122 THEORY OF THE SHOCK WAVE 



As a result, the pressure at any point for a given explosive depends only 

 on the ratio {R/a^ and the time scale at this point is proportional to 

 the charge radius a^, which is thus the linear scale factor required by 

 the principle of similarity. 



The calculation of x and 7 as functions of (R/ao) is straightforward, 

 once the necessary values of 12 (a^) and 61/ ao have been found from the 

 equation of state, as described in section 3.8. Values of x and 7 for 

 three explosives at several values of R/ao are given in Table 4.1, to- 

 gether with values of peak pressure Pm and reduced time constant d/ao. 



20 40 60 80 100 



REDUCED DISTANCE R/Oq 

 Fig. 4.1 Calculated dissipation and time spread parameters for TNT. 



The values of x and 7 for TNT plotted in Fig. 4.1 illustrate the vari- 

 ation of these quantities with distance. 



It is often convenient to have an approximate functional relationship 

 for these theoretical results in terms of charge weight and distance 

 rather than a set of tabular values. It has been found that for limited 

 ranges of the argument W^^'^IR the peak pressure Pm can be approxi- 

 mated by power laws of the form 



-\r) 



where W is in pounds and R in feet. This formula is a fairly accurate 

 expression of theoretical results ])etween 10 and 100 charge radii, as will 

 be seen from Fig. 4.2, in which the tabular values of theory for TNT are 



