
298 Ballistics: Theory and Design of Guns and Ammunition
When this is substituted back into Equation 8.346, we get
−+⋅+ =− ++
CV
CCvCv
DDLR
p
vlgl
g()
αα
2
α
α
(8.365)
which can be rewritten as
V
Cv Cv
LRNR
p
lglgl=+×+−⋅
αα
2
αααα
()
(8.366)
and by neglecting the Magnus force term as it is small and noting that l × (g × l) = g −
(l · g)l, we get
V
Cv
LR
lgl=+××
α
2
αα
(8.367)
Remember that we wish to nd a useful form with which we can calculate the quasi-
steady state yaw of repose as shown in Equation 8.363. That equation encompasses differ-
ent vector functions and time derivatives of l, but our ultimate goal is to nd expressions