
379Penetration Theories
therefore
′
=
=md
t
dt
ρθ
3075
75
se
ec
(15.37)
If we now assume that
mV hm V
ii
n
=
′
=
∑
r
(15.38)
This is equivalent to stating that m′ is the mass of material pushed ahead of the penetrator,
m′ is ejected with speed V
r
(plugging theory), and the total momentum of the ejecta jumble
is proportional to m′V
r
. We can also write, in the limiting case, that the residual momentum
approaches the initial momentum or, mathematically
r
→ 1
(15.39)
If we substitute Equation 15.38 into Equation 15.34, we get
mV hm VmV
rrss s
as V+
′
∞→→
(15.40)
which can be rearranged to yield
V
V
m
mhm
V
r
s
s
r
s
as
+
′
∞
(15.41)
We know that if ...