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.^[1] The term ballistic limit is used specifically in the context of armor; limit velocity is used in other contexts.^[1]

The ballistic limit equation for laminates, as derived by Reid and Wen^[2] is as follows:

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

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

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

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

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

References