Capsize experiment of box-shaped vessels

8010

CAPSIZE EXPERIMENT OF BOX-SHAPED VESSELS

by

Shin TAMIYA

Department of Naval Architecture University of Tokyo

Tokyo, Japan

SESSION 4-4

International Conference

on

Stability of Ships and Ocean Vehicles

March 26, 1975

Unìversity of Strathclyde

International Conference on Stability

of Ships and Ocean Vehicles Session 4-4

University of Strathclyde

Glasgow, Scotland March 26, 1975

CAPSIZE EXPERIMENT OF BOX-SHAPED VESSELS

by Shin TAMIYA *

Introduction

In a general treatment of the capsizing of ships, a finite

angular displacement must be considered. Dimensions and arrangement of deck houses, hatch coarninys, bulwarks and

freeing ports, etc., are also relevant to the actual ship

safety problem. However, taking all of these ship aspects into consideration makes the problem too cumbersome for investigating the basic mechanisms in the dynamics of ship

capsizing.

In this paper the author describes briefly the capsize experiments of simple box-shaped models ) 2)

under the com-bined actions of transverse waves and wind. Combinations of critical wind force and wave height were determined for the models restrained only in yaw and surge with the other motions

unrestrained. Some theoretical considerations are also de-scribed for understanding these experimental results.

Model Experiments 1. Box-Shaped Models

Two nearly box-shaped models, A and B were tested. In

Table 1 their principal particulars are summarized. They

resemble standard two-dimensional test models both having flat decks and differing in the extent of the bilge radius. Four

blocks of airex buoy (45.24 cm3 in total volume) were installed over the upper deck to limit excessive heel as well as actual

capsizing. Bilge keels (60 cm x 0.8 cm) were also fitted.

The statical stability curves for these models are shown in

Figs. 1 and 2. For model A, the following average logarithmic

-2-decrement of free rolling was obtained:

ln(A1/A)

- 0.16 in half period

2. Procedure and Experimental Results

The experiments were carried out in a small basin (21 m 1.8 m) at the Institute of Industrial Science, University of Tokyo. The basin is equipped with two axial wind blowers capa-ble of maintaining an uniform air stream _{over the water surface.} The models were subjected to beam waves and wind, their motions other than yawing and surging were unrestrained.

Keeping the period and height of the waves constant, the wind velocity was gradually increased until the model capsized. In these experiments capsizing was defined by the immersion of

a part of the buoy blocks. By repeating this procedure, a set of critical wave heights and wind velocity were obtained for

each prescribed wave period. The results are shown in Figs. 3

and 4. _{Rolling amplitude, heel angle and drifting velocity} are also shown in Figs. 5 through 9.

From a study of these _{figures, the following may be} de-duced:

For the same wave height, model A capsizes more

eas-ily in heaving-synchronism than rolling synchronism,

Fig. 3.

In the case of model B, the capsize did not occur in waves of half the rolling period. This again con-firms the danger of heaving-synchronism, Fig. 4.

Both cases of capsizing in shorter waves are not supposed possible from the concept of superposition of heeling action due to wind and rolling excitation

due to waves.

Deck edge immersion (leeside) possibly motivates the

capsizing of the models. The observation of the record of heeling angle and the motion pictures taken through the transparent side window in the basin wall supports this hypothesis.

the wind heeling moment only compared with the angle

where statical stability is maximum. Model B exhi-bited no such a pecularity (from the static point of view).

6. In the range of low wind velocity, the occurance of

capsizing appears small.

An example of the results of the rolling experiment of a small cargo ship in beam wind is shown in Fig. 10 in which the mean angle of heel and the amplitude of rolling are given

as functions of wind force. In the full load condition (small

freeboard) the mean angle of heel is affected by the addition

of wave excitation. Moreover, the roll amplitude increases remarkably in both loading conditions with increasing wind

velocity.

These experimental results also seem to support the

impor-tance of taking the interactions among rolling, heaving and

drifting (and possibly swaying) , as well as the effect of

deck edge immersion into the dynamics of finite ship motions.

Considerations

3. Non-linearity of GZ-curve and the effect of heaving

In order to grasp large amplitude ship rolling quantita-tive effects on ship stability, the following non-linear equa-tion of rolling was used to model the ship tability:

I + N

+ yW.GZ() = Mo + Mi (1)

where = absolute angle of heel =

- = relative angle of heel

= surface slope of wave = sinwt = S±nT (2) I = total moment of inertia

W = displacement of ship

N = coefficient of resistive moment

y = coefficient of effective wave slope

Mo ,Mi heeling moment other than wave excitation For simplicity we hereafter assume that I and N are

con-stant and set y = 1.0. M0 is a moment due to constant wind velocity and M1 is an additional moment due to heaving of the

-4-ship with heel. Fig. 11 shows the principle of generation of

this moment. M1 for model A with 2 cm freeboard is calculated

and shown in Fig. 12. ç refers to the relative wave height, positive ç corresponding to ship dipping.

In equation (1) GZ is non-linear with respect to

a' also M1 is non-linear with respect to ç . However, we can suppose

that

a and ç will vary in an oscillatory fashion with the

wave encounter period, so that GZ and M1 may be expanded in a Fourier time series and approximated using the first and-second

terms only.

Assuming a solution in the form:

X0 + Xsin(t-c) = X0 + Xsint1 (3)

and using approximation for GZ

GZ = g0/2 + h1sint1 (4)

and for M1

M1 a0/2 + b1sin(r-ó) (5)

with the expression

ç = Zsin(-r-ó) (6)

we obtain the following three equations:

G0 = 2f0 + A0 (7)

-x

+ bmH1 = 'cosE + bmß1cosft-ó) (8)

aX = sinc + bmB1sin(E-ó) (9)

where

G0 = go/GZ , H1 _{= hi/GZm} fo= M0/W.GZ

b = A2/w2 A2 = W.GM/I

m =GZm/GM

a = N/lw , A = ao/W.GZm

, B1 = b1/W.GZ

GZth = maximum of GZ,

GM = dGZ/d0

which is sufficient to determine X0 ,X and .

The calculation for model A with 2 cm freeboard was com-pleted and the results are shown in Fig. 13. If we increase

wave height under a constant wind force, only the roll ampli-tude increases at first, the mean heel X remains almost

con-stant. There is a critical wave height, above which X0 in-creases suddenly and X0 becomes maximum. The point X = maximum was verified to correspond to the instability of the motion and the curve of critical wind velocity and wave height deter-mined from this criterion is plotted in Fig. 3(a) showing

fairly good agreement with the experiments.

For fo = 0.6 where no critical point exists, the staring point of sudden increase of Xo was assumed to be critical.

The same calculation and procedure were carried out for model B and the results are shown in Fig. 14 and 4(b) respec-tively. Again there is good agreement with the experimental

results.

4. Unstable Moment

Equation (1) was used only from the practical convenience of calculation of the non-linear motions. After Prof. S.

Motora s) the more rigorous equation of rolling is described

as follows (Fig. 15)

(I

+J

)E=

(m -m )vw+ (I

- I

+J -J )qr+L

x

xdt

y z y z y z

(10) Usually we can neglect the first and second terms in the right hand side because of the smallness of the motion and the same order of magnitude of m etc.. Added masses m and

however, are of the order of m = W/g and moreover, their rela-tive magnitude varies with ship form and the frequency of the

motion. For example m and m for models A and B are shown

in Fig. 16, in which onz is shown to become larger than m at high frequencies and also at the vanishing frequency. In the

high frequency zone where heaving synchronism occurs, we can expect that the time average of vw has a positive value. At

the vanishing frequency a constant positive value of vw in-creases as the steady wind drives the ship leeside and gives

her a steady heel. Quantitative estimation of the heeling moment due to this term results in 1 2 kg-cm of heaving

synchronism which is not of negligible order.

Lacking reliable data for the added masses of the experi-mental models used, we can not at present arrive at any

deci-sive conclusions as to the actual effect of the unstable

moment, however, its importance should be recognized as a new

topic of future research in capsizing.

Closure

The author has proposed the usefulness of adopting a non-linear finite displacement equation of rolling and presented some calculated results which include the additional heeling

moment due to heaving. The importance of the so-called

un-stable moment is also pointed out.

Future work must be concentrated to clarify the resistive moment at finiteangular displacement and to obtain a more

correct expression for wave excitation.

References

Shin Tamiya, "Experimental Research on Ship Capsize", Journal of the Society of Naval Architects of Japan,

Vol. 125, 1969 (in Japanese).

Shin Tamiya, Hideaki Miyata and Toru Ìiyazawa,

"Critical Conditions of Capsize of Box-shaped Ships",

Journal of the Society of Naval Architects of Japan, Vol. 128, 1970 (in Japanese).

Shin Tamiya, "On the Characteristics of Unsymmetrical Rolling of Ships", Selected papers from the Journal of the Society of Naval ¡rchitects of Japan, Vol. 4, 1970.

Shin Tamiya, "A Calculation of Non-linear,

Non-symrnet-nc Rolling of Ships"., Journal of the Society of Naval Architects of Japan, Vol. 126, 1969 (in Japa-nese)

Seizo Motora, "On the Virtual Mass Effect", Journal of the Society of Naval Architects of Japan, Vol. 87,

TABLE 1. Particulars of Box-Shaped Models

Description Model A Model B

L B X D (cm) 100 X ₂₀

X ll5

loo X 20 X 20.25

Freeboard f (cm)

2.0

1.6

1.2

2.0

1.6

Displacement (kg)

17.81 18.61 19.41

36.20

36.95

Section Area Ratio

_.938

_.940

_.942

_.989

_.990

KG (cm)

7.89

7.93

8.00

10.45

10.65

GM (cm)

0.831

0.590

Rolling Period (sec)

1.52

1.51

1.50

2.80

3.10

Heaving Period (sec) ca

0.77

1.02 1.07

Wave Period (sec) 1.54

0.92

1.49

1.55

0.88

0.92

1.40

1.02

1.55

1.07

4 i

18

o

.0

O G

0E

_-J..

LU

o

z

e

IO

20

(de g)

Fig. i Curves of Statical Stability of Model A

1

IO

20

30

40

& (deg)

Fig. 2 Curves of Statical Stability of Model B

¡(a)

o

0000

_{\.00 o o}

o f 2Omrr,

o1 aTR'2

-NTwTH

0

I $

0

2

4

6

8

IO

WAVE HEIGHT(cm)

J 4

8

o..--J Iii

o

_z

0

--Fig. 4 _{Critical Wave Height and Wind Velocity}

.

(cl f12rnni

4e

i ?

4r

2

?,-o-000

t

_I

_1k

I 4 8 ₁₂ - H (cm)

Fig. 3 _{Critical Wave Height}

and Wind Velocity

0 f =16 mm

oTw1T/2

-2

₄

₆

₈

_IO

WAVE HE$GHT(c,m)

ç, ? t E + 81 o 6

-6Q

'(a)

f=2Omm o T =1.5s' wn =ags _wnl 4 8 (b) f=1mm

00

.s-4 8

00

00

12 12

E6

o

N

(D

I

u. u 20 6 f -20mm

/

f 4 8 WIMO vti.octry(.ia)

Fig. 7 Drifting Speed due to Wind

Fig. 9 Heel Angle due to

Wind 20 -5' '5 4 -li (m/s) t.

fr

o.d E t 8-o

_jo

--o A ,o"

9c"

o,

/

cbo

/

£ ' i o'

_-

o,A-4 .

U(m/s)

4

Fig. 8 Drifting Speed due to Waves

A

A

e.

*4

Fig. 10 Heel Angle % and Roll Aiiplitude 01

( E1 ; Full Loat, E2 ; Half Load

without Waves

Fig. 6 Heel Angle due _{to Wind} Fig. 5 Rolling Amplitude due to Wave

12

E2

A L :ZIO E L) o o 4 8 H(cm)

ig. 11 Generation of Heeling

Moment due to Heaving under constant

t'

z

5 O 5

Xd.g)

1g. 13 Mean Heel Angle (X0) and Rolling Amplitude (X).

(Model A)

Fig. 12 M1 for Model A

w

r4

2

.30

E -2.0 E E,_.0 00

d

-0.4 -0.8 0.5 Ed -u2T/g z0. 2013 -0.12B 5 10 15 20 Xo (deg)

Fig. 14 Mean Heel Angle (X0) and

Rolling Amplitude (X). (Model B) _-_ MODEL A -- m!/m

-1.0 X

Fig. 16 m and rnz of the Mode1s

Fig. 15