Ballistic limit

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:

$V_{b}={\frac {\pi \,\Gamma \,{\sqrt {\rho _{t}\,\sigma _{e}}}\,D^{2}\,T}{4\,m}}\left[1+{\sqrt {1+{\frac {8\,m}{\pi \,\Gamma ^{2}\,\rho _{t}\,D^{2}\,T}}}}\,\right]$
where

• $V_{b}\,$ is the ballistic limit
• $\Gamma \,$ is a projectile constant determined experimentally
• $\rho _{t}\,$ is the density of the laminate
• $\sigma _{e}\,$ is the static linear elastic compression limit
• $D\,$ is the diameter of the projectile
• $T\,$ is the thickness of the laminate
• $m\,$ is the mass of the projectile

Additionally, the ballistic limit for small-caliber into homogeneous armor by TM5-855-1 is:

$V_{1}=19.72\left[{\frac {7800d^{3}\left[\left({\frac {e_{h}}{d}}\right)\sec \theta \right]^{1.6}}{W_{T}}}\right]^{0.5}$
where

• $V_{1}$ is the ballistic limit velocity in fps
• $d$ is the caliber of the projectile, in inches
• $e_{h}$ is the thickness of the homogeneous armor (valid from BHN 360 - 440) in inches
• $\theta$ is the angle of obliquity
• $W_{T}$ is the weight of the projectile, in lbs