NSWC/WOL TR 76-15 5 



25. At cut-off time, TPOS, the measured outside water 

 pressure drops to about 13 psi (Figure A2). Table A2 lists limiting 

 case results for the final maximum radius (in State 2) which were 

 calculated from the above parameter values by assuming cut-off times 



TPOS occurina at A.,, A , and also sufficiently late that the 



Mm ■* _ 



oscillation has damped-out (so that A = constant = A) . 



26. Two sets of values for A /A. are given in Table A2 , 



M 2 1 

 one for a final outside pressure p_ = p. =32 psi, the other for 



the measured value of p„ = 13 psi. The results listed in the top 



row of Table A2 (cut-off at bubble maximum) are the same as if the 



positive outside overpressure, p. - p., had never occurred. In 



other words, the upper right hand value of A /A. also applies to a 



simple step decrease in the ambient pressure p. to a new value, 

 p_ = 13 psi. 



27. It is apparent from these crude results that both 

 positive and negative excursions of the outside pressure significantly 

 influence the final overshoot; and that time-of-occurrence of cut-off 

 relative to the phase of the bubble oscillation cycle is of critical 

 importance for positive excursions. It also looks like a good bet 

 that underwater explosions do kill or cause serious damage to nearby 

 fish by extending their swim bladders . 



28. Figures A3 and A4 sketch the qualitative behavior of 

 the inside air pressure and the bubble radius as functions of time 

 for the six cases listed in Table A2 . 



A-17 



