# Ballistic limit

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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

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.