486 



282 



B . ARONS 



bubble radius. Combining Eq. (13) with the ex- 

 pression for k, the non-dimensional minimum 

 radius becomes 



a„ = 0.0210ZoS, (37) 



and the dimensional minimum radius, 



A^ = Q.29>(>W', (38) 



where Zo = absolute hydrostatic depth (ft.), 

 yl„, = minimum radius (ft.), and VF = charge 

 weight (lb.). 



Unfortunately there is no direct experimental 

 evidence available to check Eq. (38), since the 

 bubble minimum cannot be measured on the high 

 speed motion pictures owing to obscuration by 

 carbon particles, etc. left behind in the water. 



V. SUMMARY 



5.1. It has been demonstrated in the preceding 

 sections that if the parameters r, e, and k are set 

 equal to 1.25, 490 cal./g, and 0.0552Zo^-', re- 

 spectively, the theoretical equations provide a 

 satisfactory fit to all the available experimental 

 data. This fact increases the utility of the theory 

 in that it should now be possible to make reason- 

 ably accurate predictions of stationary bubble 

 behavior under various circumstances, and the 

 same parameters should apply to Friedman's 

 more general theory' which includes effects re- 

 sulting from migration and the influence of 

 neighboring surfaces. 



It should be emphasized, however, that any 

 detailed physical interpretation of the parameters 

 7 and k is tenuous at best. It is somewhat sur- 

 prising that so satisfactory a fit to the peak pres- 

 sure and impulse data can be obtained with the 

 same parameters which fit the maximum bubble 

 radius and period data. One would expect, for 

 example, the true pressure-volume relationship to 

 deviate appreciably from the ideal gas adiabatic 

 which was used in the theoretical formulation, 

 and the deviation would be most pronounced 

 during the high pressure, high temperatures phase 

 in the neighborhood of the bubble minimum. 



In view of the multitude of approximations 

 and assumptions involved, it would appear to be 

 more rational to regard the numerical values of y 

 and k as parameters affording a useful fit of 

 simplified theory to experimental results rather 

 than as actual physical properties of the deto- 

 nation products. The distinction may appear to 

 be subtle, but it is probably significant. 



VI. ACKNOWLEDGMENTS 



6. 1 . The author wishes to express his gratitude 

 to Dr. J. C. Decius and Dr. B. Friedman for per- 

 mission to reproduce the curves of Fig. 1 and to 

 the Underwater Explosive Research Laboratory, 

 Woods Hole Oceanographic Institution, Woods 

 Hole, Massachusetts where all the experimental 

 data quoted in this report were obtained. 



