Ship Hydrostatics and Stability Second Edition by Adrian B Biran

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Ship Hydrostatics and Stability Second Edition by Adrian B Biran

Preface to the Second Edition

Six years have passed since the issue of the enlarged reprint of the book. New intact and
damage stability regulations have been adopted in the meantime, mainly by IMO, but also
by the German Navy. While in the past the regulations were prescriptive and based on
deterministic models, the new orientation turns towards goal-based and risk-assessment
approaches. New ship forms increased the vulnerability to parametric roll and the occurrence
of large roll angles and loss of containers have been frequently reported. Extensive research is
carried on for a better understanding of this phenomenon, as well as of not-yet fully understood
capsizing modes, such as dead ship condition, pure loss of stability and broaching-to. One aim
of the research is to develop so-called second-generation criteria of stability. As it is recognized
now that stability depends not only on the design of ships, but also on their loading and
operation, as well as on environmental conditions, another aim of the research, and of IMO, is
to issue guidance documentation for ship masters. The old deterministic approach to damage
calculations has been replaced in large part by the probabilistic approach. Nevertheless, as the
old mariners’ saying states, ‘There is always stormy weather ahead,’ the accident of the cruise
liner Costa Concordia, in 2012, will trigger new changes as it has unveiled new challenges for
Naval Architects and experts in maritime regulations.
All these developments made a new edition necessary. We updated the sections that have
become obsolete and inserted the highlights of the recent regulations and research results.
In doing so we are taking advantage of the fact that our contributor Javier de Juana has
been attending the IMO meetings during years, and one of the authors has been Permanent
Delegate as Spanish representative to the IMO. In addition, we corrected errors and added a
few exercises and explanations that proved useful during the lectures delivered by one of the
authors at the Technion.
We are pleased to thank those who helped us in our endeavour. While translating the previous
edition into Turkish, Professor Hüseyin Yilmaz reported several errors. Thomas Wardecki and
Andreas Rinke provided details on the German-Navy regulations presently in force. We thank
Miguel Palomares and Lorenzo Mayol of IMO for their help, and Luis Pérez-Rojas, Leonardo
Fernández-Jambrina, Antonio Rodriguez, Jesús Valle, Antonio Souto, and Jorge Vicario for
providing important insight for some chapters and the cover figure, a modification of the hull
forms of the DTMB combatant 5415. We acknowledge the courtesy of Luis García Bernáldez
and Verónica Alonso of Sener who allowed us to describe some of the main features of the
FORAN computer system. We thank The Mathworks for their continuing support and permit
to use their marvelous and powerful software throughout the book. This second edition was
made possible only by the dedicated work of Hayley Gray, Charlie Kent and Susan Li, all of
Elsevier, UK.
Finally, the authors want to thank their wives, Suzi and Noelia, for their patience, understanding
and forgiveness for the time stolen from that due to their families.

Preface to the First Reprint

Using the book in two consecutive academic years we discovered several typos and errors.
They are corrected in this reprint and the author thanks those students, and especially
Eyal Lahav, who have read the book with attention and transmitted their comments.
Several Naval Architects involved in university education or in maritime legislation sent
comments and suggestions. Bertram Volker corrected orthographical errors in German terms.
Lawrence Doctors recommended to insert a theorem regarding wall-sided floating bodies
with negative initial metacentric height. Dan Livneh drew the attention of the author to the
new approach of classification societies to the parametric roll of container ships. The most
extensive contributions are due to Rubén López-Pulido who corrected a few examples,
transmitted updated information on IMO, volunteered to add the Spanish translations of
important technical terms and prepared a Spanish index for the end of the book. All these
contributions are implemented in this reprint.
Additional software was included on the companion sites of this book. Short descriptions
appear in an Appendix at the end of the book.1
The author acknowledges the continuous support of The Mathworks, and personally that of
Courtney Esposito who provided the latest updates of MATLAB.
Finally, the author thanks Jonathan Simpson and Miranda Turner for their encouragement to
update the book and for their editorial help.


This book is based on a course of Ship Hydrostatics delivered during a quarter of a century
at the Faculty of Mechanical Engineering of the Technion–Israel Institute of Technology. The
book reflects the author’s own experience in design and R&D and incorporates improvements
based on feedback received from students.
The book is addressed in the first place to undergraduate students for whom it is a first course
in Naval Architecture or Ocean Engineering. Many sections can be also read by technicians and
ship officers. Selected sections can be used as reference text by practising Naval Architects.
Naval Architecture is an age-old field of human activity and as such it is much affected by
tradition. This background is part of the beauty of the profession. The book is based on this
tradition but, at the same time, the author tried to write a modern text that considers more
recent developments, among them the theory of parametric resonance, also known as Mathieu
effect, the use of personal computers, and new regulations for intact and damage stability.
The Mathieu effect is believed to be the cause of many marine disasters. German researchers
were the first to study this hypothesis. Unfortunately, in the first years of their research
they published their results in German only. The German Federal Navy—Bundesmarine—
elaborated stability regulations that allow for the Mathieu effect. These regulations were
subsequently adopted by a few additional navies. Proposals have been made to consider the
effect of waves for merchant vessels too.
Very powerful personal computers are available today; their utility is enhanced by many
versatile, user-friendly software packages. PC programmes for hydrostatic calculations are
commercially available and their prices vary from several hundred dollars, for the simplest,
to many thousands for the more powerful. Programmes for particular tasks can be written by
a user familiar with a good software package. To show how to do it, this book is illustrated
with a few examples calculated in Excel and with many examples written in MATLAB.
MATLAB is an increasingly popular, comprehensive computing environment characterized
by an interactive mode of work, many built-in functions, immediate graphing facilities and
easy programming paradigms. Readers who have access to MATLAB, even to the Students’
Edition, can readily use those examples. Readers who do not work in MATLAB can convert
the examples to other programming languages.
Several new stability regulations are briefly reviewed in this book. Students and practising
Naval Architects will certainly welcome the description of such rules and examples of how to
apply them.
About this book
Theoretical developments require an understanding of basic calculus and analytic geometry.
A few sections employ basic vector calculus, differential geometry or ordinary differential
equations. Students able to read them will gain more insight into matters explained in the
book. Other readers can skip those sections without impairing their understanding of practical
calculations and regulations described in the text.
Chapter 1 introduces the reader to basic terminology and to the subject of hull definition. The
definitions follow new ISO and ISO-based standards. Translations into French, German and
Italian are provided for the most important terms.
The basic concepts of hydrostatics of floating bodies are described in Chapter 2; they include
the conditions of equilibrium and initial stability. By the end of this chapter the reader
knows that hydrostatic calculations require many integrations. Methods for performing such
integrations in Naval Architecture are developed in Chapter 3.
Chapter 4 shows how to apply the procedures of numerical integration to the calculation of
actual hydrostatic properties. Other matters covered in the same chapter are a few simple
checks of the resulting plots, and an analysis of how the properties change when a given
hull is subjected to a particular class of transformations, namely the properties of affine
Chapter 5 discusses the statical stability at large angles of heel and the curve of statical
Simple models for assessing the ship stability in the presence of various heeling moments
are developed in Chapter 5. Both static and dynamic effects are considered, as well as the
influence of factors and situations that negatively affect stability. Examples of the latter
are displaced loads, hanging loads, free liquid surfaces, shifting loads, and grounding and
docking. Three subjects closely related to practical stability calculations are described in
Chapter 7: weight and trim calculations and the inclining experiment.
Ships and other floating structures are approved for use only if they comply with pertinent
regulations. Regulations applicable to merchant ships, ships of the US Navy and UK Navy,
and small sail or motor craft are summarily described in Chapter 8.
The phenomenon of parametric resonance, or Mathieu effect, is briefly described in Chapter
9. The chapter includes a simple criterion of distinguishing between stable and unstable
solutions and examples of simple simulations in MATLAB.
Ships of the German Federal Navy are designed according to criteria that take into account
the Mathieu effect: they are introduced in Chapter 10.
Chapters 8 and 10 deal with intact ships. Ships and some other floating structures are also
required to survive after a limited amount of flooding. Chapter 11 shows how to achieve
this goal by subdividing the hull by means of watertight bulkheads. There are two methods
of calculating the ship condition after damage, namely the method of lost buoyancy and the
method of added weight. The difference between the two methods is explained by means
of a simple example. The chapter also contains short descriptions of several regulations for
merchant and for naval ships.
Chapters 8, 10 and 11 inform the reader about the existence of requirements issued by bodies
that approve the design and the use of ships and other floating bodies, and show how simple
models developed in previous chapters are applied in engineering calculations. Not all the
details of those regulations are included in this book, neither all regulations issued all over
the world. If the reader has to perform calculations that must be submitted for approval,
it is highly recommended to find out which are the relevant regulations and to consult the
complete, most recent edition of them.
Chapter 12 goes beyond the traditional scope of Ship Hydrostatics and provides a bridge
towards more advanced and realistic models. The theory of linear waves is briefly introduced
and it is shown how real seas can be described by the superposition of linear waves and by
the concept of spectrum. Floating bodies move in six degrees of freedom and the spectrum
of those motions is related to the sea spectrum. Another subject introduced in this chapter is
that of tank stabilizers, a case in which surfaces of free liquids can help in reducing the roll
Chapter 13 is about the use of modern computers in hull definition, hydrostatic calculations
and simulations of motions. The chapter introduces the basic concepts of Computer Graphics
and illustrates their application to hull definition by means of the MultiSurf and SurfaceWorks
packages. A roll simulation in SIMULINK, a toolbox of MATLAB, exemplifies the
possibilities of modern simulation software.
Using this book
Boldface words indicate a key term used for the first time in the text, for instance length
between perpendiculars. Italics are used to emphasize, for example equilibrium of moments.
Vectors are written with a line over their name: KB, GM. Listings of MATLAB programmes,
functions and file names are written in typewriter characters, for instance mathisim.m.
Basic ideas are exemplified on simple geometric forms for which analytic solutions can
be readily found. After mastering these ideas the students should practise on real ship data
provided in examples and exercises, at the end of each chapter. The data of an existing vessel,
called Lido 9, are used throughout the book to illustrate the main concepts. Data of a few
other real-world vessels are given in additional examples and exercises.
I am closing this preface by paying a tribute to the memory of those who taught me the
profession, Dinu Ilie and Nicolae Pârâianu, and of my colleague in teaching, Pinchas Milch.
The first acknowledgements should certainly go to the many students who took the course
from which emerged this book. Their reactions helped in identifying the topics that need more
explanations. Naming a few of those students would imply the risk of being unfair to others.
Many numerical examples were calculated with the aid of the programme system
ARCHIMEDES. The TECHNION obtained this software by the courtesy of Heinrich Söding,
then Professor at the Technical University of Hannover, now at the Technical University of
Hamburg. Included with the programme source there was a set of test data that describe a
vessel identified as Ship No. 83074. Some examples in this book are based on that data.
Sol Bodner, coordinator of the Ship Engineering Program of the Technion, provided essential
support for the course of Ship Hydrostatics. Itzhak Shaham and Jack Yanai contributed to the
success of the programme.
Paul Münch provided data of actual vessels and Lido Kineret, Ltd and the Özdeniz Group, Inc.
allowed us to use them in numerical examples. Eliezer Kantorowitz read initial drafts of the
book proposal. Yeshayahu Hershkowitz, of Lloyd’s Register, and Arnon Nitzan, then student
in the last graduate year, read the final draft and returned helpful comments. Reinhard Siegel,
of AeroHydro, provided the drawing on which the cover of the book is based, and helped in
the application of MultiSurf and SurfaceWorks.
Richard Barker drew the attention of the author to the first uses of the term Naval
Architecture. Our common love for the history of the profession enabled a pleasant and
interesting dialogue.
Naomi Fernandes of MathWorks, Baruch Pekelman, their agent in Israel, and his assistants
enabled the author to use the latest MATLAB developments.
The author thanks Addison-Wesley Longman, especially Karen Mosman and Pauline Gillet,
for permission to use material from the book MATLAB for Engineers written by him and
Moshe Breiner.
And finally the author thanks the editors of Elsevier Science, Rebecca Hamersley,
Rebecca Rue, Sallyann Deans and Nishma Shah for their cooperation and continuous help.
It was the task of Nishma Shah to bring the project into production.
Adrian Biran, 2003