NSWC/WOL TR 76-155 



where L is the fork length of the fish. For our 5.4" Spot this gives 

 an initial bubble radius 



A. = 0.0178 ft (A44) 



The initial ambient pressure p^^ = 32 psi, which corresponds to a depth 

 of 40 feet in fresh water. The magnitude of the pressure step, 

 P l " P i' is 50 P si; and its time duration TPOS = 2.3 milliseconds. 

 The period ^ at p = 82 psi turns out to be 0.569 milliseconds, so 

 that the oscillation in State 1, which starts at maximum bubble size 



A 



the time cut off occurs 



M = A i , goes through 2.3/0.569 =4.04 periods of oscillation by 



(Footnote from page A-14) 



*This gives a rough approximation to the bladder volume of a 5.4" lone 



fish at 40ft-depth and 500 feet distant from a 68-lb pentolite charge 



(Shot 525) . Equation A43 was conjured up by the author for a 



"nominal fish". It represents the radius of a sphere of 1/20 of 



g 

 the estimated volume of the fish (after Weston) . The volume of the 



fish is taken as an ellipsoid whose semi-major axes (A,B,C) bear the 



relation, A = 0.38 L, B = 0.30 A, C = 0.25 B, where L is the overall 



length of the fish. The above coefficients are average values taken 



from crude measurements of sketches of fish shown by Lippson. 



9. Weston, D. E. , 1966, "Sound Propagation in the Presence of Bladder Fish", 

 published in Vol. II of "Underwater Acoustics", edited by V. M. Alters, 

 1967, Plenum Press 



10. Lippson, A. J., 1973, "The Chesapeake Bay in Maryland — an Atlas of 

 Natural Resources", John Hopkins University Press 



A-l( 



