lj^6 THEORY OF THE SHOCK WAVE 



from experimental pressure-time curves integrated to 6.7 times the 

 initial time constant are also tabulated. 



It is seen from Table 4.2 that the energy remaining in the shock 

 wave falls off rapidly near the charge as the wave progresses outward, 

 about thirty per cent of its initial energy being dissipated in the volume 

 within five radii of the charge and forty-eight per cent in the volume 

 within twenty-five charge radii. The energies computed from measured 

 pressure-time curves are approximately twenty-five per cent lower than 

 the theoretical values, but show corresponding decreases with distance 

 over the range of measurement. The difference in absolute value is 

 consistent with the fact that the experimental figures were obtained by 

 numerical integration to an arbitrary, finite time after arrival of the 

 shock front, in order to exclude significant contributions of noncom- 

 pressive flow energy to the integral. For comparison, values of the 

 afterflow integral to the same time are also tabulated. 



The energy of 561 cal./gm. at 1 charge radius represents the total 

 energy radiated by the shock wave, and is 53 percent of the estimated 

 total energy of explosion of 1,060 cal./gm. of TNT. The remaining 

 47 per cent, or 500 cal./gm., is thus the remaining energy for later mo- 

 tion of the gas sphere and the surrounding water. This energy can, 

 however, be computed rather accurately from the observed period of 

 pulsation of the gas sphere (see section 8.3), and for TNT a value of 

 480 cal./gm. is obtained. This figure is in remarkably good agreement 

 with the less directly estimated value of 500 cal./gm. Similar calcu- 

 lations for other explosives give correspondingly good agreement be- 

 tween calculated shock wave energies and indirect estimates from ex- 

 perimental measurements of the gas sphere motion. These agreements 

 are to within the combined accuracy of the measurements and calcu- 

 lations, and thus give a very satisfactory accounting for the energy 

 distribution in underwater explosions. 



The rapid dissipation near an explosive charge represents a de- 

 grading or wastage of available energy to heat, this loss occurring at the 

 steep gradient of the shock front. The fact that some twenty-five per 

 cent of the total energy of explosion is lost for useful work within 

 twenty-five charge radii of the explosion illustrates Avhat might be 

 termed the inefficiency of the shock wave for transmission of energy. 

 This inefficiency has led to suggestions that greater effectiveness might 

 be obtained by using slow burning propellant charges which did not 

 develop steep pressure fronts. Whether or not an improvement would 

 be reaUzed depends of course on the necessary magnitude and duration 

 of pressure for the purpose of interest, and whether the necessary energy 

 could conveniently be released in the most suitable way. 



