# 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 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:

$V_b=\frac{\pi\,\Gamma\,\sqrt{\rho_t\,\sigma_e}\,D^2\,T}{4\,m} \left [1+\sqrt{1+\frac{8\,m}{\pi\,\Gamma^2\,\rho_t\,D^2\,T}}\, \right ]$
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:

$V_1= 19.72 \left [ \frac{7800 d^3 \left [ \left ( \frac{e_h}{d} \right) \sec \theta \right ]^{1.6}}{W_T} \right ]^{0.5}$
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 projetile, in lbs

## References

1. ^ a b Donald E. Carlucci, Sidney S. Jacobson (2008). Ballistics: Theory and Design of Guns and Ammunition. CRC Press. p. 310. ISBN 978-1-4200-6618-0.
2. ^ SR 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.