(c) 
955 
The procedure, then, for determining 9. for a given point on a given film is 
to choose several values of @,. ®, min and ¥o calculate pinta 1 0.) by numerical 
, , 
integration. 
rt =D, n, \RI sin 4, adr 
(II-13a 
toa 8. = 
é(r Dy, ®r) i eUnt et = a 2nl* sine 1, , 
R 
where n is given as a function of @, and r in Eq. (II-15). g is then plotted against 
@, and r in Eq. (II-15). é is then plotted against 0, at the value of r' - D, deter- 
mined by the point studied. ¢ can easily be shown by physical arguments or by 
mathematical considerations to be a monotonically decreasing function of @,, The 
value of @ giving a value of § = gg (Fig. 134), that is, that value of ¢ obtained in 
the course of the calculation of p.. for the given point, is taken as the correct 
value of @,. for the shock wave as determined by that point. If no value of 0, @. 
gives a value of ¢ as large as g,, the ray of light studied is assumed to have paakedn 
through the point of total reflection after it left the diffuse light source, the 
lucite grid. In this case (Eq. II-13a) must be replaced by 
aa '-D,. 
d(et-aayeeye n, \R)sin 4, dr n,\RI sin 4, dr 
IR 
+ 
{7 (n22-n, (aI Zin, rain t n*r“enp* |B“ sin“l, — (II-13b) 
Again the integration is carried out numerically. In the numerical integration 
near r_,., the intervals chosen must, of course, be very small, Again a plot of ¢ 
ve. @, is made, and @, is then determined for the given point as that value which 
givesag= 6, for that point. 
Values of @, are calculated for several points ona given film. The tacit 
assumption has been made that @, can be a function of the value of r' - D, for the 
point for which it is calculated. The conversion of this exponential decay constant 
with distance behind the shock front to an exponential decay constant with time 
behind the front is discussed below. 
Calculation Procedure for Time Constant onential Decay Con with T 
Behind Front). In the conversion of 0, to 6, the exponential parameter in 
apes 
Ot 
Por, (+) * Puax ° , (11-20) 
@4 is assumed constant, but the possibility is admitted of dependence of @, on 
the value of r' - D, for the point for which @, is calculated. Py (t) is the 
pressure that would have been recorded by a piezoelectric gage at time t after 
the passing of the shock front of peak pressure Pax. P (r) is the pressure 
at t = o and at a distance ( [RJ - r) behind the shock f#OAt of pressure p,.. and 
radius |RI. That is, 
( {Ri =r) 
®, 
Po.p, () = Pus® (I-21) 
Q, can be a function of r if it is necessary to make Eqs. (II-20) and (II-21) 
compatible. 
The assumption is mace that 6, changes very little with|Rlover distances of 
length of the order of 6. Under this assumption, the decay of p with (R| will 
follow the same law as the decay of p(r) (where r = (RI - C and where C isa 
constant distance of the order of magnitude of @,) with R. That is, since for a 
given weight of some explosive, 
7% 16518 
