SONFIDENTTAL
It is not difficult to show that the survival probability is really asymptotically proportional
to
(1/n) exp [— en/(1 + Acs)] (n> &).
(A16)
BOMBS AIMED AT DIFFERENT POINTS
a ee ee
aeee
Suppose that at each of the points (21, y1), .- ., (Zn) Yn), the bomb of Result 2 is aimed
(with og = 72).
This does not rule out the possibility that certain of these points may
coincide; thus the discussion really includes the case of several bombs at each of several
points and in particular the case of n bombs aimed at the center of the city. The expected
level of casualties is clearly given by
re
v?
c
—A (-a)?+ (u-)
I-sae i exp ( - 5 - 33)[1- 1+ Aad &xP ~~
2
1 + Aah
“|
—A Saeko
x [1- iwi
iF
EXP “>
4
wae
1+ ro3
(Al?)
x [1 - T+ cro} PQ”
5°BY
dhe? dé dv.
—d
a
When this expression is expanded and integrated, there result 2" — 1 terms, of which the
first n are of the form
c
V{i+ koi +o)[1+ Mos+1)]
ex
—4
2
zi
LIFNos+o0%)
+
vi
"1+ Xo +7)
|
the next l¢n(n — 1) of the form
eC
1
1+Aoe Vf1 + X(o3 + 202)[1 + X(o8 + 273)]
x ex —A k + rok + do?) (a? + 22) — 2r022,2,
2
(I+ do8)(1 + Ao} + 2A0%)
(A19)
+ ditio | ,
and so on, the terms growing progressively more complicated.
If, however, only two
or three aiming points are considered, the resultant formulas are still practicable.
It is
interesting to remark that the terms in Eq. Al18 are what would result if the casualties
from one bomb might be compounded with those of another by simple addition; the terms
in Eq. A19 may be considered ‘‘ first-order corrections,”’ and so on.
EVACUATION
It would be well to close with a brief examination of the effect of evacuation efforts.
Manycities have detailed plans about where they will transfer their populations and how
long they will need to do so. From the point of view of this annex such reallocations of
population constitute new cities for which a new bivariate analysis must be performed in
order to arrive at casualty estimates.
In this annex it is not a controlled evacuation, but rather a more or less unsupervised
exodus, that is of interest. Certainly there is no overwhelmingly compelling evidence that
this will not be the case, however good the intentions may be.
ORO—R-17 (App B)
79
CONPB-ENTAGE
PITAL IE TO
NPs
TTI
SW ett ede ty be. Spe
prin msess oat ce sree EETTDE ee
PeM: War pitieWeere Papen
—ppegren
phepiphelaphatbtan rhmaddted
peett
geeetsire Peed aeeqepagtiresreeseieoat! peerage
5