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APPENDIX A
COMPUTATION OF RANGE FROM SHOCK TRAVEL TIME
For the purpose of computing slant ranges from the observed travel times, the following
procedure has been adopted. First consider an isothermal atmosphere at constant pressure P,
and sound velocity c, with no wind. Tiw travel {ime of a spherical shock wave toa radial distance R from the source is then
t= {* un" dR
(A.1)
where U is the shock-wave velocity given by the Rankine-Hugoniot equation
U
. e(1+ net
ay ar)"
OP,
(A.2)
where y {s 1.4 for air and AP ig the peak overpressure.
The integral A.1 has been evaluated numerically using the dependence of peak overpressure
on distance given by Eqs. 3.4 and 3.5. This integration gives travel time as a function of range
for a 1-K¢ source {a a hypothetical constant-pressure {sothermal al.nosphere. From this time
ve distance function the average velocity, V = R/t, to a given distance may be computed. Then,
using the assumed overpressure vs distance function, V may be tabulated and plotted as a
function of peak overpressure. Since the yield scaling law transforms distances and times In
the same ratio and leaves velocities and pressures unchanged, the relation between V and aP
is independentof the yield of the source. It is, moreover, rather insensitive to the precise
form of the assumed peak overpressure vs distance function. Values of V for a given AP computed from Eqs. 3.4 and 3.5 in the present report differ by a few tenths of 1 per cent at most
from the values computed froin the slightly different overpressure function used in the report
on Operation Snapper, Project 1.1, over the range of overpressures covered by the present
measurements,
To go from the hypothetical homogeneous isothermal atmosphere to the conditions of the
actual athaosphere, use {a made of a simplified acaling law for the effect on peak overpressure
of variations in ambient atmospheric pressure and temperature, which Bond! has ghownto be
approximately equiva.snt to the more complex Fuchs scaling law. In this approximation overpressure is changed everywhere in the same ratio as ambient pressure; so SP/P, is unchanged,
and the shock velocity ia changed in the eameratio as the velocity of sound. Thus, if ¢ is an
average value of the sound velocity over the path from source to gauge, the ratio V/c, when
expressed as a function of AP/P,, ia approximately independent of the ambient pressure and
temperature at either source or gauge as well as of the yield of the source. This function,
when computed for 1 Kt in a homogeneous atmosphere,is then directly applicable to any yield
fa any atmosphere. With the use of this relation in determining the average shock velocit, for
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