the kinetic energy,
K.E.
|
and the heat energy,
BLseu ate
r°
= an (
o
dr -
R pr2
H.E.
47 {
dr
° y-l
He starts with the equations of motion and continuity and the equation of
state of a perfect gas.
He determines the boundary conditions in terms of
the Rankine-Hugoniot relations, which describe the conditions at the shock
front.
He finds it necessary to use approximations for these relations. The
approximations are excellent as long as the pressures are very large com-
pared with the ambient pressure.
He concludes, on page 163, that the total
energy release is given in equation (1) and that K is the sum of two integrals,
each depending only on gamma.
Two errors may be noted in his derivation.
On page 162, his equation
l6a, the coefficient (2y/y +1) is inverted but is corrected in equation 16b.
On page 161 a more fundamental error occurs, when he expresses the veloc-
ity of sound in air in terms of the variable parameter gamma; he should have
used the value Yo = 1.40.
the final result.
It turns out that this causes but a small error in
It should also be noted that in calculating the energy re-
lease of the New Mexico shot, Taylor assumed an ambient air density of
1.25 x 1073 g/cc, considerably greater than the true value 1.006 x 1073.
Taylor evaluates his integrals by means of step-by-step numerical
integration, assuming several different values of gamma,
marized in his Table 3, page 180.
These are sum -
He also derives some approximate for-
mulae to facilitate these numerical calculations.
We have re-stated his
integral expressions, using Yo = 1.40, and have evaluated them using the
approximate methods.
The calculated values of K are found to be:
Y
K (Taylor)
K (re-calculation)
1,20
1.727
1.740
1.30
1.167
1,175
1,40
0, 856
0,856
Several sources of data are available, from which the probable magni
tude of gamma may be estimated.
ff, ote tp
my
-
t
7
mR
Juoghay
An estimate is all that can be made,
-
S
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