37 
95- The cavitation front travels back through the water with a velocity 
greater than the velocity of the individual pulses, and finally the orly 
part of the reflected pulse which "escapes" from the neighbourhood of the 
plate is the part P'Q'R' in fig. 17d in which the pressure is either positive 
or, if negative, of magnitude less than the tension R'N to cause cavitation 
96 Summing up, the essential features of the motion according to these 
assumptions are first the plate is projected away from the water, secondly, 
the water cavitates and follows up the plate and thirdly, only the initial 
portion P'Q*R® of the reflected pulse escapes to large distances from the 
plate. 
97- The velocity v. with which the plate leaves the water is greater than 
the velocity of the water which follows up, but as the plate is slowed 
down by the resistance kx of the supporting structure, the first layer of 
water will catch up the platee As the succeeding layers of water also 
catch up, the plate will have an increasing thickness of water moving with 
it as it is slowed down by the resistance of the supporting structure. 
Some of the kinetic energy of the water which follows up will be lost on 
impact as each layer catches up the plate and water ahead, but the rest 
of this kinetic energy must ultimately be absorbed by the resistance of the 
supporting structure. The final maximum displacement of the plate, 
representing "damage", will thus be greater in case 3 when the water 
follows up than in the previous case 2 where there was no such phenomenon 
To illustrate the potential magnitude of such increase in damage, the 
simplest case where the water cavitates at zero tension is considered, the 
energy lost on impact as the succesive layers catch up the plate and water 
ahead being neglected 
98 With the above simplifying 
assumptions, the total energy to 
be absorbed by the val istance kx 
is the total energyS 1; of the 
original incident pulse less the 
energy fof the positive portion 
P'Q'Z' in fig. 17d of the 
reflected pulse which travels away 
to large distances fron the plate. 
With the assumed neglect of kx in 
the initial stages of the motion 
when the positive portion of the 
reflected pulse is produced, the 
energy (1 in this positive portion 
depends only on€ ani the remaining 
fraction of the incident energy 
which is to be absorbed by the 
resistance kx is shown plotted as 
the upper curve in fig. 18 against 
an abscissa Y/éE< 1° For most 
practical conditions of non- 
contact explosions against single- 
_ hulled vessels the value of € is 
relatively large corresponding to 
small values of the abscissa, less 
< than 0.2 in fige18 The upper 
O90 
CASE 3 WHEN WATER CAN 
WITHSTAND NO TENSION 
AND IMPACT LOSSES 
ARE NEGLECTED 
o7 
CASE 2 
curve indicates that for such 
cases, over 90% of the incident 
iy energy has to be absorbed by the 
resistance of the plate to 
displacement For comparison, 
° O2 o4 o6 oe ro the lower curve in fig. 18 shows 
€ the fraction of the incident energy 
given to the plate, according to 
equation 38, for case 2 where 
there is no follow-up effect. 
For practical cases corresponding 
Fig. 18 - Energy transferred to target 
from _pressure pulse 
