65

A Proposed(昭 和29年5月

造 船 協 会 春 季 講 演 会 に於 て講 演)

Standardof Stability

forPassenger

Ship

Smooth Water Area)(Part I

Kogakushi,Member.
By Mitsuo Sato,
Yasubumi Yamanouchi, Kogakushi,Member.
Seizo Motora,
Kogakushi,Member.
Mamoru Uchida,
Kogakushi,Member.
§ 1.

Introduction

Need of a suitable standard of stability for ships has long been recognized, in view of promoting safety of lives and vessels at sea. The problem is, however, rather complex .and involves
so many difficulties, and it may be said that little development of significance has been madein this field in Japan.
At present, in conjunction with the program to revise various regulations under the new Ships
Safety Law, a drafting board has been set up within Ministry of Trasportation, and the workon establishing standards of stability for various types and duties of vessels are now being in
steady progress with the cooperation of Tokyo and Kyushu Universities, Nippon Kaiji Kyokai(Japan Maritime Corporation), etc.. As the first step, a standard of stability for ships engaged
in Smooth Water Service has been developed, and inspections based on this standard have been
in force since the beginning of this year. The authors intend to describe the basic principles
and process followed in preparing this standard, and would like to have wider recognition andcriticism on our scheme.
The standard cannot be declared, of course, to be a perfect one, containing many an open
question in itself, and any unreasonable provisions are subject to`amendment in the future. It
would be nevertheless of interest to note that a standard has been established, in that it may
at least be utilized as a measure to compare stabilities of different vessels. It is strongly hoped
that, making this standard as an initiative, an improved criterion for ship's stability may be
developed.

As the heelingforces,was aimed to require

2.

Basic

wind pressureandPrinciples
movement

the ship to have an iiitialstabilityof passengers

were consiaered,over and beyond a certain limitation by these heeling moments.
The following basic principles were assumed to proceed with the preparation(1)

Use of staticalstability

and itwhich will not allow the ship to heelof this standard:

for the final criterion.

(2) As thee heeling forces, only the wind pressure and the shifting of passengers
were considered, and the effects of wave, steering, etc. were excluded from the considerations.
(3) Overloading of passengers
in excess of permissible
there are other existing regulations prohibiting it.

capacity(4) Passengers
them.

to move within the(5)of the capacity

The maximum

numberangle of inclination

were assumed
waslimitedwould notto 80 w of the

be dealt with, as
space allotted

freeboard,

allowing

for
for

66

造 船 .協 会 論 丈 集

第95号

other effects such as waves. The freeboard in the calculation was also limited to the depthof side which will submerge at the angle of heel of 20°, thus preventing at the same time
the ship from inclining to an excessive angle.
§ 3.

heeling

Momentdue to Wind

Pressure

When considering the heeling moment caused by wind pressure, let us first assume the centerof pressure is located at the geometrical center of the projected lateral area of portion of ship
above waterline, as shown in Fig. 1. Then the heeling moment due to wind pressure, 111W,
in
ton-m, may be expressed by the equation :Mω=⊥ρCpん2乃2

where,ρ=densityofair,intonssec2加4

Fig.1=,19只>1n‑4fnhqqρr・21、

C D= lateral

air drag coefficient

A =projected

lateralv = wind velocity,
h =verticalThe

measuredarea of portion of vessel above waterline,

in n2

in m/sec

distance

sistance

results…4

betweenof water,the centerof pressure

which is the geometricalof the hull under waterline,
values of CD have been madein m.
available

and the center

centerby manyof lateralre-lateralareaof projected
observers

and some of theare listed in Table 1.
TABLE1.ValuesofCn

On the other hand, the actual magnitude
measuredby Mr. Okada and the resultsof heelingpublishedpressure is located considerably
above the geometricalof ship above waterline.
If we now take :
ho=verticaldistancefrom the actual

momentdue to windpressure

directlyin the paper(4J , reveals that the center ofcenter of projected lateral area of portion

centerof pressure

to thecenterof lateralh =vertical distance from the centerr of area A to the center of lateral
ratio of ho to h has been found to be in the order exemplified in Table 2.

resistance,

resistance

TABLE2.Ratioofhotoh

0A

Therefore,of Stability

Standard

Proposedforh may be used in lieu of ho to simplify

Passenger

Ship

the calculations,

67

providedthatthe valuesof CD should be increased to incorporate the effect of rise in actual center of pressure.
Weighing the averge value of CD. ho(h shown in Table 2, and also with reference to papers (1) & (2),the value of 1.25 for CD was adopted
In passing,different

for our purpose.

1VIZ~= 0.78 x 10-4Ahv2
Mr. Kato's paper shows

angle of heel.

the variation

Therefore:of heeling moment

In view of far less magnitude(1)
due to wind pressureof heeling momentatdue to wind pressurecompared to that due to movement of passengers,
with the •ships engaged in Smooth Water'Service, equation (1) was adopted for simplification.
In the United States, as shown in Appendices II & (6) ; III & (7), the steady wind velocity
sof 37 miles per hour (or 16.5 m/sec) is adopted for fully protected areas such as rivers, harbors,-etc ., and the value of 45 miles per hourlakes, bays,
clear-cutsounds,standard(or 20.1 m/sec)

etc., as well as for Great Lakes

for partially(summer).

for steadywind velocity

for ships engaged

seems not too unfit to assume

the averagewindvelocity

protected

areassuch as

It is diff=icult to determine

in Smoothof about

Water

Service,

10,m/sec.

thebut itIn actual cases

however, it is essential to take into consideration'averge wind velocity, and therefore the standard

the sudden gusts of the order of 1.4 times thewind velocity of 15 m/sec was adopted by theboard.

(1), we have :Substituting

this value with v in equation.1VIw= 0.0176 Ah(2)§ 4. Heeling Moment due to Movement of Passengers
In the case of passenger ships for Smooth Water Service, which carry on board a relatively

large number of passengers compared to the size of these ships, heeling moment due to movement of passengers is of considerable magnitude, but little useful informations on this subject
may be found. Whereupon, authors have decided to determine the heeling moment due to:normally incidental movement of passengers by the method described below.
(1) Distance of movement of passengers' load
Let us suppose that a number n of passengers in the passenger spaces are first distributed at
the density r per unit floor area (in persons/m2), and then these passengers have moved andformed the density ro (in persons/m2), and their center of gravity has moved the distance d(in m). When,,as shown in Fig. 2, the x-axis is taken along the athwartship direction, and y-axis along the longitudinal direction of the passenger space in the ship, within the small strip

aready,thedistributed
breadthofpassengers
is2x•y afterthepassengers
havemoved,
and'therefore

it follows

numberof passengers

that

thei
in thisr centerof gravity

strip

is r•2x•dy,

has

moved

it further

thefollows

Where 12 i x2•dy lx •du is not hing but the athwartship dis00
lance from the centerline of passenger space to the center

distancex•

1- rro

Fig.

2

While

the

68

造 船 協 会 論 丈 集ofspace on one side of centerline,

passenger

第95一 号

namely,b (in m), thenathwartship

distance,d=2(1-_!)
b
ro

are

When

we

t2 ke

free

to

m ovc,B (in m) as the average
the resultsb-1

The actual grouping
normaltest of passengers

conditions.

in a limited

The investigation

conducted

was confirmed

to assume

demonstrated

by the authors

may easily move from the centerline

In Fig. 3, where r is the abscissa,
A which corresponds

area

2 d/B the ordinate,

to ro of 7 persons/m2.

(Appendix

to eitherLine A is correct

attainedI) also indicatesside abreast(ro=-2r).

Therefore,

under actual

equation

the maximum

is readily

ro comes to 6.66 persons/m9.

here as readily attainable

that all the passengers

thatand the value of 7 persons/m2of these ships was 3.33 persons/m°,

value of 7 persons/m2

rigorous

passengers

ships indicate(3)

for ro may be reached,that all the passengers
the r-value

the

r 1B
ro )

value of 9 persons/m2
underwith the various

which

B4

d- 12\

Thereforeof our calculations

withincircumstances.

(3) can be illustrated
in theory,by linewhile i` would be too

move at the same time to a uniform
nsity.
The authors' field investigations
pendix I) involved
moving passengers.
of passengers'As

the ro-(Ap-

the experimentsofWhen the distance

CG movement

is asses-

sed from the actual angle of heel inthese experiments,
it comes as plottedd
in Fig. 3, showing

the

fact

each

that

ship

was

could not be accomplished

Fig.
line

3

B of Fig.

3, namely,d - 41 ~
l1~

r
ro

B and

about

the height of line A. Thismay be attributed
to theand that the movement

measure,valuesone-halftendency

under

way

of passengers
to a uniformm

density

due to various obstructions

board.

The authors

on .
therefore ,.
the optimum

seen

fit to adopt,

have,
as

ro = 7 persons/m2

Let us now attempt to translate the meaning. of equation
the passengers move from the density r to r' , then :(4) in otherwords .

Supposingthatd=-1 1---1 B
2r')
By equating this equation to . (4), we have :1 _ 1(1-+--- 1
r ' _ 2\rroThat is to say, the passengers condensate to the arithmetical mean value'between the original
and the possible per capita floor area .
The recommendationsby American Marine Standards Committee (See Appendix II and C6)).
may be interpreted to have assumed the movement of all the passengers from the centerline toA Proposed
either one side of the centerline

Standardof Stability

for Passenger(d= b), and U.S. Coast Guard

Ship

Regulations

69(See Appendix

III and(7)) to have reduced it to d=0.31 b, and therefore these requirements may be expressed by lines
C and D respectively in Fig. 3. In both cases however, the maximum angle of heel is limited
to one-half the freeboard or 7 degrees whichever is less.
There are also shown in Fig. 3, rvalues of 3.333 persnos/m2
sengerand 2.222 persons/m2,

ships for Smooth Waterof the space by a (in m2), the average
Kitei (Regulations

ships engaged
TABLE

It appears
authors

therefore

area

per

for the Arrangements

in Table 3 for the passenger

are

most

frequently

foundwith the pas-

Service.

(2) Density of passengers before movement
When the passenger capacity of the passenger
Setsubithatpermissible3.

indicate,

however,passengers

TABLE

4. Valuesof a, ai andby n persons,passenger

is a/n.

Articleof Ships)

providesin Smooth Water

Minimum

to takespace is denotedArean~a for the

do not occupy

the values of a/n as shown

Service.

valueswhen

the area
Sempaku

Passengerperthe areaa2

and93 of our

of r.

As

in between
the area

the investigations

couches,

occupied(intables,by theseby theetc.

Thus,

obstructions

is denotedby alm°), r thenn/(a-ai).

It should be noted again thatarea a in these Regulations

becomestheconsists

only ofthe space fitted for the accomodationof pas-sengers,

and do not include

passage-ways,

stairways,

such spaces

etc.,

where

as
the

passengers may also freely move about. When the area of these spaces totals a2, then :nr=a-at+a2
Table 4 lists the values of a, al and a2 of some ships, and indicates that al is larger than a2 forthe smallest ships, but becomes smaller than a2 as the size of the ship increases. It follows
that it is not necessary to consider couches, tables, etc., except for smallest ships, and it would
not constitute too heavy a demand in general even though r were represented by n/a. Eventually, n/a was adopted for the value of r with ordinary ships in question. Incidentally , values ofr(=n/a)are mostly either 3.333 or 2.222 persons/m2.

(3) The maximum athwartship distance of free passenger movement
The average athwartship distance of free passenger m~}vement within the passenger spaces is,in ordinary cases, equal to the average extreme breadth of the passenger spaces, as shown in
Fig. 4. When there are such spaces as passage-ways outside the proper passenger-carrying
spaces, as shown in Fig. 5, these should be included to assess the mean breadth. When theseoutside spaces are narrower than 40 cm, as shown in Fig. 6, they are to be excluded in obtaining B, as being impassable by passengers.

a

70

造

舟合 協

会 論:交:集第95一号・Fig. 4君

Mp = Heeling moment
passengers,
w=Average≧'4・ocmFig.5(4) Heeling moment
When,
due to movementofin ton-m
weight of a passenger,

in

tons
then,

of heeling

moments

due to movement

Mp is the sumof passengers

in. eachpassenger-carrying

space,

Fig.6

Mp = Enwd
entering d(4) into this equation,

Therefore,

名 く40C肌that is :we haveMP=+4 wE~(l- yoy nB
Assuming

w=0.06 ton, ro = 7 persons/m2,

and Y= n

Mp=0.00214
E(7- n~nB
a~5.
Maximum
degrees,quoted
as

angle

but

of heelto eitherin Appendicesa sumof theMaximum

adoptedwindpressure

momentsandeffects.

That

StatesIn ourto 800wind

is limited

Heel
the

of passengers,

independent

on eachstandard,heelingpressure

theand movement
makinga certain

freeboard

momentwas

冗

O=Maximum

angle of heel,in

B = Beam of the ship, in m
f = Freeboard
write,of the ship, in mtan 8=2(0.8fB-)-=-- 1.6fBf

degreesFig.9

asand the
for

1

Fig.8

T

assumedof passengers,
allowanceorother,

is,

Fig.7

may

of

to one-halfof the freeboad,

when,

We

Angle

or movement

due to combined

angle of heel was limited●7〆

in the United'

II & (6) ; III & (7).

maximumotherPermissible

waves

n

A ProposedStandardof Stability

for

Ship

Passenger

71

Even though the ship may have sufficient freeboard, excessive angle of heel must be avoided..
Therefore, it was decided to limit the value of freeboard, f, in the formula toobe not in excess
of depth of side submersion at the angle of heel of 20 degrees.
fc 1 B tan 200 2
or f~B/5.5(8)
The freeboard should be measured in general to the top of the upper deck as shown in.
Fig. 7, but in such cases as Fig. 8 where the side plating is watertight to a certain level above
the upper deck, or where there is an opening below the upper deck, Fig. 9, it should be measured to the lowest edge of non-watertight portion.
§ 6.

Standardof Stability

As stated, the ships must have an inital stability which will not allow the ships to heel inexcess of the limited angle under wind pressure and movement of passengers. This is expresse l by the following equation, where GM is the metacentric height (in m) and a the displacement(i z tons) of the ship :GM>(Mw+Mp)/4 tan 0
Substittuting equations (I) and (5) into above, it follows :

(9)

GM>
{0.78
x104Ahv2+
1~ w 1-rro nBJ./dtan0
The working
generalformulaequation (9)GM>(1.1

is obtainedby introducing

equations(10)(2), (6), (7) and (8) into the above

Ah±EknB)B/100fd

TABLE

fB/5.5(11)

k=0.134(7--)
awhore valuesof k may be obtained

Table

5, because

n/a may be substituted
by n/a from Table 3.
Table 6 illustrates
the results derived fromthe actual

ships using the formula
ed by U.S.

Coast

Guard

(11).

The calculated

Regulations
TABLE

from

6.

results

requir-

also

shown

for comparison.

Calculated

ResultsareforActualShips

5.

Values

of

k

?2

造 船 協

§ 7.

会 論 丈 集Additional

第95・ 号

Notes

There are some features to be born in mind when using this standard above outlined. They are:(1) The standard assumes that the stability curve forms a sine curve, as may be seen fromequation (9)'. This is justified on account of the limitation of the maximum angle to about
16° (which is 800 of the freeboard corresponding to the inclination of 20°), and also because the maximum GZ's of the majority of ships are found between 20 and 25 degrees ofheel. The assumption, GZ=GMsin 0, is therefore always on the safety side for the ordinary
ships, and it does nbt give too different a value from the ,actual GZ. For the ships withpronounced flare or tumble-home, and those with bulge, etc., it is necessary of course toderive and use the actual GZ.
(2) Passengers were supposed to be of capacity number and to move on athwartship direction on a predetermined level. If the passngers were to move on to higher decks , for example, GM would be reduced, and the ships passable under this requirement might notnecessarily remain safe.
(3) The ships were supposed to carry capacity number of passengers.
into equation (5).
Mp= 1 war 1- r
4The

heeling

momentBy substituting n = raaBrodue to movementof passengers

variesaloilga parabola, as shownin Fig.

10,reaching
toa maximum
at r= 2 . Thevalueof ro
was taken 7 persons/m2,

and as seen from Table 3, r neverreaches
to v. Therefore,
fromFig. 10,Mpbecomestherlargestwhen

On thecontrary,

less

the

passengers,

ship

carriespassengers

M0 is of course
butis still far

to thecapacitywhencarrying

greatersmallerthan.

Mp in magni-

tude. This condition, however, gives greater freeboard, and thence greater angle of heel permissible, and furthermore increased GM in ordinary vessels. For these reasons, the consideration of the only case when carrying a total of capacity passengers is justifiable.
§ 8.

Conclusions

In the foregoing, authors have attempted to describe the principles and procedures in preparing the standard, which may be summarized as follows :(1) The standard of stability was selected so that a safe initial stability would be maintained
against the average wind velocity of about 10 m/sec (steady wind velocity of 15 r/sec)
abeam the ship, and under the movement of passengers normally incidental .
(2) Heeling moment.due to movement of passengers is far greater than that due to wind pressure.
(3) The athwartship movement of CG of passengers was determined according to the originaldensity of passengers, a departure from the conventional uniform practice.
As admitted in the introduction of this paper, this standard may hardly be asserted as perfect, and contains many problems yet to be solved. For instance, there are some places in thescope of smooth Water Area, where the effect of waves cannot be neglected . But the patternsof waves are so various and complex at the different places in the same Smooth Water Area ,that even the attempt to determine standard wave profile presents a very difficult problem . Including a solution of this important problem, it is strongly hoped that a more reasonable standand of stability will be developed in the future.

Standard

A Proposed

APPENDIXREPORTof Stability

OF INVESTIGATIONS

for

Ship

Passenger

ON STABILITY73

OF SHIPS

ON " ASHI-NO-KO " AND " BI WA-KO " LAKESThe authors

have conducted

and " Biwa-Ko " lakes.
available

investigations

There

at the time of these investigations.

decks due to the unfavourable

on stability

were not many
weather.

of cruising

tourists,
Besides,andvessels

therefore

passengers

did not

With these disadvantages,on " Ashi-no-Ko "few full-load conditions
come out to weather

the objects,

as previouslyex-pected, were not fully attained.
Many groups of higher-and middle-school students on excursion
were available, on the other hand,' and they were willing to cooperate with our experiments on
the movementof passengers.

The tests conducted

were of the nature
TABLE

For the continuousrecording7.

listed in Table

Vessels

testedof angle of heel,

Ashi-no-Ko " and that of pendulum

and

7
types

rollingoftest

recorderof U-tube

type wvas used ontype on " Biwa-Ko."

Ship L 2
From the results
calculated(1) Normal
As indicatedstarboardof inclining

and are shown

experiment,

displacement,

GM, etc.

undereach condition

were

in Table 8.

angle of heel and normal
by the continuous record

following the guide's

movement of passengers
of angle of heel, Fig. 11, theexplanations,

and

also

when

a pleasure

ship heels to port andboat comes close and°74

造 船 協 会 論 文:集attracts

passengers

on

one

side.

A maximum

TABLE

8.

angle

第95号
of 5° was registered

GM under

when

the

pleasureboateach . condition

appeared on the starboard side. Heeling moment of 5.73 t-m is required to heel the ship to thisangle, and this moment would have caused the ship under full load condition (4=127.07 t) toheel, when GM= 0.410 m, i.e., passengers at proper position, to 0=7°, and when GM =0.297 m,i.e., all passengers on promenade deck, to 0=9.8°.
Assuming that this moment was caused by the movement of all the passengers on each deck,
the change in the density is derived from :355X0.055X 2BX 1- r =5.73
roTherefore, r = 0.893, or r=1.12 r. Further, athwartship movement of CG of passengers =0.30m
Yo
B
A
20
ssuming that only the passenger, who spotted the pleasure boat, moved, and thatthey were 200 persons in number, ro =1.23 r.
(2)

Passenger movemont experiment
The results of this experiment is shown in Fig. 12.

(a) Movement only within promenade deck house
No. of passengers moved : 95. Moved to starboard side on centerline.

Registered

0=1.4(b) Movement only within upper deck house
No. of passengers moved : 225. Moved to starboard side on centerline. Registered

0=6°

Estimated heeling moment= 95X 0.050 X B 4
When=

Breadth of the deck house, or 4 m, 0=3°

WhenB = 3 m, i.e., bench spaces do not admit passengers, 0=2.25°

Estimated heeling moment = 225 x 0.050 x B
WhenB= 3 m, 0=6°.
(3)

Turing experiment
The results are shownin Fig. 12.

At -1 ahead and 10° helm, registered

0 =2.3° 2

The equivalentheeling moment(4= 127.07 t) as much as:

would

When GM=0.410 m, or passengers

at proper

When GM= 0.297 m, or all passengers

haveheeledposition,on promenade

the

ship

8=3.7°
deck, 0=5.1°

under

load

condition

.

A

ProposedStandardof

StabilityforPassenger

Ship

75

Next, at 1 ahead and 20° helm, registered 6=3.5°
2The equivalent moment would have caused the ship under load condition (d =127.07 t) and with:
GM= 0.410 m, to heel 0=5.7
or
GM= 0.297 m, to heel 0=80
(4) Rolling experiment(a) During inclining experiment,GMB=1.069 m, T=4.9 sec, K=2.53 m = 2.37(b) During the first trip (Fig. 11)
T was not measured, but from Fig. 11,
GM= 0.570 m,, T=7.4 sec, K=2.78 . m
(c)

-2B
.60

During the 2nd trip (Fig. 12)
GM= 0.740 m, T = 6.0 sec, ' K = 2.33 m

2B .37

Ship L 3
From the results of inclining experiment,
calculated and given in Table 9.

displacement,

GM etc. under each condition were

TABLE9.GMundereachcondition

Continuousrecordof angle of heel is shown by Fig. 13.

(1) Normal angle of. heel
Normal angle of heel is very small.
acteristics

giving a good command

This can apparently

be accreditedof view from the promenadeto theship'schar-

deck and also having a rela-

tively high GM.
(2)

Passenger

moventexperiment(only on promenade

deck)(a) When the passengers
on one side of centerline
moved to centerline
gistered 0=3°
Since r= 4.12 persons/m2, and ro = 5.75 persons/m° =1.39 r
B =3.00 m

gives

the passengers
0=50

moved

Since r=4. 12 persons/m°,
B= 3.00 m
To give actual
(3)

0=50,

re-

0=4.5°

which is in excess of the observed value.
was not uniform, but was higher adjacent(b) Whenregisteredpassage-way,fromThis is accredited
to the centerline.
thecenterline

and ro = 8.24 persons/m2=2.0

gives
B must0=8°
be B = (3.00-1.1)

Turning experiment
At full ahead and 30° helm, registered0=7.9°

mto the fact thatto starboardrside

the densityof centerline,

76

造 船 協 会 論 丈 集

(4)

第'95号

Rolling experiment= 2.210 m,

5 sec, K=1.85

n=2experiment

give

following

5I

Ship LThe results

B GM

.22

T=2.

of

incliningthevaluesofdisplacement,

GM

etc.

for

each

condition.
TABLE

10.

GM

under

each

condition

Continuous record of angle of heel was obtained, but the angles were very small, as the rain
and fog confined the passengers within the lounge.
(1)

Turning experiment
At full ahead and 85° helm, registered 0=4°

(2) Rolling experiment
GM= 2.500 m, T=2. 6 sec, K=2. 05 m = 1B-- ,.90
Ship L 7
The values of displacement, GM etc. under each condition were calculated as shown in Table 11.
TABLE

11.

GM undereachcondition(1)

Continuous recording of angle of heel and turning experimentThis ship had a very large GM and sufficient stability.

(2)

Rolling experiment
GM= 2.630 m, T = 5.2 sec, K= 4.20 m = 2 B.02Conclusions

The investigations

revealedmany

features,unrecognizedin the past,andsome of which arelisted below(1) Angle of heel due to movement of passengers
is greater when a novel thing appears ona side of ship than while passengers
coming on or off board.
When coming on board, evenwith a rush,

passengers

usually

run to the

other

side

and

when

leaving,

passengers

onpromenade deck converge to foreward and after stair-ways
and only those on upper deckshift to one side. Thus, the angle of heel is not so large in both cases.
(2)

Angle of heel while turning

is sometimes

too important

to be neglected.

Even thoughA Proposed

turning

while underStandardof Stability

forPassenger

way full ahead is not imaginable,

exceptShip

whenship in a dense fog, and turning

alone should not cause

excessive

speed when nearing

sometimes

appreciable

when arriving

to pier may

at pier, combined

give rise to large

registerconcentration

anof passengers

77

encountering

the otherheel,

at a slow

turningheel.

This is to say,to one side and turning

may

angle of heel.

(3) When passengers
move, it is safe to assume that they do not come into the area where
couches and sofas are placed.
Therefore,
the effect of couches must be taken into account.
This point has been re-examinedin § 4 of this paper.

(4) The ratio of densities before .and after the passenger movement was, under normal conditions, in the order of : ro =1. 12 r for ship L 2. Under intentional conditions,ro = 2 r, or
the movementfrom centerline(5) When passengers
does not necessarily

to one side of centerline,

is fully possible.

move to one side under nomal conditions, the existence
separate the movement in and out of the house.
rof deck house

/l.
First

continuousrecordof angle of heel

for Ship L2.

Date: ~+June 1953, 3.30 to 3.50 p.m., cloudy
Trip:
Rojiri to Moto-Hakone
Passengers:
355 higher-school
students
average weight per person, 55 kg.

Fig
oeconn

coati

:oua

r ecorr

of

cnsle

of

ocel

Crew and Measu~ere:1:?
= 115.5 t
GM a 0.57
Rolling
Period:7.4 sec.
C Clinometerreading.

m

/2
for

3 .U pI....

[note:
j Jute 1953, 0.30 to IO.C'..,. ,. cloudy
Trio:"oto- <~:'.koneto•Kojiri
Pnese:r:ers:
320 rnidale-scn
ool )rd-dear
it ud eonscei Tit. ~0.'kg/person

Crewand measurers:
1~ persona
ll!*.g3t,
GM = 0 .74 m

マ8

造'船

協 会 論 丈 集

第95号

(6) Heeling moment due to: mbvement of passengers
extraordinary cases.

may be considered statical, expcet in(7) Rolling experiment can be accomplished more effectively by bringing the ship alongsidea pier and giving a seesaw by the rail, than the ordinary method of moving weights on board.
(8) This sort of experiments and recordings of angle of heel when underway should be conducted several more times, preferably under full load conditions, to obtain data under more
severe circumstances.
Fig.
PDntimuousrecord

of

angle

of

heel

l3

Ship L3.
~.m., cloudy

for

Date:
~+ June 1953, 5.30 to 6. cc
Trip:
Kojirito Hakone-macni
Passengers:
143 girl
students.
averareweight,
4S kg/oerror

APPENDIXII.

STABILITY

AND LOADING OF SHIPS (FINALAMERICAN
The American

MarineMARINE

Standards

1-In

all groups

half of the freeboard
if

REPORTersonsn

OF THECOMMITTEE)

recommended

Group II.-Partially9
1.11

the following standard

protected

waters.

of stability:

Group III.--Smoothwaters.

(2) Minimum initial stability
The minimum initial stability
FormulaSTANDARDS

Committee(1) Groups of vessels
Group I.-Ocean
and coastwise.
and protected

Crew and meosurers:= 23.01

when operating

is given by three

the heel is limited to thatand a maximum

formulas.

which will immerseof 7° when the vessel is subjected

not more than oneto a steady beam wind

about 55 miles per hour for Group I, 45 miles per hour for Group II, and 37 miles per hourfor Group III.
Formula2-In

all groups

half of the freeboard
Formula .3-In

the heel is limited to thatand a maximum

ill groups

which will immerseof 7° when passengers

the heel is limited to thatwith limit of 7° when any two adjacentvessel are assumed

flooded due to damage.

(3) Required minimum GM
The minimum initial stability
following(a)formulaswhen

operatingcrowd to one side.

which will immerse

half the freedboar.d

not moree than onenot more than one-compartments

on one side of theshall be the maximum

GM as .given by the:

GM= CAhB/df.. •••f must not be greaterthan either

0.246 B or 4 (fw -1)

,A ProposedStandardof Stability

Ship

Passengerfor79(b) GM= 0.005MB/4f.. •••f must not be greater than either 0.123 B, 2 (f,- 1), or 2(fc =1).
(c) GM= (Bwd+fi)/f (u4+w) ••.••f must not be greater than either 0.123 B or 2 (fm -1).
In the foregoing formulas the symbols have the following significance :GM= Metacentricheightin feet.

B= Molded beam in feet.
fo = Shell-opening freeboard in feet.
A = Exposed longitudinal area in square
act in the upright
M =Sumfeet above

waterline

on which the wind may

vessel,in feet3, of the total net

position.

of the moments

about

the centerlineof thepassenger-deckareas on one side of the vessel.
d= Distance in feet from the vessel's centerline
to the center
partments.
G= Displacementf,=of the com-in long tons.

Weather-deck
0.0050+of gravity-00
2

freeboardin feet.

, 0.00, 000

for

Group

I.

2

c= 0.0033+

L
for Group II.
X00,000,000

0.0025+ 200 L- 000 for Group III.
, 000,
h = Vertical distance in feet from center of A to one-half the draft.
w=Capacity in cubic feet to waterline of at least two adjacent compartments.
u=35 for salt water, 35.9 for fresh water.
L = Length in feet on waterline.
i = Transeverse moment of inertia of the compartments, in feet4, at the level of waterline about an axis passing through the center of gravity of the free surface andparallel to the vessel's centerline.
APPENDIXThe U.S.C.G.
Marinefrom

RULES AND REGULATIONS

Committee,
criteria
minimumand they give the minimum

metacentric

the following formula

FOR PASSENGER

VESSELS(UNITED STATES COAST GUARD)
appears to be the modification of the Final Report

Regulations

Standards(1) Weather
The requiredIII.

height(GM)of the American

GM by the following formulae.

in feetat anyparticular

draft is obtained:

GM= PAh/d tan 0
where :

L = Length

between

A = Projected
h = Verticalperpendiculars

lateraldistancearea
inapproximately

one-half

d = Displacement

in

long

in feet.

in square

feet

from
draft

feet of portion

centerofA

toof vessel above waterline.

centerofunderwater

lateralareaorpoint.

tons.

P=O.
0050+(_14)tons/f12
foroceanandcoastwise
service.
, 200=0.0033+(

L

lrtons/ft2or partiallyprotectedwaterssuchas lakes,bays, and\ 14, 200 ~sounds, and Great Lakes= 0.0025+L
14 200(summerservice).

2
tons/ft2 for protectedwaterssuch as rivers,

harbors,

etc.

80

造 船 協 会 論 文 集
d= Angle of heel to one-halfis less.

(For

vessels

the angle to one-half(2) Passenger
criteria
The required minimum

the freeboard
havingto the decka discontinuous

the freeboard

metacentric

第95号
edge or 14 degrees*eather

may be suitably

whicheverdeck or abnormal

sheer,

modified.)height (GM) in feet is obtained from the following formula:

GM= Nx b/244 tan awhere :
N=Numberof passengers.
d = Displacement
in long tons.
a=Angleof heel to deck edge or 14 degrees,b = Distancein feet from the vessel's

sengerwhichevercenterline

is less.

to the geometricalcenterof the pas-deck area on one side of centerline.
References(1) G. Hueghes :of Superstructures,"

The Air Resistance of Ship's Hulls with various Types
Trans. I. E. & S. in Scotland, 1931-32, Vol. 75.

(2)

D. W. Taylor(3)

H. Araki & T. Hanaoka:

and Distribution

Speed and Power of Ships.": "Wind-Tunnel

Japanese),read in 1948, and publishedof Japan, Vol. 84.
(4) S. Okada : "Heeling Moment
read in 1952, and to be published

Experiments

on Models of Trainin 1952 in Journal

Ferries"(inof the Society of Naval Architects

due to Wind Pressure for Small Vessels"(in Japanese),
in Journal of the Society of Naval Architectsof Japan,Vol. 92.
(5) H. Kato : "On the Stability of Small Sea-going Vessels," read in 1948, and published1951 in Journal of the Society of Naval Architects of Japan, Vol. 83.
(6) The American Marine Standards
Report of A.M.S.C., 1929.
(7) United States
19, 1952.

Coast Guard(8) J. Rahola : "The Judging
Amount of Stability ", 1939.

:

Committee:"Stability

Rules and Regulations

andLoading

for Passenger

Vessels,of the Stability of ships and the Determination(Translated by Kazuyo Nakayama, Member.)of Ships,"

in

Final

CG-256, Nov.

of the Minimum