1181 
-7T= 
APPENDIX 
fe. Numerical values for underwater explosion waves. 
let 
Po = maximum pressure in explosion wave, tons/square inch. 
A = total impulse in explosion wave, 1b.seconds/square inch, 
W = weight of charse, Ibs. 
0 = distance from charge, feet. 
C = velocity of explosion wave, feet /second, 
h = plate thickness (inches) 
Then for distances at which Py € 2 tons/square inch the following empirical relations 
have been estaolished for T.N.T., aiatol and juncotton. 
1/3 
ti can tons/square inch 
D (31) 
2/3 
A BON 1b.second/square inch 
D 
Since the experimental curve is not exactly of the exponential form assumed theoretically the value 
to be assigned to n will vary to a sinall extent according to the criteria used in fitting an 
exponential to the experimental curve. Since we are concerned here only with the order of 
quantities involving n it will ve sufficient to take the simple criteria that theoretical and 
experimental curves nave the same Py and A. Then since n= psa for the theoretical curve, the 
same will hold for the experimental n romembdcring that Po and A must be expressed in the same 
units. On this basis the empirical formulae (31) yive 
1/3 
= ——" seconds (32) 
8250 
Te Dd 
whence taking c = 4900 feet/second for a small emplitude wave we have 
Cea Es tec (33) 
n 1.68 
In order to decide on a reasonable value for tne distance, Do Say, beyond wnich the explosion 
wave may be regarded as of small amplitude we note tnat the empirical relations (31) agree with the 
inverse distance law valid for a small amplitude wave. Since these relations have been established 
for Py < 2 tons/square inch this sugjests that D, be taken as the distance for which p, = 2 tons/square 
inch. 
On this basis 
3 1/3 
0, 3.5 W? feet (34) 
For a spherical charge this value of D_ corresponds to about 13 Charge diameters and for a charge 
of 390 1b, T.N.T. gives 0, = 25.6 feet = 780cm. for this latter charge Penney has calculated 
the theoretical variation of Po O with D and from his paper we see that D = 780 cm. is a reasonable 
value for the distance beyond which Po D is constant. It may be noted that the equilibrium radius, 
Dy Say, of the bubble as given by Ramsauer's formula is 
o, = =— feet 
1 Vian ee (35) 
WhHEFE ceaes 
