MOTION OF THE GAS SPHERE S8S 



and if the difference in initial deptli can be neglected, so that Zj = Zi, 



(8.13) 



''^'iW 



Eq. (8.13) is a very useful and interesting result, for it permits an 

 estimate of energy losses in successive contractions from the easily ob- 

 tained ratio of periods. Data of this kind have been obtained from the 

 200 pound charge tests mentioned in part (B), which show that the 

 ratios T2/T1 and Tz/T2 are indeed nearly constant, independent of 

 depth, for depths greater than about 320 feet. At smaller values of 

 depth the ratios increased, this change being attributable to migration 

 of the bubble and effect of the surface on period. Disregarding this 

 change, the data give the values r2 = 0.34ri, n = 0.54r2. If a theo- 



Table 8.2. Energy losses in contractions of the gas bubble from 200 pound charges 



of a mixed explosive. 



retical value Q = 1.62 kcal./gm. is used for the detonation energy of the 

 explosive, Eq. (8.12) gives ri = 0.41. This is therefore the fraction of 

 the original energy remaining after emission of the shock wave, and the 

 values of r2 and rs, representing the fractional energies remaining after 

 the first and second contractions, are also determined. Table 8.2 sum- 

 marizes the results obtained in this way. 



The period data thus indicate that more than half of the original 

 energy of the explosion is lost before the first expansion of the bubble 

 has developed appreciably, and that about two-thirds of the remaining 

 energy is dissipated in the first contraction, leaving only a small residue 

 for later oscillations. Only a relatively small fraction of the energy 

 loss at the first contraction is accounted for by the radiated bubble 

 pressure pulse, the rest being dissipated, as discussed in section 9.4. 



Very similar results have been obtained from period ratios for small 

 charges. In experiments on small charges of tetryl and TNT (less 

 than % pound) fired in 23 feet of water (2), first and second bubble 

 periods were observed for charge depths from 4 to 20 feet. In many 

 cases, migration of the bubble had an appreciable influence on the second 

 period T2, but when a value T2 corrected for the measured migration 

 of the bubble was used, the ratio T2/T1 was found to be essentially con- 



