NSWC/WOL TR 77-90 



k = 



Y-1 



Y-1 2 



\a_.Yp 



i.pp. 



-Y 



(3.4.5) 



Damage Parameters X and Y . The problem is to calculate the 

 damage parameters X and Y, Equations 3.3.2 and 3.3.3, respectively. 

 Thus we must calculate AMIN/A. and AMAX/A.. We proceed as follows. 

 First, using k (Equation 3.4.5) we look up AMIN/AMAX in Table A-1 

 of Reference 1. Next, we calculate the pressure ratio 



(Y-1) 



PMIN 

 P. 



K 



AMIN 

 AMAX 



(3.4.6) 



"^ / amin \ "^ 



I AMAXy 



1 - 



AMIN 



3 (Y-1) 



AMAX / 

 where PMIN is the air pressure at the first compression. 



Finally, using the adiabatic pressure-volume relationship 



we get 



AMIN ^ / PMIN Y 



_1_ 

 3y 



(3.4.7) 



and 



AMAX _ / AMIN ] / ( 



AMIN 

 AMAX 



(3.4.8) 



With increasing both the first compression and the subse- 

 quent expansion calculated by this approximation become too large. 

 Thus both damage parameters, X = -100 In AMIN/A. and Y = lOO In 

 AMAX/A. become progressively too large with increasing values of 9. 



4. Snay, H. G. and Christian, E. A., 1952, "Underwater Explosion Phenomena: The 

 Parameters of a Non-Migrating Bubble Oscillating in an Incompressible Medium," 

 NAVORD Report 2437, Equation 14a. 



15 



