
84 Ballistics: Theory and Design of Guns and Ammunition
This simplies our distance–web fraction relationship to
d
f
M
f
=−
+
1
θ
(3.95)
The dimensionless nature of M can be shown if we note that c and w
1
are mass units. We
can also write the units of the burning rate coefcient as
[] []
=
⇒=
D
p
f
t
B
2
d
d
LT
M
(3.96)
The units of the propellant force, λ, are
[]
energy
ML
L
L
velocity
2
2
λ
=
=×
=
=
2
(3.97)
Using these in our denition of the central ballistic parameter, we can show
[]
M =
×
=
L
LT
M
MM
L
T
6
2
2
2
0
(3.98)
thereby demonstrating that M is dimensionless. Equation 3.95, repeated here,
d
f
M
f
=−