MOTION OF THE GAS SPHERE 



845 



value of 456 cal./gm. corresponds to the values r = 0.43, Q = 1,060 

 cal./gm. used to plot the straight line depth-period relation of Fig. 8.21. 

 The theoretical relation including surface effects, also plotted in this 

 graph, lies about 3 per cent below the experimental points for d less 

 than 60 feet, but is otherwise an excellent representation of the free sur- 

 face effect. 



The overestimate of the effect of the sea bottom for both small and 

 large charges, obtained by assuming the bottom to be a perfectly rigid 

 plane surface, is surprisingly great. The actual bottoms in these in- 

 vestigations were of course not perfectly rigid, being fairly hard packed 



9 



35 



30 



^ 25 



tsl 



20 



-10 



Fig. 8.22 



-5 



10 



15 



lO^F(x) (pf^/3) 

 d (d+33)'/3 



Test of correction for effect of free surface on bubble periods of 

 300 pound TNT charges. 



sandy mud. During most of the bubble pulsation, however, the pres- 

 sures are low and the assumption of a rigid bottom, which should refer 

 primarily to resistance against mass flow of water rather than its acous- 

 tic properties, ought on this basis to be at least a fair approximation. 

 A possible explanation of the discrepancy for charges fired near the bot- 

 tom may be that the bottom below the charge is hollowed out, or cra- 

 tered, sufficiently by the action of the shock wave and initial large veloci- 

 ties of outward flow that the subsequent motion of the bubble is not 

 affected as much as it would be by an undisturbed bottom. It is inter- 

 esting in this connection to note Ward's comparison of craters (119) 

 formed by charges fired under the ground with the maximum bubble 

 size from underwater explosions, which he found to be not very dif- 

 ferent in radius. Whatever the explanation,^^ there appears to be little 

 13 The effect of a nonrigid bottom has been taken into account in unpublished 

 calculations by B. Friedman by assuming that its effect is that of a fluid of arbitrary 

 density p, i.e., in the noncompressive approximation a medium is characterized by its 

 inertia to flow. Small charge period data are predicted quite accurately by assum- 

 ing a bottom density of 3.0, but this picture is hardly very reaUstic if cratering occurs. 



