The principles of naval architecture series : Intact stability

The Principles of

Naval Architecture Series

Intact Stability

Colin S. Moore

J. Randolph Paulling, Editor

Published by

The Society of Naval Architects

and Marine Engineers

601 Pavonia Avenue

Jersey City, New Jersey 07306

Copyright O 2010 by The Society of Naval Architects and Marine Engineers.

The opinions or assertions of the authors herein are not to be construed as of cia1 or

re ecting the views of SNAME or any government agency.

It is understood and agreed that nothing expressed herein is intended or shall be construed

to give any person, rm, or corporation any right, remedy, or claim against SNAME or any of its

of cers or member.

Library of Congress Cataloging-in-Publication Data

Moore, Colin S.

Intact stability 1 Colin S. Moore. -- 1st ed.

p. cm. -- (Principles of naval architecture)

Includes bibliographical references and index.

ISBN 978-0-939773-74-9

I. Stability of ships. I. Title.

VM159.M59 2010

623.8'171--dc22

2009043464

ISBN 978-0-939773-74-9

Printed in the United States of America

First Printing, 2010

Nomenclature

A

&I

AP

B

B

BI

BL

-

BM

-

BML

b

C

CL

CB

CG

Gcp

D

D

DWT

E

e

F

F

FP

FW

G

G,

GM

-

GML

-

GZ

9

9

H

h

I

IL

IT

i,

i,.

K

-

KB

KG

-

KM

KMI,

k

L

L

stands for area, generally

area of waterplane

after perpendicular

maximum molded breadth

center of buoyancy

etc., changed positions of center of buoyancy

molded baseline

transverse metacentric radius, or height of M

above B

longitudinal metacentric radius, or height of ML

above B

width of a compartment or tank

constant or coefficient

centerline; a vertical plane through centerline

block coefficient, VILBT

center of gravity

waterplane area coefficient, &/LB

molded depth

diameter, generally

deadweight

energy, generally

base of Naperian logarithms, 2.7183

force, generally

center of flotation (center of area of

waterplane)

forward perpendicular

fresh water

center of gravity of ship's mass

etc., changed positions of the center of gravity

transverse metacentric height, height of M

above G

longitudinal metacentric height, height of MI,

above G

righting arm; horizontal distance from G to Z

acceleration due to gravity

center of gravity of a component

head

depth of water or submergence

moment of inertia, generally

longitudinal moment of inertia of waterplane

transverse moment of inertia of waterplane

longitudinal moment of inertia of free surface in

a compartment or tank

transverse moment of inertia of free surface in

a compartment or tank

any point in a horizontal plane through the

baseline

height of B above the baseline

height of G above the baseline

height of M above the baseline

height of ML above the baseline

radius of gyration

length, generally

length of ship

LBP

LPP

LOA

LwL

Lw

LCB

LCF

LCG

LWL

I

M

M

ML

MT

MTcm

MTI

m

m

rnL

0

ox

OY

OZ

P

P

P

Q

R

S

SW

T

T

Tw

TCB

TCG

TPcrn

TPI

t

t

v

Vk

vc

VCB

VCG

vcg

W

WL

WL1

v

v

W

length between perpendiculars

length between perpendiculars

length overall

length on designed load waterline

length of a wave, from crest to crest

longitudinal position of center of buoyancy

longitudinal position of center of flotation

longitudinal position of center of gravity

load, or design, waterline

length of a compartment of tank

moment, generally

transverse metacenter

longitudinal metacenter

trimming moment

moment to trim 1 em

moment to trim 1 inch

mass, generally (W/g or w/g)

transverse metacenter of liquid in a tank or

compartment

longitudinal metacenter of liquid in a tank or

compartment

origin of coordinates

longitudinal axis of coordinates

transverse axis of coordinates

vertical axis of coordinates

(upward) force of keel blocks

pressure (force per unit area) in a fluid

probability, generally

fore and aft distance on a waterline

radius, generally

wetted surface of hull

salt water

draft

period, generally

period of a wave

transverse position of center of buoyancy

transverse position of center of gravity

tons per em immersion

tons per inch immersion

thickness, generally

time, generally

linear velocity in general, speed of the ship

speed of ship, knots

speed of a surface wave (celerity)

vertical position of center of buoyancy

vertical position of center of gravity

vertical position of g

weight of ship equal to the displacement (pgV)

of a ship floating in equilibrium

any waterline parallel to baseline

etc., changed position of WL

volume of an individual item

linear velocity

weight of an individual item

xvi NOMENCLATURE

x distance from origin along X-axis

Y distance from origin along Y-axis

x distance from origin along Z-axis

Z a point vertically over B, opposite G

A,, displacement mass = pV

A displacement force (buoyancy) = pgV

6 specific volume, or indicating a small change

0 angle of pitch or of trim (about OY-axis)

P permeability

P density; mass per unit volume

4) angle of heel or roll (about OX-axis)

$ angle of yaw (about OZ-axis)

V displacement volume

cc) circular frequency, 2r/T, radians

Preface

Intact Stability

During the twenty years that have elapsed since publication of the previous edition of this book, there have been

remarkable advances in the art, science and practice of the design and construction of ships and other floating

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 finite element analysis, computational fluid 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 flexibility

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 analytical,

numerical, experimental and computational tools available to the naval architect and also the fundamentals 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 participating 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 sub￾division 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 transi￾tion is not yet complete. In shipbuilding as well as other fields, we still find 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 engineer￾ing 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 particu￾larly in illustrations taken from other, older publications. The symbols and notation follow, in general, the standards

developed by the International Towing Tank Conference.

Several changes from previous editions of PNA may be attributed directly to the widespread use of electronic com￾putation for most of the standard and nonstandard naval architectural computations. Utilizing this capability, many

computations previously accomplished by approximate mathematical, graphical or mechanical methods are now car￾ried out faster and more accurately by digital computer. Many of these computations are carried out within more com￾prehensive software systems that gather input from a common database and supply results, often in real time, to the

end user or to other elements of the system. Thus the hydrostatic and stability computations may be contained in a hull

form design and development program system, intact stability is often contained in a cargo loading analysis system,

damaged stability and other flooding effects are among the capabilities of salvage and damage control systems.

x PREFACE

In this new edition of PNA, the principles of intact stability in calm water are developed starting from initial stability

at small angles of heel then proceeding to large angles. Various effects on the stability are discussed such as changes

in hull geometry, changes in weight distribution, suspended weights, partial support due to grounding or drydocking,

and free liquid surfaces in tanks or other internal spaces. The concept of dynamic stability is introduced starting from

the ship's response to an impulsive heeling moment. The effects of waves on resistance to capsize are discussed not￾ing that, in some cases, the wave effect may result in diminished stability and dangerous dynamic effects.

Stability rules and criteria such as those of the International Maritime Organization, the US Coast Guard, and other

regulatory bodies as well as the US Navy are presented with discussion of their physical bases and underlying assump￾tions. The section includes a brief discussion of evolving dynamic and probabilistic stability criteria. Especial atten￾tion is given to the background and bases of the rules in order that the naval architect may more clearly understand

their scope, limitations and reliability in insuring vessel safety.

There are sections on the special stability problems of craft that differ in geometry or function from traditional

seagoing ships including multihulls, submarines and oil drilling and production platforms. The final section treats

the stability of high performance craft such as SWATH, planing boats, hydrofoils and others where dynamic as well

as static effects associated with the vessel's speed and manner of operation must be considered in order to insure

adequate stability.

J. RANDOLPH PAULLING

Editor

Table of Contents

An Introduction to the Series ...................................................................... v

Foreword ....................................................................................... vii

Preface ......................................................................................... ix

Acknowledgments ............................................................................... xi

AuthorlsBiography ............................................................................... xiii

Nomenclature ................................................................................... xv

ElementaryPrinciples ........................................................................ 1

Determining Vessel Weights and Center of Gravity ................................................ 9

MetacentricHeight ........................................................................... 11

CurvesofStability ........................................................................... 17

EffectofFreeLiquids ......................................................................... 30

Effect of Changes in Weight on Stability ......................................................... 38

Evaluation of Stability ........................................................................ 41

Draft, Trim. Heel. and Displacement ............................................................ 53

The Inclining Experiment ..................................................................... 59

SubmergedEquilibrium ....................................................................... 66

TheTrimDive ............................................................................... 72

Methods of Improving Stability. Drafts. and List .................................................. 73

StabilityWhenGrounded ...................................................................... 74

AdvancedMarineVehicles ..................................................................... 76

References ...................................................................................... 79

Index ........................................................................................... 83

1

Elementary Principles

1.1 Gravitational Stability. A vessel must provide

adequate buoyancy to support itself and its contents or

working loads. It is equally important that the buoyancy

be provided in a way that will allow the vessel to float

in the proper attitude, or trim, and remain upright. This

involves the problems of gravitational stability and trim.

These issues will be discussed in detail in this chapter,

primarily with reference to static conditions in calm

water. Consideration will also be given to criteria for

judging the adequacy of a ship's stability subject to both

internal loading and external hazards.

It is important to recognize, however, that a ship or

offshore structure in its natural sea environment is sub￾ject to dynamic forces caused primarily by waves, wind,

and, to a lesser extent, the vessel's own propulsion sys￾tem and control surfaces. The specific response of the

vessel to waves is typically treated separately as a ship

motions analysis. Nevertheless, it is possible and advis￾able to consider some dynamic effects while dealing

with stability in idealized calm water, static conditions.

This enables the designer to evaluate the survivability

of the vessel at sea without performing direct motions

analyses and facilitates the development of stability

criteria. Evaluation of stability in this way will be ad￾dressed in Section 7.

Another external hazard affecting a ship's stability is

that of damage to the hull by collision, grounding, or

other accident that results in flooding of the hull. The

stability and trim of the damaged ship will be considered

in Subdivision and Damage Stability (Tagg, 2010).

Finally, it is important to note that a floating struc￾ture may be inclined in any direction. Any inclination

may be considered as made up of an inclination in the

athwartship plane and an inclination in the longitudi￾nal plane. In ship calculations, the athwartship inclina￾tion, called heel or list, and the longitudinal inclination,

called trim, are usually dealt with separately. For float￾ing platforms and other structures that have length to

beam ratios of nearly 1.0, an off axis inclination is also

often critical, since the vessel is not clearly dominated

by either a heel or trim direction. This volume deals pri￾marily with athwartship or transverse stability and lon￾gitudinal stability of conventional ship-like bodies hav￾ing length dimensions considerably greater than their

width and depth dimensions. The stability problems of

bodies of unusual proportions, including off-axis stabil￾ity, are covered in Sections 4 and 7.

1.2 Concepts of Equilibrium. In general, a rigid body

is considered to be in a state of static equilibrium when

the resultants of all forces and moments acting on the

body are zero. In dealing with static floating body sta￾bility, we are interested in that state of equilibrium as￾sociated with the floating body upright and at rest in a

still liquid. In this ease, the resultant of all gravity forces

(weights) acting downward and the resultant of the

buoyancy forces acting upward on the body are of equal

magnitude and are applied in the same vertical line.

1.2.1 Stable Equilibrium. If a floating body, ini￾tially at equilibrium, is disturbed by an external mo￾ment, there will be a change in its angular attitude. If

upon removal of the external moment, the body tends to

return to its original position, it is said to have been in

stable equilibrium and to have positive stability.

1.2.2 Neutral Equilibrium. If, on the other hand,

a floating body that assumes a displaced inclination be￾cause of an external moment remains in that displaced

position when the external moment is removed, the

body is said to have been in neutral equilibrium and has

neutral stability. A floating cylindrical homogeneous log

would be in neutral equilibrium in heel.

1.2.3 Unstable Equilibrium. If, for a floating body

displaced from its original angular attitude, the dis￾placement continues to increase in the same direction

after the moment is removed, it is said to have been in

unstable equilibrium and was initially unstable. Note

that there may be a situation in which the body is stable

with respect to "small" displacements and unstable with

respect to larger displacements from the equilibrium

position. This is a very common situation for a ship, and

we will consider cases of stability at small angles of heel

(initial stability) and at large angles separately.

1.3 Weight and Center of Gravity. This chapter deals

with the forces and moments acting on a ship afloat

in calm water. The forces consist primarily of grav￾ity forces (weights) and buoyancy forces. Therefore,

equations are usually developed using displacement,

A, weight, W, and component weights, w. In the "Eng￾lish" system, displacement, weights, and buoyant forces

are thus expressed in the familiar units of long tons (or

lb.). When using the International System of Units (SI),

the displacement or buoyancy force is still expressed

as A=pgV, but this is units of newtons which, for most

ships, will be an inconveniently large number. In order

to deal with numbers of more reasonable size, we may

express displacement in kilonewtons or meganewtons.

A non-SI force unit, the "metric ton force," or "tonnef,"

is defined as the force exerted by gravity on a mass of

1000 KG. If the weight or displacement is expressed in

tonnef, its numerical value is approximately the same as

the value in long tons, the unit traditionally used for ex￾pressing weights and displacement in ship work. Since

the shipping and shipbuilding industries have a long

history of using long tons and are familiar with the nu￾merical values of weights and forces in these units, the

tonnef (often written as just tonne) has been and is still

commonly used for expressing weight and buoyancy.

2 INTACT STAB1 llTY

With this convention, righting and heeling moments are

then expressed in units of metric ton-meters, t-m.

The total weight, or displacement, of a ship can be

determined from the draft marks and curves of form,

as discussed in Geometry of Ships (Letcher, 2009). The

position of the center of gravity (CG) may be either cal￾culated or determined experimentally. Both methods

are used when dealing with ships. The weight and CG of

a ship that has not yet been launched can be established

only by a weight estimate, which is a summation of the

estimated weights and moments of all the various items

that make up the ship. In principle, all of the compo￾nent parts that make up the ship could be weighed and

recorded during the construction process to arrive at

a finished weight and CG, but this is seldom done ex￾cept for a few special craft in which the weight and CG

are extremely critical. Weight estimating is discussed in

Section 2.

After the ship is afloat, the weight and CG can be ac￾curately established by an inclining experiment, as de￾scribed in detail in Section 9.

To calculate the position of the CG of any object, it

is assumed to be divided into a number of individual

components or particles, the weight and CG of each be￾ing known. The moment of each particle is calculated

by multiplying its weight by its distance from a refer￾ence plane, the weights and moments of all the particles

added, and the total moment divided by the total weight

of all particles, W. The result is the distance of the CG

from the reference plane. The location of the CG is com￾pletely determined when its distance from each of three

planes has been established. In ship calculations, the

three reference planes generally used are a horizontal

plane through the baseline for the vertical location of

the center of gravity (VCG), a vertical transverse plane

either through amidships or through the forward per￾pendicular for the longitudinal location (LCG), and a

vertical plane through the centerline for the transverse

position (TCG). (The TCG is usually very nearly in the

centerline plane and is often assumed to be in that

plane.)

1.4 Displacement and Center of Buoyancy. In Sec￾tion 1, it has been shown that the force of buoyancy is

equal to the weight of the displaced liquid and that the

resultant of this force acts vertically upward through a

point called the center of buoyancy, which is the CG of

the displaced liquid (centroid of the immersed volume).

Application of these principles to a ship, submarine, or

other floating structure makes it possible to evaluate

the effect of the hydrostatic pressure acting on the hull

and appendages by determining the volume of the ship

below the waterline and the centroid of this volume.

The submerged volume, when multiplied by the specific

weight of the water in which the ship floats is the weight

of displaced liquid and is called the displacement, de￾noted by the Greek symbol A.

1.5 Interaction of Weight and Buoyancy. The attitude

of a floating object is determined by the interaction of

the forces of weight and buoyancy. If no other forces are

acting, it will settle to such a waterline that the force of

buoyancy equals the weight, and it will rotate until two

conditions are satisfied:

1. The centers of buoyancy B and gravity G are in the

same vertical line, as in Fig. l(a), and

2. Any slight clockwise rotation from this position,

as from WL to WILl in Fig. l(b), will cause the center

of buoyancy to move to the right, and the equal forces

of weight and buoyancy to generate a couple tending to

move the object back to float on WL (this is the condi￾tion of stable equilibrium).

For every object, with one exception as noted later, at

least one position must exist for which these conditions

are satisfied, since otherwise the object would continue

to rotate indefinitely. There may be several such posi￾tions of equilibrium. The CG may be either above or be￾low the center of buoyancy, but for stable equilibrium,

the shift of the center of buoyancy that results from a

small rotation must be such that a positive couple (in a

direction opposing the rotation) results.

An exception to the second condition exists when the

object is a body of revolution with its CG exactly on the

Fig. 1 Stable equilibrium of floating body

INTACT STAB1 llTY

I

Fig. 2 Neutral equilibrium of

axis of revolution, as illustrated in Fig. 2. When such an

object is rotated to any angle, no moment is produced,

since the center of buoyancy is always directly below

the CG. It will remain at any angle at which it is placed

(this is a condition of neutral equilibrium).

A submerged object whose weight equals its buoy￾ancy that is not in contact with the seafloor or other ob￾jects can come to rest in only one position. It will rotate

until the CG is directly below the center of buoyancy. If

its CG coincides with its center of buoyancy, as in the

case of a homogeneous object, it would remain in any

position in which it is placed since in this case it is in

neutral equilibrium.

The difference in the action of floating and sub￾merged objects is explained by the fact that the center

of buoyancy of the submerged object is fixed relative to

the body, while the center of buoyancy of a floating ob￾ject will generally shift when the object is rotated as a

result of the change in shape of the immersed part of

the body.

As an example, consider a watertight body having a

rectangular section with dimensions and CG as illus￾trated in Fig. 3. Assume that it will float with half its

volume submerged, as in Fig. 4. It can come to rest in

either of two positions, (a) or (c), 180 degrees apart. In

either of these positions, the centers of buoyancy and

gravity are in the same vertical line. Also, as the body

is inclined from (a) to (b) or from (c) to (d), a moment

is developed which tends to rotate the body back to its

original position, and the same situation would exist if

it were inclined in the opposite direction.

1- 20 cm -4

Fig. 3 Example of stability of watertight rectangular body.

floating body.

If the 20-em dimension were reduced with the CG still

on the centerline and 2.5 em below the top, a situation

would be reached where the center of buoyancy would

no longer move far enough to be to the right of the CG as

the body is inclined from (a) to (b). Then the body could

come to rest only in position (c).

As an illustration of a body in the submerged condi￾tion, assume that the weight of the body shown in Fig.

3 is increased so that the body is submerged, as in Fig.

5. In positions (a) and (c), the centers of buoyancy and

gravity are in the same vertical line. An inclination from

(a) in either direction would produce a moment tending

to rotate the body away from position (a), as illustrated

in Fig. 5(b). An inclination from (c) would produce a mo￾ment tending to restore the body to position (c). There￾fore, the body can come to rest only in position (c).

A ship or submarine is designed to float in the upright

position. This fact permits the definition of two classes

of hydrostatic moments, illustrated in Fig. 6, as follows:

Righting moments: A righting moment exists at any

angle of inclination where the forces of weight and buoy￾ancy act to move the ship toward the upright position.

Overturning moments: An overturning moment

exists at any angle of inclination where the forces of

weight and buoyancy act to move the ship away from

the upright position.

The center of buoyancy of a ship or a surfaced sub￾marine moves with respect to the ship, as the ship is

inclined, in a manner that depends upon the shape of

the ship in the vicinity of the waterline. The center of

buoyancy of a submerged submarine, on the contrary,

does not move with respect to the ship, regardless of the

inclination or the shape of the hull, since it is station￾ary at the CG of the entire submerged volume. This con￾stitutes an important difference between floating and

submerged ships. The moment acting on a surface ship

can change from a righting moment to an overturning

moment, or vice versa, as the ship is inclined, but this

cannot occur on a submerged submarine unless there is

a shift of the ship's CG.

It can be seen from Fig. 6 that lowering of the CG

along the ship's centerline increases stability. When a

righting moment exists, lowering the CG along the cen-