Impact depth
Encyclopedia
The physicist Sir Isaac Newton
Isaac Newton
Sir Isaac Newton PRS was an English physicist, mathematician, astronomer, natural philosopher, alchemist, and theologian, who has been "considered by many to be the greatest and most influential scientist who ever lived."...

 first developed this idea to get rough approximations for the impact depth for projectile
Projectile
A projectile is any object projected into space by the exertion of a force. Although a thrown baseball is technically a projectile too, the term more commonly refers to a weapon....

s traveling at high velocities.

Newton's approximation for the impact depth

Newton's approximation for the impact depth for projectiles at high velocities is based only on momentum
Momentum
In classical mechanics, linear momentum or translational momentum is the product of the mass and velocity of an object...

 considerations. Nothing is said about where the impactor's kinetic energy
Kinetic energy
The kinetic energy of an object is the energy which it possesses due to its motion.It is defined as the work needed to accelerate a body of a given mass from rest to its stated velocity. Having gained this energy during its acceleration, the body maintains this kinetic energy unless its speed changes...

 goes, nor what happens to the momentum after the projectile is stopped.

The basic idea is simple: The impactor carries a given momentum. To stop the impactor, this momentum must be transferred onto another mass. Since the impactor's velocity is so high that cohesion
Cohesion (chemistry)
Cohesion or cohesive attraction or cohesive force is the action or property of like molecules sticking together, being mutually attractive...

 within the target material can be neglected, the momentum can only be transferred to the material (mass) directly in front of the impactor, which will be pushed at the impactor's speed. If the impactor has pushed a mass equal to its own mass at this speed, its whole momentum has been transferred to the mass in front of it and the impactor will be stopped. For a cylindrical impactor, by the time it stops, it will have penetrated to a depth that is equal to its own length times its relative density with respect to the target material.

This approach only holds for a blunt impactor (no aerodynamical shape) and a target material with no fibres (no cohesion), at least not at the impactor's speed. This is usually true if the impactor's speed is much higher than the speed of sound within the target material. At such high velocities, most materials start to behave like a fluid. It is then important that the projectile stays in a compact shape during impact (no spreading).

Applications

  • Projectile
    Projectile
    A projectile is any object projected into space by the exertion of a force. Although a thrown baseball is technically a projectile too, the term more commonly refers to a weapon....

    : Full metal projectiles should be made of a material with a very high density, like uranium (19.1 g/cm³) or lead (11.3 g/cm³). According to Newton's approximation, a full metal projectile made of uranium will pierce through roughly 2.5 times its own length of steel armor.
  • Shaped charge
    Shaped charge
    A shaped charge is an explosive charge shaped to focus the effect of the explosive's energy. Various types are used to cut and form metal, to initiate nuclear weapons, to penetrate armor, and in the oil and gas industry...

    , Bazooka
    Bazooka
    Bazooka is the common name for a man-portable recoilless rocket antitank weapon, widely fielded by the U.S. Army. Also referred to as the "Stovepipe", the innovative bazooka was amongst the first-generation of rocket propelled anti-tank weapons used in infantry combat...

    : For a shaped charge (anti-tank) to pierce through steel plates, it is essential that the explosion generates a long heavy metal jet (in a shaped charge for anti-tank use, the explosion generates a high speed metal jet from the cone shaped metal lining). This jet may then be viewed as the impactor of Newton's approximation.
  • Meteorite
    Meteorite
    A meteorite is a natural object originating in outer space that survives impact with the Earth's surface. Meteorites can be big or small. Most meteorites derive from small astronomical objects called meteoroids, but they are also sometimes produced by impacts of asteroids...

    : As may be concluded from the air pressure, the atmosphere's material is equivalent to about 10 m of water. Since ice has about the same density as water, an ice cube from space travelling at 15 km/s or so must have a length of 10 m to reach the surface of the earth at high speed. A smaller ice cube will be stopped in mid-air and explode. An ice cube with a diameter of 50 m or more, however, may also be stopped in mid-air, as long as it comes in at a very low angle and thus has to pierce through a lot of atmosphere. The Tunguska event
    Tunguska event
    The Tunguska event, or Tunguska blast or Tunguska explosion, was an enormously powerful explosion that occurred near the Podkamennaya Tunguska River in what is now Krasnoyarsk Krai, Russia, at about 7:14 a.m...

     is sometimes explained this way. An iron meteorite with a length of 1.3 m would punch through the atmosphere, a smaller one would be stopped in the air and drop down by the gravitational pull. The Black Stone
    Black Stone
    The Black Stone is the eastern cornerstone of the Kaaba, the ancient stone building towards which Muslims pray, in the center of the Grand Mosque in Mecca, Saudi Arabia. It is revered by Muslims as an Islamic relic, which according to Muslim tradition dates back to the time of Adam and Eve.The...

    , for example, with a diameter of 0.76 m would fit into this category.
  • Impactor, Bunker buster
    Bunker buster
    A bunker buster is a bomb designed to penetrate hardened targets or targets buried deep underground.-Germany:Röchling shells were bunker-busting artillery shells, developed by German engineer August Cönders, based on the theory of increasing sectional density to improve penetration.They were tested...

    : Solid impactors can be used instead of nuclear warheads to penetrate bunker
    Bunker
    A military bunker is a hardened shelter, often buried partly or fully underground, designed to protect the inhabitants from falling bombs or other attacks...

    s. According to Newton's approximation, a uranium projectile at high speed and 1 m in length would punch its way through 6 m of rock (density 3 g/cm³) before coming to a stop.
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