4.2
DEVELOPMENT OF THE EXTRAPOLATION METHOD
It was decided to study first the effect of soil type, second
the effect of depth, and third the effect of yield. In looking at the
available information it was at once apparent that in regard to both
soil type and depth the data on megaton explosions are useless, since
these shots were all fired at one depth (essentially zero) and in one
godl type (“coral” atoll); hence, it was finally recognized that the
: Bermane approach appeared to be to look first only at TNT data and from
: these data to establish an extrapolation procedure; second, to adjust
“the values of the parameters so that the JANGLE underground and JANGLE
surface: shots would be consistent; and finally, to investigate the sensi-
tivity|of the procedure and compare the results with the measurements
of nuclear craters in the Marshalls.
Nevada soil is an appropriate one to look at first since there
are considerable HE data and data from two nuclear shots. In that soil
data are available in the range A,=
-0.13 to+ 1.0.
Within this range
greatest interest lies in the neigiborhood of A, =.0.14. The data on
the TNT shots of ‘this scaled depth are plotted in Fig. 4.1 which shows
crater radius plotted against yield on log paper both ways. Figure 4.2
is a similar plot. for date on TNT at scaled depthA,= 0.50 andA,=
-O.14 (minus indicates above the surface).
The scatter of the points
shown on thesé graphs’ is typical of the scatter shown in every case
where several essentially identical shots have been fired. It is be-
lieved conservative to day.that the uncertainty in the value of radius
for any specific combination.of soil type, charge size, and charge depth
is at least 10 per cent. Consequently the plus and minus 10 per cent
limite at the maximand minimmcharge sizes shown here are marked
on Fig. 4.1. For extrapolation‘gukposes, the reciprocal slope, m, of
the most probable line is found:LObe 3.4.% To permit an estimate of
the uncertainty in extrapolatidg,//jheccLmum and minimum slopes within the
10 per cent uncertainty just mention] have also been plotted.
slopes are found to be m= 3.0 and n =| 4.1.
These
This elementary analysis
has been undertaken with the data on Fig. 4.1 only and lines of the
slopes so determined have then been drawn on Fig. 4.2. The analysis
has been limited to Fig. 4.1 both because the! scaled depthA, = 0.14 is
of major interest and also because a greaterrange of ylelds “Sor TNT
shots is available for this scaled depth than for any other.
It is apparent that m, the reciprocal ofthe slope when crater
radius is plotted against yield on a log-log basis, is related to R and
W in the following way:
1
fa
mn
R =
KW
°
In the remainder of the report "m" is referred to as the "sealing ex-
ponent."
Now, using the best fit value for m, 3.4, and the experimental
data of Tables A.4 and A.6, the solid line on Fig. 4.3 has:een
*
The actual value measured on the graph is 3.39.
It is believed,
however, that the second figure is of somewhat doubtful validity
and hence all such numbers are rounded off to two figures.
43