478 



ARONS, SLIFKO, AND CARTER 



Table III. Bubble pulse peak pressures for various 

 charge orientations. Notation for position of measurement: 

 G2,3 — gauge facing cylindrical surface of charge, G2 — • 

 gauge facing cap end of charge, G3 — gauge facing butt 

 end of charge. Gauge distance from center of bubble: 

 R = Wi/0.352 (ft.), W=charge weight (lb. T.N.T.), AP„ 

 = excess peak pressure of nth pulse (Ib./in.^). 



pressure-time curve illustrated in Fig. 1, an 

 arbitrary subdivision has been adopted. The 

 shock wave is defined as that portion of the 

 curve lying between the shock front (where 

 the time, / = 0) and the point of first bubble 

 maximum {t=Ti/2). Similarly, the first bubble 

 pulse is the portion between first and second 

 bubble maxima, i.e., T1/KKT2/2, etc. 



4.2. The impulse delivered by the pressure 

 wave during a fixed interval of time is defined : 



'= r Apdt. 



(2) 



During a bubble pulse, the pressure is initially 

 negative, becomes positive, and then again nega- 

 tive. It can be shown from acoustic theory that 

 the integral in Eq. (2) taken over the entire 

 pulse as defined above must be very nearly 

 equal to zero. (Actually, there is a small negative 

 residual.) Of principal interest, however, is the 

 magnitude of the positive impulse, the integral 

 being taken only over the region of positive 

 pressure. A summary of average positive im- 

 pulse values is given in Table IV. 



4.3. Impulses measured at Gl vertically above 

 the charge are systematically high and those at 

 Gi below the charge are systematically low, as 

 would be expected on the basis of the migration 

 results given in Table II. As with the peak 

 pressure (Table III), the impulse is higher at 

 points off the cap end and lower off the butt 

 end than off the cylindrical surface of the 

 charge. 



Using the G2,3 position (off the cylindrical 

 surface) as being representative of the unper- 

 turbed impulse, it is seen that at each depth the 

 impulse scales according to the ideal similarity 

 law within the experimental precision which is 



Table IV. Positive impulse: First and second bubble 

 pulses (no correction applied for bubble migration). Dis- 

 tance of point of measurement from center of initial charge 

 position: ^ = H'VO.352 ft., H' = charge weight (lb. T.N.T.), 

 Z = depth of charge below surface (ft.). 



• See Section 3.3 and Table III for key to position notation. 



of the order of 4 percent. This agreement indi- 

 cates that the pressure differences noted in 

 Table 1 1 are confined to a very narrow region in 

 the immediate vicinity of the peak of the pulse 

 and do not affect the remainder of the pressure- 

 time curve appreciably. 



Thus, the effect of migration on peak pressure 

 is more than would have been expected on the 

 basis of the theoretical predictions, but the other 

 parameters of the pressure-time curve remain 

 virtually unaffected. Since the impulse obeys 

 the ideal scaling law, it is presumed that the 

 peak pressure also would if the effect of migration 

 could be reduced still further, but this is not 

 conclusively demonstrated and further measure- 

 ments would be necessary to test the presumption. 



4.4. Theoretical analysis' shows that to a first 

 approximation the positive impulse in a bubble 

 pulse would be expected to vary as the inverse 

 sixth root of the absolute hydrostatic pressure 

 at the depth at which the bubble is located. 

 A test of this prediction is given in Table V. 

 Since the quantity IZo^'^/W^" is essentially 

 constant with depth, it is seen that the prediction 

 is confirmed within the available experimental 

 accuracy. 



4.5. Integrations of the pressure-time curves 

 were also performed for the purpose of deter- 

 mining the irreversible energy flux which is 

 given by acoustic theory as : 



1 r' 



flnCn "la 



F= — I {^p)-dt, 

 PoCo 



where A/) = excess pressure (Ib./in.^), / = time 

 (sec), poCo = acoustic impedance of water (slug 

 ft./in.' sec), and i^=energy flux (in. Ib./in.^). 



