THEORY OF THE SHOCK WAVE 141 



The low values of peak pressure predicted by Penney and Dasgupta 

 at the distances of the experimental observations are to be attributed 

 primarily to the low energy release assumed in the initial conditions. 

 In addition, these values are the results of an extrapolation of the cal- 

 culations, which were made from the surface of the charge out to six 

 charge radii, and are subject to errors inherent in any such process. In 

 view of these factors, it seems reasonable to suppose that an extension 

 and revision of these calculations would give results in good agreement 

 with experiment. 



The assumption that the initial conditions are adequately repre- 

 sented by adiabatic conversion of an explosive into its equilibrium prod- 

 ucts is of course a rough one, and makes calculations of Kirkwood and 

 co-workers rather inaccurate at distances of a few charge radii. Initial 

 conditions similar to those employed by Penney and Dasgupta, which 

 take account of the detonation wave front, are logically more satis- 

 factory in this respect. Another approximation, in which the variation 

 of conditions on the gas sphere boundary with time has been represented 

 by the peak approximation, causes error in description of variations of 

 pressure behind the shock front. 



Despite the limitations of the calculations which have been based on 

 the Kirkwood-Bethe theory, their analytical convenience has permitted 

 the prediction and comparison of shock wave parameters for a number 

 of explosives and conditions. These results are in good agreement with 

 experiment in describing the nonacoustic variations of these parameters 

 with distance from the charge, and further predict the relative order of 

 explosives for pressure and duration with remarkable accuracy (see sec- 

 tion 7.5). The methods of calculation developed by Kirkwood and 

 collaborators therefore realize rather successfully the goals of any theory 

 to predict and make understandable experimental results. 



The more direct approach developed by Penney, based on numerical 

 integration of the Riemann equations outward from the charge and using 

 calculated detonation wave conditions, is undoubtedly inherently more 

 satisfactory for calculation of the initial formation and development of 

 the shock wave. Unfortunately its extension to greater distances in- 

 volves a great deal of step-by-step numerical computation, with at- 

 tendant danger of cumulative errors, unless precautions are taken of 

 using very small intervals and providing adequate internal checks and 

 controls. Penney (84) has suggested that calculations of shock waves 

 could profitably be made by using the step-by-step calculations out a 

 few charge radii to provide initial conditions for use of the Kirkwood- 

 Bethe propagation theory at greater distances, but at the time of writ- 

 ing nothing of this kind has been done. Calculations along these lines 

 would be of considerable value, particularly if compared with predic- 

 tions from the alternative propagation theory of Kirkwood and Brinkley. 



