165 
5 [II. THE EXPLOSION 
point of firing. The order of magnitude of the period of oscillations due to such 
causes may be estimated very roughly by dividing twice the diameter L (in feet) of 
the mass of explosive by an estimated average velocity of 10,000 feet per second, 
giving a period of 2L/104 seconds, or about 10~ seconds for ordinary heavy charges. 
The statements made in this section concerning the explosion process rep- 
resent, for the most part, theoretical conclusions. Little is known experimentally 
beyond the values of the detonation velocity D, nor have many theoretical calcula- 
tions been made. Plausible equations, differential and algebraic, can be set up, 
but their solution requires numerical integration. 
The calculation of G. I. Taylor 
2.5, 
deserves mention (3). He considers the is | 
case of a sphere of TNT in which the deto- 
nation is initiated at the center. The re- ae 
sulting distribution of pressure p and of SC Hig? 
outward particle velocity u are shown in a i F :, 
Figure 3. The abscissa represents x = r/R, 2 at 
or the ratio of the distance r from the aot = 
center of the sphere to the distance R of 4 Ne 
the detonation front from the center. Ma- 2 
terial for which r>RF is not yet detonated. 
The same plot holds good at all times, un- 2 2 ath 6 ? ie 
til the detonation front reaches the sur- Figure 3 - Detonation of TNT Sphere 
face of the sphere of explosive. As time 
goes on, the point r = R moves outward at the detonation velocity D. At any instant 
the exploded material is at rest within a sphere whose radius is 2/5 that of the det- 
onation front. No experimental evidence exists to check these results. 
III. PRESSURE WAVE 
III. THE PRESSURE WAVE AND AFTERFLOW IN THE WATER 
Only a few observations and calculations have been made of the wave pro- 
duced in water by an explosion. Experimental observations are made difficult by the 
fact that the density of the material composing the instrument is necessarily com- 
parable with the density of the medium in which the wave exists, in contrast with the 
case of blast waves in air. Theoretical calculations are hampered both by lack of 
knowledge of the properties of matter under very high pressure and by mathematical 
difficulties. 
Properly to understand the phenomena requires familiarity with certain 
physical ideas and theoretical results concerning compressive waves. For convenience 
of reference, these ideas and results are collected together in Appendix I, and fa- 
miliarity with the material in that section will be assumed. 
