Tank formula

The armor formula is a numerical equation that can be used to estimate the penetration power of full metal jacket bullets on sheet steel .

It was developed by Krupp and reads:

${\displaystyle S_{b}=0{,}0194\cdot {\sqrt[{4}]{\frac {E^{3}}{k^{5}}}}}$

with the armor thickness in millimeters, of the impact energy of the projectile in Joules and the caliber in centimeters. ${\displaystyle S_{b}}$ ${\displaystyle E}$ ${\displaystyle k}$

An early formula for estimating the penetration power of bullets was developed by Isaac Newton .

When deployed, the above formula provides a lower armor thickness than the armor formula from the Weapons Technical Manual :

${\displaystyle S_{b}={\sqrt[{0{,}7}]{\frac {m_{G}^{0{,}5}\cdot v_{z}}{A\cdot d^{0{,}75}}}}=C{\sqrt[{7}]{\frac {E^{5}}{k^{7{,}5}}}}}$

with the armor thickness in decimeters, the bullet weight in kilograms, the impact speed in meters per second and the bullet caliber in decimeters. ${\displaystyle S_{b}}$ ${\displaystyle m_{G}}$ ${\displaystyle v_{z}}$ ${\displaystyle d}$

${\displaystyle A}$is an empirical factor that takes into account the projectile structure and properties of the armor material. Reference values ​​are = 2000 to 2500 for full tank bullets and 1400 to 1800 for hard core bullets . In comparison with the first-mentioned formula, you can see the empirically determined dependency / uncertainty of the armor thickness on the exponent of the impact energy and the bullet diameter. ${\displaystyle A}$

In the event of deviations from the angle of impact, i.e. not vertical fire on the armor, the armor thickness required becomes smaller. The armor is assumed to be an armored layer of constant thickness around the object to be protected at a constant distance. The angle is the deviation from the vertical, so that the armor layer lies in the tangential direction and the vertical fire corresponds to an angle of . The armor thickness required in millimeters for non-vertical fire can be passed through ${\displaystyle \alpha }$ ${\displaystyle \alpha =90^{\circ }}$ ${\displaystyle \alpha =0^{\circ }}$

${\displaystyle S_{a}=S_{b}\cdot {\cos ^{n}(\alpha )}}$ With ${\displaystyle n\approx 1{,}5}$

estimate from the armor thickness under vertical fire. ${\displaystyle S_{b}}$

literature

• Krupp, Rheinmetall, Waffentechnisches Handbuch , 1985, p. 512
• B. Buchmayr, T. Hatzenbichler, F. Kessler: Comparative studies on the penetration and pull-through behavior of thin sheets. In: BHM Berg- und Hüttenmünnische monthly books. 153, 2008, p. 443, doi : 10.1007 / s00501-008-0416-z .