An estimating method for stability qualities of ships in confused seas, including the effect of shipped seawater

ARCH1EF

IaL

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Scheepsbouwkink

Technische Hogeschool

i 47

((fl 36

5

D.fft.

An Estimating Method for Stability QuaÌities of Ships iñ

Confused Seas, including the Effect of Shipped Seawater

By Hiroshi Kato, Member*

Sum mary

This paper is concerned with the estimation of stability qualities of ships in rough seas subjècted to steady winds and gusts, and influenced by irregular waves and shipped seawater. Analysing results of experiments on the wind force, apparent centre óf wind pressure and apparent centre of water pressure with several ship models, new formulae for. ivind moments acting on a ship in

the upright and inclined conditions were obtained.

The ship is assumed to be rolling among non-fully developed irregular seas generated by winds 'of given mean velocity, the period of component waves of most predominant energy being equal

to the period of roll ci ship. and the expectéd maximum amplitude among 100 swings is taken as the standard absolute amplitude. After many kinds of resonance curves of ships were utilized with Neumann's spectrum, a simple relation was found between this standard amplitude and the angle

of roll of ship on imagined synchronous regular waves with heights equal to the expected maximum

height among 50 irregular waves.

The ship is inclined to an angle by the action of steady wind and rolls about that angle. She

is assumed to be struck by a gust that has the velocity i/1.'5 times that of the steady wind, when she rolls up tó the maximum angle corresponding to the standard amplitude on the wiñdward side -relative to the effective wave surface.

The effect of seawater shipping on the deck is divided into two kinds. The first effect is due

-to shipped water stagnating on the deck when she is struck by the gust and the second one is

due to water shipping on the deck when she is rolling leeward after the striking of the gust. Formulae for these two effects were determined by investigating stability qualities of a cargo ve-ssel with minimum stability in her critical conditions.

The work ratio R is defined as the ratio of useful reserve dynamical stability to the maximum kinetic energy of ship after being struck by the gust. The critical value of work ratio R of 1. 53

was obtained from the fact that the torpedo-boat 'Tomozuru" of 744-ton displacement wascapsized

in a storm of mean wind velocity of about 20 rn/sec when she was acting together with other two sister ships. A ship may be judged to be stable in given rough seas when the factor of safety for stability Co which is shown by R/Rc is greater than unity.

i

Introduction

For the sake of establishing the standard to estimate stability qualities of ships in rough seas,

in-vestigations have been made actively in Japan after the Second World War, and a number of papers'-5)

have been published about the results. The Research Committees were organized, and they also madè quite a few and important contributions to the progress in this field(7). Utilizing some parts of these

results, the new Stability Regulations, one of the world mostoutstanding, were established after rather a short period of time, and nowadays we can approximately estimate the stability qualities of ships in rough seas, and by the enforcement of this Regulations, the sea disaster is expected to decrease

( 35 . 12 )J 20

considerably. Relations, however, between the irregular wind and sea, their inclining moment acting on the ship, and the motion of ship induced by them, are very much complicated. Since the Regula.

tions are based on schematic approximations, it is natural that they 8till include many unsatisfactory

points in considering these relations. In order to make this more satisfactory, further investigations.

are now under study by the Research Committee.

Generally, stability qualities of ships in rough seas have been estimated considering the rolling

mo-tion induced by waves and the heel angle by the wind pressure. In Stability Regulamo-tions, they regulate

the metacentric height GM, the maximum righting lever GZm, and the ratio of works C. Based on the calculated value C of a number of ships in beam sea, developed by winds of various velocities, the

value of 1. 0 for Cthe ratio of worksand the standard wind velocity were decided as the criteria

for this regulation. _{In doing this, we assumed that the roll damping coefficient (in Bertin's form)} is always O. 02 for all types of ships for the calculation of roll amplitude, and taking the absolute

rolling angle as one of the criteria, we assumed that this becomes maximum at the crest of the wave. Besides, iñclining moments by wind were assumed to be constant, regardless of the ship's heel angle, upright or inclined. The effect of shipped seawater was neglected in the calculation because of its. complicated behaviour, but it was taken into considerations as the modification of the value GZm. Accordingly, by the effect of shipping water, or by the shift of cargo aboard, even the ship which has the GZni value that the Regulations gives as sufficient, and C value of i to 2 or even the ship

which has C value greater than 2 could be in danger, or might even capsize. It seems that this.

happened in the case of the aNankaimaru in 1958.

The method, proposed by the author in his previous paper(3), is to estmate the stability quality from.

the comparison of the work ratio of the ship with the critical value of the ratio that corresponds_to the value of Kv or Ah/W. _{Accordingly it is not necessary, in this method, to regulate the vàlue of} GZm especially. _{It might not be a satisfactory method, and may involve the same deffects,} because-the effect of because-the shipping water was not taken into considerations in doing calculations..

In this paper, the effect of shipped seawater is considered in addition to the rolling _{motion by the} wave and the inclining moment by the wind. _{As the effects of the shift of the cargo, and the effect} of steering' are rather small for ordinary ships, they are included in the margin in the ratio of works. Changes' of the wind pressure, the apparent center of wind pressure and the apparent center of water pressure were taken into account in The calculation of the inclining momet by the wind. _{As to the} synchronous rolling in irregular waves, a calculation formula for the relative _{rolling amplitude was}

obtained and used in considering the active resistance besides the _{passive one, and the magnification} façtor of amplitude. _{The effect of shipped seawater was calculated, considering the effect of}

free-board, the sheer, the form of the upper deck, the inclining angle to the'wave surface, the height of

bulwark and the size of freeing ports on this phenomenon. _{Applying this new calculating method,} the critical value of the work ratio which is _{necessary and sufficient to estimate the stability qualities} of any ship under any circumstances of wind, wave and the shipping water on her deck, was obtained.

2 Standard Condition to estimate Stability Qualities

_{of Ships}

The standard condition to estimate the safety of a ship under a certain atomospheric and _{sea condition} is as follows. The ship is supposed to have an initial heel angle Os due to the stationary wind pressure,

and to oscillate around that angle, affected by the passive and active resistance, in irregular waves

developed by the fluctuating irregular wind, which has mean value equal to the stationary_{wind velocity.}

When the ship inclines to the weather _{side by the standard ainpliludc of ¡'oil, relative to the effective}

wave surface at the resonance condition, the wind _{pr-ssure instantly increastes to 1.5 times that of} the stationary wind and keeps its value till thc ship finally inclines to the other side. _{After the gust}

An Estimating MethodShipped Seawater I4

ac:d on the ship, she is supposed to keep the resultant oscillation of damped free rolling and forced

rollingthe free rolling damped by the passive and active resistance, and the forced rolling which has its neutral at the inclined angle Os' where th'e inclining moment by the wind shows the equal

value with that oi the restoring rnnnlent of the ship. We also assume that the motion of ship is

influenced by the shipped seawater, which stagnated on the deck witilout ejected out completely from the freeing ports and flows to the lee side with the inclination of ship, and also by the newly shipped

seawater. The stability qualities of ship in this state is estimated by the ratio of the works, i. e.. the maximum effective potential energy and the work done upon the ship by the resultant moment

which is the difference between the inclining moment and the restoring moment.. Besides, the qualities

are judged by the factor of safety for stability that is the ratio of the above mentioned ratio and the critical work ratio.

Assuming the standard wind velocity according to the navigating region, we are able to estimate

-the stability qualitiés of ship which is operated in this region referring to the ratio of works, or the

value of the factor of safety for stability as was mentioned. As the value of standard wind velocities, the values which were used in the Stability Regulations were adopted here also.

Namely

Group I for Ocean-going ship wind velocity 26 rn/s

Group II for Coasting-I service ship wind velocity 19 rn/s

Group III for Coasting-Il service ship wind velocity 15 rn/s

Ships which belong to the Group III are those of limited coasting service, and they are operated only

in the Seto Inland Sea, or in the place where their operated ranges are within two hours at the

highest speed.

3 Moment due to Wind Pressure

The moment due to the wind pressure is an important factor to estimate the stability qualities, and the method, which has widely been used is to assume the moment by the wind to be constant2.'

or to be proportional to the projected area at the inclined state múltiplied by the vertical distance between

ihe centre of wind pressure and the centre of water pressure(5). However, the computed results come out to be quite different from the actual values which have been shown lately by the results of model experiments(8), and so, this simplified way can not be considered so reliable in the stability estimation.

3.1 Wind Pressure and Position, of its Centre of Efforts

Based on the facts that the wind velocity increases gradually with the increase of the height above

the sea9, and the value of the wind velocity in 'Beaufort scale is indicated by the velocity at the

height 5 meters abóvé Ïhé sea level, the total wind pressure and its center of efforts for the ship in upright condition is given approximately by the following formulae

P=0.78X10"f,Av2

(1)

ho=fchi '

(2)

where

P= the total wind pressure in upright condition (t)

A=the lateral area of the ship above W. L. in upright condition (m2) v=the wind velocity at the height 5 meters above the sea (m/s)

ho= the vertical distance from the water level to the apparent center of wind pressure (m) h1 = the vertical distance from the water level to the center of lateral area (m)

f, = the wind pressure coefficient =0.43h10.45

Fig. 1 Apparent centre of water pressure of

ship models with bilge keels, drifting with velocity Vd/1/gB =0. 12 (From Report of the 17 th Research Comm-ittee) o 0' D' DI 05 06 _{c Ql}

Fig. 2 Curve of h2/de for ships with bilge keels in.

upright condition

= 1. 33 h1°.°4

Eq. (1) and (2) show good agreements, with the values of the total wind pressure and the position of the wind pressure centre obtained from the results of wind tunnel tests6 for several ship models, and therefore, they are supposed to be reliable sufficiently.

3.2 Apparent Centre of Water Pressure

The 17 th Research Committee, Japan Shipbuilding Research Association, carried out a number of model tests about the height of the centre of water pressure. According to the results, when the ship drifts by the wind pressure, the vertical force due to the flow of water, in addition to the horizontal force, acts on the hull, and these forces build up inclining moments with the wind pressure itself and the added buoyancy. Another additional moment results from the fact that the water level in weather Side of the ship falls down and that of the lee side rises up. The sum of these moments is equal to the statical restoring moment of the ship at that inclining angle, and accordingly, the lever, obtained from the restoring moment devided by the wind pressure, will give us the position .of the apparent centre of water pressure. This apparent centre of water pressure changes its position with the

dri-fting velocity t'4. When the wind, which ranges 15-26 rn/s in its velocity, acts on the ship, the:

drifting velocity of the ship vill become to be 2-3 knots, and the Froude's number va/y,/jB is in the

range of 0.10-0. 14. In case when the Froude's number is 0.12 as an average, the ratio h2/de of the vertical distance h2 of the apparent centre of water pressure from the sea surface to the mean draft d varies considerably with the ship form and the heel angle as is shown in Fig. 1('), for ordinary types of ship with bilge keels. The ra'io h2/d in upright condition can be represented as a function of the

block coefficient of the hull, as is shown iñ Fig. 2, and can be obtained approximately from the

following equation,

h2fde=5. 24 (CbO. 475)-5.43 ICo-0. 475P.

(3)

As is easily found from this equation, when the block coefficient Cb is less than 0. 475, the apparent

P: P4SUqJP Vessel centre of water pressure in upright condition is above

C : Carp Vessel the water surface.

f: Fsheq Boit 3.3 Equivalent Length of the Lever of Wind

Pre-ssure Moment

Let L20 represent the corresponding equivalent

len-gth of the lever of the moment due to the wind.pre-ssure, which is obtained from the wind pressure

moment in upright condition devided by the

displace-ment, then it is given by the following equation

-o,

-o'

-o,

L50=0. 78x10-'fpA?2

w (ho+h2) (m). (4)

As the wind pressure and the centre of

wind pressure, varies remarkably with 6 the heel angle as are shown in Fig. 3,

and as the apparent centre of water

pressure also vàries with the heel an- 2 Wind PTeSSUTV Ratio

gle, it needs quite a laborious work to ¿o

____

obtain the wind pressure moment exa-ctly in an inclined condition. It is

ne-cessary, therefore, to get a practical

and simple approximate method even

k

though the accuracy is inferior to the

exact method. Experiments about the total wind pressure, the position of the

apparent centre of wind pressure and

that of water pressure, using a number of models, were carried out by the 17

th Research Committee. Based on these

results, the wind pressure moment in

various inclined conditions was calcula-ted, considering the effect of drifting

velocity. The curves of ratio L5/L50 of -/0 ₀ 10 30

the equivalent lever of the wind pre- 8 (44.)

Fig. 4 Curves of ratio of wind moment k ver ssure moment for inclined condition to

that for the upright condition are shown in Fig. 4, on the basis of the heel angle. The shapes of the

curves are effected by the ratio of the wind pressure area to the underwater area, the shape of the

wind pressure area, the drifting velocities, etc, however, it appears that the block coefficient of the hull influences most dominately. As iS clearly shown in Fig. 4, the behaviour of the curve is quite

different by the sides,the 'veather side or the lee side, and when the ship heels to lee side,

the wind pressure moment gets its maximum at about 5°, and after that, it decreases with the incre-ase of the heel angle, and gets smaller extremely at 35°-..45°. We can see a tendency that the more slender the ship is, the smaller value it reaches. The decrease of the wind pressure moment is less

in the case of the heel to weather side, and the more slender the ship is, smaller this amount of

decrease becomes. Let Lm represent the equivalent lever at 0 =5°, the ratio L5/L, is given approxi-mately by the following equation.

When 05°,

2.8

T=0.55+0.45C0sI (0-5),

₍₅₎

I-rb where L30

Lni._i00397c

We assume that this ratio is constant when O 64.3 C0 +5°,

i.e., Ls/L,n=0.3. When-35° <0<5°,

=1O. 43 Cb(lcos 4.5(0-5°)}.

(6.

An Estimating MethodShipped Seawater ₁₅₁

Passen jer.tz ro Vessel

= ñ000'r/O.JûtSOD

Full Lo4dC,jadjtaa. 4-oS34

-io -Jo -zu -is o io io ¿o w

à

Jzdtagta ûWq

Fig. 3 Curves of centre of wind pressure and wind pressure ratio

c-....c.-07

1.2

Caatre 4 WielP,sswe

We assume that the wind pressure moment given by eq. (5) and (6), which stands for ships in

still water, can be applied for ships rolling in waves. This assumption appears to be sufficiently correct according to the experimental invesiigations made by Prof. Hishida and his coauthor°>..

Usually it is believed that the fluctuation rate of gust is about 1.4 in tii case of typhoon and the low pressure zone and about 1.25 in the front line and the pressure gradient, however, we ought to takcthe higher value of this rate for the estimation of the stability qualities of ship in stormy weather and rough

sa. Considering the work given by the wind to the ship, it is reasonable4 to take the value Vl.5 for

velocity fluctuation of gust, for we assume that the gust acts on the ship at the instant when she

inclined to the weather side, and gets its maximum at that moment, and keeps its value till the ship

inclines to lee side. Accordingly the equivalent lever of the moment is given by the following equation

L1=1.5L5.

(7)

4 Synchronous Rolling in Irregular Waves

4.1 Absolute Amplitude of the Synchronous Rolling in Irregular Waves

The synchronous rolling in irregular waves is defined as thé rolling in irregular waves which has the most prominent peak in energy at the period that is equal to the natural period of rollng of the ship. This synchronous rolling is induced by the developing irregular waves generated by winds of

given velocity. Let T represent the natural period of rolling of the ship, w, the circular

fiequ-ency, v(m/s) the wind velocity. According to G. Neumann('"), the energy spectrum (r(w)]2 of the irregular waves developed by this wind velocity at the widely open sea, is given by the following equation

(y()]3= ! £e2g21&v2 _{(me. sec)}

₍₈₎

where

C=3.05 (m2. sec5).

The circular frequency Wmftx, where the energy shows the maximum, is

/2 g

Wmax

- j - ;

The energy spectrum of the undeveloped irregular waves, where the period of the most prominent waves is equal to Ts, takes the maximum value at W as is shown in Fig. 5, and the cumulative energy density E1 is represented by the shadowed area in the figure, that is

El=f

(r(w)]2Sw, (in2) ₍₁₀₎

O.Uwj

and, the significant wave height is given by

ft113=2.832,/E (m). (11)

Now, the resonance curve (Fig. 6) is necessary to obtain the rolling amplitude of the given ship in

such irregular waves. For this purpose, we have to abopt the resonance curve that is obtained from model experiments in regular waves which have the slope ® approximately equal to that of the ima-ginary regular waves as will be mentioned later, _{thinking of the non-linearity in the roll damping}

and the restoring moment. _{This resonance curve is influenced not only by the passive and active} resistances but also by the true effective wave slope coefficient for every element wave. The response amplitude operator [A(w)] (Fig. 7), _{that is, the absolute roll angle of ship induced by the wave of} unit amplitude can be obtained as follows,

[A(w)] = [rww2p/g] =[00 Wfl - g

j

(rad/m)

(9)

(12)

4 3 F

00

5 85i ¡.0 w 20 Wau W, Fig. 5

Energy spectrum of waves

I

.85w,

u

Fig.

7

Response amplitude operator

(4)

Fig. 6

Resonance curve

Fig. 8

where r= the effective wave slope coefficient for the wave of circular frequency w

p = the magnification factor

=0a/r)

= the absolute roll amplitude.

Then, the energy spectrum of rolling of ship [0(w)]2 (Fig. 8) and the cumulative energy density of

rolling Es are obtained as fol1ows"),

(0(w)]2=[r(w)]2[A(w)]2 (rad2. sec) (13)

Es=f

[0(w)]2dw (rad2). (14)

O. OBwj

The significant roll amplitude and the maximum amplitude in n rolls are as follows by M. S.

Lo-nguet-Higgins("),

Oiial. 416)/&

Jo=1.870/E,

j,=2. 12VE

Îioo2. 28,/ES

zoo 2. 43/ oo = 2.60/E5 Öi000 = 2.73/ E,

42 Standard Amplitude ßoj of the Relative Synchronous Rolling In Irregular Waves

The absolute amplitude 0.,., of the synchronous rolling in regular waves, when the ship has only the

passive resistance, is given by the following equation

(deg). ₍₁₅₎

where r=the effective wave slope coefficient for the synchronous wave

=0.74( )O.0

d=the draft moulded (m)

e=the maximum slope of wave surface (deg)

N=

On the other hand, the results of model

experi-ments show that the real angle of absolute

synch-ronous rolling in regular waves Oae does not

coin-cide with 0.,., obtained by equation (15), and the

t=iio

-o o (18) the relative where (19)

7)

tanwt1=- _cosecpacotpa 00e (20)

An Estimating Method Shipped Sea water 155

From the results of model experiments, the author found that when the ship has maximum inclinatùr. toward the lee side, the value of wt1 is about 12O023O0. The ship oscillates around a certain heel angle O induced by the steady wind, and as the modified stability curve, which is determined by the

righting arm and the lever of heel moment by wind pressure, is not symmetrical against O. the amplitude of roll is different by the sides. weather side or lee side. The amplitude úbtained by the eq. (19) can be considered to be the mean value for both sides, however, and so it can be said

that the amplitude in weather side is approximately Oo. Even in case of rolling in irregular seas, we assume that the similar relation exists. Namely,

Oot=O sin(wttpa)re sin wt,

(21)

where tan

(L)tj= cosecpacotpa

wtt = 12O023O0

.

Oat the standard amplitude of absolute synchronous rolling in irregular waves

Ootthe standard amplitude of relative synchronous rolling in irregular waves.

4.3 Standard Amplitude Oat of the Absolute Synchronous Rolling in Irregular Wav.

As for the standard amplitude of absolute rolling, contained in eq. (21), we have to decide it by

our experience. In our previous paper(4), considering the small probability of occurence of the

condi-tion when the ship is suddenly exposed to a gust when she is at the extreme heel angle to the wind side by rolling, we assumed the maximum angle among 20-50 swings as the standard amplitude, and abotped the value of 70% of the amplitude of the synchronous rolling in regular waves which has the same slope as that of the significant wave given by Sverdrup-Munk's steepness curve. This method

had been decided by the 17 th Research Com&ttee of JSRA, and was adopted in the Stability Regula-tions, however lately, it came out clear to be not abequate by some reasons. That is, a strikingly large difference was found at certain wave ages between the steepness of significant wave in irregular

waves in the growing stage calculated from Neumann's Spectrum, and the steepness given by Sverdrup

and Munk's steepness curve. In deciding the relation between the expected maximum roll angle and the amplitude of synchronous rolling in significant regular waves, we should abopt the significant

wave obtained from Neumann's Spectrum, as the maximum angle among 50 swings is computed using

that Spectrum. As the ratio of the standard amplitude to the synchronous rolling amplitude in regular

waves also varies by the difference in the roll period, and also by the roll resistance, it is not adequate to use the 70% of the synchronous rolling as the standard ampitude in all cases. Then in order to decide the standard amplitude, let us examine the case as follows. The "AMaru", a 300 Gross Tons cargo-passnger ship, leaving port in early Oct. 1947 into heavy seas, was reported to have rolled about

21' in relative roll amplitude, under the wind 15 rn/sec in velocity and induced waves on her beam. If we assume that: the irregular waves were generated in sufficiently extended sea by 15 rn/sec wind, the circular frequency of the significant waves, when the ship rolls synchronously by her own natural

period of 6.3 sec, is 0.977. Obtaining the energy spectrum [O(w]2 of roll from the energy spectrum

of developing irregular waves multiplied by the square of roll response amplitude operator of this

ship, and computing the cumulative energy density Es from it, we obtain 22° as for the maximum

amplitude u(=2.01VEs) among 32 swings. Substituting the value of d and the computed values

of wtt (182.9°) and Pa(70.6°) into equation (21), we will obtain 20.8° as the relative amplitude. This computed amplitude almost coincide with that of real rolling of 21°.

However, as this OE32 seems to occur rather frequently on heavy seas, we consider, to adopt the maximum amplitude Öioo among 100 swings as the standard amplitude Oat is rather realistic in judging

the stability characteristics of ships under considerable severe conditions. That is because this value is greater than Ö,i in some degree, and this means it has some margin for other heeling moments,

which do not appear in the computation of the critical ratio of works as will be mentioned later. Now from the practical point of view, we must get some approximate method, because it requires a

con-siderable efforts to compute this standard amplitude Oaf, that is oo. after obtaining the amplitude re-sponse curve for individual ship, and the energy spectrum of waves. For this purpose, we suppose an imaginary regular wave which is related closely with the energy spectrum of the developing irre-gular waves having the most dominent energy in the circular frequency Wi of the ship's rolling fre-quency, and obtain the relation between the synchronous rolling amplitude Oce in this imaginary regular

wave and oo. The significant wave is used most commonly as the equivalent regular wave which represents the effect of an irregular sea, however it was made clear that there is no simple relation between Oae and generally. Therefore, as the equivalent regular wave for our purpose, we adopt an imaginary wave which has same period with that of the ship's natural rolling and the height that is the same with the maximum height Ño among 50 waves. The height of this imaginary regular wave is 1.5 times that of the significant wave, and is equal to the mean of the highest 2.7% waves of the

total number of many consecutive wave trains. Accordingly the maximum wave slope of the imaginary

regular wave is given by

(deg). (22)

The values of 0 for winds of 15, 19, 26 and 30 rn/sec in velocity were computed corresponding to several

periods, using the Neumann's Spectrum, and are shown in Fig. 10. _{In order to get the relations} be-tween Oae and ioo. let us at first assume the simplest case when _{no active resistance exists, the}

passive resistance is proportional to the absolute angular velocity namely _{the rolling decrement in still}

water is represented by öOGOm, and the effèctive wave slope coefficient has no relations with the

wave period and is constant. We assume that the sea has developed to such _{an extent that the signif}

i-cant wave has reached its maximum in wave slope, and as the equivalent regular wave with them,

we choose as follows

3C)

Fig. 10 Maximum slope of imaginary regular waves

I£ ,aioci't___!O

Iri

.1

dl:ii

8

Ñ,è

0L77r

Table 1

we obtain the amplitude Oae of the synchronous rolling of

ships which have the roll decrement coefficient0.3, 0.4. and 0.5 respectively in this equivalent imaginary regular

waves, and also computate ioo of these ships, in synch-ronous rolling in the irregular waves which have developed

to such an extent as above mentioned, and finally get&oo/Oae, the ratio of these amplitudes, as are

shown in Table 1.

Next, as the most general case, we assume that the ship is subjected to both active and passive

resistances, and that restoring force is not linear, the effective wave slope coefficient varies with the wave period as it actually does, and also that the apparent moment of inertia varies according to the.

rolling amplitude. We can obtain the resonance curve for these cases only by the model experiments.

Namely, we select the resonance curve which is obtained by the model experiment in regular waves,

in which & is almost constant in the range of 9°-15°. A part of the resonance curves is shown in Fig. 11, and the results of computations are shown in Table 2. As we can see in this table, the ratio

1oo/Oae varies in the range of 0. 75-0. 94, and generally the smaller is the magnification factor, which

4

j

2

/

04

An Estimating Method-Shipped Seawater 157

08 12 16 20.

Fig. 11 Some of resonance curves used in calculation

Table 2

Wind velocity

a rn/s Resonance curve 00./e -

.ej,e

A 237 266 0-907 B1 2-60 084 309 0897 19 C 3.44 105 3 28 0-860 D1 1.05 362 0851 E1 2-74 0.81 3.39 0875 A2 2-18 0-89 245 0.937 26 B2 2 33 0-84 278 0920 C3 305 105 290 0895 f'2 3.36 105 320 0855 Is E2 286 081 3.53 Wind Velocity t rn/s a 0.4 i 3.93 0.88 0.5 3.14 0.877 19 0.5 3.14 0.876 0.3 5.24 0.750 26 0.4 3.93 0.837 0.5 3.14 0.882 y _(mIs) 15 19 26 Tw(sec) 5.8 7.48 10.13 (deg) 10.38 11.52 13.46

i

oc

07

Z 3 4 3 6

a,4(isiFdsr p

-Fig. 12 Standard amplitude of absolute rolling among irregular waves

is the ratio of the absolute rolling amplitude Oae and the effective wave slope rO, the larger the ratio

°100/Oae becomes. Taking the values Oae/TO shown in the table as the abscissa, we plotted the value

O100/Oae. The results are represented in Fig. 12, and approximately a linear relation is obtained as

follows

OaZ 0100

Ooe - Oae

=1. looo. 0688 (23)

From the equation (23), 100 or the standard amplitude Oatof the absolute synchronous rolling in

irre-gular waves is obtainable. We can conclude that when we want to get approximately the standard amplitude of the synchronous rolling in irregular waves, we can always use the value of the effective

wave slope coefficient for the synchronous waves, and that we can compute the standard amplitude of roll, approximately and simply using the magnification factor of the synchronous rolling in equivälent imaginary regular waves.

4.4 Decrement of Free Rolling

After the ship has suddenly been subjected toa gust when she has reached the maximum inclination toward the weather side on her rolling, the motion becomes the resultant motion of the forced rolling by waves and the free rolling induced by the sudden variation of wind pressure. After the first swing toward the lee side, the first amplitude of the free rolling O decreases by JO1, and the amount of

decrement is obtained approximately as follows

01=03,-03. (24)

Assuming as

01=the resultant amplitude=Oot+Or

Nt=the damping coefficient corresponding to the amplitude 01, then

ôO1=O1(1_-e11}. (25)

From the results of this calculation for many ships _{this decrement JOG' came out to be a small angle} of 0.3°-.-O.8°, and the ratio of this to 01 is in the order of 1.5--3.5%. Accordingly, in order to sim-plif y the calculations and because we estimate the stability characteristics by the method of compa-risons, we can neglect this decrement practically.

An Estimatiog MethodShipped Seawater 159

5

Effects of Shipped Seawater

5 . I The Point of View _{on Effects of Shipped Seawater}

The effects of shipped seawater upon the stability characteristics are very much complicated, and the accurate calculations _{are difficult. Accordingly, it is necessary to establish a well designed} app-Toximate method based upon simple and adequate assumptions. _{At first, assuming a ship which is} under the least influence of shipping seawater, namely a ship without bulwarks or a ship which has very high freeboard, and assuming such wind and sea conditions as will give this ship the critical

stability qualities, we calculate the ratio of works, and use this as the criterion. Next, taking a ship which is under the severe influence of shipping _{seawater, namely a ship which has low freéboard}

with bulwarks and large well as the other extreme, _{we establish a calculation method under some}

assumptions. _{This approximating method should be the one that will give the critical value to the} ratio of works for this ship, under the critical wind velocity _{and irregular waves induced.} Applying this approximating calculation method to the _{case of a ship which is moderately influenced by the} shi-pped seawater, and if the ratio of works calculated for this _{ship under the critical condition also comes} out to be eguali to the critical ratio of works, this method _{can be recognized as is reasonable}

appro-ximation.

For the case when a ship heels Os _{on her . lee side, under the effect of a steady wind, rolls} synchro-nously around this heel angle, and finally capsizes by the effect of shipped seawater, we found from model experiments, that the seawater rushed into the ship many times from the lee side or weather side, and finally the ship capsized on the side where the seawater rushed in. Generally, the ship cap-sizes on her lee side to which she has the initial heel angle. Therefore, we consider the case when the seawater ships from the lee side. Namely, we assume the following sequence of conditions, that is, when

the ship heels to a large angle toward the lee side, in the vicinity of wave crest, by her synchronous

Tolling, the seawater ships from that side, and secondly when the ship heels extremely toward the weather side, in the vicinity of wave trough, the ship is subjected to the gust and heels toward the lee side again with the seawater, which remains on her board without ejected out completely through the freeing ports, and then the seawater 'rushes on her board again from the lee side and finally the

ship capsizes. As was mentioned before, in the well, where there are no deck houses, the seawater

'that shipped on board before the gust hit the hull, remains on the deck without ejected out completely,

runs on the deck toward the lee side and strikes the bulwark when the ship heels on the lee side by the effect of 'the gust. Therefore the effect of the seawater which remained initially on the deck is to decrease the restoring force by lifting up the centre of gravity of ship (this effect is generally Sm-all), and is also to produce the heel moment by the shift of its position and by its impact against the 'bulwark. The shipping water after the gust hit the ship, namely the second shipping water inclines the ship by its impact against the deck and the bulwark, and also produces the heel moment remain-ing on the deck. Let us express the effect of the first shipping water by M1 and the effect of the

second shipping water by M2. These are approximately proportional to the volume of the shipping seawater, and the volume of this seawater depends on the maximum inclination of the ship relative to

the surface wave, the breadth of ship, freeboard height, sheer, the height of the bulwark, and on

'the dimensions of the freeing ports.

As for the side passages between the deck house and the bulwark, the effect of the first shipping water M1 does not exist, as it is recognized that the first shipping water from the lee side is ejected out completely while the ship heels toward the weather side. We assume accordingly that only the

52 Heeling Moment induced by Shipped Water Thinking of the imaginary regular waves, the relative

waves ie represented by

0601 sin (øSPa)0 Sin wi.

Accordingly, the rolling amplitude O, against the surface wave becomes,

OOs=Oal sin (wt,Pa)t9 Sin (Uts where

tan wt8 = Cosec PaCot Pa

wts'i'130°-24O°

Fig. 13 Transverse section at any

point P.

Therefore, considering the heel angle O,, induced by the

steady wind, the maximum angle of inclination Ou

agal-then, in the case of rolling iñ irregular waves, the seawater will rush into the deck even if O,, is

considerably smaller than ÇOi'. For the convenience of comparison, we assume that the seawater starts

to ship when the deck edge submerges into the imaginary regular waves, namely when Ou is equal

to tan'

2f

Let O represent the crossing point of the centre line of ship with the water line, and Q represent the crossing point of the deck surface with the inclined line. Ou in angle of inclination to water surface, which runs through O. Representing the distance from Q to point P on the side of

ship by b, this will be given by

B' f'

b=---'

_{2 tan Ou}

We assume that the maximum value of the heeling moment induced by the first shipping water is equal to that of the second shipping water, and express it as

Mc=f«Phcbc dx (t-m), (30)

where p=the weight of the unit volume of seawater =1.025 (tIm')

a is a coefficient decided by experience, and is 0. 55 from the method which will be mentioned later. 1f we call the maximum lever of heeling moment induced by the shipping water as L. L is given by

L=M/W (m).

(31)

The heeling moment M according to the shipped seawater on the deck side passage is given by eq. (30), when b is smaller than the breadth of the passage b,,. while when b is larger than b,,, M is

given by the following equation,

M . faßhcbp(2_

t")

dx, for b > b,,. (32)

(29)

rolling angle of ships against the surface

(28)

5.3 Acting Range of Shipped Seawater

As the evaluation of the varying condition of the shipped seawater by the change of the heel angle. and of its acting range need not be so accurate for the purpose of comparison, we will take a simple approximate way which is easy to calculate for this purpose. Now we a.sume the followings. The effect of the first shipped seawater M1 acts on the motion from the time when the ship becomes

upr-ight after the gust hit the hull, until the time when the bulwark top at midship immerses. The effect of the second shipped seawater M2 acts from the time when the deck edge at midship reaches the

wi-ter surface until the time when an imaginaiy point at midship which has double height of the bulwark

from the deck side immerses. The varying effects of

these shipped seawater can be expressed by a sine or cosine function. Then the various notations in Fig. 14

which represents the midship section of the ship are

used as follows

fo=the freeboard t midship in ni.

2/o

(00= tan'---- =the approximate value of the heel angle relative to the surface wave,

when the deck edge at midship reaches the

water surface,

2(fo+hb)

ço= tan '--j--- -- (deg) 2(fo+2hb) ç2=tan

B (deg)

O=the heel angle relative to the effective wave when the ship becomes in upright conditiori

after the gust hit her (deg).

'Poe,(Oie, Ç02e=the heel angles of the ship relative to the effective wave corresponding to Po. çOi and

(02 which represent the heel angle relative to the surface wave, respectvely.

Let t,. denote the time when the ship becomes upright then since the absolute heel angle must be zero

for this t, we can write that

Oat Sifl(WtuPa) +Os =0

Os

WtuPaSifl' ,

then

OuOat Sin(WtuPa)T0 sin wt+Os

=_resin{a_sin-'

_{: }.}

(33)

In the next place, if we let to denote the time, when the deck edge at midship immerses, we can write that

(Po = Oat Sin (wtoPa) (9 sin wto+ Os (34)

(OoOsOat sin(wtoPa)(9 sin wto

or

An Estimating MethodShipoed Seawater 161

Fig. 14 Midship section

øsin(wto+a) then

wto=a+

where Oatsin Pa (9Od! COSPa

01/ O+&22 Oatt9

COS Pa

wto.,80°-2O0°

o'ai.6O°-12O°

therefore

v'o.. Oat Sin (utoPa)

r&J

sin wto-F O,

=çOo+ (lr) sin'wto

=çoo+

(lr)

sin{18O°_a+sin-'()}

( .

=çPo+(1r)es1n10s1n

___ö_)J (35)

As the heel angles and Çse, relative to the effective wave, when the bulwark top and the point which has the double height of the bulwark immerse, are generally very large be>ond the ordinary

roll angle, we can not obtain these values by the method above mentioned. Therefore as the appro-ximate values of çeil and 0se, we take the sum of the difference between the effective wave slope and the surface wave slope, when the ship heels to leeway side on its extreme, and the value of 40i or ço

respectively,

i. e.,

çe=çOi+(lT)ø sin øtt

(deg) (36)

çu=ps+(1T)ø sin wts (deg), (37)

where

tanwt&= cosec Pacot Pa.

The heeling moment by the first shipped seawater M1 acts from to and its lever L1 is given by 900

L1=L sin

(OOs).

(38)

(Die - u,,

The heeling moment by the second shipped seawater M3

0,10

y..

Jacliaatas 9

Fig. 15 Equivalent levèr of inclining couple due to shipped seawater

6 -(0ie,

6 Factor of Safety for Stability

61 Factor of Safety for Stability

From the method mentioned above in detail, the work ratio of rolling when the ship rolls under the

'effect of winds, waves and shipped seawater can be obtained, _{The procedure of this method can be} summarized as follows as is in Fig. 16. Get the heel angle Os by the steady wind _{as the angle where}

the curve of lever by wind pressure crosses the curve of righting lever of stability. _{From Os. take}

the standard amplitude of relative synchronous rolling Oo _{to the weather side. Draw a curve of lever}

of wind moment by gust from Oot, and to this curve add the_{curves of lever of heeling moment by the}

shipped seawater L1 and L2. The area S1, which is enclosed by the_{curve of righting lever, the curve}

of lever of resultant heeling moment and two vertical lines at the heel angle (OoL+Os) when the

gust acts and at (0ie, _{represents the maximum kinetic energy of the ship at the heel angle}

_{. The}

.area S3, which is enclosed by the curve of righting lever, the curve of lever ai resultant heeling

An Estimating MethodShipped Seawater 163

Fig. 16

sents the heel angle when the seawater starts to enter from some opening and °e represents the heel angle where the curve of lever of moment by gust pressure crosses the curve of rightihg lever, repre-sents the effective reserve dynamical stability, or the effective potential energy of the ship. Then we calI the ratio of S2 to S1 as the work ratio, namely

work ratio R=S2/S1. (41)

When the stability performance of the ship is just in critical condition, we call the work ratio of this

ship as the critical work ratio and write it as R.

Then the factor of safety for stability Co of ships is given by

Co=R/R. (42)

For the safety of ships in rough seas this safety factor Co should be larger than unity.

By the way, the above mentioned angle of flooding Çse is taken relative to the effective wave surface

and is approximately given by

çoseçOs+(1T)esifl (Vtj, (43)

-where ÇO represents the heel angle relative to the surface wave when seawater starts to flood into the

'ship.

62 Critical Work Ratio R

The critical work ratio R is the work ratio of the ship which capsized just under the critical con-ditions. Examples of these ships are scarce. The torpedo-boat "Tomozuru" capsized in a stormy sea of 20 rn/s mean wind velocity under the fleet operation on Oct. 3, 1934. We may regard that the sta-bility performance of "Tomozuru" had been critical for the sea condition at that time, considering the fact that both two sister ships operating together with "Tomozuru" escaped from capsize. Calculating by the method in the Stability Regulations, using the damping coefficient N obtained by model

expe-riments of this shfp, we have C=l.0 for D=0.0700m, 1.5D=0.1050m, Oo=27.20°, and N=0. 0142

under wind velocity of 20Th/s. For such a ship with slender hull (Cb=O.5O for Tomozuru) with large

wind pressure area (lateral area above water/lateral area under water=2. 20) and without the bulwarks which means with very small effects of shipping seawater, we can estimate the stability performances

of the '

even b'- the method of the Stability Regulation. However calculating by the new method

abo'e mentioned, it cornes out that Lo=0. 0518 , L,?L=O.OS2 nl. L40.0777 m and ô - ti,

ro!! angle Oa!=29.5e for N0.0134, PaB4.7° and Or=3O. 7 c.rrcspending to the su:tcc wave skpe

fl. 83' and finally as the work ratio, R-=1. 53. This value of the work ratio 1.53 i.

:al

value in which O. 3 means a margin, which is for many uncalculated heeling nmrnents, such as tie nument by shipped seawater on decks besides the moment concerning bulwark, the rudder trest:re.

.1

-make this margin to be moderate and not too large, themaximum amplitude among 100 swings 0100 is

adopted as the standard amplitude of rolling Oat., Then, the critical work ratio is decided to be

R=J.53.

(44)

63 Determination of Coefficient a

About 1947, many F-type cargo ships (750 DW-type) were constructed in Japan. As the stability

performances of these ships, however, appeared rather poor, the investigating committee for stability performances of F-type cargo ships was organized and many investigations were carried out. As the

results of the investigations about many stability data of this type of ship collected from many shi-pbuilding yards, as well as about the research data, this committee proposed the minimum stability

performances which should be fulfilled by F-type cargo ships ; that was, its GZ value should be larger than 0. 140 m at heel angle of 20°, 0.200 m at 30° and 40° and thestability range should be larger than

75 degrees. After that, in 1953, however the ship safety division wasorganized in the Ship's Technical Considering Committee, and as the result of investigations the committee proposed that the ships with

breadth narrower than 13m should have GZ, as CZm0. 0215 B. Accordingly the F-type cargo ships. (B=8.40m) must have as the minimum stability the values that GZm=0. 181m, 75degrees for

stabili-ty range, and the righting lever of

O(deg.) 0 10 20 30 35 40 50 60 70 Tb

GZ(m) 0 .09 .154 .179 .181 .176 .150 .102 .037 0

If we assume a F-type cargo ship which has the stability curve as above mentioned, with aftengine. large well and small freeboard (lateral area above water/lateral area under water =0. 98) which means the ship is under the severe effect of shipping seawater, and also assume that GM=0.55 m,

T=7.3

sec. and the stañdard wind velocity of 26m/s, then the ship should be under the severest condition and

the stability of this ship must be critical. Performing the calculations for such a condition using the

proposed new method, we can obtain L50=0. 0321 m, Lo=0. 0482m, Os=3. 60 and also Oat=22. 4° for N= 0.0171, Pa43.5°, Oo=l7.5S° using the imaginary regular wave having the maximum slope O of 13.1°,

by making use of the N value obtained from the model tests. As to the effects of shipped seawater,

we get O=-4.42°, ÇOoe=ll.730, ÇOie=2l.9O°, Ç'2e=33.lO° for its

acting range, and L=0.1888a for

the maximum value. From thess values we determined the coefficient a that makes the work ratio te

be just 1.53 and obtained 0.55. Then the formula to calculate the maximum value- of heeling moment.

M by shipped seawater is given by

M ₌f 0. 55 phb dx (45)

64 Examination about the Applicability of this Method

-Now by adopting this method to the ship which is moderately affected by the shipped seawater, let us investigate the justification and the applicability of this method for calculation of the critical work: ratio and the effects of shipped seawater, which were determined thinking of two extreme cases of the ship, the one is the case when the ship is scarcely affected by shipped seawater, and the other is the case when she is severely affected by it. The ship chosen for this purpose is a 500G.T. type

cargo-passenger ship "K-Maru". The tabiliIy performance of this siip is rather poor, and it was con-sidered in the author's previous paper3 thai she was critical under wind velocity of 27 rn/s. This r,hip has a well at fore part, and deck houses aft from the middle part of the deck, with deck side passages. on both sides, having the ratio 1. 39 of the lateral area ;IbOVC water to the lateral area under water.

Therefore the effect of the shipped seawater can be considered to be moderate. When this ship is

under the wind of 27 rn/s. it comes oUI that L00. 0517 tu. L40=O.0775 in and O=3. O6, and also

co--rresponding to the irn:ginary wave having the maximum slope C'-) of 12.6", _{O 2l. 9' for V- 0. (1147,}

* Upper values are for wells, lower values for ship side passages.

in a coasting service. Although this ship has only a narrow space in stern to. be affected by the

shi-pped seawater, ve regarded that the stability qualities of this ship was insufficient, since the safety

factor was 0.889 under 19m/s wind. At present, however, this ship is engaged in a limited coasting service (in this case its standard wind velocity is 15 m/s) and its safety factor comes up to about 1. 1.

Moreover being increased the rolling resistance by changing the bilge keels, this ship is not in danger

now. Ship B was a cargo-passenger ship, and even though her C value by the Stability Regulations at wind velocity of 19 rn/s was 1. 20, she was capsized on her side in a storm of average wind velocity .of 17-20 rn/s off the coast, in Jan. 1958. This ship B had deck side passages of length 41 m and

Ship I tern Condition A Full L. i Dep. B Full L. Dep. C D E Full L. Dep. F G H I J Full L.

Arri. Full L.Dep. Full L. BallastCône. Dep. Full L.Dep. Full L.Dep. Full L.Dep. L0, (ni) 4000 46.50 46.50 4805 50.00 60.00 6200 8300 5900 2650 B (ni) 750 8.10 8.10 8.00 8.40 10.00 1050 1280 9.50 5.00 D (ni) 3.40 3.60 3.50 3.50 430 490 580 6 40 460 265 (ni) 244 242 2.30 2.68 382 327 351 540 425 234 W (t) 399 479 433 682 ¡ 1153 1123 1136 4030 1533 177 Cb .528 .500 .485 .682 P700 .556 P491 .690 .619 .535 AG (ni) 274 3.31 332 318 3.02 429 441 465 3.78 2.05 GM (ni) 1.060 .74 58 .63 526 .420 .870 . CZ,,, (ni) .292 .313 3% .217 .202 .245 .646 .691 .335 .123

e',,, (deg) 254 260 340 25.0 420 29O 67.5 489 5l0 260

9,. (deg) 484 52.7 775 46.7 77.7 495 >90 >80 >80 54O A (ni2) 203 249 258 275 184 398 425 666 222 67 h, (ni) 273 279 2.96 266 241 372 374 347 283 134 T, (see) 630 795 8.07 8.16 6.80 9.41 11.20 969 6.50 5.28 y .81 .95 1015 .90 .60

.92:

90

.65:

.67 .71 y (ni/s) 19 19 19 19 26 19 26 26 26 20 L,0 (m) .0395 .0387 .0463 .0403 .0320 .0453 .Ó73 0547 .0315 .0163 9, (deg) 2.2 3.0 3.5 I 4.03 3.3 5.0 9.8 37 30 24 (deg) 1144 1145 11.44 1142 12.85 I 1097 13.32 13.49 127O 11.66 O (deg) 32.7 32.1 31.6 I 30.4 25.7 350 430 27.3 300 29.4 N 0136 .0165 .0182 .0175 .0183 .0127 .0103 .045 .0148 .0150

8,

p,, (deg) (deg) (deg) 30.2 69.5 24.8 28.7 27.8 73.3 75.5 25.4 25.7 27.6 63.6 22.7 245 318 37.5 25.5 28.1 fl7 425 788 74.4 46.6 49.4 45.3 16.7 27.9 321 18.1 20l 19.2 L (ni) .0169 .1%5 .1588 .1810 .1007

{".

1027 O559 .1254 : 9,, e',, ,, Qi. (deg) (deg) (deg) (deg) -84

43: 94

-101 57 : 57 -53 162 168 17.8 16.0 11.9 19.1 249 13.5 86 142 : 27.6 284 293 274 288 : 32-6 196 175 27-7 383 38.2 393 37.4 33.3 375 40-0 273 278 399 9", R (deg) 36.4 1360 .795 53.5 . 344 398 55.6 1.984 .705 1.806 .135 1.570 3038 2249 .95(1 Co .889 .519 1297 461 1180 .088 1026 1986 1470 621

An Estimating Method-Shipped Seawater 165 actual thip. As to the effect of shipped seawater. O?L= -6.21°, oc=2O. 78°, Çic=22. 73° and 4'r=

33.23° for its acting range, and Lic=O.O-197m. L2C=O.1229m for its maximum value. The work ratio

calculated by using these values becomes 1.53 and is just equal to the critical work ratio. Therefore it may be concluded that this method of calculation for the effects of shipped seawater with the criti-cal work ratio of 1. 53 is exceedingly appropriate for judging the stability performances of ship.

7

Examples of Applications

By the above mentioned new judging method, the safety factor for stability performances for several

ships are calculated as the results shown in Table 3. Ship A has been a cargo-passenger ship engaged

breadth 10m, from the forecastle to the stern on both sides, and the sea water shipped in this space. From the fact that the safety factor of this ship under this circumstance is only 0.519, we are con-vinced that this ship capsizes easily by the influence of the shipped seawater. On the contrary, ship C has sufficient stability performances having Co value of 1.297, since though ship C is almost the same type with ship B. she has a water-tight poop deck and the length of deck side passage is 29 rn with breadth 1.Orn in which seawater ships. Ship D was also a cargo-passenger ship, and capsizçd by the Typhoon 'Della' at the Inland Sea of Seto in June 1949. This ship has deck side passages ha-ving 38m in length from the forecastle to the stern and 1.3m in breadth, and the C value for wind

veiocity of 19 rn/s becomes 1. 18 by the Stability Regulations while the o value comes out to be only

0. 461. Though this ship is considered to be safe fion the C value, it is clearly recogr.ized from the

C0 value that this ship may capsize easily by the effécts of shipped seawater on the deck. Ship E is a F-type cargo ship and has the large C value of 3. 11 by the stability Regulations, however since the. Co value of this ship is 1. 18 because of the shipping seawater, this ship can not be considered to have such a good stability. Ship F is a cargo-passenger ship, and since the C0 value is smaller than. 0. 1 because of the large area for wind pressure, small GZm value and small flooding angle o about 34.

degrees for the shipping of water from square windows of the deck house, we should consider that this ship is very dangerous for the coasting service. Ship G has almost critical stability performance,

while ship H and ship I have sufficient stability performances. Ship J is a 75 G.T. type dragnet fishing

boat, and as the C. value for wind velocity of 20 rn/s is only 0.62 which is insufficient for stability performance, the sufficient caution is required in operating on rough sea.

8 Conclusions

The stability performances of ships in rough seas are estimated approximately with a synthetic consideration of main causes of heeling moment, suchas the moments by wind pressures, rolling by waves and the effects of shipped seawater. In this paper a new method based on the experimental, theoretical as well as on the empirical considerations was proposed for calculation of these elements.

of stability qualities. Namely,

(i) Considering the experimental results that the wind velocity varies with the height from the-ea surface, and the wind pressure, its centre of effort and the centre of virtual water pressure vary

remarkably with the heel angle of the ship, a formula of calculation of the moment by the wind

pressure was introduced, which is entirely different from the traditional method based on many

assu-mpt ions.

As for the absolute standard amplitude of synchronous rolling on rough seás, the maximum: amplitude among 100 swings of synchronous rolling on developing irregular sea which is represented by the Neumann's Spectrum was adopted, and a very simple formula for approximating the above

standard amplitude was obtained by introducing the synchronous rolling in specific imaginar _regular

waves defined from this energy spectrum of rough seas. Also the formula for calculating the relativeS

standard amplitude corresponding to this absolute standard amplitude was obtained.

As for the effects of shipped seawater, a simplified calculating formula _{was introduced} con-sidering the deck form, the height of freeboard, the amount of the sheer of deck, the height of the bulwark, the size of freeing ports, the heeling of ship relative to the surface wave etc., and the

acting range of the shipped seawater was also made clear.

Based on these methods, calculations were performed for the ship _{which is considered to be} in the critical state of stability qualities, and the value of critical work ratio _{was decided to be 1.53.}

The stability qualities of any ship in rough seas can easily be evaluated by _{comparing the'} work ratio of the ship with this critical work ratio in either case that the seawater ships or not. In

An Estimating MethodShipped Sea water i 6

other words the stability qualities are estimated to be sufficient _{or not by the fact that the factor of} safety for stability represented by the ratio of the work ratio of the ship to the critical work ratio k greater than unity or not.

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