Ballistic limit

Template:Short description 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. 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 Wen is as follows:

$V_b=\frac{\pi \mathrm{\Gamma }\sqrt{{\rho }_t{\sigma }_e}{D}^{2}T}{4m}[1+\sqrt{1+\frac{8m}{\pi {\mathrm{\Gamma }}^2{\rho }_t{D}^{2}T}}]$
where

• $V_b$ is the ballistic limit
• $\mathrm{\Gamma }$ 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:

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

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