1115 
along a given direction from the charge were obtained on each shot. 
The pressure-time curves obtained from the ends (Positions A and B) 
of these long cylindrical charges were characteristically different from 
those of spherical charges or cylindrical charges with the ratio of 
length to diameter not greater than 2. In addition, the pressure-time 
curves with gauges off the detonator end, off the non-detonator end and 
off the sides, are distinctly different from one another (records from 
Position A, B, and C, respectively). The characteristics of pressure- 
time curves from various positions about long cylindrical charges are 
illustrated in Figs. 4 and 5, where t; is the arrival time of the first 
signal to reach the gauge, tr the arrival time of the signal from the 
charge element producing the final signal to reach the gauge, t, the 
arrival time at the gauge of the signal from the detonator end of the 
charge, t_Z/5 the arrival time of the signal from the midpoint of the 
charge, and ty the arrival time of the signal from the non-detonator 
end of the charge. The pressures corresponding to tp and ty are 
Pr and Pye The actual time of detonation of the charge element at 
x = 0 is the zero point on the time scale. The pressure measured at 
the gauge between times t; and tp does not show the initial exponential 
decay obtained with spherical or more symmetrical charges, but is 
sustained by the finite detonation time of the charge. Not until 
detonation is complete, and no further contribution to the shock wave 
from detonating explosive is reaching the gauge, does the shock wave 
begin decaying more rapidly (at time t,). 
6. Experimental Data 
Table I gives the experimental pressures (p, and p,), durations 
(tg - ty), and momenta ( f pdt) and energies (1/7 6° f pedt) together 
with their integration times for the various gauge positions and 
distances used. In Table II are presented the experimental data for 
the UERL diaphragm gauges, with thin (0.038 in. standard thickness) 
and medium (0.085 in. standard thickmess) diaphragms at various 
distances from the charge for the three charge orientations. 
IV. DISCUSSION 
7. Non-Linear Interaction of Shock Waves 
The treatment of the pressure-time function at a given point in 
space as a summation of the contributions of the elements of a line 
charge is extremely difficult because of the complicated non-linear 
manner in which shock waves of finite amplitude interact. A linear 
super-position theory would, under the conditions employed for the 
off-end shots in these experiments, fail to account for the observed 
initial peak pressure, but would predict instead a finite and 
measurable time of build-up to a maximum pressure. A more nearly 
correct theory is no doubt possible, but no quantitative discussion 
of the pressure-time relationships as a function of distance and 
orientation from the charge will be attempted here. The qualitative 
features which appear to be related to the times of detonation of each 
charge element and to the corresponding transit-time of the shock wave 
from each element to the gauge, as estimated by the acoustic approxi- 
mation, will be discussed in detail. 
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