# Penetrating power

1st floor; 2. target material; 3. Newtonian depth of penetration; 4. length of the projectile (L); 5.speed (V)

The punch or punch is the ability of an impacting object to travel a certain distance in turning destination before it is stopped. If the object has its own drive, e.g. B. rocket propulsion, it means the path to the point at which the propulsive force and the braking effect of the medium are in equilibrium. This ability is commonly referred to as penetrating power or penetrating performance , even if it is not a question of forces and performances in the sense of physical quantities.

The penetration of armor by a projectile or by its kinetic energy is a central research topic in defense technology .

## Penetration according to Newton

The expected depth of penetration in gases and liquids can be estimated according to Newton , neglecting some of the numerous parameters that are effective in practice. The only parameters considered are the density of the medium and the density and length of the impactor. It is also assumed that the impactor does not change shape and that the medium is a structureless fluid . The shape of the impactor and other aero- and hydrodynamic effects when displacing the medium are not taken into account.

Under these conditions, an impactor penetrates a medium as many times its own length as its density is relatively greater than that of the medium. On this route he displaces a mass that corresponds to his own and transmits his impulse completely to the medium:

Penetration depth ${\ displaystyle L = l \ cdot {\ frac {\ rho _ {i}} {\ rho _ {m}}}}$

With

${\ displaystyle l}$ Length of the impactor
${\ displaystyle \ rho _ {i}}$ Dense impactor
${\ displaystyle \ rho _ {m}}$ Dense medium

Under these conditions, the impact speed is irrelevant. The momentum of the impactor is used up by displacing a mass, the value of which, according to the law of conservation of momentum, has a fixed ratio to the mass of the impactor, i.e. a variable that is independent of velocity. To illustrate this, billiard balls can be cited, in which a complete impulse transmission in the event of a frontal impact also takes place independently of the speed. In solids the impactor stops after the momentum has been completely transferred. In fluids, it moves on due to external forces such as gravity.

When it hits a solid, the estimate is based on the assumption that the impactor overcomes the strength limit of the material without loss due to the pressure on impact, so that here, too, a simplified assumption is made of displacement according to the laws of fluid dynamics .

## Impact in practice

Armor-piercing APFSDS bullet with a high length-to-diameter ratio and an ignited flare
U-anchor of the ammunition of a GAU-8 / A Avenger , length approx. 10 cm, laid out on the inch scale of a ruler

In the military, penetration is important when fighting bullet-proof targets ( hard targets ). The penetration power is often given in RHA (English: rolled homogeneous armor = rolled homogeneous armor). Projectiles for fighting such targets are designed taking into account the relationships that determine the penetration power. Since the penetration force depends directly on the density and the ratio of length and diameter, for example, balancing projectiles contain a core made of a dense, hard material that is as long as possible, or special arrow-shaped, sub-caliber APFSDS projectiles with sabot . As materials are u. a. Tungsten carbide or depleted uranium ( uranium ammunition ) are used, which have a high density and low deformability. In order to overcome the strength limit of armor , they are fired at the highest possible muzzle velocity . In addition to the pure Newtonian impulse analysis, the penetration power of armor can also be estimated using the armor formula .

For use in infantry weapons, there are ammunition with improved penetration. The penetration power is increased above all through the use of hard projectile materials that are only slightly deformed when hitting an armored target or a protective vest . The bullets can be solid brass bullets or, as in the case of the bullets in the 5,45 × 39 cartridge , contain a hardened steel core.

The penetration effect in soft target media ( soft targets ) depends on numerous target ballistic factors. Solid metal jacket and solid bullets can overturn after penetrating into the target medium due to the bullet's precession , which is highest immediately after firing and then decreases, and can break under certain circumstances, which affects the penetration depth in a hardly predictable way. Due to the decrease in precession with increasing shooting distance and the resulting reduced tendency to roll over, the penetration effect can initially increase with decreasing impact speed. The movement of deformation bullets can remain stable even at high speed due to the mushrooming after penetrating the target. Due to the large cross-section of the deformed bullet, the kinetic energy is quickly transferred to the target medium, which reduces the penetration effect. A high energy output in the target is usually aimed for when hunting .

The penetration effect of armor-piercing weapons with a shaped charge also depends on the density and shape of the penetrating metal beam. When the charge explodes, the metal insert is cold-formed into a metal beam that should have the greatest possible length and density. Because of the high speed of the jet of up to more than 10 km / s, the hardness of the material is irrelevant, since at this impact speed the flow limit of each material is exceeded. The decisive factor is therefore the density, which is why u. a. Copper and tantalum are used as the metal insert.

The Newtonian rule also determines the size of meteorites in order not to be slowed down to speeds of 150–300 km / h (depending on the shape) before they reach the surface of the earth. The density of air, averaged over the altitude at which the braking effect of the atmosphere begins (approx. 70 km), is around 1.75 · 10 −4 g / cm³. A stone meteorite with a length to diameter ratio of 1: 1 and a typical density of 3.4 g / cm³ must therefore have a size of at least 3.6 meters in order to move the earth's surface at a speed greater than the above. Speed, as the density ratio is a little below 1: 20,000. Iron meteorites with a typical density of 7.8 g / cm³ are no longer slowed down to the free fall speed from a size of about 1.5 m.

Special projectiles such as Bunker Buster can be used to destroy heavily bunkered systems. According to the approximation formula described here, for a massive uranium body (density around 19 g / cm³) 1 m in length, a penetration depth of more than 6 m in stone (density slightly more than 3 g / cm³) can be predicted.

## literature

Newton's approximate solution for the penetration power of bullets is dealt with in many standard physics textbooks, for example in Gerthsen Physik .

## Individual evidence

1. Eisnecker, Finze, Hocke, Skrobanek: Kammer-Diener, 120 years 8x57, visor, international weapons magazine, issue 12/2008, pp. 6-18.
2. Dieter Meschede (Ed.): Gerthsen Physik , 22nd edition, Springer Verlag, ISBN 3-540-02622-3 ), or 25th edition (2015), page 34.