25A Proposed(昭 和29年11・月造 船 協 会 秋 季 講 演 会」こ於 て 講 演)

Standardof Stability(PartBy Mitsuo

II:SmallSato,Yasubumi
Seizo

Yamanouchi,Ships.

Crafts)

Kogakushi,Member,

Kogakushi, Member,Motora,and Mamoru

for Passenger

Kogakushi, Member

Uchida,Kogakushi, Member.
§ i.

Introduction

Small crafts of less than 5 gross were outside the scope of "Ship Safety Law," but even suchcrafts intended to carry passengers have become subject to the application of the Law by its
Amendment made in July, last year. A standard of stability for these crafts has been preparedaccordingly and is now in force in the form of " Small Crafts Safety Ragulations."
This standard was worked out in a similar manner as that for Smooth Water Area, that is by
the Ministry of Transportation with cooperation of Tokyo and Kyushu Universities, and Nippon
Kaiji Kyokai (Japan Marine Corporation).
Notations used in this paper are shown in Table 1 unless expressly defined else*here.
TABLE

§ 2.

1.

Basic Principles

It was decided to adapt and simplify the standard for vesselss in the Smooth Water Area, andthus to follow the same basic principles with the following modifications :-(1) Stability of a small craft must be determined in terms of L, B, D and do or fo as the exact
form or displacement of such a craft may not be readily available in most cases, Incidental inac*

A ProposedStandard

Soc,

Nay,Japan,

Arch,of Stability
Vol.

95for

Passenger

Ships-PartI :SmoothWater

Area , Journal

26造

船 協 会 論 交集

curacyof a certain

第96号

degree must be tolerated,(2) Go•G0M0 (-So) will be determined
mated from data on existing crafts,by means of inclining

experiment,

and thence

L\•GM esti-(3) Steady wind of 10 m/sec strength can incline small crafts only as little as about 2 degrees,
Therefore,
heeling moment due to movement of passengers to be considered .
(4) Maximum permissible inclination, or side immersion,ante for wind pressure, to 70°0 of available freeboard ,3.

z •GM whencarrying

will be limited,witha certain

allowPassengers

When zo•G°M0 is known, ~.GM can be estiYnated by the following formulaGM-==KB+BM-KG
therefore,a•GM=~•KB+O•BM-Z•KG
whereKB= d- 1 1 d + V = 5 d- 1 A
and BM= -I. _• TI
3 2Aw
63Av w
V L\Assuming that the center of gravity of passengers is located 1.00 m above the top of floor,
KG ={Do • KGo+wn(h+1)}/02Thence,.GM = 5 D d +6
3 6 Aw
2and~o•GoMo= 56 dodo-

I- DoKGo - w n (h + l)

- °- +cTIo-DO•KGO
3 o AlTherefore Do•GoMo-0.GM=
5(0d0-~d)- 1 (-IlBy~ itA,..n0? ±a(Io-I)+wn(h+1)
A,

substituting,

4=loo+wn

d±do+(A2wn k5Awo=LBCwoA,,=LBCWo' zuo'+ w)
fo=k0LB3
I=kLB34o=oLBdoC,,o CI0=rCcvo
The above formula can be written~4r-15(3r-2)doCboo•GoMo-~.GM=_ -3 r (1 + r) QL B- Cwo- (wn)-+ (h + 1) - -do-- -----6 - 3r(1+ r) Cwo (wn)(r --1)QL B d02Cbo2
3r CIUo
6 (k - ko)LB3
By dividing this by. LBdo2,and writing ~o•GOM0.S0and also assuming 6=1, we have:90-.GM- _ 4r-1 _wn_ °+ h+1 r 5 _ (3r-2)CbownLBdo23r(1+r)Cwo LBdodo
6 3r(1+r)Cwo LBdo
- (r -1) C-bo
3Crdw00Hence, (So-O.GM)/LBdo2
appears to be dependent mainly on n/LBdo and (h+1)/do . The change in• GM due to change in h may be determined , when, for instance,•G1M at hi is known, by theformublaz•GM-~•G1M=-wn{(h+1)-(h1+1)}
-wndo
Thus,

h+1 -h---1U0•
doassuming

a certain+1)/do [= (h1+l)/do-p]
actualvalues of So, z,

determined(1)
value of (h, and whentheG1M, etc.

arefrom availabl&ship

curve of (So-zon the basis

data, andG1M)/LBdo° plottedof n/LBdo, then (So -x'7ti/L~doFig. 1

A ProposedStandardofStabilityfor

Passenger

Ships

27GM)/LBdo° of an, given ship corresponding to an arbitrary value of (h+1)/do may be approximately estimated.
Fig. 1 illustrates such a curve plotted from actual ship data with p=3.00. (So- 0 •GiM)/LBdo° may be regarded to vary linearly with n/LBdo. When, for instance, writing (So-0•G1M)/LBdo°=awn/LBdo for (h1+1)/do=p,S0-z. GSM=awndo
Introducing into this equation allowance for change in h,S
la+1
o-OGM=awndo+wndo
do -p =wn~h+1-(p-a)do}(2)

From Fig. 1, p=3.00 and a=1.25, and also taking w=0.06 (ton),
So-0.GM=0.06n(h+1-1.75do)

(3)

§ 4.

Lo •GoMo when carrying

Do• GoMo, or So, could be determined
without

passengers,

by inclining

no Passengers
experimentof the craftat standby

conditionand from the formula
So=Wb

So thus obtained,(4)

however,will not give real So on accountof the effects of shifting

weights

and measurers
on board during the experiment. In order to minimize the error, the test must be
made without the crew aboard, and also the total weight of shifting weights and measurers shouldbe less than that of (No, of crew+2)
weightmen. This is practicableof 60 kg on each side is sufficient

To obtain the real So, complete
the order of (No, of crew+2)-No,
be omitted

and formuladifference

betweenexperimental§ 5.

Inclination

to carrywith small crafts,

for which shiftingout the experiment.

with crew on board,correction

must be made for weightof crew =2 persons and for its position. But such correctionofmay(4) used as it is, because it is on the safe side, and also because of small
So and real So(-So'),due to Shiftas shown on Table 2.

of Passengers

and its Limit

if the inclination of a ship due to shift of passengers is limited to an angle B,
D•GM_c•wnmtano,The

resultsofcalculations

or So_So-4•GM+cCwntwith

thevariousships

anBB(5)indicate

B=0:9B

Where, taking

the density of passengers

of Smooth Water

before and after

to the previous

case

is limited to that in the case of Smooth Water

AreaArea, as 3.33 and 7.00 persons/m°
crl l 1_ 3.33

4~7the shift,= 0.131

If the maximum

inclination

plus a certain

for wind pressure, i.e. to 70% of freeboard,tan 8=2(0.7 f)/B=1.4 f/B
w=0.06 (ton) into equation (5)Also introducing

similarrespectively,or side immersion,

allowance

S. nBAo?(So-~.GM)+001
2f(6)Where, limiting f to the depth of side immersion at 20' angle of heel, similar to the previous casef

1 Btan20'

orNext, f may be estimated by
f2wn= f o- -:~`Cwo+Cw)LB

JAB/5.5`7) 2

sn28造船 協 会 論 文 集第96号

Where, 1 (Cwo+C2U)_ 0.7 for ordinary small crafts, and taking+ 1 and w=0 .06 (ton), 2

f =fo- 0.085 n
L~(8)
On Table 3 are shown f-values of ships, of which data are known , calculated from formula(8)
in comparison with f(f')
values obtained from their hydrostatic curves , It may be said
that formula ($) is acceptable for practical use
TABLE

2TABLE

G.
Standardof stability

may be written,

So>wnTo transformthisStandardformulaof Stability

from equations

l+h-(p-a)do+(2)~Btan B
one, substituteinto a practical

3and (5) , asequations(g)(3) , (6), (7) and (8), ar.d

we haves00 106+6 h-10.5 do+ B±2f

f= fo _ _0.085n
B(10)
LB
5.5
Whereas, Article 16 of Small Crafts Safety Regulations provides that area of passenger space
be not less than 0.25 m° per person, n(=nA) may be determined from available area for passengers, and substituted into formula (10) to check the stability. In practice, however, it is moreconvenient to find n(=ns) from formula (10) at first, then compare it with nA, and determine
the capacity of passengers. For this purpose, the next method is recommended to simplify thecalculation, which may be otherwise complicated, as -the formula (10) is a quadratic equation ofvariable n. First, substitute n in equation (8) with nA-A/0.25, and from equation (7) , wehaveTherefore,comparethanfr f° ^ 0.34A
LB -< 5B _.5solution is to use this f-value

thethe resultwith nA. When, however,B/5.5, it will give

too rigorous

for f in equation (10) , determine fl(-fl),andns is found less than nA, and fo-0.34 AILB also lessa result,

since a freeboard

more than ns, has been used to obtain 'is, In this case, equation
To sum up the foregoing discussions, the standard of stability
lation procedure

may be numerated

with nA numberof passengers(8) must be used .
for small crafts and its calcu-as follows(1,) Inclining experiment to be made at the condition without passenger and crew but with fuel,water, equipment and outfit aboard at their normal position . But the total weight of shifting
weightsand measurers

should not exceed 0.06 x (No. of crew+2)

So=ti~bjtons ,(11),A Proposed

TABLE

Note :

showsStandardofStability

Passenger

Ships

29

4

n to be adopted.

(2)

Determinemaximum No, of p ssengers
nA=A/0.25=Ai/0.25(3)

Find maximum

No, of passen

ers allowable(Predetermine

h from h=EAhi/EAj)

nssns or fA, whicheverforallowable

1 OSo6±6h-1.5do+2f B

ns'~nA, an

6+6h -f - fo -fo- 0.34 AILB
00S0
0.5d0+ispace,(12)

by stability

the less, is ado ted as the maximum(4)
When ns is less thanto be assigned.

by area of passenger

B2'2f

point of view,

0.34 A C B LB - 5.5n allowable,(13)

except in the next case (4),also less than B/5.5, the next n5' givesf = fa -. O.O85n 5' < B
LB
5.5(14)then230:造船'協 会 論 丈 集

第96号

on Table 4 are shown some of the results of calculation on actual ships,§ 1.

Review(1)
For small crafts, their stability must be determined with limited informations available, andconsequently inaccuracy of a certain degree cartnot be avoided. There are involved (a) adoptionof mean line in Fig, 1, (b) neglect of effects of shifting weights as inclining experiment, and (c)uniform assumption of 0.7 for any 1 (Cw+Cwo).Combined errors of these simplifying measures
2are shown in Table 5, where F is 70 of the freeboard with n passengers (calculated by theproposed method) or 70of -B tan 20°, whichever the less, and F' is the depth of side im 2mersion when inclined by a heeling moment of cwn, B. These values were obtained from detailed
calculations on ships for which complete data were available. In effect, our method shows theship to incline as much as F while the ship actually inclines as much as F'TABLE

5TABLE6(2)In order to assure
thestandard, the authors conducted

practicabilityof thispassenger-shiftingex-periments on actual ships at Tokyo Port and Kawaguchi and Yamanaka Lakes, and their results are shownon Table 6. where, F is 70 of the freeboard with ns passengers aboard, or 70 of
B tan20°, whichever the less, and F" is the loss of freeboard due to inclination effected by shift of ns
passengers. Both values were obtained from direct measurement. The table shows in effect thatthe ship should incline as much as F according to our method, but it did incline as much as F"
in fact.
(3)
As d emonstrated "above, the proposed standard may be deemed efficiently practicable atpresent, but when more informations are gathered to construct Fig. I for each type of ship, andmore realistic values of -2- (Cw+Cwo) determined, higher accuracy maybe obtained in the future ,§ g.

Conclusions

The authors have attempted to describe the principles and procedures in preparing the proposed
standard and are pleased to note in conclusion(1)
that the standard of stability has been selected as such that will give sufficient initialstability to the ship against normally feasible shift of passengers, and(2)that the method of determining ship's stability only by its length, breadth, stability
without passengers, draft and such has been developed. Finally, it is the authors' sincerest wish
that many a weak points in this standard will be remedied and more reasonable standard d~veloped in the future,(Translatedby Kazuyo Nakayama, Member)