42 
modifies its motion accordingly. Infact, the news of such reflection 
travels through the water with the velocity c of sound and takes time 
a/c to reach the centre of the piston by way of the water. Moreover, 
the assumption of a rigid piston implies that the effect of any increase 
of pressure near the edge of the piston is shared out instantaneously over 
the whole piston; in fact, appreciable effects travel relatively slowly 
from the edge to the centre of a thin plate - more slowly than the velocity 
c of effects in the water. The net result is that in an actual drum target 
the element of the plate at its centre is unaware of the existence of the 
baffle until time a/c and up to this time it will behave as part of an 
infinite plate and the theory of para. 85-102 is relevant 
408 From equations 3), and 32 it can be shown that t. increases as n 
decreases, that is as the length of the pulse c/n increases; this time to 
corresponds to the first occurrence of tensions with possible cavitation 
in the water. Hence, in the present problem, with a sufficiently long 
pulse the diffraction wave from the edge will reach the centre of the 
plate (in the time a/c) before the occurrence of any tension. The increase 
of pressure due to this diffraction wave may prevent any tensions 
developinge For a sufficiently long pulse, therefore, cavitation will 
not occur and the ultimate motion of the piston will be ths same as that 
indicated by the assumption of incompressible flow MThe effect of 
compressibility is then merely to produce a decaying oscillation superimposed 
on the motion for incompressible flow 
109. For the other extreme of a very short pulse, the position is quite 
different In this case, the process of case 5 involving cavitation will 
be virtually complete at the centre of the plate before the diffraction 
wave arrives from the edge and since the diffracted pressure is feeble for 
a short pulse it can have little effect on the amount of energy camunicated 
to the target 
110. For intermediate lengths of pulse, there may be both appreciable 
cavitation and appreciable diffraction!’ Physically, in such cases 
cavitation will tend to commence at the centre of the plate and spread back 
through the water as a beard of bubbly water, the bubbles being 
subsequently closed up both by the diffracted pressure from the baffle 
and by the water piling up on the decelerated plate. Quantitatively, 
this process is difficult to analyse,” but qualitatively it seems fairly 
certain that the effect of the diffraction from the baffle must be to 
communicate more energy to the target than that deduced for the preceding 
case 3 on infinite plate theory. The previous estimate for case 3 
that about two-thirds of the directly-incident energy is transferred to 
the target should thus form a lower limit for single=plate targets of 
box or drum type subjected to explosives causing appreciable damage. On 
the other hand for the longer pulses where equation 49 indicates an energy 
transfer in excess of the lower limit, the use of this equation should 
provide an upper limit since it neglects any impact losses associated with 
the closing up of the cavitated water. 
111. The essumption that the baffle is infinite in extent will be a 
reasonable approximation for a baffle of finite size only if the baffle 
width is large compared with the length of the pulse. For actual drum 
targets the outer diameter of the baffle is usually about twice the diameter 
of the air—backed plate and the assumption of an infinite baffle will not 
be justified for pulses of length comparable with, or greater than, the 
plate radius. Most experiments with drum targets have, however, been 
carried out with small charges for which the length of the pressure pulse 
is only about one-fifth of the plate radius so that the assumption of an 
infinite baffle is a fair approximation As an exception, gauges” 
composed essentially of a stout cylindrical body closed at each end by a 
copper diaphragm with a small baffle, have been used for many years in 
trials with full-scale charges, the volume of dishing of the diaphragms 
being taken as an empirical measure of the potential damaging power of the 
