
404 Ballistics: Theory and Design of Guns and Ammunition
B =
−
−
+−
+−
1
21
341
11
3
3
4
(*)
(*)
(*)
η
η
ξ
γ
η
ξ
γ
3
m
m
33
(15.150)
These equations account for the fact that the yielding is Mohr–Coulomb outside of ξ = ξ
m
.
If V > V
max
, the yielding is completely according to the Tresca model. Thus, A and B are
given by
A
=−
+
2
3
2
1
τ
τ
γ
τ
m
c
c
ln
(15.151)
B
EE
=
−
+
+−
−
+
+
+
3
21
1
21
1
31
2
2
2
4
(*)
*
η
τ
η
τ
γ
γ
τ
τ
33
2
cc
c
c
EE
−
3
1 ( *)
η
(15.152)
To approximate the normal stress on the ogive, we can replace the spherically symmetric
velocity, V, in our previous equations with V
z
cos θ. We can write an equation for the ...