od 
oa 
% a 
= LMT oF 
s PEZOELECTRIC s 
= oh 
5 
2 10 
= 3 
=a 
x 
x ; 
“ 
e 
1 | | : 4 
CHARGE SURFACE L 
wy (Leet) wha» 7.38 
Fic. 3. Peak pressure similarity curve for TNT. Legend: 
A isolated experimental points based on measurement of 
spray dome velocity. experimental curve based on 
piezoelectric measurements, extrapolated to a theoretical 
value at the charge surface based upon the results of 
reference 5, 6. — — — — similarity curve arbitrarily extrapo- 
lated to a value of 108 Ib./in.? at the charge surface. 
As an example, the amount of energy dissi- 
pated between the charge surface, (W!/R) =7.35, 
and a radius given by R= W?!/0.352 is approxi- 
mately 3,400,000 in. lb. per pound of charge or 
200 cal./g of charge. 
A calculation based on the dashed curve of 
Fig. 4 for the same limits of integration would 
yield roughly 25 percent additional dissipated 
energy. The actual error is probably smaller 
than this, but the above value is an indication, 
at least, of the uncertainties involved in the 
assumption of the form of the pressure-radius 
curve in the region very close to the charge. 
It must be remembered that an additional 
error, the magnitude of which cannot be esti- 
mated, is present because of uncertainty with 
respect to the equation of state data in the high 
pressure region. The equations used are based on 
extrapolation of experimental data‘ from pres- 
sures of 10 kilobars, and at high pressures 
actually imply applicability to metastable liquid 
water in the ice VII region. 
. 14 
It is now possible to compare the measured 
shock-wave energy flux at different radii with 
the loss caused by dissipation. Unfortunately, 
A. BY ARONS” AND DD. >Re YENNTE 
er | =LB) 
Lp LA 
bY 
DISSIPATED ENTHALPY INTEGRAND (Sh ( 
i) 
Rew's (FT/LAYs) 
Fic. 4. Dissipated enthalpy integrand, (R/W1})?h, versus 
R/W3 for TNT. Legend: based on solid curve, 
Fig. 3. - - — — based on dashed curve, Fig. 3. 
there is considerable scatter in the shock-wave 
data available, so that it is hard to state precisely 
what the energy flux is at a given radius, As a 
result, the total energy flow through a surface is 
known only to within about 5 to 10 percent, and 
although the total flow at a given radius may be 
known to within these limits, the experimentally 
measured dissipation, which is given by the small 
difference between flow at each of two radii, 
will be very appreciably in error. 
To illustrate this, for TNT the flux at W#/R=1 
is 2700+250 in. lb./in.2 Ib.4, and at W?/R=0.1 
it is 20.5-+1.5 in. lb./in.? lb.#. The total energy 
flow at W!/R=1 is then 4,900,000+450,000 in. 
Ib./lb. and at Wt/R=0.1 it is 3,700,000 + 270,000 
in. Ib./Ib. The energy dissipated in the interval 
W/R=1 to 0.1 calculated from these figures is 
1,200,000+720,000 in. lb./lb. The large uncer- 
tainty in the dissipated energy is immediately 
apparent. (These values are obtained from data 
taken at Woods Hole by J. S. Coles and his co- 
workers.) 
By the use of Eq. (28), the energy loss resulting 
from dissipation between W!/R=1 and W!/R 
=0.1 would be 1,760,000 in. lb./lb. This value is 
to be compared with that of 1,200,000--720,000- 
in. lb./lb. obtained above from the Woods 
Hole data. It will be noted that the two results 
agree within the limit of error of the experi- 
mental measurement. The calculated value, 
