

Computer

Symbol

Definition or

Explanation

242 Sea Keeping

system

spectively

Frequency

Alias horizontal

Alias vertical

moment

Alias horizontal

ing moment

Alias vertical

lution in waves

Symbol

Computer

Symbol

Definition or

Explanation

Sη(f) Sηη(f)

Sη(ω) Sηη(ω)

density

roll pitch yaw

rad TAW

Wave period

Yz(ω)

Azζ(ω)

tory motions

za(ω) ζa(ω) or

za(ω) ηa(ω)

Yθζ(ω)

Aθζ(ω)

motions

Θa(ω) ζa(ω) or

Tuning factor

w w wL L L

w w w= = =

q fL L L= = =

(short crested)

Symbol

Computer

Symbol

Definition or

Explanation

I991241

- I991242

lever curve

cording to ISO 8666

IMOIS IMOHSC2000

acter sets

Symbol

Computer

Symbol

Definition or

Explanation

curves of stability

volume

centre of buoyancy

metacentre M

volume

needed for crew

sons on board

ficient - I991243

proximately equals

hull - I99121

Symbol

Computer

Symbol

Definition or

Explanation

merged test weights

ter plane

pendicular

dicular

pendicular

(mass)

weight addition

101 GGKGKG m

weight addition

101 GGKGKG m

Symbol

Computer

Symbol

Definition or

Explanation

height

to the metacentre

KGKMGM

face effect)

tion effects

height

metacentre ML

KGKMGM LL

TAG cos φ

IMOtable

profile

K Keel reference

base of keel or K

Symbol

Computer

Symbol

Definition or

Explanation

base of keel or K

metacentre M to the

condition - IMOIS

IMOtable

ment due to crew

is taken of rolling

Symbol

Computer

Symbol

Definition or

Explanation

inclination

centimetre

meter CMTL Nmm

due to wind

above waterline

PV Wind pressure Pa

s Wave steepness 1

according to hellip

value see hellip

Symbol

Computer

Symbol

Definition or

Explanation

TL Turning lever m

IMOHSC2000

ancy (LCB)

of buoyancy B

tion (LCF)

of flotation F

ity (LCG)

of gravity G

gravity G

Symbol

Computer

Symbol

Definition or

Explanation

centre of buoyancy

force g N

gle during hellip

Symbol

Computer

Symbol

Definition or

Explanation

according to hellip

gle seehellip

bility

the compartment

stability curve

Symbol

Computer

Symbol

Definition or

Explanation

E Entrance

F Fore

Z Heave

θ Pitch

φ Roll

Symbol

Computer

Symbol

Definition or

Explanation

3 SPECIAL CRAFT

Planing bottom area

strips

gravity

Beam over chines

Transom breadth

spray strips

chines

spray strips

bossings

bottom

section

Shaft angle

inclined downwards)

Symbol

Computer

Symbol

Definition or

Explanation

derway

water surface level

(flange mounting)

forces underway

ing surface

(LK + LC) 2

planing hull

water line

SWS SS

spray edge

Symbol

Computer

Symbol

Definition or

Explanation

ALFBAR

Barrel flow angle

LM LWL

TRIMDWL

design waterline

(positive bow up)

θS θ0

Static trim angle

θV θD

LM (BLCG)

TAUDWL

reference line

Spray angle

plane of bottom)

tal friction area

normally to NA)

normally to NB)

Symbol

Computer

Symbol

Definition or

Explanation

force NPN

ler pressure forces

normally to NPP)

suction forces NPS

normal to NPS)

pressure forces NRP

normal to NRP)

normal to RAA)

normal to RAP)

normal to RF)

sistance RK

normal to RK)

drag ΔRRP

normal to ΔRRP)

thrust

normal to RT)

Symbol

Computer

Symbol

Definition or

Explanation

deadrise

Δ (BCG

surface

Δ (BCG

breadth

V (BCG g)12

Load coefficient

Δ (BCG

3 ρ g )

1 LVHD

drodynamic lift

Hydrostatic lift

Due to buoyancy

reference line

ence line

reference line

Symbol

Computer

Symbol

Definition or

Explanation

reference line

Keel drag

Induced drag

g ρ tg τ

Parasitic drag

openings

Total resistance

spray drag

CF SWS qS

of the hull

Spray velocity

the spray

Symbol

Computer

Symbol

Definition or

Explanation

Box beam

Beam of main deck

Hull spacing

Tunnel width

Hull diameter

submerged hulls

dinal position X

Deck clearance

ANENIN

nel (inner) side

of demihull

ANENOU

outer side

of demihull

Box length

Length of main deck

Symbol

Computer

Symbol

Definition or

Explanation

to trailing edge

Symbol

Computer

Symbol

Definition or

Explanation

hull vessel

ence correction

RFMH - Σ RF

tion of multi-hull

RTMH - RFMH

ence correction

RRMH - Σ RR

vessel

correction

RTMH - Σ RT

33 Hydrofoil Boats

Symbol

Computer

Symbol

Definition or

Explanation

33 Hydrofoil Boats

cluding foils

Span of struts

tance of struts

Mean chord length

section with foil

Weight of foil

Dihedral angle

Submerged foil area

take-off speed

33 Hydrofoil Boats

Symbol

Computer

Symbol

Definition or

Explanation

Foil span wetted

distance

V (g LF)12

chord length

V (g cM)12

foilborne

Flight height

at rest

Keel clearance

centre of gravity

and rear foils

lF + lR

centre of gravity

Foil immersion

ALFIND

with twist

33 Hydrofoil Boats

Symbol

Computer

Symbol

Definition or

Explanation

33 Hydrofoil Boats

Symbol

Computer

Symbol

Definition or

Explanation

Foil drag

CDF AFR q

CDF AFF q

DRIND Induced drag

of motion

Interference drag

secting foil

Streamline drag

Spray drag

Strut drag

Wave drag

Ventilation drag

Lift force on foil

CL AFT q

CL AFF q

CL AFR q

attack of zero

CL0 AFT q

CLTO AFT q

33 Hydrofoil Boats

Symbol

Computer

Symbol

Definition or

Explanation

DP (AFS q) 1

L0 (AFS q) 1

condition

LTO (AFS q) 1

34 ACV and SES

Symbol

Computer

Symbol

Definition or

Explanation

34 ACV and SES

Cushion area

Cushion beam

At the water line

neath craft

Bow seal height

Skirt depth

Stern seal height

Cushion length

at rest off cushion

to structure

needs clarification

34 ACV and SES

Symbol

Computer

Symbol

Definition or

Explanation

structure

needs clarification

to structure

needs clarification

to water contact

SSHC SSH0

cushion periphery

of air

the skirt

34 ACV and SES

Symbol

Computer

Symbol

Definition or

Explanation

coefficient

R0 (ρA VR2 AC 2) 1

PCU LC Pam

in general

ρA QT VA N

of cushion

ρA QCU VA N

of skirt

ρA QTS VA N

34 ACV and SES

Symbol

Computer

Symbol

Definition or

Explanation

Symbol

Computer

Symbol

Definition or

Explanation

sistance

RI (ρI g h2 B)

of ice

RIW (S qIW)

normal

rection of motion

thickness

V (g hI)

ice force

ice (dynamic)

ice (static)

condition)

Thickness of ice

KQICMS

in ice

QIA (ρW nIA

KTICMS

in ice

TIA (ρW nIA

FRICMS

revolution in ice

Symbol

Computer

Symbol

Definition or

Explanation

in ice

2 π QIA nIA

Net ice resistance

RIT - RIW

in presence of ice

in ice

ciency in ice

ηID ηD

36 Sailing Vessels

Symbol

Computer

Symbol

Definition or

Explanation

36 Sailing Vessels

Area of mainsail

Area of spinnaker

(P E + I J) 2

Beam overall

Mainsail base

Fore triangle base

Mainsail height

olds Number

noe body

Effective draught

FH (ρVB

tical centre plane

36 Sailing Vessels

Symbol

Computer

Symbol

Definition or

Explanation

Displacement force

(weight) of keel

Displacement force

(weight) of rudder

36 Sailing Vessels

Symbol

Computer

Symbol

Definition or

Explanation

cient (upright)

RFU (S q)

cient (upright)

RRU (S q)

Total resistance

RTU (S q)

(upright)

RTφ (S q)

Cx Cy Cz

Force coefficients

Side force

right)

RTU + Rφ

Rφ RH

Vessel velocity

36 Sailing Vessels

Symbol

Computer

Symbol

Definition or

Explanation

True wind velocity

course

leaway angle

to boat course)

boat course)

Version 2014 130

4 BACKGROUND AND

REFERENCES

421 Classification

cross-references

list of symbols

drawing

standard itself

exponentiation

operators

matrix components

quantities

A ( eg Area in

msup2)

Version 2011 133

Numbers in roman

(power of n)

SYMBOLS

in italic

NUMBERS

in roman

(T = Thrust)

(M = Model) Fig 1

1 Scope

TK 102

A=A-[A]

as described above

NUMERICAL VALUES

AB = A B - [A] [B]

Version 2014 135

EXAMPLE

Ek = 2

1mvsup2

rived quantities

intensity J

51992 annex A)

dim Q = AαBβCγ

becomes in general

EXAMPLES

Quantity Dimension

velocity LT-1

force LMT-2

energy L2MT-2

relative density 1

Version 2014 136

23 Units

merical values

- base units

2321 Base units

Name Symbol

length metre m

mass kilogram kg

time second s

thermodynamic tem-

perature kelvin K

tary units

L rarr m I rarr A

M rarr kg Θ rarr K

T rarr s N rarrmol

J rarr cd

Derived quantity

SI derived unit

EXAMPLES

Version 2014 138

expressed in terms

of the seven base

units (and the sup-

plementary units in

some cases)

velocity ms

force kg ms2

energy kg m2s2

relative density 1

2323 SI prefixes

Factor Prefix

Name Symbol

1024 yotta Y

1021 zetta z

1018 exa E

1015 peta P

1012 tera T

109 giga G

106 mega M

103 kilo k

102 hecto h

10 deca da

10-1 deci d

10-2 centi c

10-3 milli m

10-6 micro micro

10-9 nano n

10-12 pico p

10-15 femto f

10-18 atto a

10-21 zepto z

10-24 yocto y

fixes see 324

233 The unit one

EXAMPLE

EXAMPLES

Plane angle α = 05

rad = 05

1 with a prefix

for the number 001

shall not be used

neous units

stance

51992 Annex A

with the Sl

Quantity Unit

Name Sym-

bol Definition

time minute

1 min= 60s

1 h = 60 min

1 d = 24 h

plane an-

degree

minute

second

1 deg =

(π180)rad =

(nl80) rad

1 = (160)deg

1 = (160)

= 1 dm

Name Sym-

bol Definition

the kinetic energy

tron in passing

through a potential

in vacuum 1 eV

1602 177 times10-19 J

mass unified

atomic

mass unit

(1 12) of the mass

of an atom of the

nuclide 12C 1u

1660 540 times10-27kg

Tables 5 and 6

the curie

and numbers

311 Symbols

sentence

use of subscripts

right) type

EXAMPLES

Upright sub-

number)

numbers)

(sloping) type

eg a∙ b-1

EXAMPLE

EXAMPLES

m metre

s second

A ampere

Wb weber

N∙m N m

symbol for a prefix

EXAMPLE

Version 2014 142

m ms m∙s-1

mendation

EXAMPLE

units (see 322)

EXAMPLES

1cm3 = (10-2m)3=10-6 m3

1 μs-1= (10-6 s)-1 = 106 s-1

1 kAm = (103A)m = 103 Am

crokilogram (μkg)

33 Numbers

man (upright) type

332Decimal sign

for the quantities

EXAMPLES

l = 12 m - 7 m= (12 - 7) m = 5m

clides

EXAMPLES

H He C Ca

A and 150 31-91992 annex A

script position

4O or (PO4)3-

types)

alpha Α a Α a

beta Β β Β β

gamma Γ γ Γ γ

delta Δ δ Δ δ

epsilon Ε ε Ε ε

zeta Ζ ζ Ζ ζ

eta Η η Η η

theta Θ θ Θ θ

iota Ι ι Ι ι

kappa Κ κ Κ κ

lambda Λ λ Λ λ

mu Μ μ Μ μ

nu Ν ν Ν ν

xi Ξ ξ Ξ ξ

omicron Ο ο Ο ο

pi Π π Π π

rho P ρ Ρ ρ

sigma Σ σ Σ σ

tau Τ τ Τ τ

upsilon Υ υ Υ υ

phi Φ φ Φ φ

chi Χ χ Χ χ

psi Ψ ψ Ψ ψ

omega Ω ω Ω ω

52 Computer symbols

Version 2014 145

52 Computer Symbols

- 9 have been used

near future

53 Documentation

Version 2014 146

53 Documentation

531 ITTC Documents

No500 1976

No6 1978

CETENA Genova 1984

532 Translations

malisation (AFNOR)

No28 Zagreb 1974

truccion Naval

53 Documentation

Version 2014 147

Table of Contents

1 General


111 Uncertainty















122 Loads

1221 External Loads



1231 Motions

1232 Attitudes

13 Fluid Mechanics

131 Flow Parameters




132 Flow Fields

1321 Velocities etc



1331 Geometry


1333 Forces


134 Boundary Layers


135 Cavitation


1352 Flow fields

1353 Pumps


141 Waves

1411 Periodic waves





142 Wind


143 Ice Mechanics


15 Noise


2 Ships in General

21 Basic Quantities


221 Hull Geometry






2222 Ducts


2224 Pods


























235 Water Jets


241 Manoeuvrability





2415 Linear Models




242 Sea Keeping




3 Special Craft











33 Hydrofoil Boats






34 ACV and SES





36 Sailing Vessels






421 Classification





52 Computer Symbols

53 Documentation

531 ITTC Documents

532 Translations


Symbol

Computer

Symbol

Definition or

Explanation

mate xi

mate y

estimates xi and xj

U = k uc(y)

Up = kp uc(y)

tion i ix X

measurand Y depends

variable

Symbol

Computer

Symbol

Definition or

Explanation

quantity Xi

servation of Xi

Output estimate

same measurement

Y A measurand

certainty Up

root of 2

Symbol

Computer

Symbol

Definition or

Explanation

n estimated by

tive square root of

tities

in the following

tion if any

Axes coordinates

Body axes (xyz)

platforms or ships

upwards

section

flight dynamics

ular case

differential

Name of coordi-

nate system

Remarks

11-121

cartesian

coordinates

system See Figure 1

11-122

cylindrical

coordinates

11-123

(-) r φ r=rer

r sin dφ eφ

spherical

Figures 3 and 5

Symbol

Computer

Symbol

Definition or

Explanation

lar quantity

scalar distribution

εikjxkds

εklixlεjkm xmds

Sij = S0ij

Si 3+j = S1ij

S3+i j = S1ij

S3+i 3+j = S2ij

tesian coordinates

fixed in the body

Tijs + Tij

tensor

( Tij - Tji ) 2

Symbol

Computer

Symbol

Definition or

Explanation

V3+i = V1i

X X(1)

Y X(2)

Z X(3)

the body

x0 x01

y0 x02

z0 x03

X0 X0(1)

Y0 X0(2)

Z0 X0(3)

xF xF1

yF xF2

zF xF3

XF XF(1)

YF XF(2)

ZF XF(3)

1 ijk = 321 213 132

0 if otherwise

Symbol

Computer

Symbol

Definition or

Explanation

f FR Frequency Hz

functions

1 TC Hz

Laurent transform

Laplace transform

t TI Time - + s

Symbol

Computer

Symbol

Definition or

Explanation

pled function

= X(0)2 + fSXF(f + jfS)

inverse form

XF(f)=XL(f)

t = 0 TC

XF = xFjδ(f - jTC)

inverse form

Hilbert transform

(1t)F = -i sgn f

if X(tlt0) = 0 then

= (X(t)exp(-at))F

ie = 0 for f lt 0

rier series

XFj(1 + sgn j)

line spectra

Symbol

Computer

Symbol

Definition or

Explanation

component

zl ZLG (Phase) Lag

component

Symbol

Computer

Symbol

Definition or

Explanation

gE gM gMR

E(g) = g(x)fx(x)dx

Random quantities

x(ζ) y(ζ)

X(I) Y(I)

i = 1 n

n sample size

quantity

xD xDR σx

dom quantity

xVR frac12

xDS sx

dom quantity

xVS 12

xxR xxMR Rxx

dom quantity

xyR xyMR Rxy

dom quantities

xE xM xMR

xA xMS mx

a random quantity

1n xi i = 1n

xAE = xE

xVSE = xV n

xPD fx

dom quantity

d Fx dx

xyPD fxy

2 Fxy (x y)

xPF Fx

xyPF Fxy

random quantities

Symbol

Computer

Symbol

Definition or

Explanation

xV xVR xxVR

XVR XXVR

x2 E - xE 2

xVS xxVS

XVS XXVS

dom quantity

1 (n - 1) (xi - x

i = 1n

xyV xyVR

quantities

x yE - xE yE

periment

dom quantity

t =-T2 +T2

T =- +

A(g(t)) = 1T g(t)dt

t =0 +T

x(ζt) y(ζt)

xxC xxCR Cxx

(x(t) - xE)(x(t + τ) - xE)E

xyC xyCR Cxy

(x(t) - xE)(y(t + τ) - yE)E

xxR xxRR Rxx

Rxx(τ) = Rxx(-τ)

= x(t)x(t + τ)MR

τ = 0

xyR Rxy

Ryx(τ) = Rxy(-τ)

if x y are ergodic

Symbol

Computer

Symbol

Definition or

Explanation

xxS Sxx

chastic process

xxRRSR

xyS Sxy

processes

xyRRSR

periment

Average sample mean

Sample covariance

Sample deviation

E M MR

Probability density

(Power) Spectrum

Sample spectrum

Sample correlation

Population variance

Sample variance

Symbol

Computer

Symbol

Definition or

Explanation

control volume

Inward positive QUs

control volume

quantity stored

dq dt QUs

Symbol

Computer

Symbol

Definition or

Explanation

AM(IJ)

DA(IJ)

RF(IJ)

uv DH(UV)

damping

u FH(U)

uv IH(UV)

inertia

of water-plane area

Iy Iyy

IY IYY

M2(22)

MA(55)

Iz Izz

IZ IZZ

M2(33)

MA(66)

Ixy I12

Iyz I23

Izx I31

IXY I2(12)

IYZ I2(23)

IZX I2(31)

kx kxx

(Ixxm)12

Symbol

Computer

Symbol

Definition or

Explanation

ky kyy

(Iyym)12

kz kzz

(Izzm)12

M0(IJ)

MA(IJ)

tensor

mij = m δij

ij M1(IJ)

M2(IJ)

IN(IJ)

MA(UV)

system

Mij = M0

Mi 3+j = M1Tij

M3+i j = M1ij

M3+i 3+j = M2ij

Symbol

Computer

Symbol

Definition or

Explanation

122 Loads

1221 External Loads

in body coordinates

u = MMu

Fi = F0i

F3+i = F1i

gi = g1

g3+i = 0

in body coordinates

F11 F4

K M(1)

F1(1) F(4)

F12 F5

M M(2)

F1(2) F(5)

FN13 F6

N M(3)

F1(3) F(6)

F01 F1

F0(1) F(1)

axis x

F02 F2

F0(2) F(2)

axis y

F03 F3

F0(3) F(3)

axis z

Gu = muv gv

G0i Gi

in body coordinates

Gi = G0

i = m0ij gj

i G1(I)

in body coordinates

G3+i = G1

i = εikj xk G0

= m1ij gj

dW dx1

Symbol

Computer

Symbol

Definition or

Explanation

section coordinates

FSi = FS0

FS3+i = FS1

i = MBi

FS11 Nm

Symbol

Computer

Symbol

Definition or

Explanation

1231 Motions

v01 v4

V0(1) V(4)

body axis x

v02 v5

V0(2) V(5)

body axis y

v03 v6

V0(3) V(6)

body axis z

v11 v1

V1(1) V(1)

v12 v2

V1(2) V(2)

v13 v3

V1(3) V(3)

body axes

vi = v1

v3+i = v0i

tive to body axes

Symbol

Computer

Symbol

Definition or

Explanation

1232 Attitudes

Angle of attack

the z-axis

about the xo axis

X(4) RO

X(5) TR

X(6) YA

course

13 Fluid Mechanics

Symbol

Computer

Symbol

Definition or

Explanation

13 Fluid Mechanics

131 Flow Parameters

Velocity of sound

(E ρ)12

Weight density

ρg (See 111)

Viscosity

Kinematic viscosity

DN RHO

Mass density

Capillarity

length

Boussinesq number

V (g RH)12

Cauchy number

V (E ρ)12

Froude number

V (g L)12

Froude depth number

V (g h)12

V (g 13)12

Mach number

Reynolds number

Strouhal number

Thoma number

Cavitation number

(pA ndash pV)q

Weber number

V2 L κ

07R Ac V nDRe

13 Fluid Mechanics

Symbol

Computer

Symbol

Definition or

Explanation

Sand roughness

surface

Hydraulic radius

wetted perimeter

13 Fluid Mechanics

Symbol

Computer

Symbol

Definition or

Explanation

132 Flow Fields

1321 Velocities etc

energy

ρ V2 2 + p + ρ g h

Mass specific force

Total head

e w = h +pw +qw

flow energy

turbed flow

ρ V2 2

Rate of flow

Total head loss

ij SR(IJ)

ρ vivj

Pa sij

ST(IJ)

Total stress tensor

change

ij SV(IJ)

Viscous stress

u vx v1

v vy v2

w vz v3

Velocity

V = vivi

Wall shear stress

μ (U y)y=0

13 Fluid Mechanics

Symbol

Computer

Symbol

Definition or

Explanation

Induction factor

Vortex density

Circulation

intV ds

along a closed line

Potential function

Stream function

ψ = const

surface

13 Fluid Mechanics

Symbol

Computer

Symbol

Definition or

Explanation

1331 Geometry

Projected area

Wing or foil span

Flap span

Mean chord length

Tip chord length

Root chord length

Sweep angle

tion (general)

edge of struts

(general)

of foil

section

tS cSTH

Taper ratio

Aspect ratio

13 Fluid Mechanics

Symbol

Computer

Symbol

Definition or

Explanation

Induced velocity

and the chord line

or incidence

Geometric angle of

attack or incidence

Hydrodynamic angle

of attack

zero lift

Angle of zero lift

at zero lift

13 Fluid Mechanics

Symbol

Computer

Symbol

Definition or

Explanation

1333 Forces

Foil drag

DRIND Induced drag

of motion

Interference drag

secting foil

zero lift

Streamline drag

Lift force on foil

CL AFT q

of zero

CL0 AFT q

Lift-Drag ratio

13 Fluid Mechanics

Symbol

Computer

Symbol

Definition or

Explanation

134 Boundary Layers

τ (ρ Ue

Entrainment factor

1 (Ue dQ dx)

rameter

(δ - δ) Θ

Static pressure

Total pressure

Entrainment

U δ v or Ue δ

RTHETA

U Θ v or Ue Θ v

boundary layer

from surface

(τ ρ)12

boundary layer

from the surface

(Ue- U) uτ

13 Fluid Mechanics

Symbol

Computer

Symbol

Definition or

Explanation

from the wall

y uτ v

δ (τw dp dx)

layer at U=0995Ue

δ δ1

boundary layer

(Ue- U) Ue dy

von Karman constant

δ995 (v dUe dx)

Energy thickness

(U Ue) (1 - U2 Ue

Momentum thickness

(U Ue) (1 - U Ue)dy

Local skin friction

μ (U y)y=0

13 Fluid Mechanics

Symbol

Computer

Symbol

Definition or

Explanation

135 Cavitation

Gas content ratio

α αS

Gas content

temperature

Cavitation number

(pA - pC) q

(pA - pV) q

1352 Flow fields

Cavity drag

Cavity length

region

Ambient pressure

Critical pressure

takes place

Cavity pressure

quasi-steady cavity

Critical velocity

takes place

Volume loss

13 Fluid Mechanics

Symbol

Computer

Symbol

Definition or

Explanation

WL WTLS

Weight loss

specified time

1353 Pumps

turbo-engines

Thoma number

(HU - pV w) HN

Symbol

Computer

Symbol

Definition or

Explanation

141 Waves

1411 Periodic waves

lerity LW TW =

2WgL in

deep water

odic wave

const = cW

lerity

i fW Hz

wave crest to wave

wave ηC - ηT

advance

Symbol

Computer

Symbol

Definition or

Explanation

at a given location

ηFSα m

ηFSp rad

crossing

trough

crossing

and crest

wave heights

crossing

of zero in a record

Symbol

Computer

Symbol

Definition or

Explanation

in a record

Negative values m

crossing

visual observation

cant wave height

wave heights

wave height

heights

visual observation

wave propagation

samples

visual observation

Symbol

Computer

Symbol

Definition or

Explanation

lution

points

tude function

4 (m0)12 m

fn S(f)df m2 sn

Si(ω)

tral density

Sr(ω)

tral density

Sη(f)

Sη(ω)

2πfP s

and first moment

m0m1 s

and second moment

(m0m2)12 s

Symbol

Computer

Symbol

Definition or

Explanation

DX(fθ)

DX(ωμ)

SIGMAOX

Sζ (ωμ)

Sθ (ωμ)

density

Sρ(fθ)

Sζ(ωμ)

θm MWD

THETAMOX

rection

Symbol

Computer

Symbol

Definition or

Explanation

142 Wind

(008 + 0065U10)10-3

Fetch length

wind blows

DURATN

Wind duration

Return period

ceeded

uz uzi

UFLUCT

USHEAR

Wind shear velocity

12 U10 or 071U10123

Reference mean wind

U10 = (10z)17 Uz

(Uz + uzi)

UzA = (z10)17 U10 or

see section 141

True wind velocity

see section 141

Dimensionless Fetch

face in meters

see section 26

True wind angle

see section 26

Wind direction

Symbol

Computer

Symbol

Definition or

Explanation

143 Ice Mechanics

weight of ice

volume of ice

unit volume of ice

15 Noise

Symbol

Computer

Symbol

Definition or

Explanation

15 Noise

acoustic centre

= 10 log10

(119903119898119904

1199011199031198901198912 ) dB 119901119903119890119891

tance of 1m

119871s

= 119871p

+ 20 log10 [119889

119889119903119890119891] dB 119889119903119890119891

Symbol

Computer

Symbol

Definition or

Explanation

2 SHIPS IN GENERAL

21 Basic Quantities

dv dt ms2

A A AR

Area in general m2

B B BR Breadth m

(forces)

d D D DI Diameter m

E E EN Energy J

F F0 F F0 Force N

h DE Depth m

H H HT Height m

mass distribution

L L LE Length m

tory velocity

m M MA

Mass kg

Symbol

Computer

Symbol

Definition or

Explanation

distribution

M MO Momentum Ns

P P PO Power W

r R RD Radius m

locity

t TI Time s

t TE Temperature K

harmonic process

of a body

ds dt ms

V VO Volume m3

specific weight

dW dV = ρg Nm3

acting on a body

tilled water at 4C

Symbol

Computer

Symbol

Definition or

Explanation

Symbol

Computer

Symbol

Definition or

Explanation

221 Hull Geometry

gitudinal plane

perpendicular

the final rounding

aft perpendiculars

port and starboard)

waterline

relative wind

midship

of midship

section

of ships hull

Symbol

Computer

Symbol

Definition or

Explanation

water line

at stem

the perpendiculars)

maximum section

verse section

Symbol

Computer

Symbol

Definition or

Explanation

point of the stern

pendicular

dicular

perpendicular

with straight keel

water surface level

bare hull

ΔBH (ρ g) m3

pendages

ΔAP (ρ g) m3

Symbol

Computer

Symbol

Definition or

Explanation

ancy) g ρ N

= TS TM

cient B 13 1

GM 13 1

GZ 13 1

cient KG T

12 IL ( B L3) 1

12 IT (B3 L) 1

AM (B T) 1

body A (AX L 2) or

A (AM L 2)

trance E (AX LE) or

E (AM LE)

body F (AX L 2) or

F (AM L 2)

Symbol

Computer

Symbol

Definition or

Explanation

R (AM LR)

AWA (B L 2) 1

forward

AWF (B L 2) 1

coefficient

maximum area

ABL (L T) 1

ABT AX 1

transom stern

AT AX 1

L 13 1

cient T 13 1

A AB After body

APP APP Appendages

B BH Bare hull

DW Design waterline

E EN Entry

Symbol

Computer

Symbol

Definition or

Explanation

F FB Fore body

FS Frame spacing

H HE Hull

LR Reference Line

LP LP Based on LPP

LW LW Based on LWL

M MS Midships

PB Parallel body

R RU Run

SS Station spacing

W WP Water plane

S WS Wetted surface

Symbol

Computer

Symbol

Definition or

Explanation

boss or hub

radius

hub to the tip

Symbol

Computer

Symbol

Definition or

Explanation

blades

2 π r sin (φ) z m

positive rake

the propeller plane

iG + iS = cS sinφ

shoulder

Symbol

Computer

Symbol

Definition or

Explanation

ing aft shoulder

rh RH Hub radius m

ler blade

ler axis

dicular

above base line

Symbol

Computer

Symbol

Definition or

Explanation

cal skew angle

Symbol

Computer

Symbol

Definition or

Explanation

2222 Ducts

LD LD Duct length m

ler plane

of duct

tion s

Jet System Head m

at station 1A

Symbol

Computer

Symbol

Definition or

Explanation

2224 Pods

Main Body

tom Fin

Bottom Fin

under pod main body

D Duct (subscript)

Symbol

Computer

Symbol

Definition or

Explanation

appendage

of rudder

propeller race

hydrofoil

lel to keel

Symbol

Computer

Symbol

Definition or

Explanation

rudders

of flanking rudders

BK Bilge keel

BS Bossing

FB Bow foil

FR Flanking rudder

FS Stern foil

KL Keel

RU Rudder

RF Rudder flap

SA Stabilizer

SH Shafting

SK Skeg

ST Strut

TH Thruster

WG Wedge

Symbol

Computer

Symbol

Definition or

Explanation

curves of stability

volume

Centre of buoyancy

volume

ter plane

(mass)

Keel reference

XCB LCB

ancy (LCB)

from Midships

XCF LCF

tion (LCF)

from Midships

Symbol

Computer

Symbol

Definition or

Explanation

from Midships

XCG LCG

ity (LCG)

from Midships

gravity G

centre of buoyancy

curves of stability

Symbol

Computer

Symbol

Definition or

Explanation

centre of buoyancy

metacentre M

pendicular

dicular

pendicular

weight addition

101 GGKGKG m

height

to the metacentre

tion effects

centric height

metacentre ML

KGKMGM LL

TAG cosφ

KB-KM =I =BM T

BM KM KB

Symbol

Computer

Symbol

Definition or

Explanation

base or keel K

metacentre M to the

ing arm

Heeling moment Δ m

GM 13 1

GZ 13 1

cient KG T

ficient

proximately equals

Symbol

Computer

Symbol

Definition or

Explanation

ficient

proximately equals

one centimetre

one meter

ΔCMTL Nmm

force g ρ N

flooded water

Δfw (ρg) m3

Symbol

Computer

Symbol

Definition or

Explanation

the compartment

bility

a apparent

A att attained

d dyn dynamic

e EFF effective

f false

KL keel line

L longitudinal

MAX maximum

s Static

S sqt Sinkage squat

TC Trim in cm

TM Trim in m

T transverse

V vertical

0 Initial

at heel angle

θ at trim angle θ

Symbol

Computer

Symbol

Definition or

Explanation

231 Hull Resistance

cross section area

lowance

propulsion tests

[(1 + k) CFM + CR]

surface of the body

bare hull

SBH + SAPP m2

Symbol

Computer

Symbol

Definition or

Explanation

area underway

area at rest

area underway

area at rest

lation

RA (S q) 1

ficient

RAA (AV qR) 1

RAPP (S q) 1

cient of a body

RF (S q) 1

RF0 (S q) 1

RP (S q) 1

coefficient

RPV (S q) 1

Symbol

Computer

Symbol

Definition or

Explanation

RR (S q) 1

g R L (ΔV2) 1

efficient

RV (S q) 1

efficient

RW (S q) 1

efficient

1000 R (Δ(KC)2)

1000 RF (Δ(KC)2) 1

sliding bodies

(CV - CF0) CF0 1

(4πg)12VK16

sponding to KQ KT

R (ρ D4 n2) 1

ρ V2 2

see 332

qR PDWR

apparent wind

ρ VWR2 2

see 342

Symbol

Computer

Symbol

Definition or

Explanation

tio in general

R Δ 1

placement ratio

RR Δ 1

FW Fresh water

MR Raw model data

OW Open water

SW Salt water

Symbol

Computer

Symbol

Definition or

Explanation

of revolution

Brake power

Delivered power

propeller power

Effective power

resistance power

Indicated power

Shaft power

Thrust power

Torque

Running trim

Ship speed

or torque identity

2 π n

Symbol

Computer

Symbol

Definition or

Explanation

(T - RT) RT

Δ23 V3 PS

PD (ρ V3 23 2)

identity

PDT PDS

ηDS ηDM

factor

Sinkage dynamic

Trim dynamic

by length

(T - RT) T

(V - VA) V

(V - VA) VA

Symbol

Computer

Symbol

Definition or

Explanation

wTM - wTS

1978 method

diction

ηD PD PE - 1

resistance

PT PD = T VA (Q ω)

coefficient

PE PD = PR PP

Gearing efficiency

Hull efficiency

PE PT = PR PT

= (1 - t) (1 - w)

and propeller

water tests

ηB ηO

Shafting efficiency

PD PS = PP PS

Symbol

Computer

Symbol

Definition or

Explanation

lution

ler blade surface

advance speed

ρ VA2 2

ρ VS2 2 Pa

QS=QSC+ QSH

torque

peller unit

peller

Symbol

Computer

Symbol

Definition or

Explanation

at 07 R

(VA2+ (07 R ω)2)12

n PDfrac12 VA

with n in revsmin

VA in kn (obsolete)

n PTfrac12 VA

with n in revsmin

VA in kn (obsolete)

T (AP qA)

= (TP AP) qA

V (D n) = VH (D n) 1

ducted propeller

VP (D n)

identity

coefficient

QSC (ρ n2 D5) 1

Symbol

Computer

Symbol

Definition or

Explanation

torque coefficient

QSH (ρ n2 D5) 1

ficient

TP (ρ n2 D4) 1

KTP+ KTD 1

KQηR 1

feet VA in kn

efficiency

PJ PD = PJ PP 1

ηJP0 ZET0

zero advance speed

T (ρ π 2)13 (PD D)23 1

η0 ηTP0 ETA0

water tests

ducted propeller

TP TT 1

Symbol

Computer

Symbol

Definition or

Explanation

propeller

peller

by propeller

blade section

arctg (VA r ω)

Symbol

Computer

Symbol

Definition or

Explanation

u = 1 6

u = 1 2 3 force

u = 4 5 6 moment

coefficients

KFi and KMi

cients

Mi (ρ n2 D5) 1

p PR Pressure Pa

ing reaction

u = 1 6

u = 1 2 3 force

u = 4 5 6 moment

from the x-axis

Symbol

Computer

Symbol

Definition or

Explanation

placement

u = 1 6

u = 1 2 3 linear

u = 4 5 6 angular

u = 1 6

u = 1 2 3 linear

u = 4 5 6 angular

eration

u = 1 6

u = 1 2 3 linear

u = 4 5 6 angular

Symbol

Computer

Symbol

Definition or

Explanation

235 Water Jets

210 n2

at station s

cient at station s

rate transducer

Ej = (ρ2)VEj2dQj

j j i i

pg x u n dA

j j i i

pu g x u n dA

sion point

several pump stages

in i direction

u u n dA

Symbol

Computer

Symbol

Definition or

Explanation

dition)

impeller

turbed flow

tion s

boundary layer

msup3s

water jet system

msup3s

jet xT

dition)

system on the hull

Symbol

Computer

Symbol

Definition or

Explanation

at station s

station 7

station 1

tion 1A

surface

in x direction

ciency E

ciency JSE0

stream conditions

the pump

Symbol

Computer

Symbol

Definition or

Explanation

ciency

pump loop test

P duct I

Symbol

Computer

Symbol

Definition or

Explanation

241 Manoeuvrability

of rudder

(AR + ARmov) 2 m2

root to tip

AHL (L T) 1

h DE Water depth m

der axis

Symbol

Computer

Symbol

Definition or

Explanation

dp dt 1s2

dq dt 1s2

dr dt 1s2

du dt ms2

dv dt ms2

dw dt ms2

body axes

χ YX Yaw angle rad

Symbol

Computer

Symbol

Definition or

Explanation

RO Roll angle rad

Pitch angle

the hull

Drift angle

the hull

ANWIRL

ANRUEF

Bow fin angle

Stern fin angle

Rudder angle

ANRUOR

COWIAB

COWIRL

Symbol

Computer

Symbol

Definition or

Explanation

N r Nms2

N v Nms2

along body x-axis

X u Nsm

eration

X u Ns2m

tion of body axis y

Y r Ns2

Symbol

Computer

Symbol

Definition or

Explanation

Y v Ns2m

along body z-axis

2415 Linear Models

ship length

turning diameter

DC LPP 1

ameter δR = δ0

D0 LPP 1

unstable ship

Symbol

Computer

Symbol

Definition or

Explanation

unstable ship

turning rate

change of heading

heading

(starboard)

(port)

tr TIR Reach time s

Symbol

Computer

Symbol

Definition or

Explanation

track reach

Symbol

Computer

Symbol

Definition or

Explanation

242 Sea Keeping

system

spectively

Frequency

Alias horizontal

Alias vertical

moment

Alias horizontal

ing moment

Alias vertical

lution in waves

Symbol

Computer

Symbol

Definition or

Explanation

Sη(f) Sηη(f)

Sη(ω) Sηη(ω)

density

roll pitch yaw

rad TAW

Wave period

Yz(ω)

Azζ(ω)

tory motions

za(ω) ζa(ω) or

za(ω) ηa(ω)

Yθζ(ω)

Aθζ(ω)

motions

Θa(ω) ζa(ω) or

Tuning factor

w w wL L L

w w w= = =

q fL L L= = =

(short crested)

Symbol

Computer

Symbol

Definition or

Explanation

I991241

- I991242

lever curve

cording to ISO 8666

IMOIS IMOHSC2000

acter sets

Symbol

Computer

Symbol

Definition or

Explanation

curves of stability

volume

centre of buoyancy

metacentre M

volume

needed for crew

sons on board

ficient - I991243

proximately equals

hull - I99121

Symbol

Computer

Symbol

Definition or

Explanation

merged test weights

ter plane

pendicular

dicular

pendicular

(mass)

weight addition

101 GGKGKG m

weight addition

101 GGKGKG m

Symbol

Computer

Symbol

Definition or

Explanation

height

to the metacentre

KGKMGM

face effect)

tion effects

height

metacentre ML

KGKMGM LL

TAG cos φ

IMOtable

profile

K Keel reference

base of keel or K

Symbol

Computer

Symbol

Definition or

Explanation

base of keel or K

metacentre M to the

condition - IMOIS

IMOtable

ment due to crew

is taken of rolling

Symbol

Computer

Symbol

Definition or

Explanation

inclination

centimetre

meter CMTL Nmm

due to wind

above waterline

PV Wind pressure Pa

s Wave steepness 1

according to hellip

value see hellip

Symbol

Computer

Symbol

Definition or

Explanation

TL Turning lever m

IMOHSC2000

ancy (LCB)

of buoyancy B

tion (LCF)

of flotation F

ity (LCG)

of gravity G

gravity G

Symbol

Computer

Symbol

Definition or

Explanation

centre of buoyancy

force g N

gle during hellip

Symbol

Computer

Symbol

Definition or

Explanation

according to hellip

gle seehellip

bility

the compartment

stability curve

Symbol

Computer

Symbol

Definition or

Explanation

E Entrance

F Fore

Z Heave

θ Pitch

φ Roll

Symbol

Computer

Symbol

Definition or

Explanation

3 SPECIAL CRAFT

Planing bottom area

strips

gravity

Beam over chines

Transom breadth

spray strips

chines

spray strips

bossings

bottom

section

Shaft angle

inclined downwards)

Symbol

Computer

Symbol

Definition or

Explanation

derway

water surface level

(flange mounting)

forces underway

ing surface

(LK + LC) 2

planing hull

water line

SWS SS

spray edge

Symbol

Computer

Symbol

Definition or

Explanation

ALFBAR

Barrel flow angle

LM LWL

TRIMDWL

design waterline

(positive bow up)

θS θ0

Static trim angle

θV θD

LM (BLCG)

TAUDWL

reference line

Spray angle

plane of bottom)

tal friction area

normally to NA)

normally to NB)

Symbol

Computer

Symbol

Definition or

Explanation

force NPN

ler pressure forces

normally to NPP)

suction forces NPS

normal to NPS)

pressure forces NRP

normal to NRP)

normal to RAA)

normal to RAP)

normal to RF)

sistance RK

normal to RK)

drag ΔRRP

normal to ΔRRP)

thrust

normal to RT)

Symbol

Computer

Symbol

Definition or

Explanation

deadrise

Δ (BCG

surface

Δ (BCG

breadth

V (BCG g)12

Load coefficient

Δ (BCG

3 ρ g )

1 LVHD

drodynamic lift

Hydrostatic lift

Due to buoyancy

reference line

ence line

reference line

Symbol

Computer

Symbol

Definition or

Explanation

reference line

Keel drag

Induced drag

g ρ tg τ

Parasitic drag

openings

Total resistance

spray drag

CF SWS qS

of the hull

Spray velocity

the spray

Symbol

Computer

Symbol

Definition or

Explanation

Box beam

Beam of main deck

Hull spacing

Tunnel width

Hull diameter

submerged hulls

dinal position X

Deck clearance

ANENIN

nel (inner) side

of demihull

ANENOU

outer side

of demihull

Box length

Length of main deck

Symbol

Computer

Symbol

Definition or

Explanation

to trailing edge

Symbol

Computer

Symbol

Definition or

Explanation

hull vessel

ence correction

RFMH - Σ RF

tion of multi-hull

RTMH - RFMH

ence correction

RRMH - Σ RR

vessel

correction

RTMH - Σ RT

33 Hydrofoil Boats

Symbol

Computer

Symbol

Definition or

Explanation

33 Hydrofoil Boats

cluding foils

Span of struts

tance of struts

Mean chord length

section with foil

Weight of foil

Dihedral angle

Submerged foil area

take-off speed

33 Hydrofoil Boats

Symbol

Computer

Symbol

Definition or

Explanation

Foil span wetted

distance

V (g LF)12

chord length

V (g cM)12

foilborne

Flight height

at rest

Keel clearance

centre of gravity

and rear foils

lF + lR

centre of gravity

Foil immersion

ALFIND

with twist

33 Hydrofoil Boats

Symbol

Computer

Symbol

Definition or

Explanation

33 Hydrofoil Boats

Symbol

Computer

Symbol

Definition or

Explanation

Foil drag

CDF AFR q

CDF AFF q

DRIND Induced drag

of motion

Interference drag

secting foil

Streamline drag

Spray drag

Strut drag

Wave drag

Ventilation drag

Lift force on foil

CL AFT q

CL AFF q

CL AFR q

attack of zero

CL0 AFT q

CLTO AFT q

33 Hydrofoil Boats

Symbol

Computer

Symbol

Definition or

Explanation

DP (AFS q) 1

L0 (AFS q) 1

condition

LTO (AFS q) 1

34 ACV and SES

Symbol

Computer

Symbol

Definition or

Explanation

34 ACV and SES

Cushion area

Cushion beam

At the water line

neath craft

Bow seal height

Skirt depth

Stern seal height

Cushion length

at rest off cushion

to structure

needs clarification

34 ACV and SES

Symbol

Computer

Symbol

Definition or

Explanation

structure

needs clarification

to structure

needs clarification

to water contact

SSHC SSH0

cushion periphery

of air

the skirt

34 ACV and SES

Symbol

Computer

Symbol

Definition or

Explanation

coefficient

R0 (ρA VR2 AC 2) 1

PCU LC Pam

in general

ρA QT VA N

of cushion

ρA QCU VA N

of skirt

ρA QTS VA N

34 ACV and SES

Symbol

Computer

Symbol

Definition or

Explanation

Symbol

Computer

Symbol

Definition or

Explanation

sistance

RI (ρI g h2 B)

of ice

RIW (S qIW)

normal

rection of motion

thickness

V (g hI)

ice force

ice (dynamic)

ice (static)

condition)

Thickness of ice

KQICMS

in ice

QIA (ρW nIA

KTICMS

in ice

TIA (ρW nIA

FRICMS

revolution in ice

Symbol

Computer

Symbol

Definition or

Explanation

in ice

2 π QIA nIA

Net ice resistance

RIT - RIW

in presence of ice

in ice

ciency in ice

ηID ηD

36 Sailing Vessels

Symbol

Computer

Symbol

Definition or

Explanation

36 Sailing Vessels

Area of mainsail

Area of spinnaker

(P E + I J) 2

Beam overall

Mainsail base

Fore triangle base

Mainsail height

olds Number

noe body

Effective draught

FH (ρVB

tical centre plane

36 Sailing Vessels

Symbol

Computer

Symbol

Definition or

Explanation

Displacement force

(weight) of keel

Displacement force

(weight) of rudder

36 Sailing Vessels

Symbol

Computer

Symbol

Definition or

Explanation

cient (upright)

RFU (S q)

cient (upright)

RRU (S q)

Total resistance

RTU (S q)

(upright)

RTφ (S q)

Cx Cy Cz

Force coefficients

Side force

right)

RTU + Rφ

Rφ RH

Vessel velocity

36 Sailing Vessels

Symbol

Computer

Symbol

Definition or

Explanation

True wind velocity

course

leaway angle

to boat course)

boat course)

Version 2014 130

4 BACKGROUND AND

REFERENCES

421 Classification

cross-references

list of symbols

drawing

standard itself

exponentiation

operators

matrix components

quantities

A ( eg Area in

msup2)

Version 2011 133

Numbers in roman

(power of n)

SYMBOLS

in italic

NUMBERS

in roman

(T = Thrust)

(M = Model) Fig 1

1 Scope

TK 102

A=A-[A]

as described above

NUMERICAL VALUES

AB = A B - [A] [B]

Version 2014 135

EXAMPLE

Ek = 2

1mvsup2

rived quantities

intensity J

51992 annex A)

dim Q = AαBβCγ

becomes in general

EXAMPLES

Quantity Dimension

velocity LT-1

force LMT-2

energy L2MT-2

relative density 1

Version 2014 136

23 Units

merical values

- base units

2321 Base units

Name Symbol

length metre m

mass kilogram kg

time second s

thermodynamic tem-

perature kelvin K

tary units

L rarr m I rarr A

M rarr kg Θ rarr K

T rarr s N rarrmol

J rarr cd

Derived quantity

SI derived unit

EXAMPLES

Version 2014 138

expressed in terms

of the seven base

units (and the sup-

plementary units in

some cases)

velocity ms

force kg ms2

energy kg m2s2

relative density 1

2323 SI prefixes

Factor Prefix

Name Symbol

1024 yotta Y

1021 zetta z

1018 exa E

1015 peta P

1012 tera T

109 giga G

106 mega M

103 kilo k

102 hecto h

10 deca da

10-1 deci d

10-2 centi c

10-3 milli m

10-6 micro micro

10-9 nano n

10-12 pico p

10-15 femto f

10-18 atto a

10-21 zepto z

10-24 yocto y

fixes see 324

233 The unit one

EXAMPLE

EXAMPLES

Plane angle α = 05

rad = 05

1 with a prefix

for the number 001

shall not be used

neous units

stance

51992 Annex A

with the Sl

Quantity Unit

Name Sym-

bol Definition

time minute

1 min= 60s

1 h = 60 min

1 d = 24 h

plane an-

degree

minute

second

1 deg =

(π180)rad =

(nl80) rad

1 = (160)deg

1 = (160)

= 1 dm

Name Sym-

bol Definition

the kinetic energy

tron in passing

through a potential

in vacuum 1 eV

1602 177 times10-19 J

mass unified

atomic

mass unit

(1 12) of the mass

of an atom of the

nuclide 12C 1u

1660 540 times10-27kg

Tables 5 and 6

the curie

and numbers

311 Symbols

sentence

use of subscripts

right) type

EXAMPLES

Upright sub-

number)

numbers)

(sloping) type

eg a∙ b-1

EXAMPLE

EXAMPLES

m metre

s second

A ampere

Wb weber

N∙m N m

symbol for a prefix

EXAMPLE

Version 2014 142

m ms m∙s-1

mendation

EXAMPLE

units (see 322)

EXAMPLES

1cm3 = (10-2m)3=10-6 m3

1 μs-1= (10-6 s)-1 = 106 s-1

1 kAm = (103A)m = 103 Am

crokilogram (μkg)

33 Numbers

man (upright) type

332Decimal sign

for the quantities

EXAMPLES

l = 12 m - 7 m= (12 - 7) m = 5m

clides

EXAMPLES

H He C Ca

A and 150 31-91992 annex A

script position

4O or (PO4)3-

types)

alpha Α a Α a

beta Β β Β β

gamma Γ γ Γ γ

delta Δ δ Δ δ

epsilon Ε ε Ε ε

zeta Ζ ζ Ζ ζ

eta Η η Η η

theta Θ θ Θ θ

iota Ι ι Ι ι

kappa Κ κ Κ κ

lambda Λ λ Λ λ

mu Μ μ Μ μ

nu Ν ν Ν ν

xi Ξ ξ Ξ ξ

omicron Ο ο Ο ο

pi Π π Π π

rho P ρ Ρ ρ

sigma Σ σ Σ σ

tau Τ τ Τ τ

upsilon Υ υ Υ υ

phi Φ φ Φ φ

chi Χ χ Χ χ

psi Ψ ψ Ψ ψ

omega Ω ω Ω ω

52 Computer symbols

Version 2014 145

52 Computer Symbols

- 9 have been used

near future

53 Documentation

Version 2014 146

53 Documentation

531 ITTC Documents

No500 1976

No6 1978

CETENA Genova 1984

532 Translations

malisation (AFNOR)

No28 Zagreb 1974

truccion Naval

53 Documentation

Version 2014 147

Table of Contents

1 General


111 Uncertainty















122 Loads

1221 External Loads



1231 Motions

1232 Attitudes

13 Fluid Mechanics

131 Flow Parameters




132 Flow Fields

1321 Velocities etc



1331 Geometry


1333 Forces


134 Boundary Layers


135 Cavitation


1352 Flow fields

1353 Pumps


141 Waves

1411 Periodic waves





142 Wind


143 Ice Mechanics


15 Noise


2 Ships in General

21 Basic Quantities


221 Hull Geometry






2222 Ducts


2224 Pods


























235 Water Jets


241 Manoeuvrability





2415 Linear Models




242 Sea Keeping




3 Special Craft











33 Hydrofoil Boats






34 ACV and SES





36 Sailing Vessels






421 Classification





52 Computer Symbols

53 Documentation

531 ITTC Documents

532 Translations


Symbol

Computer

Symbol

Definition or

Explanation

quantity Xi

servation of Xi

Output estimate

same measurement

Y A measurand

certainty Up

root of 2

Symbol

Computer

Symbol

Definition or

Explanation

n estimated by

tive square root of

tities

in the following

tion if any

Axes coordinates

Body axes (xyz)

platforms or ships

upwards

section

flight dynamics

ular case

differential

Name of coordi-

nate system

Remarks

11-121

cartesian

coordinates

system See Figure 1

11-122

cylindrical

coordinates

11-123

(-) r φ r=rer

r sin dφ eφ

spherical

Figures 3 and 5

Symbol

Computer

Symbol

Definition or

Explanation

lar quantity

scalar distribution

εikjxkds

εklixlεjkm xmds

Sij = S0ij

Si 3+j = S1ij

S3+i j = S1ij

S3+i 3+j = S2ij

tesian coordinates

fixed in the body

Tijs + Tij

tensor

( Tij - Tji ) 2

Symbol

Computer

Symbol

Definition or

Explanation

V3+i = V1i

X X(1)

Y X(2)

Z X(3)

the body

x0 x01

y0 x02

z0 x03

X0 X0(1)

Y0 X0(2)

Z0 X0(3)

xF xF1

yF xF2

zF xF3

XF XF(1)

YF XF(2)

ZF XF(3)

1 ijk = 321 213 132

0 if otherwise

Symbol

Computer

Symbol

Definition or

Explanation

f FR Frequency Hz

functions

1 TC Hz

Laurent transform

Laplace transform

t TI Time - + s

Symbol

Computer

Symbol

Definition or

Explanation

pled function

= X(0)2 + fSXF(f + jfS)

inverse form

XF(f)=XL(f)

t = 0 TC

XF = xFjδ(f - jTC)

inverse form

Hilbert transform

(1t)F = -i sgn f

if X(tlt0) = 0 then

= (X(t)exp(-at))F

ie = 0 for f lt 0

rier series

XFj(1 + sgn j)

line spectra

Symbol

Computer

Symbol

Definition or

Explanation

component

zl ZLG (Phase) Lag

component

Symbol

Computer

Symbol

Definition or

Explanation

gE gM gMR

E(g) = g(x)fx(x)dx

Random quantities

x(ζ) y(ζ)

X(I) Y(I)

i = 1 n

n sample size

quantity

xD xDR σx

dom quantity

xVR frac12

xDS sx

dom quantity

xVS 12

xxR xxMR Rxx

dom quantity

xyR xyMR Rxy

dom quantities

xE xM xMR

xA xMS mx

a random quantity

1n xi i = 1n

xAE = xE

xVSE = xV n

xPD fx

dom quantity

d Fx dx

xyPD fxy

2 Fxy (x y)

xPF Fx

xyPF Fxy

random quantities

Symbol

Computer

Symbol

Definition or

Explanation

xV xVR xxVR

XVR XXVR

x2 E - xE 2

xVS xxVS

XVS XXVS

dom quantity

1 (n - 1) (xi - x

i = 1n

xyV xyVR

quantities

x yE - xE yE

periment

dom quantity

t =-T2 +T2

T =- +

A(g(t)) = 1T g(t)dt

t =0 +T

x(ζt) y(ζt)

xxC xxCR Cxx

(x(t) - xE)(x(t + τ) - xE)E

xyC xyCR Cxy

(x(t) - xE)(y(t + τ) - yE)E

xxR xxRR Rxx

Rxx(τ) = Rxx(-τ)

= x(t)x(t + τ)MR

τ = 0

xyR Rxy

Ryx(τ) = Rxy(-τ)

if x y are ergodic

Symbol

Computer

Symbol

Definition or

Explanation

xxS Sxx

chastic process

xxRRSR

xyS Sxy

processes

xyRRSR

periment

Average sample mean

Sample covariance

Sample deviation

E M MR

Probability density

(Power) Spectrum

Sample spectrum

Sample correlation

Population variance

Sample variance

Symbol

Computer

Symbol

Definition or

Explanation

control volume

Inward positive QUs

control volume

quantity stored

dq dt QUs

Symbol

Computer

Symbol

Definition or

Explanation

AM(IJ)

DA(IJ)

RF(IJ)

uv DH(UV)

damping

u FH(U)

uv IH(UV)

inertia

of water-plane area

Iy Iyy

IY IYY

M2(22)

MA(55)

Iz Izz

IZ IZZ

M2(33)

MA(66)

Ixy I12

Iyz I23

Izx I31

IXY I2(12)

IYZ I2(23)

IZX I2(31)

kx kxx

(Ixxm)12

Symbol

Computer

Symbol

Definition or

Explanation

ky kyy

(Iyym)12

kz kzz

(Izzm)12

M0(IJ)

MA(IJ)

tensor

mij = m δij

ij M1(IJ)

M2(IJ)

IN(IJ)

MA(UV)

system

Mij = M0

Mi 3+j = M1Tij

M3+i j = M1ij

M3+i 3+j = M2ij

Symbol

Computer

Symbol

Definition or

Explanation

122 Loads

1221 External Loads

in body coordinates

u = MMu

Fi = F0i

F3+i = F1i

gi = g1

g3+i = 0

in body coordinates

F11 F4

K M(1)

F1(1) F(4)

F12 F5

M M(2)

F1(2) F(5)

FN13 F6

N M(3)

F1(3) F(6)

F01 F1

F0(1) F(1)

axis x

F02 F2

F0(2) F(2)

axis y

F03 F3

F0(3) F(3)

axis z

Gu = muv gv

G0i Gi

in body coordinates

Gi = G0

i = m0ij gj

i G1(I)

in body coordinates

G3+i = G1

i = εikj xk G0

= m1ij gj

dW dx1

Symbol

Computer

Symbol

Definition or

Explanation

section coordinates

FSi = FS0

FS3+i = FS1

i = MBi

FS11 Nm

Symbol

Computer

Symbol

Definition or

Explanation

1231 Motions

v01 v4

V0(1) V(4)

body axis x

v02 v5

V0(2) V(5)

body axis y

v03 v6

V0(3) V(6)

body axis z

v11 v1

V1(1) V(1)

v12 v2

V1(2) V(2)

v13 v3

V1(3) V(3)

body axes

vi = v1

v3+i = v0i

tive to body axes

Symbol

Computer

Symbol

Definition or

Explanation

1232 Attitudes

Angle of attack

the z-axis

about the xo axis

X(4) RO

X(5) TR

X(6) YA

course

13 Fluid Mechanics

Symbol

Computer

Symbol

Definition or

Explanation

13 Fluid Mechanics

131 Flow Parameters

Velocity of sound

(E ρ)12

Weight density

ρg (See 111)

Viscosity

Kinematic viscosity

DN RHO

Mass density

Capillarity

length

Boussinesq number

V (g RH)12

Cauchy number

V (E ρ)12

Froude number

V (g L)12

Froude depth number

V (g h)12

V (g 13)12

Mach number

Reynolds number

Strouhal number

Thoma number

Cavitation number

(pA ndash pV)q

Weber number

V2 L κ

07R Ac V nDRe

13 Fluid Mechanics

Symbol

Computer

Symbol

Definition or

Explanation

Sand roughness

surface

Hydraulic radius

wetted perimeter

13 Fluid Mechanics

Symbol

Computer

Symbol

Definition or

Explanation

132 Flow Fields

1321 Velocities etc

energy

ρ V2 2 + p + ρ g h

Mass specific force

Total head

e w = h +pw +qw

flow energy

turbed flow

ρ V2 2

Rate of flow

Total head loss

ij SR(IJ)

ρ vivj

Pa sij

ST(IJ)

Total stress tensor

change

ij SV(IJ)

Viscous stress

u vx v1

v vy v2

w vz v3

Velocity

V = vivi

Wall shear stress

μ (U y)y=0

13 Fluid Mechanics

Symbol

Computer

Symbol

Definition or

Explanation

Induction factor

Vortex density

Circulation

intV ds

along a closed line

Potential function

Stream function

ψ = const

surface

13 Fluid Mechanics

Symbol

Computer

Symbol

Definition or

Explanation

1331 Geometry

Projected area

Wing or foil span

Flap span

Mean chord length

Tip chord length

Root chord length

Sweep angle

tion (general)

edge of struts

(general)

of foil

section

tS cSTH

Taper ratio

Aspect ratio

13 Fluid Mechanics

Symbol

Computer

Symbol

Definition or

Explanation

Induced velocity

and the chord line

or incidence

Geometric angle of

attack or incidence

Hydrodynamic angle

of attack

zero lift

Angle of zero lift

at zero lift

13 Fluid Mechanics

Symbol

Computer

Symbol

Definition or

Explanation

1333 Forces

Foil drag

DRIND Induced drag

of motion

Interference drag

secting foil

zero lift

Streamline drag

Lift force on foil

CL AFT q

of zero

CL0 AFT q

Lift-Drag ratio

13 Fluid Mechanics

Symbol

Computer

Symbol

Definition or

Explanation

134 Boundary Layers

τ (ρ Ue

Entrainment factor

1 (Ue dQ dx)

rameter

(δ - δ) Θ

Static pressure

Total pressure

Entrainment

U δ v or Ue δ

RTHETA

U Θ v or Ue Θ v

boundary layer

from surface

(τ ρ)12

boundary layer

from the surface

(Ue- U) uτ

13 Fluid Mechanics

Symbol

Computer

Symbol

Definition or

Explanation

from the wall

y uτ v

δ (τw dp dx)

layer at U=0995Ue

δ δ1

boundary layer

(Ue- U) Ue dy

von Karman constant

δ995 (v dUe dx)

Energy thickness

(U Ue) (1 - U2 Ue

Momentum thickness

(U Ue) (1 - U Ue)dy

Local skin friction

μ (U y)y=0

13 Fluid Mechanics

Symbol

Computer

Symbol

Definition or

Explanation

135 Cavitation

Gas content ratio

α αS

Gas content

temperature

Cavitation number

(pA - pC) q

(pA - pV) q

1352 Flow fields

Cavity drag

Cavity length

region

Ambient pressure

Critical pressure

takes place

Cavity pressure

quasi-steady cavity

Critical velocity

takes place

Volume loss

13 Fluid Mechanics

Symbol

Computer

Symbol

Definition or

Explanation

WL WTLS

Weight loss

specified time

1353 Pumps

turbo-engines

Thoma number

(HU - pV w) HN

Symbol

Computer

Symbol

Definition or

Explanation

141 Waves

1411 Periodic waves

lerity LW TW =

2WgL in

deep water

odic wave

const = cW

lerity

i fW Hz

wave crest to wave

wave ηC - ηT

advance

Symbol

Computer

Symbol

Definition or

Explanation

at a given location

ηFSα m

ηFSp rad

crossing

trough

crossing

and crest

wave heights

crossing

of zero in a record

Symbol

Computer

Symbol

Definition or

Explanation

in a record

Negative values m

crossing

visual observation

cant wave height

wave heights

wave height

heights

visual observation

wave propagation

samples

visual observation

Symbol

Computer

Symbol

Definition or

Explanation

lution

points

tude function

4 (m0)12 m

fn S(f)df m2 sn

Si(ω)

tral density

Sr(ω)

tral density

Sη(f)

Sη(ω)

2πfP s

and first moment

m0m1 s

and second moment

(m0m2)12 s

Symbol

Computer

Symbol

Definition or

Explanation

DX(fθ)

DX(ωμ)

SIGMAOX

Sζ (ωμ)

Sθ (ωμ)

density

Sρ(fθ)

Sζ(ωμ)

θm MWD

THETAMOX

rection

Symbol

Computer

Symbol

Definition or

Explanation

142 Wind

(008 + 0065U10)10-3

Fetch length

wind blows

DURATN

Wind duration

Return period

ceeded

uz uzi

UFLUCT

USHEAR

Wind shear velocity

12 U10 or 071U10123

Reference mean wind

U10 = (10z)17 Uz

(Uz + uzi)

UzA = (z10)17 U10 or

see section 141

True wind velocity

see section 141

Dimensionless Fetch

face in meters

see section 26

True wind angle

see section 26

Wind direction

Symbol

Computer

Symbol

Definition or

Explanation

143 Ice Mechanics

weight of ice

volume of ice

unit volume of ice

15 Noise

Symbol

Computer

Symbol

Definition or

Explanation

15 Noise

acoustic centre

= 10 log10

(119903119898119904

1199011199031198901198912 ) dB 119901119903119890119891

tance of 1m

119871s

= 119871p

+ 20 log10 [119889

119889119903119890119891] dB 119889119903119890119891

Symbol

Computer

Symbol

Definition or

Explanation

2 SHIPS IN GENERAL

21 Basic Quantities

dv dt ms2

A A AR

Area in general m2

B B BR Breadth m

(forces)

d D D DI Diameter m

E E EN Energy J

F F0 F F0 Force N

h DE Depth m

H H HT Height m

mass distribution

L L LE Length m

tory velocity

m M MA

Mass kg

Symbol

Computer

Symbol

Definition or

Explanation

distribution

M MO Momentum Ns

P P PO Power W

r R RD Radius m

locity

t TI Time s

t TE Temperature K

harmonic process

of a body

ds dt ms

V VO Volume m3

specific weight

dW dV = ρg Nm3

acting on a body

tilled water at 4C

Symbol

Computer

Symbol

Definition or

Explanation

Symbol

Computer

Symbol

Definition or

Explanation

221 Hull Geometry

gitudinal plane

perpendicular

the final rounding

aft perpendiculars

port and starboard)

waterline

relative wind

midship

of midship

section

of ships hull

Symbol

Computer

Symbol

Definition or

Explanation

water line

at stem

the perpendiculars)

maximum section

verse section

Symbol

Computer

Symbol

Definition or

Explanation

point of the stern

pendicular

dicular

perpendicular

with straight keel

water surface level

bare hull

ΔBH (ρ g) m3

pendages

ΔAP (ρ g) m3

Symbol

Computer

Symbol

Definition or

Explanation

ancy) g ρ N

= TS TM

cient B 13 1

GM 13 1

GZ 13 1

cient KG T

12 IL ( B L3) 1

12 IT (B3 L) 1

AM (B T) 1

body A (AX L 2) or

A (AM L 2)

trance E (AX LE) or

E (AM LE)

body F (AX L 2) or

F (AM L 2)

Symbol

Computer

Symbol

Definition or

Explanation

R (AM LR)

AWA (B L 2) 1

forward

AWF (B L 2) 1

coefficient

maximum area

ABL (L T) 1

ABT AX 1

transom stern

AT AX 1

L 13 1

cient T 13 1

A AB After body

APP APP Appendages

B BH Bare hull

DW Design waterline

E EN Entry

Symbol

Computer

Symbol

Definition or

Explanation

F FB Fore body

FS Frame spacing

H HE Hull

LR Reference Line

LP LP Based on LPP

LW LW Based on LWL

M MS Midships

PB Parallel body

R RU Run

SS Station spacing

W WP Water plane

S WS Wetted surface

Symbol

Computer

Symbol

Definition or

Explanation

boss or hub

radius

hub to the tip

Symbol

Computer

Symbol

Definition or

Explanation

blades

2 π r sin (φ) z m

positive rake

the propeller plane

iG + iS = cS sinφ

shoulder

Symbol

Computer

Symbol

Definition or

Explanation

ing aft shoulder

rh RH Hub radius m

ler blade

ler axis

dicular

above base line

Symbol

Computer

Symbol

Definition or

Explanation

cal skew angle

Symbol

Computer

Symbol

Definition or

Explanation

2222 Ducts

LD LD Duct length m

ler plane

of duct

tion s

Jet System Head m

at station 1A

Symbol

Computer

Symbol

Definition or

Explanation

2224 Pods

Main Body

tom Fin

Bottom Fin

under pod main body

D Duct (subscript)

Symbol

Computer

Symbol

Definition or

Explanation

appendage

of rudder

propeller race

hydrofoil

lel to keel

Symbol

Computer

Symbol

Definition or

Explanation

rudders

of flanking rudders

BK Bilge keel

BS Bossing

FB Bow foil

FR Flanking rudder

FS Stern foil

KL Keel

RU Rudder

RF Rudder flap

SA Stabilizer

SH Shafting

SK Skeg

ST Strut

TH Thruster

WG Wedge

Symbol

Computer

Symbol

Definition or

Explanation

curves of stability

volume

Centre of buoyancy

volume

ter plane

(mass)

Keel reference

XCB LCB

ancy (LCB)

from Midships

XCF LCF

tion (LCF)

from Midships

Symbol

Computer

Symbol

Definition or

Explanation

from Midships

XCG LCG

ity (LCG)

from Midships

gravity G

centre of buoyancy

curves of stability

Symbol

Computer

Symbol

Definition or

Explanation

centre of buoyancy

metacentre M

pendicular

dicular

pendicular

weight addition

101 GGKGKG m

height

to the metacentre

tion effects

centric height

metacentre ML

KGKMGM LL

TAG cosφ

KB-KM =I =BM T

BM KM KB

Symbol

Computer

Symbol

Definition or

Explanation

base or keel K

metacentre M to the

ing arm

Heeling moment Δ m

GM 13 1

GZ 13 1

cient KG T

ficient

proximately equals

Symbol

Computer

Symbol

Definition or

Explanation

ficient

proximately equals

one centimetre

one meter

ΔCMTL Nmm

force g ρ N

flooded water

Δfw (ρg) m3

Symbol

Computer

Symbol

Definition or

Explanation

the compartment

bility

a apparent

A att attained

d dyn dynamic

e EFF effective

f false

KL keel line

L longitudinal

MAX maximum

s Static

S sqt Sinkage squat

TC Trim in cm

TM Trim in m

T transverse

V vertical

0 Initial

at heel angle

θ at trim angle θ

Symbol

Computer

Symbol

Definition or

Explanation

231 Hull Resistance

cross section area

lowance

propulsion tests

[(1 + k) CFM + CR]

surface of the body

bare hull

SBH + SAPP m2

Symbol

Computer

Symbol

Definition or

Explanation

area underway

area at rest

area underway

area at rest

lation

RA (S q) 1

ficient

RAA (AV qR) 1

RAPP (S q) 1

cient of a body

RF (S q) 1

RF0 (S q) 1

RP (S q) 1

coefficient

RPV (S q) 1

Symbol

Computer

Symbol

Definition or

Explanation

RR (S q) 1

g R L (ΔV2) 1

efficient

RV (S q) 1

efficient

RW (S q) 1

efficient

1000 R (Δ(KC)2)

1000 RF (Δ(KC)2) 1

sliding bodies

(CV - CF0) CF0 1

(4πg)12VK16

sponding to KQ KT

R (ρ D4 n2) 1

ρ V2 2

see 332

qR PDWR

apparent wind

ρ VWR2 2

see 342

Symbol

Computer

Symbol

Definition or

Explanation

tio in general

R Δ 1

placement ratio

RR Δ 1

FW Fresh water

MR Raw model data

OW Open water

SW Salt water

Symbol

Computer

Symbol

Definition or

Explanation

of revolution

Brake power

Delivered power

propeller power

Effective power

resistance power

Indicated power

Shaft power

Thrust power

Torque

Running trim

Ship speed

or torque identity

2 π n

Symbol

Computer

Symbol

Definition or

Explanation

(T - RT) RT

Δ23 V3 PS

PD (ρ V3 23 2)

identity

PDT PDS

ηDS ηDM

factor

Sinkage dynamic

Trim dynamic

by length

(T - RT) T

(V - VA) V

(V - VA) VA

Symbol

Computer

Symbol

Definition or

Explanation

wTM - wTS

1978 method

diction

ηD PD PE - 1

resistance

PT PD = T VA (Q ω)

coefficient

PE PD = PR PP

Gearing efficiency

Hull efficiency

PE PT = PR PT

= (1 - t) (1 - w)

and propeller

water tests

ηB ηO

Shafting efficiency

PD PS = PP PS

Symbol

Computer

Symbol

Definition or

Explanation

lution

ler blade surface

advance speed

ρ VA2 2

ρ VS2 2 Pa

QS=QSC+ QSH

torque

peller unit

peller

Symbol

Computer

Symbol

Definition or

Explanation

at 07 R

(VA2+ (07 R ω)2)12

n PDfrac12 VA

with n in revsmin

VA in kn (obsolete)

n PTfrac12 VA

with n in revsmin

VA in kn (obsolete)

T (AP qA)

= (TP AP) qA

V (D n) = VH (D n) 1

ducted propeller

VP (D n)

identity

coefficient

QSC (ρ n2 D5) 1

Symbol

Computer

Symbol

Definition or

Explanation

torque coefficient

QSH (ρ n2 D5) 1

ficient

TP (ρ n2 D4) 1

KTP+ KTD 1

KQηR 1

feet VA in kn

efficiency

PJ PD = PJ PP 1

ηJP0 ZET0

zero advance speed

T (ρ π 2)13 (PD D)23 1

η0 ηTP0 ETA0

water tests

ducted propeller

TP TT 1

Symbol

Computer

Symbol

Definition or

Explanation

propeller

peller

by propeller

blade section

arctg (VA r ω)

Symbol

Computer

Symbol

Definition or

Explanation

u = 1 6

u = 1 2 3 force

u = 4 5 6 moment

coefficients

KFi and KMi

cients

Mi (ρ n2 D5) 1

p PR Pressure Pa

ing reaction

u = 1 6

u = 1 2 3 force

u = 4 5 6 moment

from the x-axis

Symbol

Computer

Symbol

Definition or

Explanation

placement

u = 1 6

u = 1 2 3 linear

u = 4 5 6 angular

u = 1 6

u = 1 2 3 linear

u = 4 5 6 angular

eration

u = 1 6

u = 1 2 3 linear

u = 4 5 6 angular

Symbol

Computer

Symbol

Definition or

Explanation

235 Water Jets

210 n2

at station s

cient at station s

rate transducer

Ej = (ρ2)VEj2dQj

j j i i

pg x u n dA

j j i i

pu g x u n dA

sion point

several pump stages

in i direction

u u n dA

Symbol

Computer

Symbol

Definition or

Explanation

dition)

impeller

turbed flow

tion s

boundary layer

msup3s

water jet system

msup3s

jet xT

dition)

system on the hull

Symbol

Computer

Symbol

Definition or

Explanation

at station s

station 7

station 1

tion 1A

surface

in x direction

ciency E

ciency JSE0

stream conditions

the pump

Symbol

Computer

Symbol

Definition or

Explanation

ciency

pump loop test

P duct I

Symbol

Computer

Symbol

Definition or

Explanation

241 Manoeuvrability

of rudder

(AR + ARmov) 2 m2

root to tip

AHL (L T) 1

h DE Water depth m

der axis

Symbol

Computer

Symbol

Definition or

Explanation

dp dt 1s2

dq dt 1s2

dr dt 1s2

du dt ms2

dv dt ms2

dw dt ms2

body axes

χ YX Yaw angle rad

Symbol

Computer

Symbol

Definition or

Explanation

RO Roll angle rad

Pitch angle

the hull

Drift angle

the hull

ANWIRL

ANRUEF

Bow fin angle

Stern fin angle

Rudder angle

ANRUOR

COWIAB

COWIRL

Symbol

Computer

Symbol

Definition or

Explanation

N r Nms2

N v Nms2

along body x-axis

X u Nsm

eration

X u Ns2m

tion of body axis y

Y r Ns2

Symbol

Computer

Symbol

Definition or

Explanation

Y v Ns2m

along body z-axis

2415 Linear Models

ship length

turning diameter

DC LPP 1

ameter δR = δ0

D0 LPP 1

unstable ship

Symbol

Computer

Symbol

Definition or

Explanation

unstable ship

turning rate

change of heading

heading

(starboard)

(port)

tr TIR Reach time s

Symbol

Computer

Symbol

Definition or

Explanation

track reach

Symbol

Computer

Symbol

Definition or

Explanation

242 Sea Keeping

system

spectively

Frequency

Alias horizontal

Alias vertical

moment

Alias horizontal

ing moment

Alias vertical

lution in waves

Symbol

Computer

Symbol

Definition or

Explanation

Sη(f) Sηη(f)

Sη(ω) Sηη(ω)

density

roll pitch yaw

rad TAW

Wave period

Yz(ω)

Azζ(ω)

tory motions

za(ω) ζa(ω) or

za(ω) ηa(ω)

Yθζ(ω)

Aθζ(ω)

motions

Θa(ω) ζa(ω) or

Tuning factor

w w wL L L

w w w= = =

q fL L L= = =

(short crested)

Symbol

Computer

Symbol

Definition or

Explanation

I991241

- I991242

lever curve

cording to ISO 8666

IMOIS IMOHSC2000

acter sets

Symbol

Computer

Symbol

Definition or

Explanation

curves of stability

volume

centre of buoyancy

metacentre M

volume

needed for crew

sons on board

ficient - I991243

proximately equals

hull - I99121

Symbol

Computer

Symbol

Definition or

Explanation

merged test weights

ter plane

pendicular

dicular

pendicular

(mass)

weight addition

101 GGKGKG m

weight addition

101 GGKGKG m

Symbol

Computer

Symbol

Definition or

Explanation

height

to the metacentre

KGKMGM

face effect)

tion effects

height

metacentre ML

KGKMGM LL

TAG cos φ

IMOtable

profile

K Keel reference

base of keel or K

Symbol

Computer

Symbol

Definition or

Explanation

base of keel or K

metacentre M to the

condition - IMOIS

IMOtable

ment due to crew

is taken of rolling

Symbol

Computer

Symbol

Definition or

Explanation

inclination

centimetre

meter CMTL Nmm

due to wind

above waterline

PV Wind pressure Pa

s Wave steepness 1

according to hellip

value see hellip

Symbol

Computer

Symbol

Definition or

Explanation

TL Turning lever m

IMOHSC2000

ancy (LCB)

of buoyancy B

tion (LCF)

of flotation F

ity (LCG)

of gravity G

gravity G

Symbol

Computer

Symbol

Definition or

Explanation

centre of buoyancy

force g N

gle during hellip

Symbol

Computer

Symbol

Definition or

Explanation

according to hellip

gle seehellip

bility

the compartment

stability curve

Symbol

Computer

Symbol

Definition or

Explanation

E Entrance

F Fore

Z Heave

θ Pitch

φ Roll

Symbol

Computer

Symbol

Definition or

Explanation

3 SPECIAL CRAFT

Planing bottom area

strips

gravity

Beam over chines

Transom breadth

spray strips

chines

spray strips

bossings

bottom

section

Shaft angle

inclined downwards)

Symbol

Computer

Symbol

Definition or

Explanation

derway

water surface level

(flange mounting)

forces underway

ing surface

(LK + LC) 2

planing hull

water line

SWS SS

spray edge

Symbol

Computer

Symbol

Definition or

Explanation

ALFBAR

Barrel flow angle

LM LWL

TRIMDWL

design waterline

(positive bow up)

θS θ0

Static trim angle

θV θD

LM (BLCG)

TAUDWL

reference line

Spray angle

plane of bottom)

tal friction area

normally to NA)

normally to NB)

Symbol

Computer

Symbol

Definition or

Explanation

force NPN

ler pressure forces

normally to NPP)

suction forces NPS

normal to NPS)

pressure forces NRP

normal to NRP)

normal to RAA)

normal to RAP)

normal to RF)

sistance RK

normal to RK)

drag ΔRRP

normal to ΔRRP)

thrust

normal to RT)

Symbol

Computer

Symbol

Definition or

Explanation

deadrise

Δ (BCG

surface

Δ (BCG

breadth

V (BCG g)12

Load coefficient

Δ (BCG

3 ρ g )

1 LVHD

drodynamic lift

Hydrostatic lift

Due to buoyancy

reference line

ence line

reference line

Symbol

Computer

Symbol

Definition or

Explanation

reference line

Keel drag

Induced drag

g ρ tg τ

Parasitic drag

openings

Total resistance

spray drag

CF SWS qS

of the hull

Spray velocity

the spray

Symbol

Computer

Symbol

Definition or

Explanation

Box beam

Beam of main deck

Hull spacing

Tunnel width

Hull diameter

submerged hulls

dinal position X

Deck clearance

ANENIN

nel (inner) side

of demihull

ANENOU

outer side

of demihull

Box length

Length of main deck

Symbol

Computer

Symbol

Definition or

Explanation

to trailing edge

Symbol

Computer

Symbol

Definition or

Explanation

hull vessel

ence correction

RFMH - Σ RF

tion of multi-hull

RTMH - RFMH

ence correction

RRMH - Σ RR

vessel

correction

RTMH - Σ RT

33 Hydrofoil Boats

Symbol

Computer

Symbol

Definition or

Explanation

33 Hydrofoil Boats

cluding foils

Span of struts

tance of struts

Mean chord length

section with foil

Weight of foil

Dihedral angle

Submerged foil area

take-off speed

33 Hydrofoil Boats

Symbol

Computer

Symbol

Definition or

Explanation

Foil span wetted

distance

V (g LF)12

chord length

V (g cM)12

foilborne

Flight height

at rest

Keel clearance

centre of gravity

and rear foils

lF + lR

centre of gravity

Foil immersion

ALFIND

with twist

33 Hydrofoil Boats

Symbol

Computer

Symbol

Definition or

Explanation

33 Hydrofoil Boats

Symbol

Computer

Symbol

Definition or

Explanation

Foil drag

CDF AFR q

CDF AFF q

DRIND Induced drag

of motion

Interference drag

secting foil

Streamline drag

Spray drag

Strut drag

Wave drag

Ventilation drag

Lift force on foil

CL AFT q

CL AFF q

CL AFR q

attack of zero

CL0 AFT q

CLTO AFT q

33 Hydrofoil Boats

Symbol

Computer

Symbol

Definition or

Explanation

DP (AFS q) 1

L0 (AFS q) 1

condition

LTO (AFS q) 1

34 ACV and SES

Symbol

Computer

Symbol

Definition or

Explanation

34 ACV and SES

Cushion area

Cushion beam

At the water line

neath craft

Bow seal height

Skirt depth

Stern seal height

Cushion length

at rest off cushion

to structure

needs clarification

34 ACV and SES

Symbol

Computer

Symbol

Definition or

Explanation

structure

needs clarification

to structure

needs clarification

to water contact

SSHC SSH0

cushion periphery

of air

the skirt

34 ACV and SES

Symbol

Computer

Symbol

Definition or

Explanation

coefficient

R0 (ρA VR2 AC 2) 1

PCU LC Pam

in general

ρA QT VA N

of cushion

ρA QCU VA N

of skirt

ρA QTS VA N

34 ACV and SES

Symbol

Computer

Symbol

Definition or

Explanation

Symbol

Computer

Symbol

Definition or

Explanation

sistance

RI (ρI g h2 B)

of ice

RIW (S qIW)

normal

rection of motion

thickness

V (g hI)

ice force

ice (dynamic)

ice (static)

condition)

Thickness of ice

KQICMS

in ice

QIA (ρW nIA

KTICMS

in ice

TIA (ρW nIA

FRICMS

revolution in ice

Symbol

Computer

Symbol

Definition or

Explanation

in ice

2 π QIA nIA

Net ice resistance

RIT - RIW

in presence of ice

in ice

ciency in ice

ηID ηD

36 Sailing Vessels

Symbol

Computer

Symbol

Definition or

Explanation

36 Sailing Vessels

Area of mainsail

Area of spinnaker

(P E + I J) 2

Beam overall

Mainsail base

Fore triangle base

Mainsail height

olds Number

noe body

Effective draught

FH (ρVB

tical centre plane

36 Sailing Vessels

Symbol

Computer

Symbol

Definition or

Explanation

Displacement force

(weight) of keel

Displacement force

(weight) of rudder

36 Sailing Vessels

Symbol

Computer

Symbol

Definition or

Explanation

cient (upright)

RFU (S q)

cient (upright)

RRU (S q)

Total resistance

RTU (S q)

(upright)

RTφ (S q)

Cx Cy Cz

Force coefficients

Side force

right)

RTU + Rφ

Rφ RH

Vessel velocity

36 Sailing Vessels

Symbol

Computer

Symbol

Definition or

Explanation

True wind velocity

course

leaway angle

to boat course)

boat course)

Version 2014 130

4 BACKGROUND AND

REFERENCES

421 Classification

cross-references

list of symbols

drawing

standard itself

exponentiation

operators

matrix components

quantities

A ( eg Area in

msup2)

Version 2011 133

Numbers in roman

(power of n)

SYMBOLS

in italic

NUMBERS

in roman

(T = Thrust)

(M = Model) Fig 1

1 Scope

TK 102

A=A-[A]

as described above

NUMERICAL VALUES

AB = A B - [A] [B]

Version 2014 135

EXAMPLE

Ek = 2

1mvsup2

rived quantities

intensity J

51992 annex A)

dim Q = AαBβCγ

becomes in general

EXAMPLES

Quantity Dimension

velocity LT-1

force LMT-2

energy L2MT-2

relative density 1

Version 2014 136

23 Units

merical values

- base units

2321 Base units

Name Symbol

length metre m

mass kilogram kg

time second s

thermodynamic tem-

perature kelvin K

tary units

L rarr m I rarr A

M rarr kg Θ rarr K

T rarr s N rarrmol

J rarr cd

Derived quantity

SI derived unit

EXAMPLES

Version 2014 138

expressed in terms

of the seven base

units (and the sup-

plementary units in

some cases)

velocity ms

force kg ms2

energy kg m2s2

relative density 1

2323 SI prefixes

Factor Prefix

Name Symbol

1024 yotta Y

1021 zetta z

1018 exa E

1015 peta P

1012 tera T

109 giga G

106 mega M

103 kilo k

102 hecto h

10 deca da

10-1 deci d

10-2 centi c

10-3 milli m

10-6 micro micro

10-9 nano n

10-12 pico p

10-15 femto f

10-18 atto a

10-21 zepto z

10-24 yocto y

fixes see 324

233 The unit one

EXAMPLE

EXAMPLES

Plane angle α = 05

rad = 05

1 with a prefix

for the number 001

shall not be used

neous units

stance

51992 Annex A

with the Sl

Quantity Unit

Name Sym-

bol Definition

time minute

1 min= 60s

1 h = 60 min

1 d = 24 h

plane an-

degree

minute

second

1 deg =

(π180)rad =

(nl80) rad

1 = (160)deg

1 = (160)

= 1 dm

Name Sym-

bol Definition

the kinetic energy

tron in passing

through a potential

in vacuum 1 eV

1602 177 times10-19 J

mass unified

atomic

mass unit

(1 12) of the mass

of an atom of the

nuclide 12C 1u

1660 540 times10-27kg

Tables 5 and 6

the curie

and numbers

311 Symbols

sentence

use of subscripts

right) type

EXAMPLES

Upright sub-

number)

numbers)

(sloping) type

eg a∙ b-1

EXAMPLE

EXAMPLES

m metre

s second

A ampere

Wb weber

N∙m N m

symbol for a prefix

EXAMPLE

Version 2014 142

m ms m∙s-1

mendation

EXAMPLE

units (see 322)

EXAMPLES

1cm3 = (10-2m)3=10-6 m3

1 μs-1= (10-6 s)-1 = 106 s-1

1 kAm = (103A)m = 103 Am

crokilogram (μkg)

33 Numbers

man (upright) type

332Decimal sign

for the quantities

EXAMPLES

l = 12 m - 7 m= (12 - 7) m = 5m

clides

EXAMPLES

H He C Ca

A and 150 31-91992 annex A

script position

4O or (PO4)3-

types)

alpha Α a Α a

beta Β β Β β

gamma Γ γ Γ γ

delta Δ δ Δ δ

epsilon Ε ε Ε ε

zeta Ζ ζ Ζ ζ

eta Η η Η η

theta Θ θ Θ θ

iota Ι ι Ι ι

kappa Κ κ Κ κ

lambda Λ λ Λ λ

mu Μ μ Μ μ

nu Ν ν Ν ν

xi Ξ ξ Ξ ξ

omicron Ο ο Ο ο

pi Π π Π π

rho P ρ Ρ ρ

sigma Σ σ Σ σ

tau Τ τ Τ τ

upsilon Υ υ Υ υ

phi Φ φ Φ φ

chi Χ χ Χ χ

psi Ψ ψ Ψ ψ

omega Ω ω Ω ω

52 Computer symbols

Version 2014 145

52 Computer Symbols

- 9 have been used

near future

53 Documentation

Version 2014 146

53 Documentation

531 ITTC Documents

No500 1976

No6 1978

CETENA Genova 1984

532 Translations

malisation (AFNOR)

No28 Zagreb 1974

truccion Naval

53 Documentation

Version 2014 147

Table of Contents

1 General


111 Uncertainty















122 Loads

1221 External Loads



1231 Motions

1232 Attitudes

13 Fluid Mechanics

131 Flow Parameters




132 Flow Fields

1321 Velocities etc



1331 Geometry


1333 Forces


134 Boundary Layers


135 Cavitation


1352 Flow fields

1353 Pumps


141 Waves

1411 Periodic waves





142 Wind


143 Ice Mechanics


15 Noise


2 Ships in General

21 Basic Quantities


221 Hull Geometry






2222 Ducts


2224 Pods


























235 Water Jets


241 Manoeuvrability





2415 Linear Models




242 Sea Keeping




3 Special Craft











33 Hydrofoil Boats






34 ACV and SES





36 Sailing Vessels






421 Classification





52 Computer Symbols

53 Documentation

531 ITTC Documents

532 Translations


Symbol

Computer

Symbol

Definition or

Explanation

n estimated by

tive square root of

tities

in the following

tion if any

Axes coordinates

Body axes (xyz)

platforms or ships

upwards

section

flight dynamics

ular case

differential

Name of coordi-

nate system

Remarks

11-121

cartesian

coordinates

system See Figure 1

11-122

cylindrical

coordinates

11-123

(-) r φ r=rer

r sin dφ eφ

spherical

Figures 3 and 5

Symbol

Computer

Symbol

Definition or

Explanation

lar quantity

scalar distribution

εikjxkds

εklixlεjkm xmds

Sij = S0ij

Si 3+j = S1ij

S3+i j = S1ij

S3+i 3+j = S2ij

tesian coordinates

fixed in the body

Tijs + Tij

tensor

( Tij - Tji ) 2

Symbol

Computer

Symbol

Definition or

Explanation

V3+i = V1i

X X(1)

Y X(2)

Z X(3)

the body

x0 x01

y0 x02

z0 x03

X0 X0(1)

Y0 X0(2)

Z0 X0(3)

xF xF1

yF xF2

zF xF3

XF XF(1)

YF XF(2)

ZF XF(3)

1 ijk = 321 213 132

0 if otherwise

Symbol

Computer

Symbol

Definition or

Explanation

f FR Frequency Hz

functions

1 TC Hz

Laurent transform

Laplace transform

t TI Time - + s

Symbol

Computer

Symbol

Definition or

Explanation

pled function

= X(0)2 + fSXF(f + jfS)

inverse form

XF(f)=XL(f)

t = 0 TC

XF = xFjδ(f - jTC)

inverse form

Hilbert transform

(1t)F = -i sgn f

if X(tlt0) = 0 then

= (X(t)exp(-at))F

ie = 0 for f lt 0

rier series

XFj(1 + sgn j)

line spectra

Symbol

Computer

Symbol

Definition or

Explanation

component

zl ZLG (Phase) Lag

component

Symbol

Computer

Symbol

Definition or

Explanation

gE gM gMR

E(g) = g(x)fx(x)dx

Random quantities

x(ζ) y(ζ)

X(I) Y(I)

i = 1 n

n sample size

quantity

xD xDR σx

dom quantity

xVR frac12

xDS sx

dom quantity

xVS 12

xxR xxMR Rxx

dom quantity

xyR xyMR Rxy

dom quantities

xE xM xMR

xA xMS mx

a random quantity

1n xi i = 1n

xAE = xE

xVSE = xV n

xPD fx

dom quantity

d Fx dx

xyPD fxy

2 Fxy (x y)

xPF Fx

xyPF Fxy

random quantities

Symbol

Computer

Symbol

Definition or

Explanation

xV xVR xxVR

XVR XXVR

x2 E - xE 2

xVS xxVS

XVS XXVS

dom quantity

1 (n - 1) (xi - x

i = 1n

xyV xyVR

quantities

x yE - xE yE

periment

dom quantity

t =-T2 +T2

T =- +

A(g(t)) = 1T g(t)dt

t =0 +T

x(ζt) y(ζt)

xxC xxCR Cxx

(x(t) - xE)(x(t + τ) - xE)E

xyC xyCR Cxy

(x(t) - xE)(y(t + τ) - yE)E

xxR xxRR Rxx

Rxx(τ) = Rxx(-τ)

= x(t)x(t + τ)MR

τ = 0

xyR Rxy

Ryx(τ) = Rxy(-τ)

if x y are ergodic

Symbol

Computer

Symbol

Definition or

Explanation

xxS Sxx

chastic process

xxRRSR

xyS Sxy

processes

xyRRSR

periment

Average sample mean

Sample covariance

Sample deviation

E M MR

Probability density

(Power) Spectrum

Sample spectrum

Sample correlation

Population variance

Sample variance

Symbol

Computer

Symbol

Definition or

Explanation

control volume

Inward positive QUs

control volume

quantity stored

dq dt QUs

Symbol

Computer

Symbol

Definition or

Explanation

AM(IJ)

DA(IJ)

RF(IJ)

uv DH(UV)

damping

u FH(U)

uv IH(UV)

inertia

of water-plane area

Iy Iyy

IY IYY

M2(22)

MA(55)

Iz Izz

IZ IZZ

M2(33)

MA(66)

Ixy I12

Iyz I23

Izx I31

IXY I2(12)

IYZ I2(23)

IZX I2(31)

kx kxx

(Ixxm)12

Symbol

Computer

Symbol

Definition or

Explanation

ky kyy

(Iyym)12

kz kzz

(Izzm)12

M0(IJ)

MA(IJ)

tensor

mij = m δij

ij M1(IJ)

M2(IJ)

IN(IJ)

MA(UV)

system

Mij = M0

Mi 3+j = M1Tij

M3+i j = M1ij

M3+i 3+j = M2ij

Symbol

Computer

Symbol

Definition or

Explanation

122 Loads

1221 External Loads

in body coordinates

u = MMu

Fi = F0i

F3+i = F1i

gi = g1

g3+i = 0

in body coordinates

F11 F4

K M(1)

F1(1) F(4)

F12 F5

M M(2)

F1(2) F(5)

FN13 F6

N M(3)

F1(3) F(6)

F01 F1

F0(1) F(1)

axis x

F02 F2

F0(2) F(2)

axis y

F03 F3

F0(3) F(3)

axis z

Gu = muv gv

G0i Gi

in body coordinates

Gi = G0

i = m0ij gj

i G1(I)

in body coordinates

G3+i = G1

i = εikj xk G0

= m1ij gj

dW dx1

Symbol

Computer

Symbol

Definition or

Explanation

section coordinates

FSi = FS0

FS3+i = FS1

i = MBi

FS11 Nm

Symbol

Computer

Symbol

Definition or

Explanation

1231 Motions

v01 v4

V0(1) V(4)

body axis x

v02 v5

V0(2) V(5)

body axis y

v03 v6

V0(3) V(6)

body axis z

v11 v1

V1(1) V(1)

v12 v2

V1(2) V(2)

v13 v3

V1(3) V(3)

body axes

vi = v1

v3+i = v0i

tive to body axes

Symbol

Computer

Symbol

Definition or

Explanation

1232 Attitudes

Angle of attack

the z-axis

about the xo axis

X(4) RO

X(5) TR

X(6) YA

course

13 Fluid Mechanics

Symbol

Computer

Symbol

Definition or

Explanation

13 Fluid Mechanics

131 Flow Parameters

Velocity of sound

(E ρ)12

Weight density

ρg (See 111)

Viscosity

Kinematic viscosity

DN RHO

Mass density

Capillarity

length

Boussinesq number

V (g RH)12

Cauchy number

V (E ρ)12

Froude number

V (g L)12

Froude depth number

V (g h)12

V (g 13)12

Mach number

Reynolds number

Strouhal number

Thoma number

Cavitation number

(pA ndash pV)q

Weber number

V2 L κ

07R Ac V nDRe

13 Fluid Mechanics

Symbol

Computer

Symbol

Definition or

Explanation

Sand roughness

surface

Hydraulic radius

wetted perimeter

13 Fluid Mechanics

Symbol

Computer

Symbol

Definition or

Explanation

132 Flow Fields

1321 Velocities etc

energy

ρ V2 2 + p + ρ g h

Mass specific force

Total head

e w = h +pw +qw

flow energy

turbed flow

ρ V2 2

Rate of flow

Total head loss

ij SR(IJ)

ρ vivj

Pa sij

ST(IJ)

Total stress tensor

change

ij SV(IJ)

Viscous stress

u vx v1

v vy v2

w vz v3

Velocity

V = vivi

Wall shear stress

μ (U y)y=0

13 Fluid Mechanics

Symbol

Computer

Symbol

Definition or

Explanation

Induction factor

Vortex density

Circulation

intV ds

along a closed line

Potential function

Stream function

ψ = const

surface

13 Fluid Mechanics

Symbol

Computer

Symbol

Definition or

Explanation

1331 Geometry

Projected area

Wing or foil span

Flap span

Mean chord length

Tip chord length

Root chord length

Sweep angle

tion (general)

edge of struts

(general)

of foil

section

tS cSTH

Taper ratio

Aspect ratio

13 Fluid Mechanics

Symbol

Computer

Symbol

Definition or

Explanation

Induced velocity

and the chord line

or incidence

Geometric angle of

attack or incidence

Hydrodynamic angle

of attack

zero lift

Angle of zero lift

at zero lift

13 Fluid Mechanics

Symbol

Computer

Symbol

Definition or

Explanation

1333 Forces

Foil drag

DRIND Induced drag

of motion

Interference drag

secting foil

zero lift

Streamline drag

Lift force on foil

CL AFT q

of zero

CL0 AFT q

Lift-Drag ratio

13 Fluid Mechanics

Symbol

Computer

Symbol

Definition or

Explanation

134 Boundary Layers

τ (ρ Ue

Entrainment factor

1 (Ue dQ dx)

rameter

(δ - δ) Θ

Static pressure

Total pressure

Entrainment

U δ v or Ue δ

RTHETA

U Θ v or Ue Θ v

boundary layer

from surface

(τ ρ)12

boundary layer

from the surface

(Ue- U) uτ

13 Fluid Mechanics

Symbol

Computer

Symbol

Definition or

Explanation

from the wall

y uτ v

δ (τw dp dx)

layer at U=0995Ue

δ δ1

boundary layer

(Ue- U) Ue dy

von Karman constant

δ995 (v dUe dx)

Energy thickness

(U Ue) (1 - U2 Ue

Momentum thickness

(U Ue) (1 - U Ue)dy

Local skin friction

μ (U y)y=0

13 Fluid Mechanics

Symbol

Computer

Symbol

Definition or

Explanation

135 Cavitation

Gas content ratio

α αS

Gas content

temperature

Cavitation number

(pA - pC) q

(pA - pV) q

1352 Flow fields

Cavity drag

Cavity length

region

Ambient pressure

Critical pressure

takes place

Cavity pressure

quasi-steady cavity

Critical velocity

takes place

Volume loss

13 Fluid Mechanics

Symbol

Computer

Symbol

Definition or

Explanation

WL WTLS

Weight loss

specified time

1353 Pumps

turbo-engines

Thoma number

(HU - pV w) HN

Symbol

Computer

Symbol

Definition or

Explanation

141 Waves

1411 Periodic waves

lerity LW TW =

2WgL in

deep water

odic wave

const = cW

lerity

i fW Hz

wave crest to wave

wave ηC - ηT

advance

Symbol

Computer

Symbol

Definition or

Explanation

at a given location

ηFSα m

ηFSp rad

crossing

trough

crossing

and crest

wave heights

crossing

of zero in a record

Symbol

Computer

Symbol

Definition or

Explanation

in a record

Negative values m

crossing

visual observation

cant wave height

wave heights

wave height

heights

visual observation

wave propagation

samples

visual observation

Symbol

Computer

Symbol

Definition or

Explanation

lution

points

tude function

4 (m0)12 m

fn S(f)df m2 sn

Si(ω)

tral density

Sr(ω)

tral density

Sη(f)

Sη(ω)

2πfP s

and first moment

m0m1 s

and second moment

(m0m2)12 s

Symbol

Computer

Symbol

Definition or

Explanation

DX(fθ)

DX(ωμ)

SIGMAOX

Sζ (ωμ)

Sθ (ωμ)

density

Sρ(fθ)

Sζ(ωμ)

θm MWD

THETAMOX

rection

Symbol

Computer

Symbol

Definition or

Explanation

142 Wind

(008 + 0065U10)10-3

Fetch length

wind blows

DURATN

Wind duration

Return period

ceeded

uz uzi

UFLUCT

USHEAR

Wind shear velocity

12 U10 or 071U10123

Reference mean wind

U10 = (10z)17 Uz

(Uz + uzi)

UzA = (z10)17 U10 or

see section 141

True wind velocity

see section 141

Dimensionless Fetch

face in meters

see section 26

True wind angle

see section 26

Wind direction

Symbol

Computer

Symbol

Definition or

Explanation

143 Ice Mechanics

weight of ice

volume of ice

unit volume of ice

15 Noise

Symbol

Computer

Symbol

Definition or

Explanation

15 Noise

acoustic centre

= 10 log10

(119903119898119904

1199011199031198901198912 ) dB 119901119903119890119891

tance of 1m

119871s

= 119871p

+ 20 log10 [119889

119889119903119890119891] dB 119889119903119890119891

Symbol

Computer

Symbol

Definition or

Explanation

2 SHIPS IN GENERAL

21 Basic Quantities

dv dt ms2

A A AR

Area in general m2

B B BR Breadth m

(forces)

d D D DI Diameter m

E E EN Energy J

F F0 F F0 Force N

h DE Depth m

H H HT Height m

mass distribution

L L LE Length m

tory velocity

m M MA

Mass kg

Symbol

Computer

Symbol

Definition or

Explanation

distribution

M MO Momentum Ns

P P PO Power W

r R RD Radius m

locity

t TI Time s

t TE Temperature K

harmonic process

of a body

ds dt ms

V VO Volume m3

specific weight

dW dV = ρg Nm3

acting on a body

tilled water at 4C

Symbol

Computer

Symbol

Definition or

Explanation

Symbol

Computer

Symbol

Definition or

Explanation

221 Hull Geometry

gitudinal plane

perpendicular

the final rounding

aft perpendiculars

port and starboard)

waterline

relative wind

midship

of midship

section

of ships hull

Symbol

Computer

Symbol

Definition or

Explanation

water line

at stem

the perpendiculars)

maximum section

verse section

Symbol

Computer

Symbol

Definition or

Explanation

point of the stern

pendicular

dicular

perpendicular

with straight keel

water surface level

bare hull

ΔBH (ρ g) m3

pendages

ΔAP (ρ g) m3

Symbol

Computer

Symbol

Definition or

Explanation

ancy) g ρ N

= TS TM

cient B 13 1

GM 13 1

GZ 13 1

cient KG T

12 IL ( B L3) 1

12 IT (B3 L) 1

AM (B T) 1

body A (AX L 2) or

A (AM L 2)

trance E (AX LE) or

E (AM LE)

body F (AX L 2) or

F (AM L 2)

Symbol

Computer

Symbol

Definition or

Explanation

R (AM LR)

AWA (B L 2) 1

forward

AWF (B L 2) 1

coefficient

maximum area

ABL (L T) 1

ABT AX 1

transom stern

AT AX 1

L 13 1

cient T 13 1

A AB After body

APP APP Appendages

B BH Bare hull

DW Design waterline

E EN Entry

Symbol

Computer

Symbol

Definition or

Explanation

F FB Fore body

FS Frame spacing

H HE Hull

LR Reference Line

LP LP Based on LPP

LW LW Based on LWL

M MS Midships

PB Parallel body

R RU Run

SS Station spacing

W WP Water plane

S WS Wetted surface

Symbol

Computer

Symbol

Definition or

Explanation

boss or hub

radius

hub to the tip

Symbol

Computer

Symbol

Definition or

Explanation

blades

2 π r sin (φ) z m

positive rake

the propeller plane

iG + iS = cS sinφ

shoulder

Symbol

Computer

Symbol

Definition or

Explanation

ing aft shoulder

rh RH Hub radius m

ler blade

ler axis

dicular

above base line

Symbol

Computer

Symbol

Definition or

Explanation

cal skew angle

Symbol

Computer

Symbol

Definition or

Explanation

2222 Ducts

LD LD Duct length m

ler plane

of duct

tion s

Jet System Head m

at station 1A

Symbol

Computer

Symbol

Definition or

Explanation

2224 Pods

Main Body

tom Fin

Bottom Fin

under pod main body

D Duct (subscript)

Symbol

Computer

Symbol

Definition or

Explanation

appendage

of rudder

propeller race

hydrofoil

lel to keel

Symbol

Computer

Symbol

Definition or

Explanation

rudders

of flanking rudders

BK Bilge keel

BS Bossing

FB Bow foil

FR Flanking rudder

FS Stern foil

KL Keel

RU Rudder

RF Rudder flap

SA Stabilizer

SH Shafting

SK Skeg

ST Strut

TH Thruster

WG Wedge

Symbol

Computer

Symbol

Definition or

Explanation

curves of stability

volume

Centre of buoyancy

volume

ter plane

(mass)

Keel reference

XCB LCB

ancy (LCB)

from Midships

XCF LCF

tion (LCF)

from Midships

Symbol

Computer

Symbol

Definition or

Explanation

from Midships

XCG LCG

ity (LCG)

from Midships

gravity G

centre of buoyancy

curves of stability

Symbol

Computer

Symbol

Definition or

Explanation

centre of buoyancy

metacentre M

pendicular

dicular

pendicular

weight addition

101 GGKGKG m

height

to the metacentre

tion effects

centric height

metacentre ML

KGKMGM LL

TAG cosφ

KB-KM =I =BM T

BM KM KB

Symbol

Computer

Symbol

Definition or

Explanation

base or keel K

metacentre M to the

ing arm

Heeling moment Δ m

GM 13 1

GZ 13 1

cient KG T

ficient

proximately equals

Symbol

Computer

Symbol

Definition or

Explanation

ficient

proximately equals

one centimetre

one meter

ΔCMTL Nmm

force g ρ N

flooded water

Δfw (ρg) m3

Symbol

Computer

Symbol

Definition or

Explanation

the compartment

bility

a apparent

A att attained

d dyn dynamic

e EFF effective

f false

KL keel line

L longitudinal

MAX maximum

s Static

S sqt Sinkage squat

TC Trim in cm

TM Trim in m

T transverse

V vertical

0 Initial

at heel angle

θ at trim angle θ

Symbol

Computer

Symbol

Definition or

Explanation

231 Hull Resistance

cross section area

lowance

propulsion tests

[(1 + k) CFM + CR]

surface of the body

bare hull

SBH + SAPP m2

Symbol

Computer

Symbol

Definition or

Explanation

area underway

area at rest

area underway

area at rest

lation

RA (S q) 1

ficient

RAA (AV qR) 1

RAPP (S q) 1

cient of a body

RF (S q) 1

RF0 (S q) 1

RP (S q) 1

coefficient

RPV (S q) 1

Symbol

Computer

Symbol

Definition or

Explanation

RR (S q) 1

g R L (ΔV2) 1

efficient

RV (S q) 1

efficient

RW (S q) 1

efficient

1000 R (Δ(KC)2)

1000 RF (Δ(KC)2) 1

sliding bodies

(CV - CF0) CF0 1

(4πg)12VK16

sponding to KQ KT

R (ρ D4 n2) 1

ρ V2 2

see 332

qR PDWR

apparent wind

ρ VWR2 2

see 342

Symbol

Computer

Symbol

Definition or

Explanation

tio in general

R Δ 1

placement ratio

RR Δ 1

FW Fresh water

MR Raw model data

OW Open water

SW Salt water

Symbol

Computer

Symbol

Definition or

Explanation

of revolution

Brake power

Delivered power

propeller power

Effective power

resistance power

Indicated power

Shaft power

Thrust power

Torque

Running trim

Ship speed

or torque identity

2 π n

Symbol

Computer

Symbol

Definition or

Explanation

(T - RT) RT

Δ23 V3 PS

PD (ρ V3 23 2)

identity

PDT PDS

ηDS ηDM

factor

Sinkage dynamic

Trim dynamic

by length

(T - RT) T

(V - VA) V

(V - VA) VA

Symbol

Computer

Symbol

Definition or

Explanation

wTM - wTS

1978 method

diction

ηD PD PE - 1

resistance

PT PD = T VA (Q ω)

coefficient

PE PD = PR PP

Gearing efficiency

Hull efficiency

PE PT = PR PT

= (1 - t) (1 - w)

and propeller

water tests

ηB ηO

Shafting efficiency

PD PS = PP PS

Symbol

Computer

Symbol

Definition or

Explanation

lution

ler blade surface

advance speed

ρ VA2 2

ρ VS2 2 Pa

QS=QSC+ QSH

torque

peller unit

peller

Symbol

Computer

Symbol

Definition or

Explanation

at 07 R

(VA2+ (07 R ω)2)12

n PDfrac12 VA

with n in revsmin

VA in kn (obsolete)

n PTfrac12 VA

with n in revsmin

VA in kn (obsolete)

T (AP qA)

= (TP AP) qA

V (D n) = VH (D n) 1

ducted propeller

VP (D n)

identity

coefficient

QSC (ρ n2 D5) 1

Symbol

Computer

Symbol

Definition or

Explanation

torque coefficient

QSH (ρ n2 D5) 1

ficient

TP (ρ n2 D4) 1

KTP+ KTD 1

KQηR 1

feet VA in kn

efficiency

PJ PD = PJ PP 1

ηJP0 ZET0

zero advance speed

T (ρ π 2)13 (PD D)23 1

η0 ηTP0 ETA0

water tests

ducted propeller

TP TT 1

Symbol

Computer

Symbol

Definition or

Explanation

propeller

peller

by propeller

blade section

arctg (VA r ω)

Symbol

Computer

Symbol

Definition or

Explanation

u = 1 6

u = 1 2 3 force

u = 4 5 6 moment

coefficients

KFi and KMi

cients

Mi (ρ n2 D5) 1

p PR Pressure Pa

ing reaction

u = 1 6

u = 1 2 3 force

u = 4 5 6 moment

from the x-axis

Symbol

Computer

Symbol

Definition or

Explanation

placement

u = 1 6

u = 1 2 3 linear

u = 4 5 6 angular

u = 1 6

u = 1 2 3 linear

u = 4 5 6 angular

eration

u = 1 6

u = 1 2 3 linear

u = 4 5 6 angular

Symbol

Computer

Symbol

Definition or

Explanation

235 Water Jets

210 n2

at station s

cient at station s

rate transducer

Ej = (ρ2)VEj2dQj

j j i i

pg x u n dA

j j i i

pu g x u n dA

sion point

several pump stages

in i direction

u u n dA

Symbol

Computer

Symbol

Definition or

Explanation

dition)

impeller

turbed flow

tion s

boundary layer

msup3s

water jet system

msup3s

jet xT

dition)

system on the hull

Symbol

Computer

Symbol

Definition or

Explanation

at station s

station 7

station 1

tion 1A

surface

in x direction

ciency E

ciency JSE0

stream conditions

the pump

Symbol

Computer

Symbol

Definition or

Explanation

ciency

pump loop test

P duct I

Symbol

Computer

Symbol

Definition or

Explanation

241 Manoeuvrability

of rudder

(AR + ARmov) 2 m2

root to tip

AHL (L T) 1

h DE Water depth m

der axis

Symbol

Computer

Symbol

Definition or

Explanation

dp dt 1s2

dq dt 1s2

dr dt 1s2

du dt ms2

dv dt ms2

dw dt ms2

body axes

χ YX Yaw angle rad

Symbol

Computer

Symbol

Definition or

Explanation

RO Roll angle rad

Pitch angle

the hull

Drift angle

the hull

ANWIRL

ANRUEF

Bow fin angle

Stern fin angle

Rudder angle

ANRUOR

COWIAB

COWIRL

Symbol

Computer

Symbol

Definition or

Explanation

N r Nms2

N v Nms2

along body x-axis

X u Nsm

eration

X u Ns2m

tion of body axis y

Y r Ns2

Symbol

Computer

Symbol

Definition or

Explanation

Y v Ns2m

along body z-axis

2415 Linear Models

ship length

turning diameter

DC LPP 1

ameter δR = δ0

D0 LPP 1

unstable ship

Symbol

Computer

Symbol

Definition or

Explanation

unstable ship

turning rate

change of heading

heading

(starboard)

(port)

tr TIR Reach time s

Symbol

Computer

Symbol

Definition or

Explanation

track reach

Symbol

Computer

Symbol

Definition or

Explanation

242 Sea Keeping

system

spectively

Frequency

Alias horizontal

Alias vertical

moment

Alias horizontal

ing moment

Alias vertical

lution in waves

Symbol

Computer

Symbol

Definition or

Explanation

Sη(f) Sηη(f)

Sη(ω) Sηη(ω)

density

roll pitch yaw

rad TAW

Wave period

Yz(ω)

Azζ(ω)

tory motions

za(ω) ζa(ω) or

za(ω) ηa(ω)

Yθζ(ω)

Aθζ(ω)

motions

Θa(ω) ζa(ω) or

Tuning factor

w w wL L L

w w w= = =

q fL L L= = =

(short crested)

Symbol

Computer

Symbol

Definition or

Explanation

I991241

- I991242

lever curve

cording to ISO 8666

IMOIS IMOHSC2000

acter sets

Symbol

Computer

Symbol

Definition or

Explanation

curves of stability

volume

centre of buoyancy

metacentre M

volume

needed for crew

sons on board

ficient - I991243

proximately equals

hull - I99121

Symbol

Computer

Symbol

Definition or

Explanation

merged test weights

ter plane

pendicular

dicular

pendicular

(mass)

weight addition

101 GGKGKG m

weight addition

101 GGKGKG m

Symbol

Computer

Symbol

Definition or

Explanation

height

to the metacentre

KGKMGM

face effect)

tion effects

height

metacentre ML

KGKMGM LL

TAG cos φ

IMOtable

profile

K Keel reference

base of keel or K

Symbol

Computer

Symbol

Definition or

Explanation

base of keel or K

metacentre M to the

condition - IMOIS

IMOtable

ment due to crew

is taken of rolling

Symbol

Computer

Symbol

Definition or

Explanation

inclination

centimetre

meter CMTL Nmm

due to wind

above waterline

PV Wind pressure Pa

s Wave steepness 1

according to hellip

value see hellip

Symbol

Computer

Symbol

Definition or

Explanation

TL Turning lever m

IMOHSC2000

ancy (LCB)

of buoyancy B

tion (LCF)

of flotation F

ity (LCG)

of gravity G

gravity G

Symbol

Computer

Symbol

Definition or

Explanation

centre of buoyancy

force g N

gle during hellip

Symbol

Computer

Symbol

Definition or

Explanation

according to hellip

gle seehellip

bility

the compartment

stability curve

Symbol

Computer

Symbol

Definition or

Explanation

E Entrance

F Fore

Z Heave

θ Pitch

φ Roll

Symbol

Computer

Symbol

Definition or

Explanation

3 SPECIAL CRAFT

Planing bottom area

strips

gravity

Beam over chines

Transom breadth

spray strips

chines

spray strips

bossings

bottom

section

Shaft angle

inclined downwards)

Symbol

Computer

Symbol

Definition or

Explanation

derway

water surface level

(flange mounting)

forces underway

ing surface

(LK + LC) 2

planing hull

water line

SWS SS

spray edge

Symbol

Computer

Symbol

Definition or

Explanation

ALFBAR

Barrel flow angle

LM LWL

TRIMDWL

design waterline

(positive bow up)

θS θ0

Static trim angle

θV θD

LM (BLCG)

TAUDWL

reference line

Spray angle

plane of bottom)

tal friction area

normally to NA)

normally to NB)

Symbol

Computer

Symbol

Definition or

Explanation

force NPN

ler pressure forces

normally to NPP)

suction forces NPS

normal to NPS)

pressure forces NRP

normal to NRP)

normal to RAA)

normal to RAP)

normal to RF)

sistance RK

normal to RK)

drag ΔRRP

normal to ΔRRP)

thrust

normal to RT)

Symbol

Computer

Symbol

Definition or

Explanation

deadrise

Δ (BCG

surface

Δ (BCG

breadth

V (BCG g)12

Load coefficient

Δ (BCG

3 ρ g )

1 LVHD

drodynamic lift

Hydrostatic lift

Due to buoyancy

reference line

ence line

reference line

Symbol

Computer

Symbol

Definition or

Explanation

reference line

Keel drag

Induced drag

g ρ tg τ

Parasitic drag

openings

Total resistance

spray drag

CF SWS qS

of the hull

Spray velocity

the spray

Symbol

Computer

Symbol

Definition or

Explanation

Box beam

Beam of main deck

Hull spacing

Tunnel width

Hull diameter

submerged hulls

dinal position X

Deck clearance

ANENIN

nel (inner) side

of demihull

ANENOU

outer side

of demihull

Box length

Length of main deck

Symbol

Computer

Symbol

Definition or

Explanation

to trailing edge

Symbol

Computer

Symbol

Definition or

Explanation

hull vessel

ence correction

RFMH - Σ RF

tion of multi-hull

RTMH - RFMH

ence correction

RRMH - Σ RR

vessel

correction

RTMH - Σ RT

33 Hydrofoil Boats

Symbol

Computer

Symbol

Definition or

Explanation

33 Hydrofoil Boats

cluding foils

Span of struts

tance of struts

Mean chord length

section with foil

Weight of foil

Dihedral angle

Submerged foil area

take-off speed

33 Hydrofoil Boats

Symbol

Computer

Symbol

Definition or

Explanation

Foil span wetted

distance

V (g LF)12

chord length

V (g cM)12

foilborne

Flight height

at rest

Keel clearance

centre of gravity

and rear foils

lF + lR

centre of gravity

Foil immersion

ALFIND

with twist

33 Hydrofoil Boats

Symbol

Computer

Symbol

Definition or

Explanation

33 Hydrofoil Boats

Symbol

Computer

Symbol

Definition or

Explanation

Foil drag

CDF AFR q

CDF AFF q

DRIND Induced drag

of motion

Interference drag

secting foil

Streamline drag

Spray drag

Strut drag

Wave drag

Ventilation drag

Lift force on foil

CL AFT q

CL AFF q

CL AFR q

attack of zero

CL0 AFT q

CLTO AFT q

33 Hydrofoil Boats

Symbol

Computer

Symbol

Definition or

Explanation

DP (AFS q) 1

L0 (AFS q) 1

condition

LTO (AFS q) 1

34 ACV and SES

Symbol

Computer

Symbol

Definition or

Explanation

34 ACV and SES

Cushion area

Cushion beam

At the water line

neath craft

Bow seal height

Skirt depth

Stern seal height

Cushion length

at rest off cushion

to structure

needs clarification

34 ACV and SES

Symbol

Computer

Symbol

Definition or

Explanation

structure

needs clarification

to structure

needs clarification

to water contact

SSHC SSH0

cushion periphery

of air

the skirt

34 ACV and SES

Symbol

Computer

Symbol

Definition or

Explanation

coefficient

R0 (ρA VR2 AC 2) 1

PCU LC Pam

in general

ρA QT VA N

of cushion

ρA QCU VA N

of skirt

ρA QTS VA N

34 ACV and SES

Symbol

Computer

Symbol

Definition or

Explanation

Symbol

Computer

Symbol

Definition or

Explanation

sistance

RI (ρI g h2 B)

of ice

RIW (S qIW)

normal

rection of motion

thickness

V (g hI)

ice force

ice (dynamic)

ice (static)

condition)

Thickness of ice

KQICMS

in ice

QIA (ρW nIA

KTICMS

in ice

TIA (ρW nIA

FRICMS

revolution in ice

Symbol

Computer

Symbol

Definition or

Explanation

in ice

2 π QIA nIA

Net ice resistance

RIT - RIW

in presence of ice

in ice

ciency in ice

ηID ηD

36 Sailing Vessels

Symbol

Computer

Symbol

Definition or

Explanation

36 Sailing Vessels

Area of mainsail

Area of spinnaker

(P E + I J) 2

Beam overall

Mainsail base

Fore triangle base

Mainsail height

olds Number

noe body

Effective draught

FH (ρVB

tical centre plane

36 Sailing Vessels

Symbol

Computer

Symbol

Definition or

Explanation

Displacement force

(weight) of keel

Displacement force

(weight) of rudder

36 Sailing Vessels

Symbol

Computer

Symbol

Definition or

Explanation

cient (upright)

RFU (S q)

cient (upright)

RRU (S q)

Total resistance

RTU (S q)

(upright)

RTφ (S q)

Cx Cy Cz

Force coefficients

Side force

right)

RTU + Rφ

Rφ RH

Vessel velocity

36 Sailing Vessels

Symbol

Computer

Symbol

Definition or

Explanation

True wind velocity

course

leaway angle

to boat course)

boat course)

Version 2014 130

4 BACKGROUND AND

REFERENCES

421 Classification

cross-references

list of symbols

drawing

standard itself

exponentiation

operators

matrix components

quantities

A ( eg Area in

msup2)

Version 2011 133

Numbers in roman

(power of n)

SYMBOLS

in italic

NUMBERS

in roman

(T = Thrust)

(M = Model) Fig 1

1 Scope

TK 102

A=A-[A]

as described above

NUMERICAL VALUES

AB = A B - [A] [B]

Version 2014 135

EXAMPLE

Ek = 2

1mvsup2

rived quantities

intensity J

51992 annex A)

dim Q = AαBβCγ

becomes in general

EXAMPLES

Quantity Dimension

velocity LT-1

force LMT-2

energy L2MT-2

relative density 1

Version 2014 136

23 Units

merical values

- base units

2321 Base units

Name Symbol

length metre m

mass kilogram kg

time second s

thermodynamic tem-

perature kelvin K

tary units

L rarr m I rarr A

M rarr kg Θ rarr K

T rarr s N rarrmol

J rarr cd

Derived quantity

SI derived unit

EXAMPLES

Version 2014 138

expressed in terms

of the seven base

units (and the sup-

plementary units in

some cases)

velocity ms

force kg ms2

energy kg m2s2

relative density 1

2323 SI prefixes

Factor Prefix

Name Symbol

1024 yotta Y

1021 zetta z

1018 exa E

1015 peta P

1012 tera T

109 giga G

106 mega M

103 kilo k

102 hecto h

10 deca da

10-1 deci d

10-2 centi c

10-3 milli m

10-6 micro micro

10-9 nano n

10-12 pico p

10-15 femto f

10-18 atto a

10-21 zepto z

10-24 yocto y

fixes see 324

233 The unit one

EXAMPLE

EXAMPLES

Plane angle α = 05

rad = 05

1 with a prefix

for the number 001

shall not be used

neous units

stance

51992 Annex A

with the Sl

Quantity Unit

Name Sym-

bol Definition

time minute

1 min= 60s

1 h = 60 min

1 d = 24 h

plane an-

degree

minute

second

1 deg =

(π180)rad =

(nl80) rad

1 = (160)deg

1 = (160)

= 1 dm

Name Sym-

bol Definition

the kinetic energy

tron in passing

through a potential

in vacuum 1 eV

1602 177 times10-19 J

mass unified

atomic

mass unit

(1 12) of the mass

of an atom of the

nuclide 12C 1u

1660 540 times10-27kg

Tables 5 and 6

the curie

and numbers

311 Symbols

sentence

use of subscripts

right) type

EXAMPLES

Upright sub-

number)

numbers)

(sloping) type

eg a∙ b-1

EXAMPLE

EXAMPLES

m metre

s second

A ampere

Wb weber

N∙m N m

symbol for a prefix

EXAMPLE

Version 2014 142

m ms m∙s-1

mendation

EXAMPLE

units (see 322)

EXAMPLES

1cm3 = (10-2m)3=10-6 m3

1 μs-1= (10-6 s)-1 = 106 s-1

1 kAm = (103A)m = 103 Am

crokilogram (μkg)

33 Numbers

man (upright) type

332Decimal sign

for the quantities

EXAMPLES

l = 12 m - 7 m= (12 - 7) m = 5m

clides

EXAMPLES

H He C Ca

A and 150 31-91992 annex A

script position

4O or (PO4)3-

types)

alpha Α a Α a

beta Β β Β β

gamma Γ γ Γ γ

delta Δ δ Δ δ

epsilon Ε ε Ε ε

zeta Ζ ζ Ζ ζ

eta Η η Η η

theta Θ θ Θ θ

iota Ι ι Ι ι

kappa Κ κ Κ κ

lambda Λ λ Λ λ

mu Μ μ Μ μ

nu Ν ν Ν ν

xi Ξ ξ Ξ ξ

omicron Ο ο Ο ο

pi Π π Π π

rho P ρ Ρ ρ

sigma Σ σ Σ σ

tau Τ τ Τ τ

upsilon Υ υ Υ υ

phi Φ φ Φ φ

chi Χ χ Χ χ

psi Ψ ψ Ψ ψ

omega Ω ω Ω ω

52 Computer symbols

Version 2014 145

52 Computer Symbols

- 9 have been used

near future

53 Documentation

Version 2014 146

53 Documentation

531 ITTC Documents

No500 1976

No6 1978

CETENA Genova 1984

532 Translations

malisation (AFNOR)

No28 Zagreb 1974

truccion Naval

53 Documentation

Version 2014 147

Table of Contents

1 General


111 Uncertainty















122 Loads

1221 External Loads



1231 Motions

1232 Attitudes

13 Fluid Mechanics

131 Flow Parameters




132 Flow Fields

1321 Velocities etc



1331 Geometry


1333 Forces


134 Boundary Layers


135 Cavitation


1352 Flow fields

1353 Pumps


141 Waves

1411 Periodic waves





142 Wind


143 Ice Mechanics


15 Noise


2 Ships in General

21 Basic Quantities


221 Hull Geometry






2222 Ducts


2224 Pods


























235 Water Jets


241 Manoeuvrability





2415 Linear Models




242 Sea Keeping




3 Special Craft











33 Hydrofoil Boats






34 ACV and SES





36 Sailing Vessels






421 Classification





52 Computer Symbols

53 Documentation

531 ITTC Documents

532 Translations
