THEORY OF THE SHOCK WAVE 



123 



plotted on double logarithmic scales. The empirically fitted straight 

 line of slope a = 1.16 gives a good fit except for W^'^/R > 0.3 

 {R/ao < 25). Similar curves for other explosives can be drawn to the 

 same order of accuracy. 



The variation of the reduced time constant B/W^'^, also plotted in 

 Fig. 4.2 for TNT, is not well represented by a power function. The 

 derived quantities, impulse and energy, equal to Pnfi and Pr,?d/2pc in 

 the peak approximation, can be fitted quite well by power laws. A 

 presentation of these laws and their agreement with experiment is given 



(a) TNT, density 1.59 



Q 



(b) Pentolite (PETN/TNT 50/50), density 1. 



Q 



(c) Tetryl, density 1.00 



Q 



Table 4.1. Shock wave parameters predicted by Kirkwood-Bethe theory 

 (from calculations of Kirkwood, Brinkley, and Richardson) . 



in section 7.4. It is interesting to note here that the variation of peak 

 pressure with distance at a rate greater than 1/R, and the spreading of 

 the wave as it is propagated outward, are both confirmed by experiment. 

 Although these departures may not appear large except at points close 

 to the charge, they persist to great distances. As an example, the peak 

 pressure at 100 charge radii is less than 60 per cent of what it would be 

 for acoustic decay, and the time constant is more than twice as great. 



The theoretical predictions as given in Table 4.1 represent only a 

 small fraction of the calculations, which have been made for forty-eight 

 different explosive compositions in all, comprising thirteen distinct 

 combinations of components. For complete tabulations of the various 

 results and variables of the theory, reference should be made to the 



