The Principles of Naval Architecture Series: Ship Resistance and Flow

243 Pages·2010·9.76 MB·English

by  Lars Larsson

The Principles of
Naval Architecture Series
Ship Resistance and Flow
Lars Larsson and Hoyte C. Raven
J. Randolph Paulling, Editor
2010
Published by
The Society of Naval Architects
and Marine Engineers
601 Pavonia Avenue
Jersey City, New Jersey 07306
Copyright © 2010 by The Society of Naval Architects and Marine Engineers.
The opinions or assertions of the authors herein are not to be construed as offi cial or
refl ecting the views of SNAME, Chalmers University of Technology, MARIN, or any government agency.
It is understood and agreed that nothing expressed herein is intended or shall be construed
to give any person, fi rm, or corporation any right, remedy, or claim against the authors or
their employers, SNAME or any of its offi cers or member.
Library of Congress Cataloging-in-Publication Data
Larsson, Lars.
Ship resistance and fl ow / Lars Larsson and Hoyte C. Raven; J. Randolph Paulling, editor.
p. cm. — (Principles of naval architecture)
Includes bibliographical references and index.
ISBN 978-0-939773-76-3 (alk. paper)
1. Ship resistance—Mathematics. 2. Inviscid fl ow—Mathematics. 3. Viscous fl ow—Mathematics.
4. Hulls (Naval architecture)—Mathematics. 5. Ships—Hydrodynamics—Mathematics.
I. Raven, Hoyte C. II. Paulling, J. Randolph. III. Title.
VM751.L37 2010
623.8'12—dc22
2010020298
ISBN 978-0-939773-76-3
Printed in the United States of America
First Printing, 2010
An Introduction to the Series
The Society of Naval Architects and Marine Engineers is experiencing remarkable changes in the Maritime Industry
as we enter our 115th year of service. Our mission, however, has not changed over the years . . . “an internationally
recognized . . . technical society . . . serving the maritime industry, dedicated to advancing the art, science and
practice of naval architecture, shipbuilding, ocean engineering, and marine engineering . . . encouraging the ex-
change and recording of information, sponsoring applied research . . . supporting education and enhancing the
professional status and integrity of its membership.”
In the spirit of being faithful to our mission, we have written and published signifi cant treatises on the subject
of naval architecture, marine engineering, and shipbuilding. Our most well known publication is the “Principles
of Naval Architecture.” First published in 1939, it has been revised and updated three times – in 1967, 1988, and
now in 2008. During this time, remarkable changes in the industry have taken place, especially in technology,
and these changes have accelerated. The result has had a dramatic impact on size, speed, capacity, safety, qual-
ity, and environmental protection.
The professions of naval architecture and marine engineering have realized great technical advances. They
include structural design, hydrodynamics, resistance and propulsion, vibrations, materials, strength analysis using
fi nite element analysis, dynamic loading and fatigue analysis, computer-aided ship design, controllability, stability,
and the use of simulation, risk analysis, and virtual reality.
However, with this in view, nothing remains more important than a comprehensive knowledge of “fi rst p rinciples.”
Using this knowledge, the Naval Architect is able to intelligently utilize the exceptional technology available to its
fullest extent in today’s global maritime industry. It is with this in mind that this entirely new 2008 treatise was
developed – “The Principles of Naval Architecture: The Series.” Recognizing the challenge of remaining relevant
and current as technology changes, each major topical area will be published as a separate volume. This will fa-
cilitate timely revisions as technology continues to change and provide for more practical use by those who teach,
learn or utilize the tools of our profession.
It is noteworthy that it took a decade to prepare this monumental work of nine volumes by sixteen authors and
by a distinguished steering committee that was brought together from several countries, universities, companies,
and laboratories. We are all especially indebted to the editor, Professor J. Randolph (Randy) Paulling for providing
the leadership, knowledge, and organizational ability to manage this seminal work. His dedication to this arduous
task embodies the very essence of our mission . . . “to serve the maritime industry.”
It is with this introduction that we recognize and honor all of our colleagues who contributed to this work.
Authors:
Dr. John S. Letcher Hull Geometry
Dr. Colin S. Moore Intact Stability
Robert D. Tagg Subdivision and Damaged Stability
Professor Alaa Mansour and Dr. Donald Liu Strength of Ships and Ocean Structures
Professor Lars Larsson and Dr. Hoyte C. Raven Ship Resistance and Flow
Professors Justin E. Kerwin and Jacques B. Hadler Propulsion
Professor William S. Vorus Vibration and Noise
Prof. Robert S. Beck, Dr. John Dalzell (Deceased), Prof. Odd Faltinsen Motions in Waves
and Dr. Arthur M. Reed
Professor W. C. Webster and Dr. Rod Barr Controllability
Control Committee Members are:
Professor Bruce Johnson, Robert G. Keane, Jr., Justin H. McCarthy, David M. Maurer, Dr. William B. Morgan,
Professor J. Nicholas Newman and Dr. Owen H. Oakley, Jr.
I would also like to recognize the support staff and members who helped bring this project to fruition, espe-
cially Susan Evans Grove, Publications Director, Phil Kimball, Executive Director, and Dr. Roger Compton, Past
President.
In the new world’s global maritime industry, we must maintain leadership in our profession if we are to continue
to be true to our mission. The “Principles of Naval Architecture: The Series,” is another example of the many ways
our Society is meeting that challenge.
ADMIRAL ROBERT E. KRAMEK
Past President (2007–2008)
Nomenclature
A wave amplitude k wave number, form factor, turbulent kinetic
A lateral area of topsides and superstructure energy
L
A area of midship section K ,k fundamental wave number
M 0 0
AR aspect ratio k roughness (Mean Apparent Amplitude)
MAA
AR effective aspect ratio k equivalent sand roughness
e s
A frontal (transverse) area of topsides and K “circular K”: nondimensional speed
T
superstructure L lift
A transom area L,L ship length (between perpendiculars)
tr pp
A((cid:2)),B((cid:2)) wave amplitude functions L length scale of pressure variation
p
a coeffi cient in discretized equations m mass
→a acceleration vector m(cid:5) mass fl ux

B ship beam m→ dipole moment

b width of channel or plate, wing span n wall-normal coordinate, inverse of exponent
c wave speed, volume fraction in velocity profi le formula
C block coeffi cient of ship P delivered power
B D
C drag coeffi cient P effective power
D E
C induced drag coeffi cient Pe Peclet number
Di
C local skin friction coeffi cient p pressure
f
C total skin friction p* approximate pressure in SIMPLE algorithm
F
C total skin friction for a fl at plate p(cid:7) pressure correction in SIMPLE algorithm
F0
c wave group velocity p hydrodynamic contribution to pressure
g hd
C ,C ,C moment coeffi cients about x,y,z-axes p hydrostatic pressure
K M N hs
C prismatic coeffi cient of ship hull, pressure p stagnation pressure
P max
resistance coeffi cient p undisturbed pressure
(cid:4)
C pressure coeffi cient Q source strength
p
C hydrodynamic pressure coeffi cient q dynamic head
phd
C hydrostatic pressure coeffi cient R distance
phs
C residuary resistance coeffi cient r radius of (streamline) curvature
R
C total resistance coeffi cient r,r principal radii of curvature of a surface
T 1 2
C viscous resistance coeffi cient R frictional resistance
V F
C ,C ,C force coeffi cients in x,y,z-directions R hydraulic radius of channel
X Y Z H
C wave resistance coeffi cient R Reynolds stress
W ij
© “circular C”: ship resistance coeffi cient Rn Reynolds number
D drag, diffusion conductance R residuary resistance
R
D induced drag R total resistance
i T
E wave energy R viscous resistance
wave V
E kinetic energy in wave R wave resistance
kin W
En Euler number S wetted surface, source term
E potential energy in wave s,t,n coordinates of local system on free surface
(cid:5)pot
E wave energy fl ux S rate of strain tensor
ij
F volume fl ux per unit area T ship draught, wave period, turbulence level
→
F force vector t time, thrust deduction fraction

→ → →
Fb ,Fp ,Fv bfoordcye , froerscpee, cptirveeslsyure force, and viscous Uu→ (cid:4) vinefll oocwit yv evleocctiotyr
Fn,Fn Froude number based on ship length u,v,w fl ow velocity components in x,y,z-directions
L
Fn Froude number based on ship beam u(cid:5) friction velocity
B
Fn Froude number based on water depth u+ non-dimensional velocity in wall functions
h
Fn Froude number based on (cid:6)(cid:3) u* approximate velocity in SIMPLE algorithm
g tr acceleration of gravity tr u(cid:7) velocity correction in SIMPLE algorithm
h water depth V ship speed
H approximate wave elevation in linearization v→ velocity vector
HM mean height of lateral projection of top- V→A → propeller advance velocity
sides and superstructure V ,V true and apparent wind velocity, respectively
TW A W
K,M,N moments about x,y,z-axes W weight of ship, Coles’ wake function
xxii NOMENCLATURE
Wn Weber number (cid:15) length of wave, measured in longitu-
x
w wake fraction dinal section
X,Y,Z forces in x,y,z-directions (cid:16) dynamic viscosity, doublet density
x,y, z coordinates of global system (cid:16) effective dynamic viscosity
eff
y+ non-dimensional wall distance in wall functions (cid:16) turbulent dynamic viscosity
t
z dynamic sinkage (cid:17) kinematic viscosity
_v
z z-coordinate of transom centroid (cid:17) effective kinematic viscosity
tr eff
(cid:6) angle of attack (cid:17) turbulent kinematic viscosity
t
(cid:7) blockage ratio, boundary layer cross-fl ow (cid:18) density
angle (cid:19) cavitation number, source density
(cid:7) ,(cid:7) true and apparent wind angle, respectively (cid:19) stress tensor
TW AW ij
(cid:7) wall cross-fl ow angle (cid:5) trim angle
w
(cid:8) surface tension, overspeed ratio in channel (cid:5) wall shear stress
w
(cid:9) v ortex strength, generalized diffusion coef- (cid:20) general dependent variable in fi nite
fi cient volume theory
(cid:10)p pressure jump due to surface tension (cid:21) velocity potential
(cid:8)
(cid:8) weight of ship (cid:21)(cid:7) perturbation of potential, in linear-
(cid:11) boundary layer thickness ization
(cid:11) boundary layer displacement thickness (cid:22) base fl ow potential in linearization
(cid:11)1 Kronecker delta (cid:23) rotation tensor
(cid:12)i j rate of dissipation of turbulent kinetic energy (cid:24)ij radial frequency, specifi c rate of dis-
(cid:3) wave elevation sipation of turbulent energy
(cid:3)(cid:7) perturbation of wave elevation →(cid:24) vorticity vector
(cid:3) w ave height deduced from double-body (cid:9) displacement
r
pressure Indices
(cid:3) height of transom edge above still-watersurface a,w air and water, respectively
tr
(cid:13) propulsive effi ciency M,S model and ship, respectively
D
(cid:13) hull effi ciency P central point in a discretization stencil
H
(cid:13) relative rotative effi ciency W,E,N,S,T,B neighboring points in a discretization
R
(cid:13) open-water effi ciency of propeller stencil
0
(cid:2) w ave divergence angle, boundary layer mo- w,e,n,s,t,b cell faces
mentum thickness x,y,z components of a vector in the x-, y-,
(cid:14) von Kàrmàn constant orz-directions
(cid:15) wave length 1,2,3 components of a vector in the x-, y-,
(cid:15) l ength of transverse wave, fundamental wave orz-directions (alternative represen-
0
length tation)
Preface
Ship Resistance and Flow
During the 20 plus years that have elapsed since publication of the previous edition of Principles of Naval A rchitecture,
there have been remarkable advances in the art, science and practice of the design and construction of ships and other
fl oating structures. In that edition, the increasing use of high speed computers was recognized and computational
methods were incorporated or acknowledged in the individual chapters rather than being presented in a separate
chapter. Today, the electronic computer is one of the most important tools in any engineering environment and the
laptop computer has taken the place of the ubiquitous slide rule of an earlier generation of engineers.
Advanced concepts and methods that were only being developed or introduced then are a part of common
engineering practice today. These include fi nite element analysis, computational fl uid dynamics, random process
methods, numerical modeling of the hull form and components, with some or all of these merged into integrated
design and manufacturing systems. Collectively, these give the naval architect unprecedented power and fl exibility
to explore innovation in concept and design of marine systems. In order to fully utilize these tools, the modern
naval architect must possess a sound knowledge of mathematics and the other fundamental sciences that form a
basic part of a modern engineering education.
In 1997, planning for the new edition of Principles of Naval Architecture was initiated by the SNAME publica-
tions manager who convened a meeting of a number of interested individuals including the editors of PNA and the
new edition of Ship Design and Construction on which work had already begun. At this meeting it was agreed
that PNA would present the basis for the modern practice of naval architecture and the focus would be principles
in preference to applications. The book should contain appropriate reference material but it was not a handbook
with extensive numerical tables and graphs. Neither was it to be an elementary or advanced textbook although it
was expected to be used as regular reading material in advanced undergraduate and elementary graduate courses.
It would contain the background and principles necessary to understand and to use intelligently the modern ana-
lytical, numerical, experimental, and computational tools available to the naval architect and also the fundamen-
tals needed for the development of new tools. In essence, it would contain the material necessary to develop the
understanding, insight, intuition, experience, and judgment needed for the successful practice of the profession.
Following this initial meeting, a PNA Control Committee, consisting of individuals having the expertise deemed
necessary to oversee and guide the writing of the new edition of PNA, was appointed. This committee, after par-
ticipating in the selection of authors for the various chapters, has continued to contribute by critically reviewing
the various component parts as they are written.
In an effort of this magnitude, involving contributions from numerous widely separated authors, progress has
not been uniform and it became obvious before the halfway mark that some chapters would be completed before
others. In order to make the material available to the profession in a timely manner it was decided to publish each
major subdivision as a separate volume in the Principles of Naval Architecture Series rather than treating each as
a separate chapter of a single book.
Although the United States committed in 1975 to adopt SI units as the primary system of measurement the tran-
sition is not yet complete. In shipbuilding as well as other fi elds we still fi nd usage of three systems of units: English
or foot-pound-seconds, SI or meter-newton-seconds, and the meter-kilogram(force)-second system common in
engineering work on the European continent and most of the non-English speaking world prior to the adoption of
the SI system. In the present work, we have tried to adhere to SI units as the primary system but other units may
be found, particularly in illustrations taken from other, older publications. The symbols and notation follow, in
general, the standards developed by the International Towing Tank Conference.
A major goal in the design of virtually all vessels as varied as commercial cargo and passenger ships, naval
vessels, fi shing boats, and racing yachts, is to obtain a hull form having favorable resistance and speed character-
istics. In order to achieve this goal the prediction of resistance for a given hull geometry is of critical importance.
Since the time of publication of the previous edition of PNA important advances have been made in theoretical and
computational fl uid dynamics and there has been a steady increase in the use of the results of such work in ship
and offshore structure design. The present volume contains a completely new presentation of the subject of ship
resistance embodying these developments. The fi rst section of the book provides basic understanding of the fl ow
phenomena that give rise to the resistance encountered by a ship moving in water. The second section contains
an introduction to the methods in common use today by which that knowledge is applied to the prediction of the
resistance. A third and fi nal section provides guidance to the naval architect to aid in designing a hull form having
favorable resistance characteristics.
xvi PREFACE
William Froude in the 1870s proposed the separation of total resistance into frictional and residual parts, the
former equal to that of a fl at plate of the same length, speed, area, and roughness as the ship wetted surface, and
the latter principally due to ship generated waves. Since Froude’s time, much research has been conducted to
o btain better formulations of the fl at plate resistance with refi nements to account for the three dimensional nature
of the fl ow over the curved shape of the hull. Simultaneously, other research effort has been directed to obtaining a
b etter understanding of the basic nature of the fl ow of water about the ship hull and how this fl ow affects the total
resistance.
The three methods currently in general use for determining ship resistance are model tests, empirical meth-
ods, and theory. In model testing, refi nements in Froude’s method of extrapolation from model to full scale are
described. Other experimental topics include wave profi le measurements, wake surveys, and boundary layer mea-
surements. Empirical methods are described that make use of data from previous ships or model experiments.
Results for several “standard series” representing merchant ships, naval vessels, fi shing vessels, and yachts are
mentioned and statistical analyses of accumulated data are reviewed.
The theoretical formulation of ship resistance began with the linear thin ship theory of Michell in 1898. The pres-
ent volume develops the equations of inviscid and viscous fl ow in two and three dimensions, including free surface
effects and boundary conditions. From this basis are derived numerical and computational methods for character-
izing the fl ow about a ship hull. Modern computing power allows these methods to be implemented in practical
codes and procedures suitable for engineering application. Today, it is probable that many, if not most, large ships
are designed using computational fl uid dynamics, or CFD, in some form either for the design of the entire hull or
for components of the hull and appendages.
Concluding sections describe design considerations and procedures for achieving favorable fl ow and resistance
characteristics of the hull and appendages. Examples are covered for ships designed for high, medium, and low
speed ranges. Design considerations affecting both wave and viscous effects are included. A fi nal section discusses
fl ow in the stern wake that has important implications for both resistance and propeller performance.
J. RANDOLPH PAULLING
Editor
Table of Contents
An Introduction to the Series . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xi
Foreword . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiii
Preface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xv
Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xvii
Authors’ Biography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xix
Nomenclature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xxi
1 Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .1
1.1 The Importance of Accurate Resistance Predictions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .1
1.2 Different Ways to Predict Resistance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .1
1.2.1 Model Testing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .1
1.2.2 Empirical Methods. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .2
1.2.3 Computational Techniques . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .3
1.2.4 Use of the Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .4
1.3 The Structure of this Book . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .5
2 Governing Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .5
2.1 Global Coordinate System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .5
2.2 The Continuity Equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .5
2.3 The Navier-Stokes Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .6
2.4 Boundary Conditions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .8
2.4.1 Solid Surfaces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .8
2.4.2 Water Surface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .9
2.4.3 Infi nity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .9
2.5 Hydrodynamic and Hydrostatic Pressure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .9
3 Similarity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .10
3.1 Types of Similarity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .10
3.2 Proof of Similarity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .10
3.3 Consequences of the Similarity Requirements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .11
3.3.1 Summary of Requirements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .11
3.3.2 The Dilemma in Model Testing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .12
iv SHIP RESISTANCE AND FLOW
4 Decomposition of Resistance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .13
4.1 Resistance on a Straight Course in Calm, Unrestricted Water. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .13
4.1.1 Vessel Types . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .13
4.1.2 Detailed Decomposition of the Resistance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .13
4.1.3 Comparison of the Four Vessel Types . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .15
4.2 Other Resistance Components . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .15
5 Inviscid Flow Around the Hull, Wave Making, and Wave Resistance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .16
5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .16
5.2 Inviscid Flow Around a Body . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .16
5.2.1 Governing Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .16
5.2.2 Inviscid Flow Around a Two-Dimensional Body . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .18
5.2.3 Inviscid Flow Around a Three-Dimensional Body . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .19
5.3 Free-Surface Waves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .20
5.3.1 Derivation of Sinusoidal Waves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .22
5.3.2 Properties of Sinusoidal Waves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .23
5.4 Ship Waves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .24
5.4.1 Two-Dimensional Waves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .24
5.4.2 Three-Dimensional Waves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .25
5.4.3 The Kelvin Pattern . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .26
5.4.4 Ship Wave Patterns . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .27
5.4.5 Interference Effects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .29
5.4.6 The Ship Wave Spectrum . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .30
5.5 Wave Resistance. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .31
5.6 Wave Breaking and Spray . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .34
5.7 Viscous Effects on Ship Wave Patterns . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .35
5.8 Shallow-Water Effects on Wave Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .36
5.9 Shallow-Water Effects on Ship Wave Patterns . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .38
5.9.1 Low Subcritical: Fn (cid:2) 0.7 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .38
h
5.9.2 High Subcritical: 0.7 (cid:2)Fn (cid:2) 0.9 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .39
h
5.9.3 (Trans)critical: 0.9 (cid:2)Fn (cid:2) 1.1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .40
h
5.9.4 Supercritical: Fn (cid:3) 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .41
h
5.10 Shallow-Water Effects on Resistance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .42