1. Introduciior&

The research on ship slamming is concerned with the following arcas of investigation:

The study of ship motions in waves. The study of the mechanism of slamming

and the prediction of slamming loads. The responsc of the local structure as well as the hull girder resporse.

The complete solution of the slamming probkm needs a combination of diese studies.

However, progress has been made by

neglect-ing the interaction effects upon the load gene-rated, and considering each of these aspects as distinct and separable parts of the total problem. The principal problem is the fundamental research on the mechanism of hydrodynarnic impact. To-gether with model experiments conducted in a seakccping tank it gives the starting

### point on

which the statistical studies on the frequency of occurrence of impact and its magnitude can be based.A survey of the impact problem is geven by Sze-behely 1L Szcheheiy and Ochi

### 2!, Chy and

Abramson 3I, Moran 4! and recently by

Meyer-hoff 5!.

In the following we will concern ourselves to the impact problem for flat-bottomed bodies which has received condiderable attention during the last few years.

2.

### The Conventioiial Approach

The hydrodynaniic impact theory based on the fundamental work of van Kármnán and Wagner usually deals with an incompressible fluid and is essentially involved in the wedge entry problem. The results of these theories become increasingly

### inaccurate as the dcadrise angle of the wedge

decreases._{In the extreme case of a flat bottom}

the theory predicts infinitely high pressures at the
instant of impact. _{Taking the compressibility of}
the water into account (von Kdrmtn IGl, Egorov
7!, Ogilvie 8!) results into an initial pressures

equa.l

### to the acoustic pressure in water.

Thehigh pressure predicted by these theories could not

be verified experimentally. _{Measurements show}
a much lower impact pressure over a longer time

period. _{Moreover, the impact pressure is} _{}

appro-APPENDIX 2

LEboratrjum icor

### cJf

21Mekewag 2,2623 CD De!ft

r$L

### On the Hydrodynarnic Impact Problem for

_{Hat-bottomed Bodies}

by J.H.C. Verhagcn

ximnately proportional to ilse square of the impact

velocity instead of linearly proportional. _{Theories}
which ìnclude the cushioning effect of the air
layer entrapped between body and water surface
at the morflent of impact arc developed by several

investigators. By this approach the essential

features of the impact phenomena obtained from

two dimensional di!op tests can be largely explained.

3.

_{Studies ou the Effect of Entrmpped Air}

### lujita

I 9I considers he impact mechanism asclue to the pressure increase caused by the rapid compression of a fLxed amount of air entrapped between the body and the water. Also ¡he first calculation of Lewison and Maclean ¡10! is based on this assumption.

The amount of air must be chosen to fit the experimental results, Egorov

_{Ill I}

_{calculated the}amount of air from the deformation of the water surface at the moment of impact.

_{An improved}

### theory considering the motion in the air layer

as a one dimensional compressible ideal gas flow
is developed by Lewisori ¡10, 12!. _{Compressible}
and incompressible movement of the water is

assumed to take place. _{Tise method of soiution}
is somewhat crude. _{Arbitrary assumptions arc}
made and factors introduced, which have to be
determinated experimentally.

_{One of the}

diffi-cuides lay in the initial conditions that were
assumed to prevail when calculations of the air
pressure began. _{The outflow of the air at the}

edge of the model desires a more careful study.
To prevent the horizontal air velocity in the
calcu-lation from increasing to unreasonably high _{values}

(several times sonic speed) Lewison introduced into

the computer program an upper bound to the
out-flow of air equal to sonic speed. _{To his opinion}
the chocking process of the air flow will be a

gradual one instead of an arbitrary discontinuity. The theoretical curves do not reproduce the ex-perimnental ones very well although their general

characters are much simnilar.

Further refinement of the theory will beneeded.

Experiments were designed to check the

theore-tical approach. _{The air velocity under tise falling}

flat bottomed model was measured _{by means of}

high-speed motion _{photography cf styrofoam}
balls carried along by the air flow.

f

Simultaneously the motion of the water surface was recorded as well as the pressure at the center

### and near the edge.

_{The results indicated that}

the air velocities were less than expected but the experimental technique could have been improved No significant downward motion of the water surface was observed before impact.

These tests were performed on the ship dynamic
test machine at the University of California _{131.}
This machine provides

_{a facility to study on a}

relatively large scale, _{two-dimensional} _{impact}
phenomena and local structuralresponse to impact
load. _{The preliminary tests results obtained by}

Maclean 1141 on this facility show that the maxi-mum peak pressure increases linearly with drop height and therefore with the square of the impact

velocity. _{The peak pressure diminished toward}

### the free edges of the model The peak

_{pressure}

at the edges time lead that on the centerline. The maximum pressure at the centerline occurred when the model has just passed the original water level.

_{The increase in peak pressure with the}

model loading as measured _{was much less than}predicted by Lewison's theory. An important result obtained from the work of Lewison and Maclean is that the peak pressure can be drastically

reduced if flanges arc fitted to the flat bottom to

entrap air.

In order to clarify the relationship between the

maximum pressure and the impact velocity,Nagai
carried Out a systematic test program on a dropping
test tower, which is a small-scaic version of the
California ship dynamic test machine 122_{I.} From
the obtained experimental data, _{he summarized}
the following results:

1 The relationship between maximum

pressure

and impact velocity depends mainly upon the weight and the angle between both bottom and water surfaces, rather than

_{upen the}

bottom width.
2 Within five degrees angle between _{bottom}

### and water surface the relationship turned

### out to be pV where l.4<n<2.2, but

no clear quantitative relation was found be-tween the weight and the maximum_{pressure.}The two-dimensional problem of the air flow between a rigid flat-bottomed body falling

_{towards}a rigid plane is solved by Johnson .1151.

_{From}his careful numerical study it is concluded that the deformation of the water surfacemust be taken into account to obtain pressures that agree with experimental data.

_{The behaviour of the free}

surface near the edge of the body_{requires a careful}study, because small changes in the exit arca will significantly affect the amount of entrapped

_{air}and hence the pressure beneath the body.

Verhagen 116 I treated the flow in the air-layer

as a one-dimensional compressible flow of a perfect

gas in the same way as Lewison. _{The disturbance}
of the water surface due to the imposed air pressure

is calculated neglecting the water compressibility.

The initial conditions at the starting point of the numerical calculation are derived under the assum-ption that initially the air flow can be considered

as _{incompressible and the water surface }

undis-turbed. _{From the theoretical treatment it} _{appears}
that the air-layer is entrapped as soon as the local
velocity of the air at the edges reaches the velocity

of sound. _{Afterwards an adiabatic compression}
of the air-layer neglecting further outflow of the
air is assumed. _{The solution of that part of the}
problem is similar to the approach of Fujita _{191.}
The numerical results gave an excellent agreement

### with the experimcntal data obtained

from his fairly lightly loaded two-dimensional test body. The increase in peakpressure with the modelload-ing accordload-ing to this theory is also overestimated.

It is concluded that compressibility effects of the water cannot be neglected when the mass of the body is large compared to the added mass.

An interesting experimental study on the import-ance of air density and fluid properties to water im-pact pressures is given by Gerlach 117 I. By

reduc-ing the environmentalpressure, he found the peak

pressure increasing with diminishing gas density,
up till quite closely the acoustic liquid _{pressure.}
The peak pressure for a given gas fluid and body
appeared to be a function of the variable _{/i/e14,}
where Im is the drop height and ße the

environ-mental pressure. The presence of waves on the
liquid surface tends to reduce the peak _{pressure.}
A theoretical study on the influence of air_{on the}
impact pressure of blunt bodies is given by _{}

Green-berg 1181. He considered the

### air as

incom-pressible because the air velocities are anticipated

in his case as sufficiently subsonic. _{Also the water}

is considered as iticompressihle. _{The non-linear}
free surface conditions are retained. The analysis
will be coded for solution.

From _{model experiments on slamming impact}
conducted in regular and irregular _{waves Ochi}

1191 obtained a relationship between maximum

pressure and relative VC1OCIty between bottom änd

wave at various locations along the ship's bottom.
A meanline representing the pressure on the keel
plate for a 13 feet Mariner model at station 2 is
drawn for comparison with results of various _{}
twa-dimensional drop-tests in Fig. 21. The reason for

the large discrepancy is not clear. 4.

### Conchsion

The theoretical treatment of the impact problem
which include the effect of entrapped air yield
results which are in reasonable _{agreement with}
results obtained from two-dimensional _{drop-tests.}
However, the results obtained from model

20 X q E Q-s Nags L.

### E.EE

E E-IJE_{E-'}370

_{8.50 J Ochi}

_{nS1 Schwartz}y LOO 6.80

### lLl56

V-shape A 375 7.58 + 50 85 (jV-Sh2pe 370 7.50 170 11.3_{U-shape}o 240 1127 L 2S 9.91 MacLean o 370

_{am}

_{iä}4 255 4.97 e3048 1.47 240 5.66 o 3048 113 n 210 6.93 220 h26 I 220 9

_{J}8 220 3.00 + 160 3.68

_{Verhagen}o 160 3.38 400 0.32 0 220 1.53 Chu a ng 508 i7ô

### A

o 4-0.5### 4

¿.7### I

2mcnts in waves cannot be _{satisfactory explained}
by theory. _{Further research is recommended.}
References

### ''J

Szcbchely, V.G.:"Hydrodynamic impact", Appl. Mech. Reviews

12, pp. 297-300, 1959.

J2J _{Szcbchclv, V.G. and Ochi, K.M.:}

"Hydrodynamic impact and _{water entry",}

AppI. Surveys. _{Spartan Books, Washington,}

pp. 951-.957, 1966.

J3j _{Chu, W.H. and Abramson, H.M.:}

"Hydrodynamic theories of ship slamming",
Rciew and Extension, _{Southw.} _{Res.} _{Inst.}
San Antonio, Texas, Techn. _{Report No. 2,}

1960. .14! Moran,J.P.:

"On the hydrodynamic theory of water-exit
and entry", Therm. Advanced _{Research Inc.,}

l'ar-TR 6501, March, 1965.

.: J .'l:c..

.';"

### -:'''-:

theory M/m oO.32Verhagen mean tine according Ochi

### .,

_{...}

,-£
y.
### /

2C### 1

### LH-iJ

SSCifiC model toad

M _{2M}

m

1. _{5}

7 10

_-___ y rn/sec

Maxirrjrn impact _{pressure} _{as a function}
o! irnpsc _{velocity}

Fig. 21. _{Maximum impact pressure} _{as a function of imptct velocity}

23

5 I Meyerhoff, W.K.:

"Uebersicht über _{grundlegende} _{theoretische}
und experimcatellc Arbeiten _{zum Problem der}
Bodenstösse by Schiffen", Jahrbuch der
Schiff-bautechn. Gesellschaft, Band 61, pp. 147--163,

1967.

6 J _{Von Kármán, Th.:}

"The impact of sea plane floats during landing",

NACA TN 321, 1929.

7 _{Egorov, I.T.:}

"Impact on a compressible fluid", _{Translation}

NACA, Tcchn. Memo. 1413, 1956. 8 J Ogilvie, T.F.:

"Compressibliity effects _{in ship} _{slamming",}

Schiffstechnik, Band 10, Heft 53, 1963.

9 J Fujita, Y.:

"On the impulsive pressure of a circular plate falling upon a water surface", Journ. S.N.A. of Japan, Vol. 94, pp. 105-110, 1954.

"The effect of entrapped air upon the slamming

of ship's bottom", Univ. of Calif. Berkeley,

College of Engineering, Report NA-66-5, 1966.

llj Egorov,I.T.:

"Free surface deformation and further

hydrody-namic phenomena by the entry of a flat plate on a fluid", Trudy, Sudostroenic, pp. 87---93,

1965, (Russian).

121 Lewison,G.:

"An experimental investigation of the role of

air in ship slamming", Univ. of California.,

Berkeley, College of Engineering, Report NA-66-12, November, 1966.

Maclean, W.M.:

"The ship dynamic test machine at the Univ. of Calif.", Thesis, Univ. of Calif. Berkeley, May,

1967.

Maclean, W.M.:

"The ship dynamic test machine at the Univ. of Calif.", Berkeley, Calif. College of Engineering, Report NA-66--1, January, 1966.

Johnson, RS.:

"The effest of air compressibility ¡n a first

approximation to the ship slamming prohlcsu",

Journ. Ship Research, Vol. 12, No. 1, March,

1968.

Verhagen, J.H.G.:

"The impact of a flat plate ori a water surface",

Journ. Ship Research, Vol. II, No. 4,

Decem-ber, 1967. l7j Gerlach, C.R.:

"Investigation of water impact of blunt rigid

bodiesReal fluid effects", San Antonio, Texas. Southwest Research Inst. Dept. of Mech. Sci., December, 29, 1967.

Greenbert, M.D.:

"Prediction of ship slamming loads: On the water impact of a circular cylinder", Therm.

Advanced Research Inc., TAR-TR 6701, May,

1967. Ochi, K.M.:

"Prediction of occurrence and severity of ship

slamming at sea", 5th Symp. on Nay. Hydrodyn.,

Bergen, 1967.

Och, K.M. and Schwartz, F.M.:

"Two-dimensional experiments on the effect of hull forms on hydrodynamic impact,"

D.T.M.B., Report 1994, 1966.

1211 Chuang, S.L.:

"Experimental investigation of rigid flat-bottom slamming", D.T.M.B., Report 2041, 1965.

22! Nagai,T.:

National Defense Lab, of Japan, Teehn. Re-ports, No. 156, November, 1965; No. 263,

May, 1967; No. 318, May, 1968.