SHOCK WAVE MEASUREMENTS 235 



pounds, and the energy flux density function is conveniently expressed 

 in units of (in. Ib./in.^). It is evident that the units chosen have httle 

 to recommend them from the point of view of logic or internal con- 

 sistency and their adoption here is justified by the convenience of estab- 

 lished usage. 



The energy flux density in any approximation is somewhat arbitrary, 

 as in the case of impulse, because of the necessity for some convention 

 as to the time t to which the integration is carried, and this must be 

 remembered in specifying or attaching significance to experimental 

 values. The dependence on P^ of the leading term in Eq. (7,4) makes 

 this integral converge more rapidly than the impulse integral, however, 

 and for most purposes the same upper limit as for impulse, of approx- 

 imately five times the time constant, is fully adequate to give a fair 

 measure of energy flux density. 



7.3. Validity of the Principle of Similarity for Shock Waves 



The most direct predictions concerning the behavior of shock waves 

 are embodied in the principle of similarity, discussed in section 4.1, and 

 conclusions drawn from it. According to this principle, if the linear 

 dimensions of the charge and all other lengths are altered in the same 

 ratio for two explosions, the shock waves formed will have the same 

 pressures at corresponding distances scaled by this ratio, if the times at 

 which pressure is measured are also scaled by the same ratio. 



A. Scale experiments for spherical pentolite charges. The most direct 

 experimental test of similarity is the obvious one of making two or more 

 experiments with charges of different weights in which all linear dimen- 

 sions have the same ratio. If the observed pressure-time curves, 

 measured at distances in this ratio, are identical when corrected for the 

 difference in time scale, the principle is verified. Since the linear dimen- 

 sions of a charge are proportional to the cube root of the volume, and 

 hence weight W, the distances in such experiments should be made 

 proportional to W^'^. The observed pressure-time curves at scaled 

 distances R satisfying R = constant X W^^^, and only at these dis- 

 tances, should be the same at times t proportional to W^'^, or what is 

 the same thing, should superpose if plotted to new scales of time taken 

 proportional to the reduced time t/W^'^. 



The simplest and most clear cut tests of this kind have been made 

 using spherical cast pentolite charges of three different weights. Pento- 

 lite is an excellent explosive material for this and other types of funda- 

 mental investigation because it can readily be cast into charges of varied 

 size and shape and is sensitive enough to be detonated with a minimum 

 size of initiating, or "boostering," material. In small charge work, 

 which is in many ways the more difficult, spherical pentolite charges 

 have been found to give more reproducible results than any other ex- 



