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:

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

References

^ ^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.
^ 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.

[carlucci-1] 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.

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