where C and § are constants, and
Dy {t) =
t
f th 1) .
(2)
Here L(t) is the intensity of the surrounding water at time t; hence, this quantity is
dependent on the contaminated water and on the ship's path through that environment.
It is evident that, as a ship spends sufficient time in contaminated water, Dy becomes
large and the hull intensity approaches a saturation value:
I (t)—> stb,
(3)
The constants $ and C were evaluated from CROSSROADS support ship intensity data,
as discussed in Reference 6. The derived values are given below.
S =
1800 mR-day
0.3
for destroyers,
(4)
1570 mR-day?*? for aj] other ships.
C=
11.0 day7! for all ships.
(5)
It was also observed at Operation CROSSROADS that steaming in clean water
reduced the accumulated contamination by about half during the first day after
departing the lagoon, but that subsequent steaming had a much smaller effect. In the
model, it is assumed that both hull and piping intensities were reduced to half their
departure values during the first day after departure from the lagoon, and that
subsequent decay while out of the lagoon followed the t
-1.3
decay rate.
The exterior hull gamma intensity (1) is then used to determine the average
interior ship intensity.
This analysis, as described in detail in Reference 6, results in
an apportionment factor Fw which relates average interior intensities (1) to exterior
hull gamma intensities (1) by the relation:
[ = Pathe
.
29
(6)