
238 Ballistics: Theory and Design of Guns and Ammunition
Recall that the Mach number is V/a where a is the speed of sound in air. Then for our at
re approximation, we can dene a constant k
2
such that
k
=
(8.81)
Then,
ˆ
C
D
*
(8.82)
From Equations 8.55 and 8.56, we see that
=−
(8.83)
and
Vk
=− −
2
(8.84)
Also from Equation 8.60, we see that
′
(8.85)
Using these three equations and proceeding in the same fashion as we did with the con-
stant C
D
, we can derive equations for the x- and y-velocities; the time of ight to any range, x;
the angle of fall, ϕ, and the trajectory ordinate at any range. These equation ...