45 
a sphere simulating some half-scale targets, the maximum bodily velocity 
would be only about 12 ft. per sec. whereas the corresponding velocity of 
the plating nearest the explosion, as deduced from equation 35, was about 
380 ft. per sece The bodily motion may thus be expected to be unimportant 
for such a case. It will be noticed, that whereas the sphere was assumed 
rigid in the analysis for estimating bodily motion, the results were used 
to derive conclusions concerning damage, which automatically implies some 
yielding of the surfacee However, it seems reasonable to expect that the 
bodily motion of a yielding target will be less than of a rigid target 
and since the theoretical conclusions refer to cases where the bodily motion 
is expected to be unimportant, the use of an over-estimation far the 
bodily motion is justifiede However, for cases where the theory of the 
rigid sphere indicates appreciable bodily motion it would be necessary, for 
practical application, to revise the theory to include sone allowance for 
yielding This problem is extremely difficult but some progress for 
specific targets can be made by approximate methods, *? 
419. The problem of bodily motion and the previous problem of copper 
diaphragm gauges represent cases where the effeat of diffraction round an 
obstacle can be of importance. This effect is also of some importance 
for piezo-electric gauges used to measure the pressure/time variation in 
thes pressure pulse. For this purpose it is desirable that the presence 
of the gauge, which is necessarily of finite size, should not modify 
appreciably the pressure in the water. The effects of diffraction round 
the gauge and bodily motion assist in this purpose by tending to equalise 
the pressure round the gauge. 
120, For actual ship targets, questions of diffraction do not arise to a 
great extent in underwater explosion theory, especially in comparison with 
the similar effects in air. Thus the typical naval target is usually 
relatively isolated and questions of screening of one target by another 
rarely arise. Similarly, the diffraction of air blast into a building via 
broken windows has no real parallel for the underwater target. 
Behaviour of gas bubble in presence of a target 
121. The attraction of the gas bubble to a rigid surface and its repulsion 
by a free surfacé have already been described. A target which suffers 
damage by an underwater explosion represents an intermediate case of a 
yielding swface. The analysis of the behaviour of the bubble near a 
yielding surfaco is very difficult, espscially as some allowance must be 
made for the prior effect of the pressure pulse on the target Since 
bubble motion is relatively much more important on the small-scale, 
theoretical and experimental attention has been mainly concentrated on the 
behaviour of the bubble for small explogions against box end drum model *! 
targetse An early theoretical analysis for this problem suggested that 
the model might behave qualitatively as a free surface at one stage of the 
plate deflection and as a rigid surface at another stage with appreciable 
motion both away and towards the target A later revised theory, however, 
suggested that repulsions effects were negligible and that the target 
behaved essentially as a rigid surface with a resultant attraction of the 
bubble towards the targete In the meantime, this latter conclusion had 
been deduced from experimental observations of the bubble motion near a 
small box model which showed clearly the attraction of the bubble to the 
target The magnitude of these displacements were in reasonable agreement 
with theoretical values calculated on the assumption that the flat target 
plate and surrounding baffle could be treated as a rigid disoor @qual area 
In general, therefore,it appears that small-scale box and drum model targets 
behave effectively as rigid surfaces and attract the gas bubble. 
122, The bubble pulses are intrinsically much feebler than the initial 
présswre pulse but due to the attraction of the bubble to the target, the 
bubble pulses emanate from a source nearer to the target and can thus 
contribute appreciably to the damage. 
