no PHOTOGRAPHY OF UNDERWATER EXPLOSIONS 



16,000 ft. /sec, corresponding to pressures in excess of 10^ Ib./in.^, and 

 measurements of the less rapidly changing plane wave velocities at a 

 flat charge surface give 19,000 ft. /sec. 



The pressures determined from these measurements are compared 

 with predictions of the Kirkwood-Bethe and Kirkwood-Brinkley theories 

 in Fig. 6.3, in which distance R is expressed as a multiple of the charge 

 radius do. The parameters of the latter theory were obtained from the 

 experimental piezoelectric gauge data plotted as open circles. The 

 velocity data (solid circles) are seen to agree within their scatter with 

 gauge measurements where the two meet, but give much higher pres- 

 sures close to the charge than either of the theoretical predictions. The 

 difference from the Kirkwood-Bethe theory is probably explained by 

 the assumed initial conditions of adiabatic conversion of the explosive 

 to its products at the same volume. The similar disagreement with the 

 Kirkwood-Brinkley theory cannot be attributed to this assumption, as 

 it is not involved, but may be the result of inadequate treatment of the 

 approximation methods employed. It is to be noted that the various 

 data of Fig. 6.3 are not strictly comparable for several reasons (dif- 

 ferent explosive loading densities, velocity results for fresh water), but 

 the necessary corrections are much smaller than the differences. 



The data obtained by any method are very meager for pressures 

 close to the charge and further investigations would be desirable. Al- 

 though the velocity method is indirect and gives only shock front pres- 

 sures, this line of attack is one of the most promising ones. The initial 

 rate of expansion of the gaseous products is also indicated in Fig. 6.2(b), 

 but the outline is distorted by refraction of light passing through the 

 high pressure region (see part B). 



B. Optical distortion methods. The velocity of light in water de- 

 pends on the pressure as a result of the difference in density, the index 

 of refraction changing from 1.344 at atmospheric pressure and 17° C. 

 to 1.365 at 20,000 Ib./in.^, an increase of 1.5 per cent. This increase is 

 great enough to cause marked refraction effects, particularly for oblique 

 incidence at a discontinuity, and has been used as a basis for optical 

 studies of pressures. The deviation in a light ray passing through a 

 spherical front is indicated diagrammatically in Fig. 6.4(a) . A ray origi- 

 nating at Q travels along the broken path through the points S and P. 

 The curved path within the shock front is drawn for decreasing pres- 

 sure and decreasing velocity at points behind the front. 



The actual path between fixed points of entry and exit is determined 

 by the requirement of geometrical optics that it be the one which mini- 

 mizes the travel time between these points. This condition leads to 

 Snell's law of refraction, and for a linear velocity gradient behind the 

 front the path is easily shown to be an arc of a circle. Rays actually 

 originating at aS or P appear to an observer at Q to have originated at 



