Ballistic limit

{{Short description|Concept in physics}}

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.{{cite book|author=Donald E. Carlucci, Sidney S. Jacobson|title=Ballistics: Theory and Design of Guns and Ammunition|publisher=CRC Press|year=2008|pages=310|isbn=978-1-4200-6618-0}} 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 WenSR Reid, HM Wen. "Perforation of FRP laminates and sandwich panels subjected to missile impact". In: SR Reid, G Zhou, editors. "Impact behaviour of fibre-reinforced composite materials and structures". Cambridge: Woodhead Publishers Ltd. 2000. In: G Reyes Villanueva, WJ Cantwell (2004). "The high velocity impact response of composite and FML-reinforced sandwich structures". Composites Science and Technology 64:35-54. {{doi|10.1016/S0266-3538(03)00197-0}}. is as follows:

$V\_b=\backslash frac\{\backslash pi\backslash ,\backslash Gamma\backslash ,\backslash sqrt\{\backslash rho\_t\backslash ,\backslash sigma\_e\}\backslash ,D^2\backslash ,T\}\{4\backslash ,m\}\; \backslash left\; [1+\backslash sqrt\{1+\backslash frac\{8\backslash ,m\}\{\backslash pi\backslash ,\backslash Gamma^2\backslash ,\backslash rho\_t\backslash ,D^2\backslash ,T\}\}\backslash ,\; \backslash right\; ]$

where

• $V\_b\backslash ,$ is the ballistic limit
• $\backslash Gamma\backslash ,$ is a projectile constant determined experimentally
• $\backslash rho\_t\backslash ,$ is the density of the laminate
• $\backslash sigma\_e\backslash ,$ is the static linear elastic compression limit
• $D\backslash ,$ is the diameter of the projectile
• $T\backslash ,$ is the thickness of the laminate
• $m\backslash ,$ is the mass of the projectile

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

$V\_1=\; 19.72\; \backslash left\; [\; \backslash frac\{7800\; d^3\; \backslash left\; [\; \backslash left\; (\; \backslash frac\{e\_h\}\{d\}\; \backslash right)\; \backslash sec\; \backslash theta\; \backslash right\; ]^\{1.6\}\}\{W\_T\}\; \backslash right\; ]^\{0.5\}$

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
• $\backslash theta$ is the angle of obliquity
• $W\_T$ is the weight of the projectile, in lbs