CHAPTER 17
For Deep bursts at increasing scaled depths approaching the Very Deep
category, the transition between the two corresponding values of ¢
will have to be determined by additional theoretical or experimental
work.
Complete derivations of the mathematical forms of N for both deep
and shallow bursts are presented in Reference 48. Summaries of the derivations are presented in the following paragraphs, along with Equations 17-10 to
17-12, which are explicit expressions for N. The dose rate, d, due to transit
radiation from underwater bursts, can then be calculated by the substitution
into Equation 17-5 of Equations 17-6 to 17-8, the appropriate form of Equation
17-9, and the suitable value of N as expressed by Equations 17-10, 17-ll or
17-12. Such calculations have been machine programmed at USNRDL.
(1)
"Deep" Geometry
Consider a solid truncated cone, (Fig.17-10) of radius Ry,
height Z, interior angle & between face and base, with the base centered
at 0; and a receiver at point P in the plane of the base at a distance
S from the axis of the cone.
Then,
Wr2 + 22
N= l/ln Ife mT? pareedz
re + 22
where cylindrical coordinates are used with center at P, z-axis
parallel to axis of cone and polar axis PO, and the integration is
over the volume of the truncated cone. (All distances are expressed in
mean-free-path units. )
To facilitate computation, the z-integration is replaced by 4
finite summation over n increments Az where n 4z = Z.
let 2, be the
midpoint of the i*® increment: z; = (21 + 1) Z. In effect, the
en
truncated cone is replaced by a set of n circular disks of thicknese
Z/n and of radius R, - z; cot a, i= 1, 2, ....n.
N= l/dx
n
z _ z/n
;
e-
.
Then,
24
eae
rdodr.
r
The value n = 10 was used in computing base surge dose rates. ‘here are
2 forms for the integral depending whether S <R, - z, cot a, or
S 2R) - 2; cot a.
entire volume:
O
Best
There are thus 3 cases fur the summation over the
PY
COP
a Ls2= C
o
“" AIL .Ao
17-53
terme reece ee
te