
394 Ballistics: Theory and Design of Guns and Ammunition
We now use a compatibility condition that at z = 2d, both Equations 15.103 and 15.91 must
yield the same answer. We shall call the time it takes the projectile to reach 2d, t
1
and the
velocity at that point will be V
1
, thus at z = 2d we have
F
d
Sf NV
t=t
c
1
=
′
+
=
π
2
1
2
2
ρ
,
(15.104)
d
2
s
z
Vt
2
1
2=− =
ωω
sin,
(15.105)
Since F = ma, we can combine the aforementioned equations to write
mV t
d
Sf NV
ωω ρ
sc
si
1
2
1
2
2=
′
+
=
π
(15.106)
Also at t = t
1
, Equations 15.101 and 15.102 can be written as
2= sin
s
1
d
t
ω
(15.107)
1
(15.108)
We now rearrange Equation 15.108 to
V
t
s
cos
=
1
ω
(15.109)
Now in ...