476 



272 



ARONS, SLIFKO, AND CARTER 



Fig. 1. Pressure-time record showing shock wave and bubble pulses. Charge: 0.505 lb. T.N.T.; 

 Gauge dist.r 2.25 ft. Depth: 500 ft. 



were made at a depth of 500 ft. in water having 

 an over-all depth in excess of 650 ft. (For com- 

 parison several 0.505- and 2.507-lb. charges were 

 fired at 250 ft.) Under these conditions, surface 

 and bottom effects were negligible. The half- 

 pound charge is deemed to be the smallest T.N.T. 

 charge which can be reliably detonated under 

 these circumstances. The twelve-pound charge is 

 the largest that could be tolerated at a distance 

 of 500 ft. below the vessel performing the experi- 

 ments; thus, the range of charge size was the 

 widest attainable with the available experi- 

 mental equipment and with T.N.T. as the 

 explosive. 



All pressure-time measurements were made at 

 a distance from the charge such that the value 

 of W^/R was constant and equal to 0.352, W 

 being the charge weight in pounds and R the 

 charge to gauge distance in feet. A typical pres- 

 sure-time record is reproduced in Fig. 1. Periods 

 of pulsation have been measured to the seventh 

 and, in some cases, to the eighth bubble pulse. 

 Peak pressures, impulse, and energy flux have 

 been obtained for the first and second pulses. 



n. PERIODS OF OSCILLATION 



2.1. Theoretical analysis shows' that to a first 

 approximation the period of oscillation of a gas 

 globf is given by 



T = KW"^/Zo"\ 



(1) 



where /C =constant of proportionality, W= charge 

 weight, and Zo = absolute hydrostatic depth. 



If the energy associated with the oscillation 

 were constant (i.e., if there were no dissipation 

 or acoustic radiation), the period would also 

 remain constant. However, appreciable energy is 

 lost, principally in the neighborhood of the 

 bubble minimum owing to the emission of the 

 pressure wave and other dissipative effects and, 



consequently, the period of successive oscilla- 

 tions decreases. A summary of the expierimental 

 results is given in Table I in terms of the pro- 

 portionality constant, K, defined by Eq. (1). 



2.2. It will be noted in Table I that the values 

 of Ki for the 2.5- and 12-lb. charges are sig- 

 nificantly lower than those for the 0.5-lb. charges. 

 The reproducibility of the period measurements 

 and the fact that charge sizes were alternated in 

 a definite sequence during the shooting program 

 make it very unlikely that the difference is due 

 to systematic experimental error in the measure- 

 ment of T or Z. The discrepancy can be in- 

 terpreted only as a slight but significant depar- 

 ture from the ideal cube root law of variation of 

 period with charge weight. (Although correction 

 has been made for the effect of the tetryl booster 

 present in each charge, one cannot be certain of 

 the accuracy of the correction, and it is therefore 

 possible that the observed discrepancy may be 

 due to the relatively larger proportion of booster 

 in the half pound charges.) 



Examination of A'„ as a function of n shows 

 that the period drops off sharply during the first 

 three oscillations and then decreases slowly but 

 steadily in such a way that the results do not 

 yield a value of K which could be regarded as 

 an accurate limiting value, applicable to the 

 ultimate small amplitude oscillations of the gas 

 globe. 



III. PEAK PRESSURE: FIRST AND 

 SECOND PULSES 



3.1. Peak pressures of the first and second 

 bubble pulses are summarized in Table II- 



As will be indicated in Section V, the cylindri- 

 cal'charges were oriented with their axes in a 

 horizontal plane. Pairs of gauges were placed 

 above, below, and to the side of the charge in 

 positions denoted by Gl, G4, and G2,3, respec- 



