NSWC/WOL TR 77-90 



The kill probability, p, is then calculated as 



1 



p = (3.3.4)* 



1 + EXP [-0.055(Z-125) ] 



This equation represents underwater explosion test data from some 

 1500 caged Spot and White Perch over a wide range of explosive test 

 conditions. Equation 3.3.4 was used for predicting the Striped 

 Bass kill as well as for White Perch, since unpublished preliminary 

 results with 16 species of fish indicate that Equation 3.3.4 applies 

 to the majority of swimbladder fish.** 



3.4 RESPONSE TO EXPONENTIAL WAVES OF SHORT DURATION . The method 

 used in Reference 1 to calculate the oscillatory response to 

 exponential waves was to patch together solutions to successive 

 square steps of half-period duration. This solution breaks down, 

 however, as the time constant 9 becomes less than the duration of 

 the calculated first half-period of the motion, and the calculated 

 size of the first compression gets too small. This comes about 

 because, in the limit as 9 becomes smaller and smaller, the first 

 approximating step takes on the value one-half PMAX, the average of 

 the initial and final pressures--and consequently, the damage para- 

 meter, X = -100 In AMIN/A. , does not go to zero as 9 approaches 

 zero. 



Impulsive Loading Approximation . This approximation is for 

 the limiting case of pulses of infinitely short duration. Under 

 impulsive loading the initial radial velocity v. of the bubble is 

 given by 



v. = 1- ~" - (3.4.1) 



1 pA. 



*Reference 1, Equation 3.2.1 



**Equation 3.3.^ describes explosion test result_s for 10 of the l6 species tested. 

 The other 6 species required larger values for Z (= 125 in Equation 3.3.^). 



13 



