# Projectile

A projectile is an object that is propelled by the application of an external force and then moves freely under the influence of gravity and air resistance.[1][2] Although any objects in motion through space are projectiles, they are commonly found in warfare and sports (for example, a thrown baseball, kicked football, fired bullet, shot arrow, stone released from catapult).[3][4]

A projectile being fired from an artillery piece

In ballistics mathematical equations of motion are used to analyze projectile trajectories through launch, flight, and impact.

## Motive force

Projectile and cartridge case for the huge World War II Schwerer Gustav artillery piece. Most projectile weapons use the compression or expansion of gases as their 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.

## In sports

Ball speeds of 105 miles per hour (169 km/h) have been recorded in baseball.[5]

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.

## As a weapon

### 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).

### Kinetic projectiles

A kinetic energy weapon (also known as kinetic weapon, kinetic energy warhead, kinetic warhead, kinetic projectile, kinetic kill vehicle) is a weapon based solely on a projectile's kinetic energy instead of an explosive or any other kind of payload.

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.

## 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.

## 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) 4.43 15.948 14.5 9.9 9.8
Object falling 10 m (in vacuum, at Earth's surface) 14 50.4 46 31 98
Thrown club (expert thrower) 40 144 130 90 800
Object falling 100 m (in vacuum, at Earth's surface) 45 162 150 100 980
Refined (flexible) atlatl dart (expert thrower) 45 162 150 100 1,000
Ice hockey puck (slapshot, professional player) 50 180 165 110 1,300
80-lb-draw pistol crossbow bolt 58 208.8 190 130 1,700
War arrow shot from a 150 lbs medieval warbow 63 228.2 208 141 2,000
Blunt Impact Projectile shot from a 40mm grenade launcher 87 313.2 285 194.6 3,785
Paintball fired from marker 91 327.6 300 204 4,100
175-lb-draw crossbow bolt 97 349.2 320 217 4,700
6 mm Airsoft pellet 100 360 328 224 5,000
Air Rifle BB 4.5 mm 150 540 492 336 11,000
Air gun pellet .177" (magnum-power air rifle) 305 878.4 1,000 545 29,800
9×19mm (bullet of a pistol) 340 1224 1,116 761 58,000
12.7×99 mm (bullet of a heavy machine gun) 800 2,880 2,625 1,790 320,000
German Tiger I 88 mm (tank shell- Pzgr. 39 APCBCHE) 810 2,899 2,657 1,812 328,050
5.56×45mm (standard round used in many modern rifles) 920 3,312 3,018 2,058 470,000
20×102mm (standard US cannon round used in fighter cannons) 1,039 3,741 3,410 2,325 540,000
25×140mm (APFSDS, tank penetrator) 1,700 6,120 5,577 3,803 1,400,000
2 kg tungsten Slug (from Experimental Railgun) 3,000 10,800 9,843 6,711 4,500,000
MRBM reentry vehicle Up to 4,000 Up to 14,000 Up to 13,000 Up to 9,000 Up to 8,000,000
projectile of a light-gas gun Up to 7,000 Up to 25,000 Up to 23,000 Up to 16,000 Up to 24,000,000
Satellite in low Earth orbit 8,000 29,000 26,000 19,000 32,000,000
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 TeV particle in LHC[6] 299,792,455 [note 1] 1,079,252,839 983571079 670,616,536 ~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.

## References

1. ^ Pius, Okeke; Maduka, Anyakoha (2001). Senior Secondary School Physics. Macmillan,Lagos, Nigeria.
2. ^ "projectile". merriam-webster.com. Retrieved 13 April 2017.
3. ^ "projectile". The Free Dictionary. Retrieved 2010-05-19.
4. ^ "projectile". Dictionary.com. Retrieved 2010-05-19.
5. ^ Pepin, Matt (2010-08-26). "Aroldis Chapman hits 105 mph". Boston.com. Archived from the original on 31 August 2010. Retrieved 2010-08-30.
6. ^ "Facts and figures". European Organization for Nuclear Research. CERN. 2008. Archived from the original on 2018-07-02. Retrieved 2018-07-02.