The physicist Sir
Isaac NewtonSir Isaac Newton FRS was an English physicist, mathematician, astronomer, natural philosopher, alchemist, and theologian who is perceived and considered by a substantial number of scholars and the general public as one of the most influential men in history...
first developed this idea to get rough approximations for the impact depth for
projectileA projectile is any object propelled through space by the exertion of a force which ceases after launch. Although a thrown baseball could be considered a projectile, the word more often refers to a weapon...
s travelling at high velocities.
Newton's approximation for the impact depth for projectiles at high velocities is based only on
momentumIn classical mechanics, momentum is the product of the mass and velocity of an object . For more accurate measures of momentum, see the section "modern definitions of momentum" on this page...
considerations. Nothing is said about where the impactor's
kinetic energyThe kinetic energy of an object is the extra 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 current velocity. Having gained this energy during its acceleration, the body maintains this kinetic energy unless its...
goes, nor what happens to the momentum after the projectile is stopped.
Discussion
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The physicist Sir
Isaac NewtonSir Isaac Newton FRS was an English physicist, mathematician, astronomer, natural philosopher, alchemist, and theologian who is perceived and considered by a substantial number of scholars and the general public as one of the most influential men in history...
first developed this idea to get rough approximations for the impact depth for
projectileA projectile is any object propelled through space by the exertion of a force which ceases after launch. Although a thrown baseball could be considered a projectile, the word more often refers to a weapon...
s travelling 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
momentumIn classical mechanics, momentum is the product of the mass and velocity of an object . For more accurate measures of momentum, see the section "modern definitions of momentum" on this page...
considerations. Nothing is said about where the impactor's
kinetic energyThe kinetic energy of an object is the extra 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 current velocity. Having gained this energy during its acceleration, the body maintains this kinetic energy unless its...
goes, nor what happens to the momentum after the projectile is stopped. It gives a similar result to Hunt's Impact Theorem, but is less precise.
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
cohesionCohesion or cohesive attraction or cohesive force is a physical property of a substance, caused by the intermolecular attraction between like-molecules within a body or substance that acts to unite them.Water, for example, is strongly cohesive as each molecule may make four hydrogen bonds to...
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 his speed, his 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 high velocities like that, 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
A projectile is any object propelled through space by the exertion of a force which ceases after launch. Although a thrown baseball could be considered a projectile, the word more often 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
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, initiate nuclear weapons, and penetrate armor...
, BazookaBazooka is the common nickname for a man-portable rocket launcher widely fielded by the US Army during World War II. 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
A meteorite is a natural object originating in outer space that survives an impact with the Earth's surface. 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 eventThe Tunguska Event, or Tunguska explosion, was a powerful explosion that occurred near the Podkamennaya Tunguska River in what is now Krasnoyarsk Krai of Russia, at around 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 StoneThe Black Stone also called as "Hijre Aswad" or "Sang-e-Sayah" in Urdu, is a Muslim relic, which according to Islamic tradition dates back to the time of Adam and Eve. Some consider it to be a tektite or a meteorite...
, for example, with a diameter of 0.5 m would fit into this category.
- Impactor, Bunker buster
A bunker buster is a bomb designed to penetrate hardened targets or targets buried deep underground.-World War II:In World War II the British designer Barnes Wallis, of bouncing-bomb fame, designed two bombs that would today be called bunker busters: the five tonne Tallboy and the ten tonne Grand...
: Solid impactors can be used instead of nuclear warheads to penetrate bunkerA 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. Such an impactor, at a speed of 5 to 15 km/s, carries more kinetic energy than an explosive warhead of the same mass carries explosive energy.