NSWC/WOL TR 76-155 



Z = i°-° In PMIN/^ + 100 In AMAX/A ± (E2) 



Note that Equation E2 is equivalent to 3.1.5. It is just our 

 point of view that has changed. 



Now let us suppose, for fish very close* to the water 

 surface, that the Shockwave peak overpressure PMAX is the only- 

 tissue damaging pressure. The damage parameter by this mechanism 

 equivalent to Equation E2 is then given by 



100 , 

 PMAX ' 3y 



^ + 1 (E3) 



. P i J 



where PMIN is replaced by PMAX + p. and the second term drops out. 



Note that Z _,..,.., must always be smaller than Z calculated by 

 PMAX J 



Equation 3.1.5 except for those cases — the ones of interest here-- 



where the pressure wave is of such short duration that the transient 



response of the swimbladder is suppressed*. Thus, when in doubt 



which damage parameter to use — z PMA v (Equation E3) or 



Z (Equation 3 . 1 . 5) -- calculate both parameters, and use the greater 



value . 



Finally, we estimate the overpressure level, PMAX, 

 associated with the assumption that all the damage corresponding 

 to the damage parameter Z is due directly to tissue compression 

 by the incident Shockwave. Solving E3 for PMAX we get 



"* 



Since Z is equivalent to the damage parameter X 



(Equation 3.1.3) calculated from the non-oscillatory steady-state 

 response of an infinitely small bubble to an overpressure PMAX 

 of finite rise time. 



E-2 



