NSWC/WOL TR 76-155 



(Equations 3.1.7 and 3.1.8) was then varied to obtain the best 

 possible correlation between the calculated and experimentally 

 observed in juries — Section 3.2 and 3.3. 



Next, we read or calculate the outside pressure at the end 

 of the first half-cycle of motion using the period estimate calculated 

 by (B8) ; and then calculate p.. , the constant outside pressure for 

 this approximate solution, as the average of the pressures at the 

 beginning and end of the half -cycle. Using p we can then calculate 

 the parameters for the first half-cycle of motion; and, in particular, 

 obtain a considerably improved value for T. Using the improved 

 value for T we then calculate from Equation B8 a better value for c< 

 which we use to calculate the next half-cycle of motion.* 



Surface Cut-off . Upon arrival of the reflected wave from 

 the water surface the outside water pressure suddenly drops to 

 below the initial ambient level. This phenomenon is known as 

 "surface cut-off". When cut-off occurred near an extremum — i.e., 

 within 0.10 cycles of a maximum size, or within 0.08 cycles of a 

 minimum — we calculated the final motion at the lowered outside 

 pressure as starting from rest from the nearby extremum . Interme- 

 diate cases were calculated as starting from rest using an interme- 

 diate initial bubble size — based on the parameter (At/T) which 

 was calculated as follows: 



If A + AMAX , then (At/T)-,, = (TPOS - t ) /T (B9) 



c , n PC c , n 



n-1 n-1 



*If necessary, we can use this improved value for T to get a better value of the 

 average pressure p . So far this has not been necessary. 



B-5 



