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Basic Ship Theory
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Basic Ship Theory
K.J. Rawson
MSc, DEng, FEng, RCNC, FRINA, WhSch
E.C. Tupper
BSc, CEng, RCNC, FRINA, WhSch
Fifth edition
Volume 1
Chapters 1 to 9
Hydrostatics and Strength
OXFOR D AUCKLAND BOST ON JOHANNESBURG MELBOURNE NEW DELHI
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Butterworth-Heinemann
Linacre House, Jordan Hill, Oxford OX2 8DP
225 Wildwood Avenue, Woburn, MA 01801-2041
A division of Reed Educational and Professional Publishing Ltd
A member of the Reed Elsevier plc group
First published by Longman Group Limited 1968
Second edition 1976 (in two volumes)
Third edition 1983
Fourth edition 1994
Fifth edition 2001
#
K.J. Rawson and E.C. Tupper 2001
All rights reserved. No part of this publication may be reproduced in
any material form (including photocopying or storing in any medium by
electronic means and whether or not transiently or incidentally to some
other use of this publication) without the written permission of the

publications visit our website at www.bh.com
Typeset in India at Integra Software Services Pvt Ltd,
Pondicherry, India 605005; www.integra-india.com
Introduction
Symbols and nomenclature
1 Art or science?
1.1 Authorities
2 Some tools
2.1 Basic geometric concepts
2.2 Properties of irregular shapes
2.3 Approximate integration
2.4 Computers
2.5 Appriximate formulae and rules
2.6 Statistics
2.7 Worked examples
2.8 Problems
3 Flotation and trim
3.1 Flotation
3.2 Hydrostatic data
3.3 Worked examples
3.4 Problems
4 Stability
4.1 Initial stability
4.2 Complete stability
4.3 Dynamical stability
4.4 Stability assessment
4.5 Problems
5 Hazards and protection
5.1 Flooding and collision
5.2 Safety of life at sea

9.9 Vibration and noise
9.10 Human factors
9.11 Problems
Bibliography
Answers to problems
Index
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Foreword to the ®fth edition
Over the last quarter of the last century there were many changes in the
maritime scene. Ships may now be much larger; their speeds are generally
higher; the crews have become drastically reduced; there are many dierent
types (including hovercraft, multi-hull designs and so on); much quicker and
more accurate assessments of stability, strength, manoeuvring, motions and
powering are possible using complex computer programs; on-board computer
systems help the operators; ferries carry many more vehicles and passengers;
and so the list goes on. However, the fundamental concepts of naval architec-
ture, which the authors set out when Basic Ship Theory was ®rst published,
remain as valid as ever.
As with many other branches of engineering, quite rapid advances have been
made in ship design, production and operation. Many advances relate to the
eectiveness (in terms of money, manpower and time) with which older proced-
ures or methods can be accomplished. This is largely due to the greater
eciency and lower cost of modern computers and proliferation of information
available. Other advances are related to our fundamental understanding of
naval architecture and the environment in which ships operate. These tend to
be associated with the more advanced aspects of the subject: more complex
programs for analysing structures, for example, which are not appropriate to a
basic text book.
The naval architect is aected not only by changes in technology but also by
changes in society itself. Fashions change as do the concerns of the public, often

go in the subjects of each chapter. It is tempting to load the books with theories
which have become more and more advanced. What has been done is to
provide a glimpse into developments and advanced work with which students
and practitioners must become familiar. Towards the end of each chapter a
section giving an outline of how matters are developing has been included
which will help to lead students, with the aid of the Internet, to all relevant
references. Some web site addresses have also been given.
It must be appreciated that standards change continually, as do the titles of
organizations. Every attempt has been made to include the latest at the time of
writing but the reader should always check source documents to see whether
they still apply in detail at the time they are to be used. What the reader can rely
on is that the principles underlying such standards will still be relevant.
2001 KJR ECT
xii Foreword to the fifth edition
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Acknowledgements
The authors have deliberately refrained from quoting a large number of refer-
ences. However, we wish to acknowledge the contributions of many practi-
tioners and research workers to our understanding of naval architecture, upon
whose work we have drawn. Many will be well known to any student of
engineering. Those early engineers in the ®eld who set the fundamentals of
the subject, such as Bernoulli, Reynolds, the Froudes, Taylor, Timoshenko,
Southwell and Simpson, are mentioned in the text because their names are
synonymous with sections of naval architecture.
Others have developed our understanding, with more precise and compre-
hensive methods and theories as technology has advanced and the ability to
carry out complex computations improved. Some notable workers are not
quoted as their work has been too advanced for a book of this nature.
We are indebted to a number of organizations which have allowed us to draw
upon their publications, transactions, journals and conference proceedings.

towards the best solution to an owner's economic aims or military demands.
Manipulation of the elements of a ship is greatly strengthened by such a `feel'
and experience provided by personal involvement. Virtually every ship's char-
acteristic and system aects every other ship so that some form of holistic
approach is essential.
A crude representation of the process of creating a ship is outlined in the
®gure.
xiv
Economics of trade
or
Military objective
Volume
Hull shape
Weight
Resistance & Propulsion
Dimensions
Safety
Architecture
Structure
Production
Manoeuvring
Flotation & stability
Choice of machinery
Design
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This is, of course, only a beginning. Moreover, the arrows should really be
pointing in both directions; for example, the choice of machinery to serve speed
and endurance re¯ects back on the volume required and the architecture of the
ship which aects safety and structure. And so on. Quanti®cation of the
changes is eected by the choice of suitable computer programs. Downstream

Before embarking on the book proper, it is necessary to comment on the
units employed.
UNITS
In May 1965, the UK Government, in common with other governments,
announced that Industry should move to the use of the metric system. At the
same time, a rationalized set of metric units has been adopted internationally,
following endorsement by the International Organization for Standardization
using the Syste
Á
me International d'Unite
Â
s (SI).
The adoption of SI units has been patchy in many countries while some have
yet to change from their traditional positions.
Introduction xv
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In the following notes, the SI system of units is presented brie¯y; a fuller
treatment appears in British Standard 5555. This book is written using SI units.
The SI is a rationalized selection of units in the metric system. It is a coherent
system, i.e. the product or quotient of any two unit quantities in the system is
the unit of the resultant quantity. The basic units are as follows:
Quantity Name of unit Unit symbol
Length metre m
Mass kilogramme kg
Time second s
Electric current ampere A
Thermodynamic temperature kelvin K
Luminous intensity candela cd
Amount of substance mole mol
Plane angle radian rad

2
Volume cubic metre m
3
Density kilogramme per cubic metre kg=m
3
Velocity metre per second m=s
Angular velocity radian per second rad=s
Acceleration metre per second squared m=s
2
xvi Introductionxvi Introduction
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Angular acceleration radian per second squared rad=s
2
Pressure, stress newton per square metre N=m
2
Surface tension newton per metre N=m
Dynamic viscosity newton second per metre squared N s=m
2
Kinematic viscosity metre squared per second m
2
=s
Thermal conductivity watt per metre kelvin W=(mK)
Quantity Imperial unit Equivalent SI units
Length 1 yd 0.9144 m
1 ft 0.3048 m
1 in 0.0254 m
1 mile 1609.344m
1 nautical mile
(UK)
1853.18 m

3
0:0283168 m
3
1 UK gal 0:004546092 m
3
 4:546092 litres
Velocity 1 ft=s0:3048 m=s
1 mile=hr 0:44704 m=s;1:60934 km=hr
1 knot (UK) 0:51477 m=s;1:85318 km=hr
1 knot (International) 0:51444 m=s;1:852 km=hr
Standard acceleration, g 32:174 ft=s
2
9:80665 m=s
2
Mass 1 lb 0:45359237 kg
1 ton 1016:05 kg  1:01605 tonnes
Mass density 1 lb=in
3
27:6799 Â 10
3
kg=m
3
1lb=ft
3
16:0185 kg=m
3
Force 1 pdl 0.138255 N
1 lbf 4.44822 N
Pressure 1 lbf=in
2

1 000000 000 000=10
12
tera T
1 000000 000=10
9
giga G
1 000 000=10
6
mega M
1 000=10
3
kilo k
100=10
2
hecto h
10=10
1
deca da
0:1=10
À1
deci d
0:01=10
À2
centi c
0:001=10
À3
milli m
0:000 001=10
À6
micro 

3
1:0252 tonne=m
3
1:025 tonne=m
3
salt water 35 ft
3
=ton 0:9754 m
3
=tonne 0:975 m
3
=tonne
Mass density 62:2lb=ft
3
0:9964 tonne=m
3
1:0 tonne=m
3
fresh water 36 ft
3
=ton 1:0033 m
3
=tonne 1:0m
3
=tonne
Young's modulus E (steel) 13,500 tonf=in
2
2:0855 Â 10
7
N=cm

b
b
b
`
b
b
b
b
X
A
w
420
tonf=in 1:025 A
w
(tonnef=m) 1:025 A
w
tonnef=m
A
w
(ft
2
) A
w
(m
2
)
NPC 100:52 A
w(N=cm)
NPM A
w

L
L
MN m
m

Force displacement Á 1 tonf 1.01605 tonnef 1.016 tonnef
9964.02N 9964 N
Mass displacement Æ 1 ton 1.01605 tonne 1.016tonne
Weight density:
Salt water 0.01 MN=m
3
Fresh water 0.0098 MN=m
3
Speci®c volume:
Salt water 99.5 m
3
=MN
Fresh water 102.0 m
3
=MN
xviii Introductionxviii Introduction
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Of particular signi®cance to the naval architect are the units used for dis-
placement, density and stress. The force displacement Á, under the SI scheme
must be expressed in terms of newtons. In practice the meganewton (MN) is a
more convenient unit and 1 MN is approximately equivalent to 100 tonf (100.44
more exactly). The authors have additionally introduced the tonnef (and,
correspondingly, the tonne for mass measurement) as explained more fully in
Chapter 3.
EXAMPLES

height of wave, crest to trough
H total head, Bernoulli
L length in general
L
w
,  wave-length
m mass
n rate of revolution
p pressure intensity
p
v
vapour pressure of water
p
I
ambient pressure at in®nity
P power in general
q stagnation pressure
Q rate of ¯ow
r, R radius in general
s length along path
t time in general
t

temperature in general
T period of time for a complete cycle
u reciprocal weight density, speci®c volume,
u, v, w velocity components in direction of x-, y-, z-axes
U, V linear velocity
w weight density
W weight in general

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GEOMETRY OF SHIP
A
M
midship section area
A
W
waterplane area
A
x
maximum transverse section area
B beam or moulded breadth
BM metacentre above centre of buoyancy
C
B
block coecient
C
M
midship section coecient
C
P
longitudinal prismatic coecient
C
VP
vertical prismatic coecient
C
WP
coecient of ®neness of waterplane
D depth of ship
F freeboard

A
D
developed blade area
A
E
expanded area
A
O
disc area
A
P
projected blade area
b span of aerofoil or hydrofoil
c chord length
d boss or hub diameter
D diameter of propeller
f
M
camber
P propeller pitch in general
R propeller radius
t thickness of aerofoil
Z number of blades of propeller
 angle of attack
 pitch angle of screw propeller
RESISTANCE AND PROPULSION
a resistance augment fraction
C
D
drag coe.

P
I
indicated power
P
S
shaft power
P
T
thrust power
Q torque
R resistance in general
R
n
Reynolds number
R
F
frictional resistance
R
R
residuary resistance
R
T
total resistance
R
W
wave-making resistance
s
A
apparent slip ratio
t thrust deduction fraction

O
propeller e. in open water

R
relative rotative eciency
 cavitation number
SEAKEEPING
c wave velocity
f frequency
f
E
frequency of encounter
I
xx
, I
yy
, I
zz
real moments of inertia
I
xy
, I
xz
, I
yz
real products of inertia
k radius of gyration
m
n
spectrum moment where n is an integer

natural period in smooth water for pitching
T

natural period in smooth water for rolling
Y

(!) response amplitude operatorÐpitch
Y

(!) response amplitude operatorÐroll
Y

(!) response amplitude operatorÐyaw
 leeway or drift angle

R
rudder angle
" phase angle between any two harmonic motions
 instantaneous wave elevation
xxii Symbols and nomenclature
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
A
wave amplitude

w
wave height, crest to trough
 pitch angle

A

b breadth of plate
C modulus of rigidity
" linear strain
E modulus of elasticity, Young's modulus
 direct stress

y
yield stress
g acceleration due to gravity
I planar second moment of area
J polar second moment of area
j stress concentration factor
k radius of gyration
K bulk modulus
l length of member
L length
M bending moment
M
p
plastic moment
M
AB
bending moment at A in member AB
m mass
P direct load, externally applied
P
E
Euler collapse load
p distributed direct load (area distribution), pressure
p

L
3
, x
H
 x=
1
2
L
2
V
2
, L
H
 L=
1
2
L
3
V
2
.
(c) A lower case subscript is used to denote the denominator of a partial derivative, e.g.
Y
u
 @Y=@u.
(d) For derivatives with respect to time the dot notation is used, e.g.

x  dx=dt.
xxiv Symbols and nomenclature
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Â
du Navire. In his book, Bouguer laid
the foundations of many aspects of naval architecture which were developed later
in the eighteenth century by Bernoulli, Euler and Santacilla. Lagrange and many
others made contributions but the other outstanding ®gure of that century was
the Swede, Frederick Chapman who pioneered work on ship resistance which
led up to the great work of William Froude a hundred years later. A scienti®c
approach to naval architecture was encouraged more on the continent than in
Britain where it remained until the 1850s, a craft surrounded by pride and
secrecy. On 19 May 1666, Samuel Pepys wrote of a Mr Deane:
And then he fell to explain to me his manner of casting the draught of
water which a ship will draw before-hand; which is a secret the King and
1
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all admire in him, and he is the ®rst that hath come to any certainty before-
hand of foretelling the draught of water of a ship before she be launched.
The second half of the nineteenth century, however, produced Scott Russell,
Rankine and Froude and the development of the science, and dissemination of
knowledge in Britain was rapid.
NAVAL ARCHITECTURE TODAY
It would be quite wrong to say that the art and craft built up over many
thousands of years has been wholly replaced by a science. The need for a
scienti®c approach was felt, ®rst, because the art had proved inadequate to
halt the disasters at sea or to guarantee the merchant that he or she was getting
the best value for their money. Science has contributed much to alleviate these
shortcomings but it continues to require the injection of experience of success-
ful practice. Science produces the correct basis for comparison of ships but the
exact value of the criteria which determine their performances must, as in other
branches of engineering, continue to be dictated by previous successful practice,
i.e. like most engineering, this is largely a comparative science. Where the

architect is being held increasingly responsible for ensuring that the environ-
mental impact of the product is minimal both in normal operation and follow-
ing any foreseeable accident. There is a duty to the public at large for the safety
of marine transport. In common with other professionals the naval architect is
expected to abide by a stringent code of conduct.
It must be clear that naval architecture involves complex compromises of
many of these features. The art is, perhaps, the blending in the right pro-
portions. There can be few other pursuits which draw on such a variety of
sciences to blend them into an acceptable whole. There can be few pursuits as
fascinating.
SHIPS
Ships are designed to meet the requirements of owners or of war and their
features are dictated by these requirements. The purpose of a merchant ship has
been described as conveying passengers or cargo from one port to another in
the most ecient manner. This was interpreted by the owners of Cutty Sark as
the conveyance of relatively small quantities of tea in the shortest possible time,
because this was what the tea market demanded at that time. The market might
well have required twice the quantity of tea per voyage in a voyage of twice the
length of time, when a fundamentally dierent design of ship would have
resulted. The economics of any particular market have a profound eect on
merchant ship design. Thus, the change in the oil market following the second
world war resulted in the disappearance of the 12,000 tonf deadweight tankers
and the appearance of the 400,000 tonf deadweight supertankers. The econom-
ics of the trading of the ship itself have an eect on its design; the desire, for
example, for small tonnage (and therefore small harbour dues) with large
cargo-carrying capacity brought about the three island and shelter deck ships
where cargo could be stowed in spaces not counted towards the tonnage on
which insurance rates and harbour dues were based. Such trends have not
always been compatible with safety and requirements of safety now also vitally
in¯uence ship design. Specialized demands of trade have produced the great

submarine, as an alternative carrier of the torpedo, led to the design of the anti-
submarine frigate; the missile carrying nuclear submarine led to the hunter
killer nuclear submarine. Thus, the particular demand of war, as is natural,
produces a particular warship.
Particular demands of the sea have resulted in many other interesting and
important ships: the self-righting lifeboats, surface eect vessels, container
ships, cargo drones, hydrofoil craft and a host of others. All are governed by
the basic rules and tools of naval architecture which this book seeks to explore.
Precision in the use of these tools must continue to be inspired by knowledge of
sea disasters; Liberty ships of the second world war, the loss of the Royal
George, the loss of HMS Captain, and the loss of the Vasa:
In 1628, the Vasa set out on a maiden voyage which lasted little more than
two hours. She sank in good weather through capsizing while still in view of
the people of Stockholm.
That disasters remain an in¯uence upon design and operation has been
tragically illustrated by the losses of the Herald of Free Enterprise and Estonia
in the 1990s, while ferry losses continue at an alarming rate, often in nations
which cannot aord the level of safety that they would like.
Authorities
CLASSIFICATION SOCIETIES
The authorities with the most profound in¯uence on shipbuilding, merchant
ship design and ship safety are the classi®cation societies. Among the most
dominant are Lloyd's Register of Shipping, det Norske Veritas, the American
Bureau of Shipping, Bureau Veritas, Registro Italiano, Germanische Lloyd and
Nippon Kaiji Kyokai. These meet to discuss standards under the auspices of
the International Association of Classi®cation Societies (IACS).
It is odd that the two most in¯uential bodies in the shipbuilding and shipping
industries should both derive their names from the same owner of a coee shop,
Edward Lloyd, at the end of the seventeenth century. Yet the two organizations
4 Basic ship theory