449 
in vf depends on the characteristics of thee xplosive. 
The results of the calculation by the methods of this section 
of the shocksewave parameters for the underwater explosion of spherical 
charges of TNT and Pentolite are listed in Tables 7.1 and 7.2. Figure 7.1 
shows the variation with distance from the charge of the peak pressure Pra 
and the time constant 8 for TNT. Figure 7.2 shows the variation with 
distance forthe same substance of the dissipation parameter X% and the 
spread parameter Y . Theoretical predictions have been made for 48 
different explosive combinations comprising 13 different explosives. 
Reference should be made to the original reports for the complete 
tabluations of the results of the theory .26/ 
8. Similarity Restraint Propagation Theory2/ 
In this section, we describe an alternative theory of the propa- 
gation of shock waves from the underwater explosion of spherical charges 
of explosive. The theory to be described results in the formulation of 
a pair of ordinary differential equations for peak pressure and shock-wave 
energy as functions of distance from the source. These equations can be 
integrated numerically for specified initial conditions, and they provide 
a particularly simple method for the extrapolation to points close to the 
charge of experimental peak pressure—distance curves, measured at large 
distances from the charge. Although less convenient than the analytical 
theory that has been described in the previous sections and less instructive 
26/ J. G. Kirkwood, S. R. Brinkley, Jr., and J. M, Richardson, 
OSRD Report No. 2022 (1943); OSRD Report No. 3949 (1944). Cal- 
culations in earlier reports by Kirkwood et al. are superseded 
by these reports. 
27/ See Reference & 
62 
