305 
-5-+ 
= -k(t - t_) 
Piste ise Gh o’ log c.t 
OL fe} t.<t 
= ie hs 
Numerscal Values 
The forms of the pressure-time curves for these cases have been evaluated for particular 
Values of the various parameters, For all cases 
Cans 20,000 ft./sec. 
cy = 5,000 ft./sec. 
Ze cents 
k = 60,000 sec.*, p, = 5,000 1b./sq.in. 
For cases Ai, A2 and A3 
dia 5 ft. 
For cases Bi and B2 
= f; 
ie 5 ft. 
respectively. 
The forms of the various pressure-time curves are shown in Figure 3(a), (b), (c) and 
Figure 4(a) and (b) together with curves observed using piezo electric gauges and Cirdtex charges 
of the same lengths and in the same positions as those in the calculations. The integrals for 
CaSes Ai, 2 and 3 were computed numerically. !n Figure 3 and 4 the time after detonation to the 
arrival of the wave is assumed to be the same for the observed curves as for the calculated curves, 
since these times were not observed experimentally. For underwater explosions of Cordtex, the 
Values of cy and cy correspond approximately with those used in the calculations. 
{t is not known what values should be taken for the pressure Poe at 1 foot from the explosion 
and for k which determines the rate of decay of the shock wave pressure, in order that they may 
correspond with the Cordtex. jt is seen, however, that for values for Py of 5,000 1b./sq.in. and 
for k of 60,000 sec. }, the relative shapes and magnitudes of the calculated curves are not very 
dis-similar from those observed. The agreement is even better than is apparent in Figure 3 and 4, 
Thus the sharp cut-off of pressure in Figure 3(b) and 3(c) which occurred about 0.6 milliseconds 
after the start of the waves was due to the reflected tension wave from the free surface. The high 
peak pressure in Figure 3(c) was probably due to the added effect of the detonator. The gradual 
rise of the pressure shown in the record in Figure 4(b) was almost certainly due to the effect 
of the finite size of the gauge. if it is assumed that the actua) wave reaching the gauge was 
shock-fronted and approximate calculation estimates the true peak to be about 4,500 1b./sq.in. instead 
of just over 2,000 1b./sq.in.s which is more in accord with theoretical predictions. 
From Figure 3(a), u(a) and 4(b) it is seen that relatively small alterations in the shape 
of the charge produced considerable changes in the forms of the pressure-time curves. For these 
Cases, however, the impulses were not very different and it is therefore possible that the damage 
produced by theee charges would not be very dependent on the shape of the charge, 
The report therefore indicates the extent to which the forms of the waves produced by line 
charges can be predicted to a first approximation, by the simple theory given in this note, It is 
to be noted, however, that the use of the theory is limited by uncertainty in the choice of values 
for Po and k. Further, the effects near to the charge will not be represented by the simple state 
of affairs assumed in the theory since the finite amplitude of the waves will result in their 
interaction in a more complicated manner than for waves of acoustic intensity. Thus, although the 
acoustic approximation may be valid at points more remote from the charge, the form of the waves 
reaching such points will have been determined to a certain extent by the condition obtaining near 
the charge. 
