477 



SECONDARY PRESSURE PULSES IN UNDERWATER EXPLOSIONS. I, 



Table I. Summary of period constants for T.N.T. r„ = iC„ W" V^o'", r„ = period of nth oscillation (sec), M' = charge 

 weight (lb.), Z = depth of charge below surface (ft.), Zo = absolute hydrostatic depth = Z+33 (ft.). 



n(ier these condil 



Results of the two shots agreed very closely. 



lively, all the gauges being positioned off the 

 cylindrical surface of the charge. It was assumed 

 that the difference between the average pressures 

 at Gl and G4 was due only to displacement of 

 the bubble toward Gl, and the pressure was 

 assumed to vary inversely as the gauge to bubble 

 distance. This treatment neglects any effects 

 resulting from possible asymmetry of the pressure 

 field, but it appears to be justified by the fact 

 that when pressures at Gl and G4 are corrected 

 to the same distance as the G2,3 position, all 

 the values agree within experimental scatter. 



The values given in Table 1 1 are the averages 

 of pressures measured at all three positions and 

 corrected (by means of the apparent migration 

 result) to the given distance from the center of 

 the bubble, R=Wi/0.352 ft. 



Because of uncertainty as to the exact location 

 of the true base-line of zero excess pressure on 

 the individual photographic records, the records 

 were read with respect to an arbitrary base- 

 line and were then adjusted to the theoretical 

 baseline value calculated by means of the theory 

 summarized by Friedman.' This is based on a 

 calculation of the negative pressure (below sur- 

 rounding hydrostatic level) existing at the time 

 of the first bubble maximum, and for the condi- 

 tions represented in Table II the values are —80 

 and -120 Ib./in.^ at depths of 250 and 500 ft., 

 respectively. 



3.2. Ideal scaling would require that all the 

 peak pressure values at a given ratio of W'/R 

 be equal regardless of charge size. Examination 

 of Table II shows that this is not the case. 

 The principal cause of the observed variation is 

 undoubtedly the migration of the bubble. Theo- 

 retical calculation of the influence of migration 

 on peak pressure' predicts very much less effect 

 than is observed, the expected decrease in peak 



pressure for the worst case (2.5 lb. at 250 ft.) 

 being less than 1 percent, whereas Table II 

 indicates 15 percent, if AP for the half-pound 

 charges at 500 ft. is used as a basis of comparison. 

 Further discussion of this result will be found 

 below in Section IV. 



3.3). The results summarized in Table II indi- 

 cated that the pressure field was cylindrically 

 symmetrical with respect to the axis of the 

 charge. A number of shots were fired with 

 the charge so placed that gauges in position G2 

 faced the cap end while gauges at 03 faced the 

 butt end of the charge. Gauges at Gl and G4 

 were still above and below the charge, respec- 

 tively. In Table III the pressures at G2 and 03 

 are compared with the pressure at G2,3 (off the 

 cylindrical surface) given in Table II. It will be 

 noted that a marked degree of asymmetry exists, 

 particularly in the case of the small charges, 

 with the pressure from the cap end being sig- 

 nificantly higher than the pressure from the 

 butt end. 



IV. POSITIVE IMPULSE AND ENERGY PULSE 

 4.1. For convenience in describing and work- 

 ing with various portions of the continuous 



Table II. Apparent bubble migration and corrected 

 peak pressures. AP„ = excess peak pressure of nth pulse 

 (lb./in.2), i? = distance from bubble center of point where 

 AP„ is measured; R = W^/0.i52 (ft.), W = charge weight 

 (lb. T.N.T.), Z = depth of charge below surface (ft.), 

 A/(„ = vertical displacement of center of bubble from initial 

 charge position at time of nth bubble minimum (ft.). 



I" Stated error is standard deviation of the mean. 



