The ballistic limit or limit velocity is the velocity required for a particular projectile to reliably (at least 50% of the time) penetrate a particular piece of material. In other words, a given projectile will generally not pierce a given target when the projectile velocity is lower than the ballistic limit. The term ballistic limit is used specifically in the context of armor; limit velocity is used in other contexts. The ballistic limit equation for laminates, as derived by Reid and Wen is as follows:
V b = π Γ ρ t σ e D 2 T 4 m [ 1 + 1 + 8 m π Γ 2 ρ t D 2 T ] {\displaystyle V_{b}={\frac {\pi \,\Gamma \,{\sqrt {\rho _{t}\,\sigma _{e}}}\,D^{2}\,T}{4\,m}}\left[1+{\sqrt {1+{\frac {8\,m}{\pi \,\Gamma ^{2}\,\rho _{t}\,D^{2}\,T}}}}\,\right]}
where
V b {\displaystyle V_{b}\,} is the ballistic limit
Γ {\displaystyle \Gamma \,} is a projectile constant determined experimentally
ρ t {\displaystyle \rho _{t}\,} is the density of the laminate
σ e {\displaystyle \sigma _{e}\,} is the static linear elastic compression limit
D {\displaystyle D\,} is the diameter of the projectile
T {\displaystyle T\,} is the thickness of the laminate
m {\displaystyle m\,} is the mass of the projectile Additionally, the ballistic limit for small-caliber into homogeneous armor by TM5-855-1 is:
V 1 = 19.72 [ 7800 d 3 [ ( e h d ) sec θ ] 1.6 W T ] 0.5 {\displaystyle V_{1}=19.72\left[{\frac {7800d^{3}\left[\left({\frac {e_{h}}{d}}\right)\sec \theta \right]^{1.6}}{W_{T}}}\right]^{0.5}}
where
V 1 {\displaystyle V_{1}} is the ballistic limit velocity in fps
d {\displaystyle d} is the caliber of the projectile, in inches
e h {\displaystyle e_{h}} is the thickness of the homogeneous armor (valid from BHN 360 - 440) in inches
θ {\displaystyle \theta } is the angle of obliquity
W T {\displaystyle W_{T}} is the weight of the projectile, in lbs
References