1066 
-2- 
Although it is not true generally that tn (1) is a function of o only, it is true at 
the shock front ana nearly true for a little distance behing. It has been assumed in the 
theory that u is a function of c so that we are justifica in regarding 1 as a function of 
Pao) 
pressure c¢, and therefore in using tne symbol as tne value of which we calculate from tables 
in O.S.R.D. 676 
Differentiating (1) with resoect to time t we jet 
a0. 20. 20 ae. 2 2) 
ot’ ot dp ot (6) 
oe a eae (3) 
t g 30 
As the wave passes over any given point tne value of o at that point changes because 
the wave is decaying in intensity ana also because the oressure behind the shock front varies 
from point to point, expressed in equation form, for coints just behind the shock front. 
Qo. o ~y 32 (4) 
font at OR 
where U = velocity of shock wave 
32 = rate of decay of ceak pressure. 
at 
Eliminating = from (3) ana (4) we get 
t 
G2. i(o , 2 gw, 2 (s) 
R U at 6 a OR ra) a0 u 
ap Op 
Written in terms of ¢< this becomes 
° 
life (ES) Q (6) 
) = a= g a0 U 
a, oP 
In (6) all symbols refer to values just behind the shock front, i.e. to the peak values. 
From equation (1) we see that the oeak value is given by 
Xa 
= ° 
Q = =< a, (7) 
g 
X and % are calculated functions of z= Q, is given in 0,S.R.D. 588 for T.N.T. at density 1.59. 
co) 
Hence using the tabular relation (c) between ana o we get c as a function of Zz, Numerical 
. . . . . . ° 
differentiation then gives us et) . It is possible therefore to evaluate the right-nand side 
a 
of (6) numerically as a function of din 
The equation connecting rate of decay 8 of a spherical shock wave and the space rate 
of change of cressure behind the shock front 92 may be written (4 
R 
EP ey eT (0 ESD Lal eG i (TE (8) 
dR R cf au R c* aul 
uy utr SH w [v-u+ So 
or for simplicity 
i 9 CL B 
GE te ye (9) 
ag OR R 
WHEE sovee 
