NSWC/WOL TR 77-90 



Which Approximation to Use . For those cases where the calculation by 

 half-period square steps showed to be the order of a half-period or less, we 

 calculated the fish damage parameter, Z = X + Y, by both approximations. Since 

 the systematic errors in both of these approximations result in values of Z which 

 are too high--square steps for values too small, impulse for 9 values too 

 large--we calculated these cases by both approximations and selected the one 

 giving the smallest value of the damage parameter Z. It turned out that the 

 crossover for the Z values calculated by the two approximations occurred for 

 e values equal to approximately six-tenths of the first half-period calculated 

 by square steps. 



3.5 PATCHING OF SOLUTIONS . The response of the equivalent bubble to the 

 pressure-time signature was determined separately for each of the two pulses 

 shown in Figures 3.1.1 and 3.1.2. To facilitate the calculations the response 

 to the second pulse was calculated as starting from rest at the initial ambient 

 radius and pressure, A^ and p.. Results of the separate calculations were then 

 scanned to obtain the extreme values of the radius, AMIN and AMAX. Table 3.5.1 

 summarizes the results of these calculations. The values of X and Y selected 

 to calculate the damage parameter, Z = X + Y, are indicated with a check mark. 

 Note that the value of X or Y selected is the maximum of the value calculated 

 for the first pulse and that second pulse value corresponding to the method of 

 calculation--square or impulsive loading--selected according to the criterion 

 given in Section 3.4. For example, for the first entry (first row) in Table 

 3.5.1, the "Impulsive Loading" calculation was used for the second pulse, since 

 this value of Z = X + Y (48 + 38) is less than the value calculated by "Square 

 Steps" (102 + 40). Thus, the value for Z representing the combined response to 

 the first and second pulse is the sum of 64_, the greatest X value (taken from 

 first pulse having discarded the value 102 ) , and 3_8' the greatest Y value (taken 

 from second pulse having discarded the value 4_0) . 



Additional Details . Response to the first pulse for the two shallowest 

 depths (Figures 3.1.1 and 3.1.2) was calculated by the method of Reference 1 

 by setting TPOS (Reference 1, Figure 3.1.1) equal to the time of arrival of 

 the second pulse. Response to the first pulse (square step) for the deepest 

 depth was calculated setting PMAX equal to the step pressure and 9 equal to 

 approximately 10^ times the duration of the step. Other parameters were =et 

 as follows: TFOS = step duration, PNEG = plateau pressure following step, 

 and DTNEG = duration of plateau pressure. 



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