250 



SHOCK WAVE MEASUREMENTS 



tained by simple addition. In order to understand qualitatively the 

 differences in pressures measured at points A, B, C, it is convenient to 

 assume that the pressure at any point and time can be obtained by 

 adding the pressures which would be developed independently by suc- 

 cessive elements of the charge. In this approximation, which has been 

 developed in a Road Research Laboratory report/ the pressure at a 

 point at a distance r from an element dx is then the sum of pressures 

 P = {P„ie~^/^/r) dx, where P^ and d are constants. If the difference in 

 times of initiation are to be taken into account properly, these contri- 



Fig. 7.13 Shock wave pressure-time curves at points on extended axis of a 



line charge. 



butions must be evaluated for a retarded time t = t — r/c — x/D, 

 where r is the path in water with velocity c, and x is the distance of the 

 element from the point of detonation. For an element to contribute 

 we must then have r ^ 0, and the pressure at any point is 



(7.7) 



P = P. 



I 



r/e 



dx 



the limits of the integral over x including all values of x from which a 

 signal can reach the point of observation (i.e., for which r ^ 0). 



Explicit evaluation of the integral Eq. (7.7) must be carried out 

 numerically and this has been done for several specific cases, but the 

 general nature of the solutions can he inferred quite simply. Consider- 

 ing point A of Fig. 7.12, it is evident that the first signal arrives from 



' The details of this theory and its appUcation to experimental results are given 

 in three reports listed as Reference (92) . 



