1442 
Vv. THE CRITICAL DISTANCE 
It is necessary to remember that all investigations in 
Section IV concerning the critical angle Os 
assuming plane waves. The case which is of direct interest for 
were carried out 
underwater explosion shockwaves is the propagation of a spherical 
wave. A small section of such a wave shall be approximated by a 
plane wave so that the results of Section IV can be applied. 
A spherical shockwave in water produced by a charge in the 
distance d from the surface propagates and hits the surface at 
first under @ = 90°. This angle of incidence decreases during 
the further propagation, the pressure in the wave decreasing also. 
Thus the intersection of wave and surface travels at first with 
c' soe, this speed c' decreasing to velocity of sound for 
@ =o. Ina certain distance corresponding to the critical 
angle the reflected wave will begin to travel along the primary 
wavefront and thus attenuate the peak pressure, if a critical 
angle exists. 
Before going into further details the critical case shall 
be investigated to determine if it always occurs for any charge 
weight and any charge depth. For this purpose a spherical shock- 
wave whose decay is given by Fig. 2 shall be considered. The 
critical angle defined by (14) is 
ead an a 2yi- (2 cw 
14 
