12 
28. Alternatively, if energy is adopted as the criterion, then for an 
exponential shape of pulse, equations A17 and 10 give 
2 
Sy bP 
Q = Fa CO) 
Taking c = 5,000 ft. per sec. for sea water of density 64 lb. per cu. ft. 
and substituting for p,, ana() in equation 17 by use of equations 11 and 12 
then, 
MB = Ls seCe. eee eee eee eee eee sala eee (18) 
29. Yet another alternative is to make the exponential form give impulse 
and energy corresponding to equations 12 and 13 whilst disregarding equation 
11. Then, by substituting from equations 12 and 13 in equations 15 and 17 
respectively, and solving for p,, and n, the values to be used in equation 
10 for T.N.T. charges would be 
x 
Pay = 603 H WEE PGP Belg Ailg “S06 5000 G06) 06) one (19) 
a 
1 we 
n = 7,00 SCCe cee eee eco eve eee eee eee (20) 
30. Thus, using variously the empirical formulae 11, 12 and 13, three 
alternative pairs of formulae can be obtained for use with equation 10, 
namely, either (a) equations 11 and 16, (b) equations 11 and 18, or 
(c) equations 19 and 20. The three sets of formulae agree for a charge 
weight of about 130 lbs., and generally for medium weight charges of this 
order of size, the choice of formulae for p,, I and n will not be of vital 
importance. Damage produced by a pressure pulse can depend primarily on 
any one of the three quantities p,, I and{l. The choice of formulae for 
Pe I and n will, therefore, depend on the mechanism of damage. Where the 
damage is not specially dependent on any one of p,,,I ana (2 equation 16 has 
the merit of giving values of n intermediate to those given by equation 18 
and 20. In general, the simplicity of the exponential form of equation 10 
for theoretical analysis more than offsets the attendant uncertainty as to 
the best values to be used for p,, and m 
31. Experimental measurements have, in general, been confined to measuring 
the pressure/time variation in the pulse at given points. However, the 
corresponding distribution of pressure in space at a given time can be 
deduced by using the preceding relationship between the pressure/time and 
pressure/distance curves for distances at which the pulse is of small 
amplitude. Thus in fig. 4, corresponding pressure/space distribution at 
the time when the front of the pulse reaches the distance r = 40 ft. will 
be given approximately by the pressure/time curve. The time scale would 
then be replaced by a distance scale with time 0 becoming r = 40 ft., time 
0.001 becoming r = 35 ft., time 0.002 becoming r = 30 ft. and so on, the 
charge centre lying off the figure to the right. 
32. Since the pulse has an indefinite tail there is strictly neither a 
definite duration of pulse at a given point nor a definite length of the 
pulse in space at a given time. However, for theoretical analysis using 
the exponential representation of equation 10, the parameter n determines 
the rapidity with which the pressure in the pulse drops to unimportant 
magnitudes. The reciprocal 1/n, which has the dimensions of time, gives 
a measure of the order of time for which the pressure is important and is 
the time constant for the pressure pulse. 
