# Projectile

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A projectile is any object thrown by the exertion of a force. [1] It can also be defined as an object launched into the space and allowed to move free under the influence of gravity and air resistance. [2] Although any object in motion through space (for example a thrown baseball, kicked football, fired bullet, thrown arrow, stone released from catapult) may be called projectiles, they are commonly found in warfare and sports. [3] [4] Mathematical equations of motion are used to analyze projectile trajectories.

## Motive force

Blowguns and pneumatic rifles use compressed gases, while most other guns and cannons utilize expanding gases liberated by sudden chemical reactions by propellants like smokeless powder. Light-gas guns use a combination of these mechanisms.

Railguns utilize electromagnetic fields to provide a constant acceleration along the entire length of the device, greatly increasing the muzzle velocity.

Some projectiles provide propulsion during flight by means of a rocket engine or jet engine. In military terminology, a rocket is unguided, while a missile is guided. Note the two meanings of "rocket" (weapon and engine): an ICBM is a guided missile with a rocket engine.

An explosion, whether or not by a weapon, causes the debris to act as multiple high velocity projectiles. An explosive weapon, or device may also be designed to produce many high velocity projectiles by the break-up of its casing, these are correctly termed fragments.

## Delivery projectiles

Many projectiles, e.g. shells, may carry an explosive charge or another chemical or biological substance. Aside from explosive payload, a projectile can be designed to cause special damage, e.g. fire (see also early thermal weapons), or poisoning (see also arrow poison).

## Sport projectiles

In projectile motion the most important force applied to the ‘projectile’ is the propelling force, in this case the propelling forces are the muscles that act upon the ball to make it move, and the stronger the force applied, the more propelling force, which means the projectile (the ball) will travel farther. See pitching, bowling.

## Kinetic projectiles

A projectile that does not contain an explosive charge or any other kind of payload is termed a kinetic projectile, kinetic energy weapon, kinetic energy warhead, kinetic warhead, kinetic kill vehicle or kinetic penetrator. Typical kinetic energy weapons are blunt projectiles such as rocks and round shots, pointed ones such as arrows, and somewhat pointed ones such as bullets. Among projectiles that do not contain explosives are those launched from railguns, coilguns, and mass drivers, as well as kinetic energy penetrators. All of these weapons work by attaining a high muzzle velocity, or initial velocity, generally up to hypervelocity, and collide with their targets, converting the kinetic energy associated with the relative velocity between the two objects into destructive shock waves and heat. Other types of kinetic weapons are accelerated over time by a rocket engine, or by gravity. In either case, it is this kinetic energy that destroys its target.

Some kinetic weapons for targeting objects in spaceflight are anti-satellite weapons and anti-ballistic missiles. Since in order to reach an object in orbit it is necessary to attain an extremely high velocity, their released kinetic energy alone is enough to destroy their target; explosives are not necessary. For example: the energy of TNT is 4.6 MJ/kg, and the energy of a kinetic kill vehicle with a closing speed of 10 km/s (22,000 mph) is 50 MJ/kg. For comparison, 50 MJ is equivalent to the kinetic energy of a school bus weighing 5 metric tons, traveling at 509 km/h (316 mph; 141 m/s). [6] This saves costly weight and there is no detonation to be precisely timed. This method, however, requires direct contact with the target, which requires a more accurate trajectory. Some hit-to-kill warheads are additionally equipped with an explosive directional warhead to enhance the kill probability (e.g. Israeli Arrow missile or U.S. Patriot PAC-3).

With regard to anti-missile weapons, the Arrow missile and MIM-104 Patriot PAC-2 have explosives, while the Kinetic Energy Interceptor (KEI), Lightweight Exo-Atmospheric Projectile (LEAP, used in Aegis BMDS), and THAAD do not (see Missile Defense Agency).

A kinetic projectile can also be dropped from aircraft. This is applied by replacing the explosives of a regular bomb with a non-explosive material (e.g. concrete), for a precision hit with less collateral damage. A typical bomb has a mass of 900 kg (2,000 lb) and a speed of impact of 800 km/h (500 mph). It is also applied for training the act of dropping a bomb with explosives. This method has been used in Operation Iraqi Freedom and the subsequent military operations in Iraq by mating concrete-filled training bombs with JDAM GPS guidance kits, to attack vehicles and other relatively "soft" targets located too close to civilian structures for the use of conventional high explosive bombs.

A Prompt Global Strike may use a kinetic weapon. A kinetic bombardment may involve a projectile dropped from Earth orbit.

A hypothetical kinetic weapon that travels at a significant fraction of the speed of light, usually found in science fiction, is termed a relativistic kill vehicle (RKV).

## Wired projectiles

Some projectiles stay connected by a cable to the launch equipment after launching it:

• for guidance: wire-guided missile (range up to 4,000 metres or 13,000 feet)
• to administer an electric shock, as in the case of a Taser (range up to 10.6 metres or 35 feet); two projectiles are shot simultaneously, each with a cable.
• to make a connection with the target, either to tow it towards the launcher, as with a whaling harpoon, or to draw the launcher to the target, as a grappling hook does.
• Bolo shotgun ammunition

## Typical projectile speeds

Projectile Speed Specific kinetic energy (J/kg)
(m/s)(km/h)(ft/s)(mph)
Object falling 1 m (in vacuum, at Earth's surface)4.4315.94814.59.99.8
Object falling 10 m (in vacuum, at Earth's surface)1450.4463198
Thrown club (expert thrower)4014413090800
Object falling 100 m (in vacuum, at Earth's surface)45162150100980
Refined (flexible) atlatl dart (expert thrower)451621501001,000
Ice hockey puck (slapshot, professional player)501801651101,300
80-lb-draw pistol crossbow bolt58208.81901301,700
War arrow shot from a 150 lbs medieval warbow 63228.22081412,000
Blunt Impact Projectile shot from a 40mm grenade launcher 87313.2285194.63,785
Paintball fired from marker91327.63002044,100
175-lb-draw crossbow bolt97349.23202174,700
6 mm Airsoft pellet 1003603282245,000
Air Rifle BB 4.5 mm15054049233611,000
Air gun pellet .177" (magnum-power air rifle)305878.41,00054529,800
9×19mm (bullet of a pistol)34012241,11676158,000
12.7×99 mm (bullet of a heavy machine gun)8002,8802,6251,790320,000
German Tiger I 88 mm (tank shell- Pzgr. 39 APCBCHE)8102,8992,6571,812328,050
5.56×45mm (standard round used in many modern rifles)9203,3123,0182,058470,000
20×102mm (standard US cannon round used in fighter cannons)1,0393,7413,4102,325540,000
25×140mm (APFSDS, tank penetrator)1,7006,1205,5773,8031,400,000
2 kg tungsten Slug (from Experimental Railgun)3,00010,8009,8436,7114,500,000
MRBM reentry vehicle Up to 4,000Up to 14,000Up to 13,000Up to 9,000Up to 8,000,000
projectile of a light-gas gun Up to 7,000Up to 25,000Up to 23,000Up to 16,000Up to 24,000,000
Satellite in low earth orbit 8,00029,00026,00019,00032,000,000
Exoatmospheric Kill Vehicle ~10,000~36,000~33,000~22,000~50,000,000
Projectile (e.g., space debris) and target both in low earth orbit 0–16,000~58,000~53,000~36,000~130,000,000
7 T eV particle in LHC [7] 299,792,455 [note 1] 1,079,252,839983571079670,616,536~6.7 × 1020 [note 2]

## Equations of motion

An object projected at an angle to the horizontal has both the vertical and horizontal components of velocity. The vertical component of the velocity on the y-axis is given as ${\displaystyle V_{y}=U\sin \theta }$ while the horizontal component of the velocity is ${\displaystyle V_{x}=U\cos \theta }$. There are various calculations for projectiles at a specific angle ${\displaystyle \theta }$:

1. Time to reach maximum height. It is symbolized as (${\displaystyle t}$), which is the time taken for the projectile to reach the maximum height from the plane of projection. Mathematically, it is given as ${\displaystyle t=U\sin \theta /g}$ where ${\displaystyle g}$ = acceleration due to gravity (app 9.81 m/s²), ${\displaystyle U}$ = initial velocity (m/s) and ${\displaystyle \theta }$ = angle made by the projectile with the horizontal axis.

2. Time of flight (${\displaystyle T}$): this is the total time taken for the projectile to fall back to the same plane from which it was projected. Mathematically it is given as ${\displaystyle T=2U\sin \theta /g}$.

3. Maximum Height (${\displaystyle H}$): this is the maximum height attained by the projectile OR the maximum displacement on the vertical axis (y-axis) covered by the projectile. It is given as ${\displaystyle H=U^{2}\sin ^{2}\theta /2g}$.

4. Range (${\displaystyle R}$): The Range of a projectile is the horizontal distance covered (on the x-axis) by the projectile. Mathematically, ${\displaystyle R=U^{2}\sin 2\theta /g}$. The Range is maximum when angle ${\displaystyle \theta }$ = 45°, i.e. ${\displaystyle \sin 2\theta =1}$.

## Notes

1. Approximate equivalent of 99,9999991% c.
2. In relation to the rest mass of proton.

## Related Research Articles

In physics, the Coriolis force is an inertial or fictitious force that acts on objects that are in motion within a frame of reference that rotates with respect to an inertial frame. In a reference frame with clockwise rotation, the force acts to the left of the motion of the object. In one with anticlockwise rotation, the force acts to the right. Deflection of an object due to the Coriolis force is called the Coriolis effect. Though recognized previously by others, the mathematical expression for the Coriolis force appeared in an 1835 paper by French scientist Gaspard-Gustave de Coriolis, in connection with the theory of water wheels. Early in the 20th century, the term Coriolis force began to be used in connection with meteorology.

In military terminology, a missile, also known as a guided missile or guided rocket, is a guided airborne ranged weapon capable of self-propelled flight usually by a jet engine or rocket motor. Missiles have five system components: targeting, guidance system, flight system, engine and warhead. Missiles come in types adapted for different purposes: surface-to-surface and air-to-surface missiles, surface-to-air missiles, air-to-air missiles, and anti-satellite weapons.

Nutation is a rocking, swaying, or nodding motion in the axis of rotation of a largely axially symmetric object, such as a gyroscope, planet, or bullet in flight, or as an intended behaviour of a mechanism. In an appropriate reference frame it can be defined as a change in the second Euler angle. If it is not caused by forces external to the body, it is called free nutation or Euler nutation. A pure nutation is a movement of a rotational axis such that the first Euler angle is constant. Therefore it can be seen that the circular red arrow in the diagram indicates the combined effects of precession and nutation, while nutation in the absence of precession would only change the tilt from vertical. However, in spacecraft dynamics, precession is sometimes referred to as nutation.

In physics, an orbit is the gravitationally curved trajectory of an object, such as the trajectory of a planet around a star or a natural satellite around a planet. Normally, orbit refers to a regularly repeating trajectory, although it may also refer to a non-repeating trajectory. To a close approximation, planets and satellites follow elliptic orbits, with the center of mass being orbited at a focal point of the ellipse, as described by Kepler's laws of planetary motion.

A warhead is the explosive or toxic material that is delivered by a missile, rocket, or torpedo. It is a type of bomb.

A kinetic energy penetrator is a type of ammunition designed to penetrate vehicle armour using a flechette-like, high-sectional density projectile. Like a bullet, this type of ammunition does not contain explosive payloads and uses purely kinetic energy to penetrate the target. Modern KEP munitions are typically of the armour-piercing fin-stabilized discarding sabot (APFSDS) type.

A bunker buster is a type of munition that is designed to penetrate hardened targets or targets buried deep underground, such as military bunkers.

Orbital mechanics or astrodynamics is the application of ballistics and celestial mechanics to the practical problems concerning the motion of rockets and other spacecraft. The motion of these objects is usually calculated from Newton's laws of motion and law of universal gravitation. Orbital mechanics is a core discipline within space-mission design and control.

A trajectory or flight path is the path that an object with mass in motion follows through space as a function of time. In classical mechanics, a trajectory is defined by Hamiltonian mechanics via canonical coordinates; hence, a complete trajectory is defined by position and momentum, simultaneously.

High-explosive anti-tank (HEAT) is a type of shaped charge explosive that uses the Munroe effect to penetrate heavy armor. The warhead functions by having an explosive charge collapse a metal liner inside the warhead into a high-velocity superplastic jet; this superplastic jet is capable of penetrating armor steel to a depth of seven or more times the diameter of the charge. The jet's effect is purely kinetic in nature; the round has no explosive or incendiary effect on the target.

An inverted pendulum is a pendulum that has its center of mass above its pivot point. It is unstable and without additional help will fall over. It can be suspended stably in this inverted position by using a control system to monitor the angle of the pole and move the pivot point horizontally back under the center of mass when it starts to fall over, keeping it balanced. The inverted pendulum is a classic problem in dynamics and control theory and is used as a benchmark for testing control strategies. It is often implemented with the pivot point mounted on a cart that can move horizontally under control of an electronic servo system as shown in the photo; this is called a cart and pole apparatus. Most applications limit the pendulum to 1 degree of freedom by affixing the pole to an axis of rotation. Whereas a normal pendulum is stable when hanging downwards, an inverted pendulum is inherently unstable, and must be actively balanced in order to remain upright; this can be done either by applying a torque at the pivot point, by moving the pivot point horizontally as part of a feedback system, changing the rate of rotation of a mass mounted on the pendulum on an axis parallel to the pivot axis and thereby generating a net torque on the pendulum, or by oscillating the pivot point vertically. A simple demonstration of moving the pivot point in a feedback system is achieved by balancing an upturned broomstick on the end of one's finger.

A sub-orbital spaceflight is a spaceflight in which the spacecraft reaches outer space, but its trajectory intersects the atmosphere or surface of the gravitating body from which it was launched, so that it will not complete one orbital revolution or reach escape velocity.

In physics, circular motion is a movement of an object along the circumference of a circle or rotation along a circular path. It can be uniform, with constant angular rate of rotation and constant speed, or non-uniform with a changing rate of rotation. The rotation around a fixed axis of a three-dimensional body involves circular motion of its parts. The equations of motion describe the movement of the center of mass of a body. In circular motion, the distance between the body and a fixed point on the surface remains the same.

Projectile motion is a form of motion experienced by a launched object. Ballistics is the science of dynamics that deals with the flight, behavior and effects of projectiles, especially bullets, unguided bombs, rockets, or the like; the science or art of designing and accelerating projectiles so as to achieve a desired performance.

In astrodynamics an orbit equation defines the path of orbiting body around central body relative to , without specifying position as a function of time. Under standard assumptions, a body moving under the influence of a force, directed to a central body, with a magnitude inversely proportional to the square of the distance, has an orbit that is a conic section with the central body located at one of the two foci, or the focus.

Rotation around a fixed axis is a special case of rotational motion. The fixed-axis hypothesis excludes the possibility of an axis changing its orientation and cannot describe such phenomena as wobbling or precession. According to Euler's rotation theorem, simultaneous rotation along a number of stationary axes at the same time is impossible; if two rotations are forced at the same time, a new axis of rotation will appear.

A banked turn is a turn or change of direction in which the vehicle banks or inclines, usually towards the inside of the turn. For a road or railroad this is usually due to the roadbed having a transverse down-slope towards the inside of the curve. The bank angle is the angle at which the vehicle is inclined about its longitudinal axis with respect to the horizontal.

In physics, a projectile launched with specific initial conditions will have a range. It may be more predictable assuming a flat Earth with a uniform gravity field, and no air resistance.

In celestial mechanics, a Kepler orbit is the motion of one body relative to another, as an ellipse, parabola, or hyperbola, which forms a two-dimensional orbital plane in three-dimensional space. A Kepler orbit can also form a straight line. It considers only the point-like gravitational attraction of two bodies, neglecting perturbations due to gravitational interactions with other objects, atmospheric drag, solar radiation pressure, a non-spherical central body, and so on. It is thus said to be a solution of a special case of the two-body problem, known as the Kepler problem. As a theory in classical mechanics, it also does not take into account the effects of general relativity. Keplerian orbits can be parametrized into six orbital elements in various ways.

Hit-to-kill, or kinetic kill, is a term used primarily in the military aerospace field to describe weapons that deliver their destructive power by hitting the target at high velocity and do not contain an explosive warhead. It has been used primarily in the anti-ballistic missiles (ABM) and anti-satellite weapons (ASAT) area, but some modern anti-aircraft missiles are also hit-to-kill. Hit-to-kill systems are part of the wider class of kinetic projectiles, a class that has widespread use in the anti-tank field.

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