29(昭 和31年5月

A Proposed

造 船 協 会 春 季 講 演 会 に 於 て 講 演)

Standard
Passengerof Stability
Ships

for

(Part III : Ocean-going and Coasting Ships)
By

andYoshihiro Watanabe,
Shosuke Inoue,
Yasubumi Yamanouchi,
Daikaku Manabe,
Mamoru Uchida,

Kogakuhakushi, Member*,)
Kogakuhakushi, Member")
Kogakushi, Member*6)
Kogakushi, Member*7)
Kogakushi, Member*9)

Hiroshi Kato, Kogakuhakushi Member")
Mitsuo Sato, Kogakushi, Member*4)
Seizo Motora, Kogakushi, Member*6)
Yoshiro Masuda, Kogakushi, Member*s>

Abstract
The authors

have developed

Coasting Services.
Water

a standard

This standard

Area and Small Craftsof stability

was workedby the Ministryfor passenger

out in a similarof Transportation

ships in Ocean-goingmannersteering,

stability

such as wind,

as well as metacentric

whereuponfollows :thewaves,

shippingheight,dynamical

stability,

judgementof the( 1 ) Criterion by dynamical stability
Among external forces, effects of wind and waves
a ship is listed under

the staticalis subjected

dynamicallywindward.

In order thattransverse

the ship has sufficient( 2 ) Criterion by maximum
As external forces, shipping
GZm≧ 0.0215of the followingBGZm( 3 ) Criterion by metacentricheightAs the criterion by GM is same as thatpressure

and shift of passengersGM§ 1.

≧ 0.275

etc. :Let us assume
wind,

as

that,,and the ship.

angle of roll due to waves＋ ΣknB)B/100

aboard,steering,

etc.

have

formulae.

(m)for ships engaged

have been taken≧ (1.1Aharm,developed

stability,

shift of heavy weights

eitheror

aboard,C> 1righting armof sea water,

GZm must satisfy

beenmoment due to steadydynamicalof external

rightinghas

have been considered.

heelingof Tokyo andelements

maximumandfor Smooth

shift of weights

stability

to a gust when the ship is at the maximum
work ratio

been considered.

of sea water,of comprehensive

methodthatwith cooperation

Kyushu Universities,
Nippon Kaiji Kyokai, etc.
In preparing this standard,
investigations
have been made on various
forces affectingasin Smooth Water

Area when wind.

into consideration.
fΔ,

f≦B/5.5.

Foreword

The authors have recently proposed standards of stability for passenger ships in Smooth Water
Area [1] and for those of small size [2]. As a further extension of this series of work, theauthors

have successfully

Services,and they are pleased

The general
原 稿 受 付.
*1)
*6)

developed

task of working

昭 和 31 年 1 月 10

九 州 大 学 教 授.

*2)

東 京 大 学 助 教 授.

to present

for passenger

ships in Ocean—going and Coasting

it in this paper.

out standardsof stability

forpassenger

ships

has

thus

been

日

東 京 大 学 教 授.

*7)

a standard*3)

九 州 大 学 助 教 授.

九 州 大 学 教 授.
*8)

*4)

日 本 海 事 協 会.

運 輸 省 船 舶 局.
*9)

*5)

運 輸 省 船 舶 局.

運 輸 技 術 研 究 所.

30

造 船 協 会 論 文 集completed,at least

tentatively,

these proposed standards

The work has been drawn
RelatedRegulãtions

and theup by Ministry

Revisory

Universities,

NipponAssociation,

Shipbuilders'

Association

In the courseof preparation

carried[3],[4] and [5].

of Transportation

is expected

Law and its related

regulations.

of Transportation's

Panel " and thenand Kyushu

wereMinistry

into the Ships Safety

Kaiji

第 99 号

reviewed" Ships Safety

by a committee

Kyokai (classificationof Japan,of these standards,

society),

Japanese

Its

Tokyo

Shipowners'

comprehensive

investigationsof theproposed standard and how it has been arrived at.
In other countries, the United States [6] and U. S. S. R. [7] have their own standardsof sta-which do not however

papers,incorporate

the authors

attempt

and analyses

by those responsible.
an accountbility,to these

Law andrepresenting

etc.

out, and some of the works were made public previously
Referringto incorporate

the effect of waves.

to give

The authors

is the first to take such an effect into account.

It does not of course follow

regardIt is the authors'

this standard.standards

as consummate

be developed,§2.

makingthis standard

as a stepping

earnestthat theirs

that

the

hope that

authors

still betterstone.

Principles( 1 ) Classificationof Ships
The current regulations classify
ing,

in itself.

believe

Coasting

and Smooth Water

it is thought

unfairInland Sea service

to applyor thosethe plying limits of vessels into Ocean-going,
Areas.

the

For the purposesamerunning

standard

only a shortof applying

for Coasting

Greatera standard

ships to ships engaged

voyage out into Coasting

Coast-of stability,

Area.

These

in Setoships

should therefore
be treated separately.
'Coasting ships encounter no noticeably

On the other hand,different sea conditions

Ocean-going ships and Greater
so that they may be dealt within the same category.

all ships,

thoseof Smoothand Greater

Coasting)

Consequently,,divided into the following( i)

Ocean-going(ii)

Coasting-I

(iii)

three

classes(Regulations'(Regulations'

Ocean-going
generalthe worst

stability

define such a worst
in every

Water

Area,

can beCoasting)

Coasting-II (Regulations'
Coasting ships but navigating in Seto Inland Sea only, orwith scheduled voyage less than 2 hours in the Coasting Area.)( 2 ) Conditions of Ships
A ship must maintain ample stability
takeexcept:condition

possible service

veral

conditions

givingdue regard

conditionin all service

conditions.

alone as the basis for criterion.

in a simple manner.

condition is a nuisance.

On the otherTheof a ship and to see if the requirement

Table

to size and plying limits of ships,
1

best

It

is therefore
However,hand,solution

sufficient

calculation

thereforeof stability

is to select se-

is met in these conditions.
have thoughtto

it is difficult to

fit to designate

The authors,thecondi-

A Proposed

tions

given

( 3 )
In

in

Table

Effective

1.

Standard

This

questionofwill

Stability

befordiscussed

Passenger

31

Ships

furtherin •˜

9.

Buoyancy

stability

calculation,itisnecessary

deemed it fit to adopt the following

todefineprinciples

thelimitsofbuoyancy.

Theauthorshave:( i ) Side-to-side erections and other similarly
ctures will be included in the buoyancy.

effective

superstru-(ii) ) If there is an opening in a part of the ship included in thebuoyancy,
and if such an opening has ineffectivemeans of closing
whetherin design,

strength

or watertightness,

it is considered open tosea. When the ship inclines past the angle of immersion of the lower
end of such an opening (hereinafter
called the angle of flooding),thebuoyancy
ntly,of the ship

the stability

is considered

no longer

effective.

Conseque-curve holds good only up to the angle fo flooding,

Fig.

1

as shown in Fig. 1.
§3.

External

Forcesandtheir

Estimation( 1 ) External Forces to be Considered
As the external forces affecting the stabilityof a ship, the following

factors

may be consi-

to ascertain

all the effects

dered :( i)Wind(ii) )

Waves

(iii)

Shipping(iv)

Shift of weightsof sea water
aboard( v)

Steering
etc.
It is very difficult, if not impossible,

under the present

circumstances,of these external forces and determine the stability required to withstand these effects. The authors have attempted to take into their account as much effects of these external forces, direct
or indirect,

as possible,and have finally adopted the methods given( 2 ) Elements of Stability to be Considered
Stability of a ship comprises various elements.
tric height,

dynamical

stability,

maximum

In usual practice,righting

in (3),(4) and (5) below.

such elements

arm and vanishingangle

as metacen-of stability

aregiven suitable values so as to insure ample stability for a ship in design.
If any two of thelast three elements, dynamical stability,
maximum righting arm and vanishing angle of stability,

are fixed, the third one may be approximatedelements

wereselectedas the measuresof stability( i)Dynamical

stability

(So)

(ii)

Maximumrightingarm (GZm)(iii) Metacentric height (GM)The authors have related these elements(1) above, and have workeda ship must conform.

automatically.

with the effects

out the following

threecriteria

of external(3),( 3 ) Criterion by Dynamical Stability
Among external forces, effects of wind and wa ves are consideredLet

us assume

heeling

momentthat,as shown

in Fig.

(due mainly to steadyand then the ship is subjected2,wind),

Thus,

the following

three

:

a ship is listed
and rolls

forces enumerated

in(4) and (5), to all of whichprimarily

Os underin the calculation .
the statical transverse

00 and 00' from side to side about Os,

to a gust when the ship is at the maximum angle of roll 00 win-

32

造 船 協 会 論 文 集

第99号

dward.

In order thator

the ship does not capsize,

Area ABC>

Area BFGD

Area AK'C>

Area K'FG'

Let Area

AK'C=b,Area K'FG'=a,

It follows

then

this

C mustis notto capsize.

and
(1)

unit,

cable to determine

It may be in orderC suggested

in the past,so many

amenableto calculation.

to add here thatthe theoretical

will be made to relate
forces

than

heavy

wind

the authors

weights

aboard,thatsteering,

therightingarm,righting

arm, in abstract

are coveredin (3) above,thatdata of sunken

it is notpracti-and exist-of other express

ions ofexamined before adopting

to ascertainHere,
terms,of ship,
ship'stheexternal

an attemptwith such other externalof seawater,

shift ofetc.

kiB=radius

centerline,

all

therefore,

as shipping

the case when a ship rolled to a swing end.

angle of roll Ca', displacement

B=breadthk2B fromfactorsthan

It contains,.

It is therefore

are aware

value is not an easy task.

the maximum

and waves

Let us consider

Letfrom available

be greater(1) above.

and calculate0', relative

elusive[4], [8], [9] and [10], which were thoroughly( 4 ) Criterion by Maximum Righting Arm
In giving an adequate value for the maximum
forcesship

however,the critical value of C empiricallying ships.

the expression

if thethat

4,

Let absoluteand moment of inertia

of gyration,

ap=accelarationand g=gravitational

acceleration,

angle of roll beI, thenof a pointP

at a distancethen

Therefore,

This equation implies that ap depends on GZ(0a')/B,
and also that the greater the value of
GZ(0a')/B, hence cep, the better the ship's righting ability from a swing end. The latter may
be expressed as :( 2)
Assuming

that

ing

conditionAsM,

a shiphas

is required

listedCa',for theship

to remain

and received

momentdue

to shipping

a suddenstableheeling

momentof M, the follow-

ofaboardthedimension

of

:

(3)
ship.
the

let

us

take

the

Then

the

arm

lengthship,

Magnitude
of

a

ship.

and henceofshippedof thistype

may be expressedseawaterandof momentof seawateror shift

is relative

to theas k4B.

If themovingweights

momentmay

athwartshipis causedbeweights

assumedby a force

relative

F,

to

the

size

Thus,

Therefore.

Substituting

this into equation(3), we have(4)

A ProposedStandardof Stability

forPassenger

Thus we have the same type of equationas (2).

abilitywith the degreeof a ship has an important

relation

33

Ships

It may be said therefore

that

the rightingof its safety.

The value of Ca' must be chosen when the ship has the least GZ and at the greatest
angle of heel.

Specifically,

it seems suitable

moment due to wind pressure

to takeand rolling due to waves

so easy and simple to obtain Ca' among irregularat GZm), and the form of GZ-curves
ships,

the maximum

it seems safe to determine

act simultaneously.

waves.

possibleangle of heel when the
It is not however

As Ca' is close to Cm (angle

does not seem to differ much from each otherof heelin different

GZm/B in place of GZ(Ca')/B.
(5)

As the criticalderivedvalue

of

is notfrom data of actual

Next,

as anotherupon the rudder

readily

amenableto theoretical

calculation,

ships.

type of M, let us take the moment due to steering.

be F,

it must be

and the distancefrom the ship's

Let the force acting

C. G. to the centerof effort F be h,

are far smaller

the critical

then,

Therefore,

In actual cases,
lues

the calculatedof GZm whichthought

unnecessary

values of this criterion

is given by equation
to take this factor(5) above and described

into consideration,( 5 ) Criterion by Metacentric Height
Ocean-going and Coasting ships must of course conformin Smooth Water
considered

Area

[1].

in a similar
Values§4.

As external

forces,exceptandto arriveat a suitablevalue of GM.

Wind

Velocity

and

of

Roll

to

be

ships.
forships

of passenger

are

Used

in

Criteria

types

by

their

:

(i )

Barometric

(ii)

Front

(iii)

Lows

gradient(iv) Typhoons
As depicted in Fig. 3, barometricfor a relatively

long duration,

gradients

but

their

and fronts

strength[2], barometricwind pressure

gradientof a margin for maximum
vessels[1] , front

In lows and typhoons,at theirangle of heel.),and for smooth water

centers,

where

steadythe wind velocity

3

crafts,momentIt seems infor Coasting—II class of ships.

as shown in Fig.

center,after that the trailingfor smallbut comes in the formof 15 m/sec have been assumed.

Fig.

of wind occur very frequently,
andIt may be recalled that, for small

directly,order then to take the front
strongestof 10 m/sec (In the standard

is not consideredblow

is not sogreat, being 10 to 15 m/sec at the strongest.
These types
are likely to attack ships near the coast without warning.
craft

vait isshift( 1 ) Type of Ocean Winds to be Used for Each Plying Limit
Ocean winds may be divided, according to the paper [3], into the following
cause

Thus,

to the basic requirements

wind pressureAngle

in § 7.

for high-speed

mannerofthanfurtherthe direction

wind continues
reaches

4, wind force is theis reversed,
to blow.

andAt theiras high as 32 m/sec in lows,

Fig.

4

due to

造 船 協 会 論 文 集34

and 50 m/sec in typhoons.
20 m/sec in typhoons
standard

In the trailingand accelerates

of stability,

steadyFrom the foregoing

discussions,

It seems appropriate

the latterlows,

sometimes

and forto setvelocity

to be used foras shown on Table 2.

2.

( 2 ) Sea Conditions in Storms 'and Their Effect on the Critical
Apart from barometric gradients and fronts as shown in Fig. 3,

Angle of Rolllows and typhoonsof theto ships

type as shown in Fig. 4 give rise to a question

as to where

it is the most dangerous

and thus the standard

us supposethat

ship'sposition.

its direction

should be based on.

At the center

180 degrees,Letof the typhoon,

thus causing

the

waves

of the ship is not so violent.

velocity

decreases

somewhat,heavierrolling

to the ship.

loped,

butwhere

eo is the angle

wind

but the waves
Amongstvelocityof rollingthat could have been developedFig.

It is impossible
wind and rolling,irregularity

As the typhoon centersteady wind,

to decrease.

and regularized

variesmoves away,inthe windregular,incurringis illustrated

in Fig. 5,

rolling among the waves

by the wind force at such a position.

angle of inclination

given in equation
as the centerathe waves become highly deve-This relation

5or C (=b/a)

and become very irregular,

and esyn is the angle of synchronous

to find how the criticalof waves

to interfere

throughbut it soon changes

grow and become increasingly

the trailing

continues

a typhoon passes

the wind is very strong,which the rolling

the

the

Ocean-going

may have to run into typh-

the type of wind and its approximate

limit rnay be summarized
Table

it may be up to 15 m/sec in lows andof the sea.

class ships as to withstandclass ships to hold against typhoons, becauseoons even though aware of such warnings.
each plying

wind,

the growthfor Coasting-I

第 99 号

(1),

Fig.

6

under

the

combined

effectsofshould vary unless it is known how themoves away.

However,in orderfor thevessels

A Proposed

havingthevalueof C=1higherwind velocity,Standardin thecalculationsof Stability

trailing

forsteadyPassenger

wind to manitain

based on a few examples

35

Ships

the conditionindicate

Tolling must be reduced

as shown in Fig. 6.

If the angle of rollingless thanthat of Fig.

6,follows

that the standard

that

at

the critical

angle

of

due to irregular

waves

is

6's AD-curve,itnamely,if Fig.

5's AD-curvecomes below

Fig.

of stability

may

be determinedbypoints,theof C=1

twocenterA andperiphery B, or by one mid-point P. The paper [4] chooses points A and B, but here the authors have chosen the other alternativeof a point in the middle of points A and B, where thewind force is a little
is a little

smallerstrongerthan that

Standard§5.

in the trailingwaves.

Value( 1 ) Steady Wind
As mentioned in §4,
selectedthan thatin the regular
of

Wind

the standard

value
the

Firstly,

from actual ship's

criticalangle

of rolling

Velocityat the middle point between

wind zone.

wind but theof thecenterstatically

incliningsteadywind velocity

of typhoon

or low,and thetrailing

data described

possible condition that may be encounteredby a ship,

later

is

steadyin § 7, and secondly from the worst

the standard

value of 26 m/sec for Ocean-going and 19 m/sec for Coasting-I have been adopted. For Coasting-II,
it was taken at 15 m/sec.
Inclining arm due to steady wind pressure will be calculated in the same manner as before :Namely,assuming

that

Where,

Da, = Inclining

the wind blows transversely,

it is given by( 6)

arm due to wind pressure(m)

V = Standard wind velocity (m/sec)
A = Lateral area of the part of the ship above waterh = Verticalheight

4 = Displacement of the ship (T)In addition, the effects of the angle of inclination( 2 ) GustinessAs shown in Fig. 2, the criterion
at the swing end to windward.

by dynamicalor the " gustiness,"must be determined.

'wholerange

In typhoons,and on the average

this value represents,of the minute features

made up of the average
duration.

only

In actual cases,

however,

may cause a ship to capsize are
ihalf

the

rolling

periodtheof ships,that a ship receivesof fluctuation
ratio

of gustiness

it is

it is 1.23.

Butof fluctuais

longthe fluctuations

thatof a duration

or , specifically

3 to 8Fig.

a gustin the wind velo-

7of a relatively
ones

here.

7 shows the( Vmax- V)/ V, which

fluctuation

point (m)assumesthe degree

for example,

1.7 at the maximum,in Fig. 8,

stability
Fig.

Fig.

tion as shownis neglected

For this purpose,(city,of storms .

line (m2)of C. G. of A above the half-draft

8

over the

造 船 協 会 論 文 集36

第 99 号

seconds.

It is apparently

too rigorous

to take-(fmax-V)/V
as the gustiness of a gust in Fig.
2. From this view point, duration and intensity ofgust are plotted along the base of average windvelocity and presented in Fig. 9. On the upper
section is shown the duration
lower section
relative

theof gust, and on the -corresponding

intensity.

gustiness,

This plot indicates

or-

that

( i ) Duration of gust may be divided roughly
into two groups :(ii)
Gusts of longer duration
intensity.
(iii)

As the averagegustiness

velocity

findings suggest

that,of a gust for the purpose
Furthermore,

9equationincreases,

the flfor the gustinessof Fig.

2,

relatively

small value should be assumed.

consideringrises above the staticalin.:decreases.

These
Fig.

are stronger

the tendency

center(6), and also thatthat,

under gusts,

under steady wind pressure,

the relative

wind velocity

the centerof reaction

thus reducing

thedecreases

due to drift

gustiness ratio of /1.5 (*1. 23) has been specified.
Consequently,
arm due to wind pressure becomes, from equation (6),of a ship

valueof thethe fluctuationof h in,
ship,

the-

in inclining
(7)

Waves

§6。

and

RollingofShips( 1 ) Relation between Wind and Wave
According to the famous paper by H. U. Sverdrup
w een wave steepness
expressed
is takenby the8 and wave

dottedthata windchronizes
thecertain

with

the

wave,

steepness

of

ship

having

that

is,

of

The

authors

adopt,

This

relation
figurebet--

can be-11 on the basis of wave period when the wind volocit,

Fig.
havingvelocity,

longersmallerin Fig. 10.

10a ship,oftheand W. H. Muuk [11], theas shown
1

Fig.

reforein Fig.

as a parameter.

Assuming
bylines

age [3 is given

the
the

that

is,

periodofseverestrolling

when

she
be

this

wave

can

periodofrollingrollingofTs,

encounters

this

ship

encountersobtained

with
from

may

only

wave

steepness

Fig.

synchronize

11
with

may

the

take

wave

11.
with

of

In

a
place
the

constant
thewave

originatedwhenperiod

she
T.

wind

wave

of

the

rollingsynThe-velocity,greaterage,

steepness.
asastandard,

thecorresponding

toperiodof.

A Proposed

the ship and standard
tion is put forthStandard

wind velocity

ofStabilityforby Fig.

11.

obtainedfor the convenience's

Passenger

Ships

In this case,the following

assump.

sake.

( i ) In the sea area where the wind of certain velocity blows, the wave originated by thewind of smaller velocity can be co-existed.
In other words, for all periods smaller than thosecorrespondingof 8.

to the maximum

values of 6-curves,

maximum

value of 8 is taken as the value(ii) ) Although Fig. 11 indicates that the steepness of the waves of longer period becomesvery small, 0.035 (*1/30) is taken as the minimum wave steepness taking into account theswell transmitted from other sea area and the irregularityof waves.
(iii)
ording6-curves between the maximum and minimum wave steepnesses
thus determined 133
to (i) and (ii) may be regarded as straight lines as obviously shown in Fig. 11.

From the above assumptions,
given by solid lines in Fig.
wind velocity.

the wave steepness

11 according

to be used for the standard

to the rolling period of actual( 2 ) Synchronized
Rolling Angle amongst Regular Waves
The synchronised rolling angle of the ship amongst regularfollowingwaves

is derived

ships and the standal

can be deserminedby theformula.
(8)

Where,

Althoughpaper
takingy as

the precise

the

to

value

into

account60

actualformulaof y has been developedof 7 is calculated
the
ships

fact
are

that
as

the

shown

by Y. Watanabeby the following

formulacalculated

of

in

Fig.

valuesfor the[14] and [15] , in thissake of simplification,

12.

( 9)
Where,

d = Draft of ship (m)OG = VerticalcenterConcerning

distance from the waterof gravity

line to theof the ship (m)(Positive above water line)
N, since there is no reliable

formula

or

Fig.

12

curve at present, it is taken as 0.02 provisionally for ships of ordinary form having bilge keel.
In determining 6 from Fig. 11, T is obtained by H. Kato's presumption method [16] and [10]or by Rollzahl method where it is unknown.
( 3) Irregularity of Waves
As both period and height of ocean waves are irregular, the rolling of ships amongst them
are not uniform. With regard to the irregularity of waves, it is known that there are a few
statistical laws ; that is, as ascertained by Jr. G. Neuman [17], when the wave frequency istaken as coand the amplitude r (co), the spectrogram of the wave [r(co)]2 has approximately
constant

distribution

It hasalso been

as faras theascertained

fully arisen sea is concernenedby M. S. Longuet-Higgins[18] thatas exemplified

in Fig.

between

area

the

14.

of this[r(o)]2
curve,
R(w)=f o[r(co)]2da)(whichis calledascumulative
energydensity),andthestatisticalquantityoftheirregularity

of

waves

the

relation

indicated

by

Table

3 exists.

造 船 協 会 論 文 集

38

Table

On

the

other

sionallythewhenobservingtheheightof thebiggestwave

of waves

passingby increases.

heightnumber

3.

hand,

come,

第 99 号

Tableof whicha series

variesincludedof waves,

accordingtoin the

group

This

relation

exceptionallythenumber

the

waves

of

big

waves

may

occa-

of waves

passingbyandusually

is indicatedin Tableincreases

as

the-t

has different

as-

4.

4.

( 4 ) Rolling of Ships amongst Irregular
It is a matter of course that the rollingWaves
of ships amongst

irregular

waves

pects from that amongst regular waves.
One of them is that, whilst the resonance curve in
irregular
waves has a steep crest at the synchronism,in irregularwaves the crest of the
curve
of

at the

waves

come

synchronism

enoughsuccessively.

trary,

there

that

waves

nally

come.

becomes

low,

cause

the

perfect

Outsideoftois a possibility,of thenearlyConsequently

the

the

numbersynchronism

synchronism,

do

not

on thecon-

due to the irregularityof waves,

synchronizedperiodmayoccasio-therolling

curve

tends

to be as

is

shown

Fig.

13.

The

other

one

waves

big

and

small

rolling

angleson therolling

amplitude

becausesimilarsinceinirregular

are

that,

mingled,theanalysesto those

on

the

wave

ampli-

tude indicate
cumulative

that

Fig.

13

the

relationis the same as those given
and Table 4 mentionedWith

regardamongstirregular

oreticalsolution.

tempt

to carry

3

rolling

waves,of ships

M. St. Denis.

[19] state on the theNow, the authors
out thecalculation

atin

with this method.

Since the significant
a seriesin Tableabove.

to theand W. J. Pierson

accordance

between-energy density and amplitude,

wave

of waves having

heighttheofspectro-gram as shown in Fig. 14 is given by
1. 416 VR according to Table 3, this,.
Fig.

14

value coinsides

with

the

wave

height..

A Proposed
when

such

amongstsolid

seriesunit

line

in Fig.

14 cancomputingarerepresentedbyhavingsuch

a height

and frequency

15.

Thence,be derived

theenergyfromof ships.

As shown

meanamplitude

is far smaller

amplitude

waves

and

lings

occasionallyoccur.

tterof the probability

be taken.

Whenrolling

amplitudeout

isconsidered

fact

that

that of a gust,

Now,

let

curve

of theirregular

waves

distributed

shownby dotted

lines

amongst
Table

4 as

us

assumethat,ship is givenbyas shown

in Fig.

15 by

that

questionbigrolma-

the maximumof rolling

the

into
rarelymaximum

account

thecoinsides

with

Fig.

it becomes approximately

On the other hand,the experiments

wave.

col, resonaceof 20 to 50 rollings

takingits phase

3 and

39

the

It is thenumbershouldangle

regularShips

significant

is

that

what

of

The

however,

among

Table

than

the

to be considered,rolling

thefor Passenger

in the figure,is also smaller.

amplitude

thedensityrolling

in irregularof Stabilityof waves

waves

in Fig.

Standard

the rolling

0.7 time the rolling

angles,calculated

15

amplitudeby equation

amongst(8) accordingof NISSEI MARU [20] and HOKUTO MARU, amongst

possibly caused by the wind velocities at the time of experiments
lines in Figs. 16 and 17 respectively ; whereas the rolling angles

regularwaves..

to the results

the synchronized

of

waves

are as expressed by the solidmeasured then are as plottedin the same figures. As these measured values indicate the heel angles including the effect of
the wind rather than the rolling angles, they must be bigger than the rolling angles theoretically.

However,valuesby equation

both in Fig.

Fig.
Takingtheintosynchronized

16 and 17, they are

considerably

smallerthanthecalculatect.

(8).

account

16
therolling

afore-mentioned
angle

amongstfact,
regulartherollinganglerolling

angle,

Fig.

17

of

a shipis takenas

0 .7 timewaves.

Accordingly,

Therefore,

from equation(8),

we have

From the above and from §4 and §5 wind,
be as given in Table 5.

wave,

etc.

eventually(10)
become to40

造 船 協 会 論 文 集
Table

5.

Determination

§7.

of

( 1 ) Critical Value of C
Fig. 18 indicates the values
ships

having

第 99 号

availabledata,

Stability

Criterions

of C (=bla)calculatedusing equations(6),

by equation
(7),

(9),

(1) as to 57 conditions(10) and Fig.

11 andvelocity of steay wind within the range of 15 m/sec to 30 m/sec.
The
made on the worst stability conditions that the ships may be subjected.

of 50

takingthecalculation has been
In determining
thecriticalvalue of C from this figure, attention is to be paid to the following ships .
C-3 indicates the condition, at the time of casualty, of a sunken passenger ship (CoastingII).
C-19 and 20 are for passenger ships which have been given warning due to the insufficie
ncy of the stability.

For these ships it is rather

C that does not reach to the critical
existing passenger ships (Coasting-II).
C-7 is for a passenger

value.

ship (Coasting-I)

GZm,

which

will be mentioned

later,

than

C-2, 6, 16, 18, 21, 22, 23, 24, 25 and 27 are forwhich

has been found safe after

rolling

to about 23

degrees under the wind of 17 m/sec velocity.
C-8-I represents
the condition, at the time ofcasualty,
of a sunken passenger ship (Coasting-I); C-8-II the full loaded condition in which
the stability

was consideredinsufficient,thewas adequate.

C-9 is for an existingstability

angle
the

of flooding

is about 24 degrees

upper deck.

present
C-13-II

and C-8-III

If this opening

Aomori and Hakodate

passenger

after
ship

due to the opened stairway

is effectively

the condition, at the time
the full loaded condition

the condition

closed,the renovation(Coasting-I)

in which

in which

located at the ship's

C will increase

considerably.

theside of

C-13-I re-of casualty, of a sunken passenger ship (Coasting-I),
andof the same ship.
C-28 to 37 are for ferry boats between(Coasting-I),

Althoughsome valuesof C, for instance

C-34-I,

represent

the condition, at the time of casualty, of the sunken ship, the critical value of C for Coasting-I can not be determinedfrom these data , because the weather condition at sea then was considered abnormal as for this coasting area.
C-35-I and 37-I represent the condition of the ships
which
are

stood against

for existing

the stormy

passenger

weatherat thattime.

C-1, 4, 5, 10, 11, 12, 14, 15, 17 and 26

ships (Coasting-I).

0-1 and 2 are for cargo ships (Ocean-going)
which were deemed to have insufficient stability.
For these ships GZm is under critical value, mentioned later, rather than the value of C. 03, 7 and 9 are for existingdeck•were

excludedpassengerfrom the effective

ships (Ocean-going).
buoyancy

for these ships, actual

due to the effect of superstructures.

0-8 to 11 are forwhich

represents

have ample stability.

a sunkentorpedo boat (Ocean-going),

the stability
sunkenFrom

0-12-Ihas been made ample.

destroyerthe(Ocean-going).

above

data,

As the structures
large

and C-12-II

the condition

0-13 represents

the condition,

0-4,

5 and 6 are for existing

it is consideredadvisable

to takein orderto compare

the above criticalships(Ocean-going)at the time of casualty,

after

the renovation

the criticalvalue of C (C =1.0)

ofin whichat the time of causalty,
passenger

standard wind velocities of 26 m/sec, 19 m/sec. and 15 m/sec according-I and Coasting-II respectively .
Next,

upper

value of C may increase

passenger

the the condition,

above theof aships (Ocean-going).
value of C as 1.0 for

as Ocean-going,with thecriticalCoasting
valueofA ProposedStandardof Stability

forPassenger

Ships

41

,C1(C1=0 .8) described in the paper [4], calculations have been made according to both methods,
whereupon it has been ascertained that C1 (Coasting)=0.8 corresponds to C=1.0 when the standard wind velocity to be used for Fig. 2 is taken as 18 to 20 m/sec, and that C1 (Greater Coasting and Ocean-going)=0.8 corrosponds to C=1.0 when taken as 25 to 27 m/sec. Accordingly
the judgement that the critical value of C is taken as 1.0 in association with the standard windvelocity of 26 m/sec and 19 m/sec for Ocean-going and Coasting-I respectively has approximately
the same severity as that presented by the paper [4].

Fig.

( 2 ) Critical Value of GZm
In Fig. 19 GZm are plottd against
havingavailable

stability,
abnormal

into accountvalues C for C-8-II,

though their

(5),

as

to 117 ships

to take the criticalor ships

havinginsufficientwindvelocity

and that

among

sunkenvalue of GZm as 0.0215 B and

12-II and 13 do not reach to 1.0 for standard

GZm are not small,stormy weather

advisable

the fact that,ships

C-28 to 30 are for ships

as for Coasting-I( 3 ) Critical Value of GM
As a a critical value of GM, the standard
adopted.

to the idea of equation

data.

From this figure it is considered
0.275 m, taking

B, according

18

al-

which

were

sunkenunder

in Smooth

Water

Area

[1] isarea.

for ships engaged

造 船 協 会 論 文 集

42

Fig.

S tandard

§8.

( 1)

Criterion

In Fig.

of

Stability

moment

lever

19

of C

20, draw

Du, parallelto theline, take rolling

angle 00 to the windward(left

K, the intersectionof Du, with the stability

curve,

draw moment lever

due to gust, 1.5 Dip, parallelline.

When the areasand "b"In this第 99 号

case stability

curve

is limited

respectively,

introducing

these

to the

angle

of

20.

wind velocities

19 m/sec and 15 m/sec for Ocean-going,asting-II

as "a"

thenflooding 01 as shown in Fig.
Since the standard

and thento the base

K'FG' and AK'C are denoted

respectively,

baseside) fromare taken

Coasting-I

Dx can be obtained

values into equation

as 26 m/sec,
and

Co-

as follows

by

(6) :
Fig.

20

Where,

00 can be obtained

from equation

7 can also be obtained
is,

8 can

Fig.

21

be determinedfrom equation

by drawing

as to the standard

windvelocity,

wn in Fig.

From

this

21.

(10), thatfigure,

(9),

is,,

that

Fig.

11 Ilcurves

which

is as sho-

we obtain

A ProposedStandardof Stability

for Passenger

Ships

43;

Where,

N is taken as 0.02 for ordinary( 2 ) Criterion of GZin
GZm must satisfy either

ships havingof the followingbilgekeel .

formulw.

In this case, GZm is taken as the maximum

value of GZ withinthefor ships

inangle of flooding 01, as shown in Fig. 22.
( 3 ) Criterion of GM
As the criterion of GM is the same
Smooth Water

Area[1], only it's

as thatresultis describedengagedbelow .

Fig.

22

Where,

Application

§9.

of

the

Standard( 1 ) Standard of Stability and Condition
Since, in applying the standard of stability,of

Stabilityof Ships
calculations

as to all service

conditionsof a ship,

are difficult and complicated,the conditions

listed in Table 1 have been adopted as mentioned§2 (2).

however,are otherIn actualservice,therevariousconditionsof the ship than

in

those

given in Table 1, and therefore even if a ship has been found to comply with the standard..
of stability in all conditions given in Table 1, the ship can not always be regarded
as having
sufficient stability.

On the contrary,failed to comply with thelstandard,as such unsatisfactorysures,

In otherconditions

even if there

are some conditions

in whichthe ship may not always be considered
can be avoided by means of ballastinga shiphas

unsatisfactoryso longor by other suitablemea-words,

the _ship may be considered satisfactory
if her conditions are restricted
to those in which she can comply with the standard.
Accordingly it is consideredmore advi
sable to adopt the following
given in Table 1.
As the factors necessary

methodthan to make calculations

for the calculationof the criterions

6, the criterions can be calculated when the draftof gravity of the ship KG (GM) are given.
Assuming
intervals
that

derivedFig.

23

are classified

as to conditions.

as shownof the ship d and the positionin Table-of the center

that the drafts of the ship are d1, d2, d3, ... taken at equal..

withinthe

GM corresponding

intervals,of the criterions

range

of minimum

to respective

value of C for eachand maximum

assumedcombination

as shown in Fig. 23. As the relation

make C=1 is obtained

from this figure,drafts

aredraftsandat equalof d and GM can bebetween(i)-curve

d and GM toin Fig. 24 can be,

14

造 船 協 会 論 文 集
Table

第 99 号

6.

Fig.

Fig.
Fig.

drawn.

With

26

25

24

regardto T8 in the calculationof C, the curvedrawnTon

GM as shownin Fig. 25 (which is an example when H. Kato's presumption

may facilitate

the calculation.

thebasis of d andmethod [16] is used)

In the calculation of GZm, the relation between d and GM to satisfy Fig. 26 and to make GZm=0.0215 B or 0.275 m can be obtained as shown by (ii)--curve in Fig . 24 in the similar manneras in the case of the calculation

of C.

The criterionof GM can also be obtained as shown by(iii)-curvein Fig. 24 when required GM for the above-mentioned
d1, d2, d3, ... are calculated.
From these curves, the relation between d and GM that the ship comply with the standard
can be determined
Therefore
easilyas illustrated

whetherbe judged by plottingThis calculation
method24.

methodin the condition given

d and GM in these condition

tions of the ship can be restrictedcalculationin Fig.

the ship complies with the standard

thecondi-

form this figure so thatby assuming

as to certain

in Table 1 canon Fig. 24, and moreover

she can comply with standard .
d and GM is advantageouscompared with the direct

chosen conditions.

( i ) When the lines of a ship are given, the range within which the ship complies withthe standard can be obtained as shown in Fig. 24 before the execution of the inclining test.

A

After

the inclining

whether

Proposed

test,Standardof

Stability

at theinclining

test,

stage

Passenger

it can be judged only by plotting

the ship complies with the standard.

estimatedforof initialdesignit is not necessary

Ships

GM against

Even where

the centerhas been found different

to calculate

45

the standard

d in eachof gravity

from thatagain,

condition,of theobtainedbut sufficient

ship

by

the

to correctthe-.

plots of GM in Fig. 24.
(ii)
Standardin Fig. 24.

of C, GZni, and GM can be expressed

only on the basic of d and GM as shown(iii) The value of GM computed by the operator of a ship can be checked from the value.
of Ts by adding Fig. 25 to the data previously supplied to the operator for the purpose of cormputing GM. Moreover,by furnishing
Fig. 24 to the operator,
GM value whether the ship complies with the standard.

he can easily

judge by only(iv) Passenger ships engaged in international
voyage are subjected to Ship Subdivision Regulations and are required to maintain the specified stability (GM) in non-damaged condition inorder to insure safety at the time of damage.
Since both standardsof stability,
proposed inthis paper and required

above, can be expressed

comply with these both standards

can readilyon the basis of d and GM, whether
be judged by plotting( 2 ) Disposition for Exceptional Ships
In applying the standard, there are some ships, for instancedirectapplicationof the standard

judged in each particular

is not consideredcase by making

those described

appropriate.

investigations

the lattertheseships,

on Fig. 24.
below,

to which

In such cases the stabilityison each ship.

(i )Ships having extraordinary
flare, tumble
the standard of GM is not appropriate.

(ii)

Ships of special form or having
applicable to take N as 0.02.

(iii)

Ships in which an excessive amount of sea water is liable to be shipped and containedon upper deck due to the special feature of the structural arrangementon the upper deck.

(iv)

Ships of speciallyetc.

bilge keels of special

high speed which are excessively

to which the application

form or size in which

heeleditofis notdue to steering,

Conclusions§10.

In thehome, bulge,

forgoing,

the authors

have attemped

to describe- the particulars

paring the standard of stability for passenger ships engaged
vices, which may be summarized as follows :and process

in Ocean-goingin pre-and CoastingSer-( 1 ) The standard of stability for passenger ships has been developed, and is in the processof legislation as the first Govermental Regulations respecting stability in Japan.
( 2 ) Previous to other countries,
ted by the Goverment.
(3)

Investigations

effect of waves

have been made on various

has been introduced

elements(steady wind and gust), wave, shipping of sea water,
well as the effect of external force, metacentric height,arm,

etc. ; whereupon

the methodof comprehensive

affectingin the standard

stability,

such

as

adopwindshift of weights aboard, steering,asdynamical stability, maximum righting

judgementof the stability

has been deve-

loped.
( 4 ) Stability of ships to be complied with the standard could be indicated by the draft andthe corresponding metacentricheight, which has enabled operators to judge the stability fromthe metacentric
Regulations,same elements

heightalone.

Accordingly

the stabilityof a ship specified

by Ship Subdivision

which was dealt with separately(draftand metacentric

It would be needlessto emphasizein the past , can be judged simultaneously
height) as dealt with in this paper .

the importanceof the stability

here .

Numberby theof countries

446

造 船 協 会 論 文 集

whichlegislateestablishedfuture,thethemoreover,ernational

stability

standard

regulations
it would

would

第 99 号

be increased,

investigations

would

be conceivable

that

be
the

and

in countries

which

in viewof revising

them.

In

of stability

be adopted

in theInt-

progressed
standard

have

already

Convention.

The

standarddeveloped

many

provisions

to be revised.

made,

the

standard

standard

would

be

by theauthorscannot

It is strongly

alwaysmaintained

be declared

hoped,
into be a complete

therefore,

modernizedthatconditionone,

furtherandcontaining

investigations

eventuallybea perfect

be developed.
References[1]

M. Sato, Y. Yamanouchi,
S. Motora
for Passenger
Ships,Part I ; Smoothchitectsof Japan,Vol. 95.

[ 2]

M.
for
of

[ 3]

Sato,

Vol.

on

tects

of

Y.

M.

[ 7]

"

United;MotoraandM.

UchidaStandard

Small

Crafts,"JournalD.

Manabe

Vol.

97.

N.

Yamagami,ofandJournalStatesS.

Architectual

JournalMizushina

Inspection,

19,

Japan,

Ships,II

Yamagami,

Naval

Watanabe,

going

[ 6]

N.

the

S.
Part

Standardof Stability
Societyof Naval
Ar-

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"A

ProposedoftheSociety:" ReportofofSociety

of

of

Naval

the

Ocean

Stability
Architects

96.

Watanabe,

Japan

[ 5]

Yamanouchi,
Ships,

Japan,
Y.

[ 4 ]

Y.

Passenger

and M. Uchida: " A Proposed
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" The

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D.

Naval

and

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the

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ArchitectsofJapan,

Regulations

for

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StabilityofStandard

of

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"

Passenger

Vol.

Archi-

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Wind about
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Vessels,

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PeH-

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MopekroлOBbIX

PerHcTpa

CYлOB",CCCP

HOЯбPЯ,:" BpeMeHHbIe

HopMbIOCTOHHHBOCTH.„|„|„`

ToproBbIX

1947.

[8]

Y. Watanabe : " Safety Criterion of a Ship Considered from the Stability, " Journal of
the Society of Naval Architects,
Vol. 79.
[ 9] H. Kato : " On the Stability of Small Sea-going Vessels, " Journal of the Society of Naval Architects,
Vol. 83.
[10] H. Kato : "A Simple Judging Method for the Stability Qualitiesof Ships, " Journal of
the Society of Naval Architectsof Japan, Vol. 98.
[11] Sverdrup H. U. and W. H. Munk : " Wind, Sea and Swell ; Theory of Relations for
Forecasting, " H. 0. Pub. 601.
[12] " Techniques for ForecastingWind Waves and Swell, " H. 0. Pub. 604.
[13] Bretschneider
C. L. : " The Generation
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[14] Y. Watanabe : " On the Characters of the Rolling Motion of Ships on Waves, " Journalof the Society of Naval Architects of Japan, Vol. 56.
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[16] H. Kato : " On a Method for Calculating
an Approximate Value of the rolling Period of
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[19]

M. St. Denis and W. J. Pierson : " On the Motion of Ships in Confused Seas, " T. S. N.
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[21]

J. Rahola : " The
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Judging" 1939.

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the

Minimum