UNDERWATER EXPLOSION PHENOMENA 
. 
based on a knowledge of the somewhat more 
accurate pressure-distance curve, is probably the 
better of the two. 
V. IMPULSE AND ENERGY FLUX ASSOCIATED 
WITH THE SHOCK WAVE 
15 
The general character of the pressure wave 
emitted by an underwater explosion is illustrated 
by the oscilloscope trace reproduced in Fig. 1. 
The first portion is generally referred to as the 
shock wave, and this in turn is succeeded by 
the first, second, etc., bubble pulses. The pres- 
sure-time record is continuous, and naturally 
there is no sharply defined demarcation between 
the various portions of the wave. For con- 
venience, an arbitrary demarcation will be intro- 
duced for the purposes of this report. 
The shock wave will be defined as the portion 
of the wave lying between the shock front (t=0) 
and the first bubble maximum (¢=¢a1) which 
occurs at the pressure minimum lying halfway 
between the shock front and the peak of the 
first bubble pulse. The first bubble pulse will be 
defined as the portion of the wave lying between 
the times of first and second bubble maxima 
(ie., between t=tfyi and t=ty2), etc., for the 
succeeding pulses. 
Usually, shock-wave pressure-time recording is 
carried only to times of the order of 100, where @ 
is the time constant of the initial exponential 
decay. Recently, a series of deep water measure- 
ments? has provided data making it possible to 
construct average or composite curves out to 
time twi as defined above. These curves are 
1145 
527 
based on measurements with 0.50-, 2.50-, and 
12.0-lb. charges of TNT at depths of 250 and 
500 ft. Gauges were placed at such distances as 
to keep the value of W!/R constant at 0.352 for 
each charge size. The curves are shown in Figs. 5, 
6, and 7. 
16 
The impulse delivered up to any time ¢ is 
defined by 
[= f “Apdl. (29) 
The shock wave has an initial positive phase 
of relatively short duration and high amplitude 
followed by a long negative phase of low ampli- 
tude. The positive portion of the impulse is of 
principal interest as far as damage considerations 
are involved. 
As the integration is carried to tari, the value 
of the integral becomes very small and in an 
incompressive system would become zero. In a 
compressive fluid the integral has a small posi- 
tive residual at ¢1, as indicated in the following. 
At tw: the bubble has attained maximum 
radius, and the particle velocity at its surface 
is zero. In the acoustic approximation the particle 
velocity as a function of time at a point in the 
fluid is given by 
Ap ae lee re 
+— f Apdt. 
polo poR Jo 
If we make an observation at R=A 41, where 
Am. is the maximum bubble radius, then at 
a 
(30) 
Fic. 5. Composite pressure- 
time curve for tail of shock wave. 
Explosive: TNT; charge depth: 
250 ft.; distance from center of 
charge: R=W}/0.352. Legend: 
@ time constant of initial shock 
wave decay, @, X 0.5-lb. and 2.5- 
Ib. charges from measurements 
of reference 2. A Points from 
shock-wave composites obtained 
EXCESS PRESSURE (PSU) 
by J. S. Coles et al., Woods 
Hole. 
REDUCED TIME T (t/e) 
