4.2
DEVELOPMENT OF THE EXTRAPOLATION METHOD
It was decided to study first the effect of soil type, second
the effect of deptn, and tnird the effect of yield.
In looking at the
available information it was at once apparent that in regard to both
soll type and deptn the data on megaton explosions are useless, since
these shots were all fired at one depth (essentially zero) and in one
soil type ("coral atoll); hence, it was finally recognized that the
germane 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 cf the parameters s0 that the JANGLE underground and JANGLE
surface shots would be consistent, and finally, to investigate the sensitivity cf the procedure and compare the results with the measurements
of nuclear craters in tne Marsnalis.
Nevada soil is an appropriate one to look at first since there
are considerable HE data anda 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 neignborhood of ro = 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 @ Similar plot for data on TNT at scaled depth r = 0.50 and A, =
-O.14 (minus indicates above the surface).
The scatter of the points
shown on these graphs is typical cf the scatter shown in every case
where several essentially identical snots have been fired.
It is believed conservative to say that the uncertainty in the value of radius
for any specific combination of scil type, charge size, and charge depth
is at least 10 per cent.
Consequently the plus and minus 10 per cent
limits at the maximum and minimum charge sizes shown nere are marked
on Fig. 4.1.
For extrapolation purposes, the reciprocal slope, m, of
the most probable line is found t«
pe +.4.*
To permit an estimate of
Rilke
the uncertainty in extrapolation, maximum and minimum slopes within the
10 per cent uncertainty just mentione: have also been plotted.
Tnese
slopes are found to be m= 3... anc m= 4.1.
This elementary analysis
has been undertaken witn tne data on Fig. 4.1 only and lines of tne
slopes so determined nave then peen drawn on Fig. 4.2.
The analysis
has been limited to Fig. 4.1 votn because the scaled depth ro = 0.14 is
of major interest and also because a greater range of yields for TNT
shots is available for this scalec depth than for any other.
It is apparent that m, the reciprocal of the slope when crater
radius is plotted against yield cr a log-log basis, is related to R and
Win the following wa,:
?o= Rw
In the remainder of tne repcr*
ponent."
Now,
uSing tne oest f1*
data of Tatles A.+ and A.t.
*
"™'’
1s referred to as the "scaling ex-
value rer m,
:.4, and the experimental
tre .. lid line on Fig. 4.3 has been
Tne actu
value measurea on tre graph is 3.39.
It is believed,
however, that the second figure is of somewhat doubtful validity
and hence all such numberc are rounded off to two figures.
aalii
fn