The physicist Sir Isaac Newton first developed this idea to get rough approximations for the impact depth for projectiles 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 momentum considerations. Nothing is said about where the impactor's kinetic energy 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 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: 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, Bazooka: 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: 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 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, for example, with a diameter of 0.5 m would fit into this category.

• Impactor, Bunker buster: Solid impactors can be used instead of nuclear warheads to penetrate bunkers. 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.

See also

• Impact force
• Meteorite
• Shaped charge
• Projectile

External links

• Impact Earth Impact Effects Program

An impact force is a high force or shock applied over a short time period. Such a force can have a greater effect than a lower force applied over a proportionally longer time period.

Theory

At normal speeds, during a perfectly inelastic collision, an object struck by a projectile will deform, and this deformation will absorb most, or even all, of the force of the collision. Viewed from the conservation of energy perspective, the kinetic energy of the projectile is changed into heat and sound energy, as a result of the deformations and vibrations induced in the struck object. However, these deformations and vibrations can not occur instantaneously. A high velocity collision (an impact) does not provide sufficient time for these deformations and vibrations to occur. Thus, the struck material behaves as if it were more brittle than it is, and the majority of the applied force goes into fracturing the material. Or, another way to look at it is that materials actually are more brittle on short time scales than on long time scales. !

Applications

• A nail is normally pounded with a series of impacts, each being a single hammer blow. These high velocity impacts prevent friction with the wood on the sides of the nail from retarding the forward motion of the nail.

• A pile driver does the same thing, on a much greater scale.

• An impact wrench is an analogous device designed to impart torque impacts to bolts to tighten or loosen them. At normal speeds, the forces applied to the bolt would be dispersed, via friction, to the mating threads. However, at impact speeds, the forces act on the bolt to move it before they can be dispersed.

• In ballistics, bullets utilize impact forces to puncture surfaces that could otherwise resist substantial forces. A rubber sheet, for example, behaves more like wood at typical bullet speeds. That is, it ruptures, and does not stretch or vibrate.

Example

Since

for a mass m accelerating at a, then assuming an ideal system, we can set the impact force as,

for a time interval dt.

For example, a train that weighs 1 kg moving at 500 m/s and that hits a 'perfect' steel wall where it uniformly decelerates from 500 m/s to 0 m/s in .02 seconds, has an approximate impact force of 25000 N. Thus, a body which decelerates more quickly has a greater effective impact than one which decelerates more slowly.

External links

• Application to mountain climbing: http://www.impact-force.info/anglais/impact1.html

See also

• Impulse
• Charpy impact test
• Cushioning
• Izod impact strength test
• Shock

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