
131Ammunition Design Practice
Inserting Equation 4.57 into Equation 4.55 yields
dF adml
cr
d==
ρπ
2
ω
(4.58)
which, when integrated from the inner to the outer radius, gives
dF lrr
l
r
r
cWAL
i
o
d
2
==−
∫
2
3
22
2
πρ ω
πρ ω
(4.59)
This is the radial force on the wall due to the inertia of the wall material only. If the pro-
jectile is lled with material, we need to account for this ller as well. Thus, if we integrate
from the centerline to the inner radius of the projectile wall, we obtain
dF lrr
l
r
r
cFILLFILL
FILL
i
d
i
∫
2
2
3
22
2
3
πρ ω
πρ ω
(4.60)
The total force acting on the projectile wall due to spin is then
FF F
l
rr r
ccWALL cFILLoiFILLi
=+=−
()
+
2