THEORY OF THE SHOCK WAVE 129 



cation is perhaps not justified, as discussed by Rice and Ginell. The 

 details of their calculations are sufficiently similar to those of Kirkwood 

 and Bethe that reproduction of them here would not be worth-while, 

 and the discussion here will be confined to the results obtained. 



The calculated peak pressure Pm for cast TNT of density 1.59 is 

 plotted in Fig. 4.3 as a function of R/aJ , where aj is the radius of the 

 cylinder and R the distance from the axis. Near the charge the pres- 

 sure falls off roughly as {aJ/Ry-^, and for greater values of R/aJ changes 

 in slope of the logarithmically plotted curve occur. These changes at 

 large values of R/ao' are, however, not likely to be realized in actual 

 experiments because cylindrical charges of length many times the dis- 

 tance R, which itself is much greater than Go', would be necessary to 

 approximate the assumed symmetry. 



As an estimate of peak pressures in the equatorial plane perpendicu- 

 lar to the axis of a charge of finite length, Rice and Ginell suggest that 

 comparison be made with a spherical charge of the same weight. At 

 small distances, the peak pressure should be essentially that for an 

 infinite cylinder, and at larger distances the pressure should approach 

 values for the sphere, the deviations from this symmetry becoming in- 

 creasingly unimportant. The spherical charge of volume equal to a 

 cylinder of radius aj and length L has a radius Go given by 



4 



- irtto^ = iraJ'^L and hence Go = {^L/iao'Y'^ao' 

 o 



The pressures for spherical charges of the same weight as cylinders with 

 length/radius ratios of 10 and 50 are plotted in Fig. 4.3, as calculated 

 from the Kirkwood-Bethe theory. The transitions from the cylindrical 

 case to the spherical ones should occur in the region R ~ L/2, and the 

 dotted lines suggest a reasonable transition. The decay of peak pres- 

 sure with distance on this basis would change rather smoothly from a 

 decay roughly as {aj /Ry-^ near the charge to a decay as {aj /RY-'^^ at 

 distances greater than the length of the charge. Similar estimates for 

 the time constant 6 as defined by P{t) = Pme~^^^ are plotted in Fig. 4.4, 

 and the differences in the changes of d/ao with increasing distance are 

 evident from this figure. 



The theory of Rice and Ginell affords an at least semiquantitative 

 prediction of the pressure variation off the side of a cylindrical charge, 

 but the equally interesting question of what happens off the ends of 

 such a charge has not been treated. The observed pressure-time curves 

 at points along the axis reveal a number of interesting features, some of 

 which can be understood qualitatively on theoretical grounds, and the 

 analysis of such results is discussed in section 7.6. A comparison with 

 the calculations of Rice and Ginell is furnished by measurements by 



