Results of experimental investigation for capsizing in breaking waves

RESULTS OF EXPERIMENTAL INVESTIGATION FOR CAPSIZING IN BREAKING WAVES

by E. 0. Balitskaja Translated by Michail Aleksandrov and Geoffrey Gardner

Department of Naval Architecture and Marine Engineering

The University of Michigan

/

College of Engineering

The problem of ship motion in breaking waves becomes par-ticularly essential for medium and small ships. Many ship

losses can be explained only as a result of capsizing in

breaking waves, Reference [1]. In the past, the theoretical solution to the problem did not go beyond stating of the problem. Thus, we conclude: that for the most part an experiment is the only source for practical recommendations.

Shallow water model tests carried out in the tank of

Leningrad Shipbuilding Institute initiated by S. N. Blagoveschensky

and combined with theoretical analysis may be considered a first attempt in obtaining a general solution of this problem. This

paper gives some results of the above mentioned tests and the

highlights of the theoretical approach to the problem.

Description of experiment

The general scheme of the experiment is given in Figure 1.

The wave breakage has been achieved by means of a raised bottom which consisted of an upper part (wooden with steel framing) with

the dimensions 5400 x 5400 mm. and a hinged sloping panel (size 5400 x 2800 mm.) to prevent any flow under the raised bottom.

The raised bottom allowed a change of depth and inclination of

the upper part so that 9. and 2 (Fig. 1) were varied independently

Mode1#

40597

L = 2500 mm

B= 200mm

T=

66mm

H =

123 mm, 198 mm

Model#

40598

L = 2500 mm

B= 360mm

T

119mm

H= 221mm

-Two models tested in last series. _(N

₄₀₅₉₇

_and

₄₀₅₉₈₎

_had the followIng particulars:

D = 26.2

kg

D = 85.1

kg

Model #

40587

was tested as follows (Fig.

₂₎

low freeboard _{(123 Trim) without superstructure} high freeboard

_{(199 mm)}

_{without superstructure}

low freeboard with open low _{(70 irim) superstructure}

high freeboard with open

_{(70 mm)}

_{superstructure}

low freeboard with open high

_{(145 mm)}

_{superstructure}

The length of the deckhouses _{were equal to the length} of models. The side.

of deckhouse opposite to side subjected to wave impact and

the superstructure deck were left open.

Model # 40598 wastested

without superstructure

with a open high (185 mm) superstructure

All models were equipped with pressure gauges located

in the middle of the side facing the waves. A block of gauges consisted of 3 or 5 devices forming a vertical line (Figs. 3

F3

Both models were tested with constant displacement and

different magnitude of initial meticentric height. In the initial stage of the experiment the model was placed trans-versely, 0.5 - 1.5 m. from the rising bottom. Under the

action of waves the model started to drift, depending upon height and length of the waves; the number of waves in any

particular test ranged from _{seven to ten. The last wave}

reached the model 1.5 to 2.5 _{m. behind the step of the}

221

f)

I,,

bottom, so that the entire tidal drift _{was 3-4 m.}

Just after the model passed the step of _{the bottom,} the oscillograph started to reôord the impulses of the

gauges and the wave parameters. _{At the same time the movie} camera started operating. _{Wave parameters were measured} at two points: _{in deep water, before the slope of the} rising bottom, and in shallow water, above the rising bottom. _{For each model the position of the center of}

gravity was determined from the period of _{roll in calm}

water. To determine the damping coefficient, a film _was

I

taken of freerolling with decaying amplitude.

WAVES

It is known, Reference [4], that with a wave moving from deep water to shallow water the wave parameters are changing. The height of the wave is increasing while its

speed and length are decreasing. The wave period, however, remains practically constant. The deformation of the wave

form depends upon the slope of the bottom. When the slope

is small, a wave with a long fetch transforms to a shallow water type with a steep crest and a flat trough. In this

case the wave crest just dissipates. With a steep slope,

the wave transformation occurs over a relatively short distance and the wave crest actually breaks.

The wave parameters in the described experiment were

selected to cover a range from sub-critical to

super-critical wave types, on a scale of their ability to capsize ships. Wave parameters aregivenin Table 2, where: J

and h = period and height of deep water wave; X = length of wave, A = 1.56

T2.

A

= relative length

H. = depth of shallow water

p-a

Sill

sec

_Capsized

D7oae? 1 40597 Table

/

frIave N

(7ã6/e2)

10,3 9,84 0 0,46 11z) 4,8 4

a

8,60 8,29 I,'70 2,01

150

1,39

II

11x) 4,8 7,85 7,50 245, 2,80 1,13 1,00

iI,I2

-4,8

10,3 0 11,15 1,4,12,13,14

b

10,0 0,30 2,80 15 4,11,12,13 8,60 1,70 1,52 15 1,4,11,12,14 10,3 0 8,11 1,4 9,84 0,48 1,38 8,11 4 C _{9,48 0,82 1,65}

_-

₈ 8,60 1,70 1,41

II

1,4,8

d

I0,3 10,0 9,84 0, 0,30 0,46 3,80 3,12 11,15 11,12,15 12

-14

-9,50 1,08 1,79 11,12,15 13,14 10,3 0

3,6,8.10

1,2,4

9,84 0,46 3,24 8,9,12 2.3 9,48 0,82 2,42

6,7,8,9

.1,3,4,5.

e

_{8,60 1,70} 1,49 3 8,00 2,30 1,12

2,6,7,9,10,

12 3,4

mthl

18,50 0 8 17,67 0,83 2,50 2,6,8 17,03 1,47 2,05 8 15,44 3,06 1,30

2,8,6

15,15 3,35 1,23 7 17,67 0,83 2,75

3,5,6,8

1,2,4 17,03 1,47 2,10

2,3.8

I

15 44 3,06 1,39

2,4,5,6

1,3 Type sm

s/il m H

h

Wave

_Ii

Thle 2

I 2 0,95 1,13 15,8 16,8 1,4.0 2,00 8,9 8,4 25 25 1,6 1,5 0,20.10' 0,26.102 3 1,00 19,9 1,56 7,8 25 1,25 0,43.102 4 1,14 I'7,6 2.03 11,5 25 1,4 0,35.102 5 1,05 21,2 1,72 8,1 25 1,2 0,54.102 6. 1,03 22,2 1,65 7,5 25 1,1 0,61.102 7 1,26 18,4 2,56 13,9 25 1,35 0,44102 8 1,11 22,6 1,91 8,4 25 1,1 0,68.102

model '/c597

I 0,85 II, I 1,12 10,1 15 1.35 0,40.102 2 0,97 11,8 1,46 12,5 15 1,3 0,53. 3 090 12,4 1,26 10,1 15

12

0,58.102 4 0,81 13,5 1,03 7,6 15 1,1 0,68.102 5 U U U 25 1,85 0,5'7 102 6 0,98 14,2 150 10,6 15 1,05 0,92.102 7 U U U 25 1,75 0, 78 8 0,95 15,8 140 8,8 15 0.95 1,22.102 9 U U 25 1,6 1,01 .io2 I0 1,00. 18,6 1,56 8,4 15

08

2,19.102 II 1,00 19,9 1,56

78

15 075 2,47IO2 12 U 25 1,25 2,08.102 13 14 0,85 U 16,6 U 1,12 6,8 15 25 0,9. 1,5 1,25 .x02 i,ob.'o2 IS 1,03 22,2 165 '75 25 1,1 2,92.102 f,700'ei O59i

Capsizing as a rule occurred in the direction of _wave

motion. The cases where capsizing occurred in the opposite

direction are marked by "X". For each test the angle of

heel was plotted against time (Fig. 5, Model #40598). In the same figure is a plot of drift against time. _{Using this}

graph we can determine the position as well _{as the linear and}

angular velocities of the model at the time of impact..

30 &'O 110 0 10 J0

F/95

(rnoa'e?

_4'O5.9c}

The depth of shallow water for model _{#40597 was equal}

to, H

= 150 mm. For model #40598 the depth _{was H = 250} mm., which provided a ratio H

_2.1

/H

= 1.7, which was very near to the scale ratio (1.8).

RESULTS OF THE EXPERIMENT

All results of the experiment _{are given in Table I. For}

each wave parameter and läading _{condition, 5 to 6 tests were}

performed to account for different _{relative positions of the}

model and wave at the time of impact. _{The wave was considered}

VERTICAL DISTRIBUTION OF PRESSURE ON A SHIP SIDE

Earlier experiments, Reference [2], [3], showed that the actIon of breaking waves is that of an impact nature. The recordings of pressure distribution reaffirmed this fact (Fig. 5).

Theplacement of 3 or5 strain

qauqes

on a

!A

4J-

_Tf1

V.

shipt s side allowed us to plot the vertical pressure dis-tribution at the time of impact. As an example, we may consider figure 6 (model no. 40597). These gauges recorded

the pressure at intervals of 0.0222 seconds so that for an impact which lasted about 0.1 seconds, the pressure was measured 4-5 times. Tests tests indicated that the total

pressure and its distribution varied, even for the same model and wave parameters. The explanation can be found

by considering that there are different phase anglesbetween the wave and ship motion.

INFLUENCE OF ROLLING AND STABILITY

The theoretical investigations indicated that the in-tensity of wave impact is proportional to the relative wave energy, jh2, steepness of the wave, h/X, and degree of

shallowness, h/H. These qualitative relations were taken as the basis for evaluation of the experimental results, in the form of these criterion:

h2JLIJT j'p;'

7;:

_vQVT.VH

It was discovered that resistance to capsizing is

cha-racterized mainly by rolling parameters and closeness of the

resonance zone, as well as by initial metacentric height.

Fic.6

We also found that

measure of this resistance. _{As an example of this we can refer} to Fig. 7, where ' is plotted against _{(p-a). The final}

ex-perimental results were plotted _{as a series of graphs. An}

example is given in. fig. 8 for _{model no. 40597 in test "a",}

2,0 10 1,5.102 0,05

p-af

1\2

8

_7;:) 1,0 2,0 30 40 htAL

ij1

V4!3 Vi Vii

2,50

I Regton of capzing _x

/ //(////Yt /,./

Reqior,

of pobe capsLzrng

2 f,OfO x , Safe regioni 0,51V2 -45 ,-2 1,0 can be used as a 1,5,02 _2,0f6 (p-a)SD?

ox

x

15iV2 0 0 0 *

r//' /

//////

SQfQ reg ofl 45it72 I.O1O2 9

///////

.r1'

7 2,0 tO2

and in figure .9 for the same model in test "d". On these graphs we can see three distinct zones:

A safe region containing the parameter i when the model. did not capsize.

Region of Capsizing.

Region of Possible Capsizing,,a transiational zone where both phenomena can take place..

In spite of their limited significance to other areas the above parameters can help to make positive distinctions

be-tween the three regions of wave parameters:

Waves which cannot capsize models.

Waves which can capsize models for all types of loading

conditions and any value of metacentric height.

Waves which can capsize models only under unfavorable

loading conditions. 4OO2 0 0 0 _{Qqton o4} capLztr?9

00

0 0 I

\ \\\

0 0 0 A

We can assume that the same conditions exist in _real sit-uations where we can determine the critical _{wave parameters,}

relative to the ships safety.

INFLUENCE OF FREEBOARD AND SUPERSTRUCTURES

To determine the influence of superstructures and free-board we can use the data given in tables 1 and 2. _For

example, in table 3 the results of tests with different

superstructure heights are given. As we can see the increase of depth due to the addition of a superstructure increases

the chances of capsizing. We can get some better insight into the influence of a superstructure by studying the

impulse distribution. _{The magnitude of the impulses and}

p-a

5m.

T

sec

sec.

"ioael YO53 wave.v 8

Resi1*

1ale. 3

their moments are given in table 4. In all examples the order

of impulses acting on a superstructure was approximately the

same as those acting on a hull, but the moments were considerably

greater. This fact explains the influence of superstructure

on capsizing. _{Evidently increasing the height of the}

super-structure will influence the capsizing, until the freeboard

a P

.Superi-1rat. 135ii, 1,4? 1,4? 2,05 2,10 1.24 1,24 0,61 0,59

co,auzea

,o

peif#-etct

1,70 1,50 0.90 0,60

5upr3trac/i 76,,'m

1,70 1,41 0,90 0,64

-/4gfl7fl7

'I -

1,70 I .49 0,90 0,60

Cops zed

mock? 4'0597

, v'e y

4',

= 491

Jest maLlet'

Iv'qve

/mpucc'

N

_p-c

_7::

_h

A ₀

s-- £?

sin Cer /7/ CIII )tzucZ

I

23

45

617 t8

911011

J7',21ent c//mpd(se

6', (Qnqt

e4)

ltola? _su,oerjt,'

4t?

Z

eJpe7lrn cafca". &c/i: Re sut'

5/77 12 13 14 _{IS IS}

_I?

_{18 19} -41900 -58500 -16600

-4,2

44

455

76,0 -30000 -34300 + 4300

-4,8

I 3,2 4,37 49,0 -7900 -13400 +5500

-1,9

2,4 2,56 28,0 IThd? , 40597 D 26,3 109 0,46 1,88 19,9 156 1,00 5,5 -0,86 2100 800 1300 236

245

1,15 19,9 156

1,00 -8,0

2,00 1770 1770 426 1,70 1,49 15,8 141

0,95 -125 -0,30

1990 1460 530 432 0,46 3,24

158

141 0,95 -I, 5 0,44 3380 2350

Io

tT',d-'? i& 40598 .0 = 85,1 E9 609 0,83 2,75 22,6 193

I," -65

-0,75 10000 5940 4060 617 3,05 1,39 16,8 199

1,13 -32,5

0,47 6290 3050 3240 639 3,06 1,39 17,6 201 1,14 0 1,04 4100 1380 2720 -4660 -5200 + 540

-2,2

6,3 6,49 52,0 4950 -1950

-1,1

3,5 4,10 40,0 -12900 -13300 + 400

-6,5

4,S 6,20 51,0 '1 -12350 -14100 +1750

-3,7

5,7 5,91 80,0 11

becomes greater than the height of the wave. h21L,

JEfE

V'1 Vi 'YH o.'o2 1,5.10' 1,2.101 04 mv(/ 40597

rndd405,

_q

de1oz/i /9'7,4 - ZC9/ai So en,fan

Figures 10 and 11 give the dependence of H _{upon the}

ratio F/T where: T-draft and F is freeboard including

super-structure. The ratios

F/T

_{for models_are as follows:}

h 2,0.1172 5IC' 1.2,02 0,8.102 4. I 0 SCALE EFFECTS 0 1,0 2,0

To consider the influence of scale,we can use the tests where the scale factor of wave parameters and model dimensions

are nearest. The best examples of this were when the small model was with wave no. 4 and the big model was tested with

wave no. 6. _{The comparison of results is given in figure 11,}

where corresponding zones for model #40598 are located in

FiqII T -- /1?idd

49?

, 1I?'e( 40598

F/T

a iS C I a e 0,86 2,0 I .. 3,1 t 9 0,86 2,0

areas of smaller values of

F,

than those for the small model.

CONCLUSIONS

Ships operating in shallow water might be subjected to

the action of breaking waves causing capsizing. The

forces which are a result of these waves depend on wave parameters, degree of shallowness, area of impact

and relative position of the ship and wave at the time

of impact.

The criterion: were adopted to

determine the critical range of wave parameters. The

magnitude of this region depends on the size of the

ship and its superstructure.

An increase in stability might lead to either positive

or negative results.

The presence of a superstructure increases the possibility

of capsizing.

The modeling process is difficult due to the scale factors

which account for existance of forces other from those

of a gravitational nature.

Subsequent work in this area should be aimed towards

theoretical investigation of impact phenomenon, scale

REFERENCES

S. N.. Biagoveschensky1 "Data of Casualties to Fishing Vessels,'! L.S.I., 1957..

A. N. Cholodilin, "Stability Norms for Small Vessels,"

Proc. of Registar of Shipping of USSR, 1963

.E. 0. Balitskaja., "SomeResults of Thvestigation _of Ship Behavior j.r _{Shallow Water," Proc. of Register of} Shipping of USSR, 196.5

A. N. Krilov, uTO the Problem of Wave Propogation,"

Meteorology, 1941.

S. N.. B]Qv chensky, "Stability Norms of Sea Vessels,".

Proc.. of C.i.M.M., 1951