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 bottomthe 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 improvedtheory 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 thatthe 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
pressureat 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 drasticallyreduced 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 122I. 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 maximumpressure. 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 bodyrequires 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 airon 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 6.80lLl56
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 9J 8 220 3.00 + 160 3.68 Verhagen o 160 3.38 400 0.32 0 220 1.53 Chu a ng 508 i7ôA
o 4-0.54
¿.7I
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./
2C1
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.
