59 73 



The time constant T^ of the shock wave would be perhaps O.06 milli- 

 second for a charge of 0.2 pound and more than 0.1 millisecond for charges of 

 a pound or larger. 



Thus, at least for the larger charges, T^ Is relatively small, and 

 Case 5 as described on page 52 Is present. Compressibility of the water can 

 be neglected; cavitation should not occur. Furthermore, there should be no 

 appreciable increase in the pressure by reflection, except during the first 

 few microseconds. 



The swing time of the diaphragm with water loading may be estimated 

 from Equation [67] as 



0.5 n 



0.000832 / ^ 0.39 

 35000 \ 8.89 h 



Here 8.89 is the specific gravity of copper and O.OOO832 its density in inch 

 dynamical units, and the yield stress has been taken as 35.000. According to 

 this formula T, varies from O.078 for a thickness h = 0.03 inch to O.O60 mil- 

 lisecond for ^ = 0.1 inch. This is of the same order as the duration of the 

 wave. Hence some increase of deflection by dynamical overshoot is to be 

 expected. 



For charges of 1 to 300 pounds of TNT, the static pressure P re- 

 quired to produce the same deflection as does the explosion was found experi- 

 mentally to vary nearly as R'^'^* where R is the distance in feet from the 

 charge to the gage; see Figure l8 in Reference (19). The exponent l.lU might 

 arise chiefly from the variation with distance of the pressure due to a 

 charge of TNT. A variation with distance of this order was found at Woods 

 Hole for tetryl (20). Similitude would then imply a general variation of P 

 as (W^V-R)''^^ or as W^'^yR^'^*; whereas the data indicate a variation more 

 nearly as w^^R^'^* 



The more rapid increase with W may be partly the result of in- 

 creased dynamical overshoot. For 1 pound, q = 2T,/{nT^) = 2 x 0.07/(0.1 1 tt) = 

 0.40, roughly, at which, in Figure 28, N= 1.22. For 200 pounds, q = 

 2 X 0.07/(0. 64 tt) = 0.07, at which N= 1 .80. Thus Equation [92] implies an 

 Increase in the deflection due to increased overshoot, as the charge is in- 

 creased from 1 pound to 200 pounds in the ratio 1 .80/I .22, or in the ratio 

 W""-" On the assumption that deflection and equivalent static pressure are 

 nearly proportional to each other, therefore, the total variation of the 

 equivalent static pressure would be about as i^o-ss +<>•<''' = w"'*^, which is not 

 too different from the observed W''-\ 



In absolute magnitude, however, the equivalent static pressures are 

 considerably below the estimated peak pressures in the explosion wave. For 



