232 SHOCK WAVE MEASUREMENTS 



Strictly, the pressure P{t) — Po in excess of hydrostatic pressure should 

 be used in this equation, but for most cases of interest the shock wave 

 pressure P{t) is so large that the difference is of no importance. 



Unfortunately for simplicity, the form of the shock wave is such 

 that the integral I{t) does not converge rapidly to a limiting value with 

 increasing values of t, and it is not practically possible or desirable to 

 define an upper limit on time for which the impulse is obtained. This 

 difficulty arises from the existence of the shock wave tail, or interval of 

 slowly decaying pressures, the area under which makes a continually 

 increasing contribution to the integral of Eq. (7.2), as shown in Fig. 7.2. 

 The reason for the tail is the onset of essentially noncompressive motion 

 exterior to the gas sphere, and the pressure associated with the motion 

 becomes zero (strictly hydrostatic) only after the gas pressure has fallen 

 to hydrostatic. This time is of the order of one-tenth the period of pul- 

 sation of the gas sphere (see section 9.3) which is many times the time 

 constant 6 of the initial high pressure region. For example, the time 

 constant 6 is approximately 0.5 msec, thirty feet from 300 pounds 

 of TNT, and the duration of positive excess pressure is of the order of 

 80 msec, for th^s charge detonated 40 feet below the surface. 



The determination of impulse out to some 200 times the initial time 

 constant of the wave would, for many reasons, be a time consuming and 

 difficult problem both in experimental arrangements and analysis. 

 Such an integration in many cases would reduce the value of the figure 

 finally obtained as a measure of a short-lived transient pressure. For 

 these reasons, impulse values for shock waves are customarily obtained 

 by integration over only the earlier high-pressure region to an arbitrarily 

 assigned upper limit on time, which should be long enough to include 

 any characteristic features of the pressure-time curve when the pres- 

 sures are a significant fraction of the initial peak value. One way of 

 assigning the upper limit on time is to specify it in terms of the initial 

 time constant, for example as five or ten times the time constant. Such 

 a measure presents difficulties if pressure-time curves from considerably 

 different explosives or from charges of different shapes are to be com- 

 pared, and in such a case a simpler measure is a specified value for a 

 given charge weight or volume. 



In order to arrive at a suitable criterion for the integration time, the 

 effect of different choices in this time on impulse ratios for charges of 

 different explosives and shapes has been examined.^ The data used in- 

 cluded pressure-time curves for charges of three explosives, in approxi- 

 mately spherical and elongated cylindrical shapes. The measured time 

 constants differed by factors as great as three, but impulse ratios for 

 times greater than five times the mean value showed little change with 

 increasing values of the limit on time, although individual values in- 



3 Unpublished analysis by the writer. 



