16 
dpe For the present problem, if the maximum pressure in the pulse is mich 
greater than a few hundred Ib. per sqein. it seems fairly certain that the 
reflected pulse will cause some cavitation or breaking of the water. This 
cavitation will be most pronounced for points near N in fig.5 where it 
leads to the formation of the spray dome. For the present, attention will 
be confined to points such as P in fig.5 at some horizontal distance from 
EN; at such points the main effect of cavitation will be to replace the 
portion K C' F of the pressure/time curve in fig.6b by a portion K G H. 
The resultant curve 0 C 0! K GH corresponds to the type of record observed 
experimentally for the pressure pulse as modified by the proximity of the 
sea surface. Since, in general, the tensile phase K GH is relatively 
small compared with the pressure phase 0 C O' K, it is reasonable and 
customary approximation to neglect the tensile phase and regard the 
pressure/time curve to be given by 0 C O' K. 
456 The reflection of the pressure pulse at the sea surface with 
subsequent cavitation of the water can be taken into account theoretically 
by a simple "surface cut-off" effect. It is only necessary to evaluate 
randr', the respective distances of any point P in fig.5 from the 
explosion E and its image E'. The pressure pulse from E is then considered 
to cease abruptly at time 00' = (r - r')/c after its commencement. This 
replaces any use of equation 24 which is invalidated by cavitation. 
46. The surface cut-off does not affect the maximm pressure in the pulse 
but it can modify appreciably the transmitted impulse and energy. Assuming 
the exponential form given by equation 10 for the original pulse 0 C D to be 
correct, the surface cut-off decreases the transmitted impulse by the 
fractional amount 
XQ' = en ME) 
oc 
eee eee eoe eee eee eee eee (25) 
The transmitted energy is decreased by the fractional amount 
2 = Qe 
x ze Bq r ) ece eee ece eee eee eee eee (26) 
The length o/n depends on the size of the e. For example, equation 21 
gives o/n fora T.N.T. charge. he distance (r' = r) depends on the 
position of any target-point P in fig.5 relative to the explosion and the 
sea surface. 
bal The effect of reflection of the pressure pulse at a free surface 
has so far been treated by the methods of the theory of sound. The second 
order terms in the hydrodynamical equation, which are neglected in the 
theory of sound, are nevertheless of decisive importance when the incident 
pulse reaches the surface at nearly glancing angles. 
A mathematical discussion 12a has shown that if the peak pressure 
in the shock wave, in pounds per sqein., reaches the free surface at an 
angle of incidence less than a critical angle =(90-0.21 )9, 
then the cut-off theory is approximately accurate. Should the angle of 
incidence be greater than the critical angle, then the cut-off theory is 
not correct in that it predicts too high a value of the peak pressure near 
the surface, and too short a duration. The failure of the simple cut-off 
theory becomes of practical importance when consideration is given to large 
explosions in relatively shallow water. 
