Recoil
Overview
 
Recoil (often called knockback, kickback or simply kick) is the backward momentum
Momentum
In classical mechanics, linear momentum or translational momentum is the product of the mass and velocity of an object...

 of a gun
Gun
A gun is a muzzle or breech-loaded projectile-firing weapon. There are various definitions depending on the nation and branch of service. A "gun" may be distinguished from other firearms in being a crew-served weapon such as a howitzer or mortar, as opposed to a small arm like a rifle or pistol,...

 when it is discharged. In technical terms, the recoil caused by the gun exactly balances the forward momentum of the projectile and exhaust gasses, according to Newton's third law. In most small arms
Small arms
Small arms is a term of art used by armed forces to denote infantry weapons an individual soldier may carry. The description is usually limited to revolvers, pistols, submachine guns, carbines, assault rifles, battle rifles, multiple barrel firearms, sniper rifles, squad automatic weapons, light...

, the momentum is transferred to the ground through the body of the shooter; while in heavier guns such as mounted machine gun
Machine gun
A machine gun is a fully automatic mounted or portable firearm, usually designed to fire rounds in quick succession from an ammunition belt or large-capacity magazine, typically at a rate of several hundred rounds per minute....

s or cannon
Cannon
A cannon is any piece of artillery that uses gunpowder or other usually explosive-based propellents to launch a projectile. Cannon vary in caliber, range, mobility, rate of fire, angle of fire, and firepower; different forms of cannon combine and balance these attributes in varying degrees,...

s, the momentum is transferred to the ground through its mount
Weapon mount
A weapon mount is a weapon component used to secure an armament. Weapon mounts can be broken down into two categories: static mounts and non-static mounts.-Static mount:...

.

A change in momentum results in a force
Force
In physics, a force is any influence that causes an object to undergo a change in speed, a change in direction, or a change in shape. In other words, a force is that which can cause an object with mass to change its velocity , i.e., to accelerate, or which can cause a flexible object to deform...

, which according to Newton's second law is equal to the time derivative
Time derivative
A time derivative is a derivative of a function with respect to time, usually interpreted as the rate of change of the value of the function. The variable denoting time is usually written as t\,.-Notation:...

 of the momentum
Momentum
In classical mechanics, linear momentum or translational momentum is the product of the mass and velocity of an object...

 of the gun.
Encyclopedia
Recoil (often called knockback, kickback or simply kick) is the backward momentum
Momentum
In classical mechanics, linear momentum or translational momentum is the product of the mass and velocity of an object...

 of a gun
Gun
A gun is a muzzle or breech-loaded projectile-firing weapon. There are various definitions depending on the nation and branch of service. A "gun" may be distinguished from other firearms in being a crew-served weapon such as a howitzer or mortar, as opposed to a small arm like a rifle or pistol,...

 when it is discharged. In technical terms, the recoil caused by the gun exactly balances the forward momentum of the projectile and exhaust gasses, according to Newton's third law. In most small arms
Small arms
Small arms is a term of art used by armed forces to denote infantry weapons an individual soldier may carry. The description is usually limited to revolvers, pistols, submachine guns, carbines, assault rifles, battle rifles, multiple barrel firearms, sniper rifles, squad automatic weapons, light...

, the momentum is transferred to the ground through the body of the shooter; while in heavier guns such as mounted machine gun
Machine gun
A machine gun is a fully automatic mounted or portable firearm, usually designed to fire rounds in quick succession from an ammunition belt or large-capacity magazine, typically at a rate of several hundred rounds per minute....

s or cannon
Cannon
A cannon is any piece of artillery that uses gunpowder or other usually explosive-based propellents to launch a projectile. Cannon vary in caliber, range, mobility, rate of fire, angle of fire, and firepower; different forms of cannon combine and balance these attributes in varying degrees,...

s, the momentum is transferred to the ground through its mount
Weapon mount
A weapon mount is a weapon component used to secure an armament. Weapon mounts can be broken down into two categories: static mounts and non-static mounts.-Static mount:...

.

A change in momentum results in a force
Force
In physics, a force is any influence that causes an object to undergo a change in speed, a change in direction, or a change in shape. In other words, a force is that which can cause an object with mass to change its velocity , i.e., to accelerate, or which can cause a flexible object to deform...

, which according to Newton's second law is equal to the time derivative
Time derivative
A time derivative is a derivative of a function with respect to time, usually interpreted as the rate of change of the value of the function. The variable denoting time is usually written as t\,.-Notation:...

 of the momentum
Momentum
In classical mechanics, linear momentum or translational momentum is the product of the mass and velocity of an object...

 of the gun. The momentum is equal to the mass
Mass
Mass can be defined as a quantitive measure of the resistance an object has to change in its velocity.In physics, mass commonly refers to any of the following three properties of matter, which have been shown experimentally to be equivalent:...

 of the gun multiplied by its velocity
Velocity
In physics, velocity is speed in a given direction. Speed describes only how fast an object is moving, whereas velocity gives both the speed and direction of the object's motion. To have a constant velocity, an object must have a constant speed and motion in a constant direction. Constant ...

. This backward momentum is equal in magnitude, by the law of conservation of momentum, to the forward momentum of the ejecta (projectile(s), wad, propellant gases, etc...) from the gun. If the mass and velocity of the ejecta are known, it is possible to calculate a gun’s momentum and thus the energy. In practice, it is often simpler to derive the gun’s energy directly with a reading from a ballistic pendulum
Ballistic pendulum
A ballistic pendulum is a device for measuring a bullet's momentum, from which it is possible to calculate the velocity and kinetic energy. Ballistic pendulums have been largely rendered obsolete by modern chronographs, which allow direct measurement of the projectile velocity.Although the...

 or ballistic chronograph
Gun chronograph
A gun chronograph is an instrument used to measure the velocity of a projectile fired by a gun.-History:Around 1800, the ballistic pendulum was used to measure the momentum of the projectile fired by a gun; dividing the momentum by the projectile mass gives the velocity.An early chronograph that...

.

Momentum

There are two conservation laws at work when a gun is fired: conservation of momentum and conservation of energy
Conservation of energy
The nineteenth century law of conservation of energy is a law of physics. It states that the total amount of energy in an isolated system remains constant over time. The total energy is said to be conserved over time...

. Recoil is explained by the law of conservation of momentum, and so it is easier to discuss it separately from energy
Energy
In physics, energy is an indirectly observed quantity. It is often understood as the ability a physical system has to do work on other physical systems...

.

The recoil of a firearm, whether large or small, is a result of the law of conservation of momentum. Assuming that the firearm and projectile are both at rest before firing, then their total momentum is zero. Immediately after firing, conservation of momentum requires that the total momentum of the firearm and projectile is the same as before, namely zero. Stating this mathematically:
where is the momentum of the firearm and is the momentum of the projectile. In other words, immediately after firing, the momentum of the firearm is equal and opposite to the momentum of the projectile.

Since momentum of a body is defined as its mass multiplied by its velocity, we can rewrite the above equation as:
where: is the mass of the firearm is the velocity of the firearm immediately after firing is the mass of the projectile is the velocity of the projectile immediately after firing

Energy

A consideration of energy leads to a different equation. From Newton's second law
Newton's laws of motion
Newton's laws of motion are three physical laws that form the basis for classical mechanics. They describe the relationship between the forces acting on a body and its motion due to those forces...

, the energy of a moving body due to its motion can be stated mathematically from the translational kinetic energy as:
where: is the mass of the firearm system, or ejecta and projectile after leaving the barrel is its velocity

This equation is known as the "classic statement" and yields a measurement of energy in joule
Joule
The joule ; symbol J) is a derived unit of energy or work in the International System of Units. It is equal to the energy expended in applying a force of one newton through a distance of one metre , or in passing an electric current of one ampere through a resistance of one ohm for one second...

s (or foot-pound force in non-SI units). is the amount of work that can be done by the recoiling firearm, firearm system, or projectile because of its motion, and is also called the translational kinetic energy. In the firearms lexicon, the energy of a recoiling firearm is called felt recoil, free recoil
Free recoil
This article is about the energy produced by small arms when discharged. For other uses, go to Recoil Free recoil is a vernacular term or jargon for recoil energy...

, and recoil energy. This same energy from a projectile in motion is called: muzzle energy, bullet energy, remaining energy, down range energy, and impact energy.

There is a difference between the two equations and events of recoil momentum and recoil energy. The momentum equation describe the conditions during discharge of the firearm, but before the projectile has left the barrel. While the energy equation describes the conditions after the projectile has left the barrel.

It should also be noted that, since usually the projectile mass is far smaller than that of the firearm system, the recoil does not affect so much the velocity (and energy) of the projectile. Thus, allowing the naval cannon from the figure above to roll freely backwards gives little prejudice to the power of the shot, while avoiding the "big kick" to the ship structures.

Impulse

The recoil impulse  of a small arm can be roughly described as:
Where: is the muzzle velocity is the mass of the projectile is the mass of the propellant charge

This equation is an approximation. The constant of 1.75 varies for differing propellants.

See physics of firearms
Physics of firearms
From the viewpoint of physics , a firearm, as for most weapons, is a system for delivering maximum destructive energy to the target with minimum delivery of energy on the shooter. The momentum delivered to the target however cannot be any more than that on the shooter...

 for a more detailed discussion.

Perception of recoil

For small arms, the way in which the shooter perceives the recoil, or kick, can have a significant impact on the shooter's experience and performance. For example, a gun that is said to "kick like a mule
Mule
A mule is the offspring of a male donkey and a female horse. Horses and donkeys are different species, with different numbers of chromosomes. Of the two F1 hybrids between these two species, a mule is easier to obtain than a hinny...

" is going to be approached with trepidation, and the shooter will anticipate the recoil and flinch in anticipation as the shot is released. This leads to the shooter jerking the trigger, rather than pulling it smoothly, and the jerking motion is almost certain to disturb the alignment of the gun and result in a miss.

This perception of recoil is related to the acceleration associated with a particular gun. The actual recoil is associated with the momentum of a gun, the momentum being the product of the mass of the gun times the reverse velocity of the gun. A heavier gun, that is a gun with more mass, will manifest the momentum by exhibiting a lessened acceleration, and, generally, result in a lessened perception of recoil.

One of the common ways of describing the felt recoil of a particular gun-cartridge combination is as "soft" or "sharp" recoiling; soft recoil is recoil spread over a longer period of time, that is at a lower acceleration, and sharp recoil is spread over a shorter period of time, that is with a higher acceleration. With the same gun and two loads with different bullet masses but the same recoil force, the load firing the heavier bullet will have the softer recoil, because the product of mass times acceleration must remain constant, and if mass goes up then acceleration must go down, to keep the product constant.

Keeping the above in mind, you can generally base the relative recoil of firearms by factoring in a number of figures such as bullet weight, powder charge, the weight of the actual firearm etc. The following are base examples calculated through the Handloads.com free online calculator, and bullet and firearm data from respective reloading manuals (of medium/common loads) and manufacturer specs:
  • In a Glock 22 frame, using the empty weight of 1.43 lb (0.6486370891 kg), the following was obtained:
    • 9 mm Luger: Recoil Impulse of 0.78 ms; Recoil Velocity of 17.55 ft/s (5.3 m/s); Recoil Energy of 6.84 ft·lbf (9.3 J)
    • .357 SIG: Recoil Impulse of 1.06 ms; Recoil velocity of 23.78 ft/s (7.2 m/s); Recoil Energy of 12.56 ft·lbf (17 J)
    • .40 S&W: Recoil impulse of 0.88 ms; Recoil velocity of 19.73 ft/s (6 m/s); Recoil Energy of 8.64 ft·lbf (11.7 J)
  • In a Smith and Wesson .44 Magnum with 7.5-inch barrel, with an empty weight of 3.125 lb (1.4 kg), the following was obtained:
    • .44 Remington Magnum: Recoil impulse of 1.91 ms; Recoil velocity of 19.69 ft/s (6 m/s); Recoil Energy of 18.81 ft·lbf (25.5 J)
  • In a Smith and Wesson 460 7.5-inch barrel, with an empty weight of 3.5 lb (1.6 kg), the following was obtained:
    • .460 S&W Magnum: Recoil Impulse of 3.14 ms; Recoil Velocity of 28.91 ft/s (8.8 m/s); Recoil Energy of 45.43 ft·lbf (61.6 J)
  • In a Smith and Wesson 500 4.5-inch barrel, with an empty weight of 3.5 lb (1.6 kg), the following was obtained:
    • .500 S&W Magnum: Recoil Impulse of 3.76 ms; Recoil Velocity of 34.63 ft/s (10.6 m/s); Recoil Energy of 65.17 ft·lbf (88.4 J)


In addition to the overall mass of the gun, reciprocating parts of the gun will affect how the shooter perceives recoil. While these parts are not part of the ejecta, and do not alter the overall momentum of the system, they do involve moving masses during the operation of firing. For example, gas-operated shotguns are widely held to have a "softer" recoil than fixed breech or recoil-operated
Recoil operation
Recoil operation is an operating mechanism used in locked-breech, autoloading firearms. As the name implies, these actions use the force of recoil to provide energy to cycle the action...

 guns. In a gas-operated gun, the bolt is accelerated rearwards by propellant gases during firing, which results in a forward force on the body of the gun. This is countered by a rearward force as the bolt reaches the limit of travel and moves forwards, resulting in a zero sum, but to the shooter, the recoil has been spread out over a longer period of time, resulting in the "softer" feel.

Mounted guns

A recoil system absorbs recoil energy, reducing the peak force that is conveyed to whatever the gun is mounted on. Old-fashioned cannon
Cannon
A cannon is any piece of artillery that uses gunpowder or other usually explosive-based propellents to launch a projectile. Cannon vary in caliber, range, mobility, rate of fire, angle of fire, and firepower; different forms of cannon combine and balance these attributes in varying degrees,...

s without a recoil system roll several meters backwards when fired. The usual recoil system in modern quick-firing gun
Quick-firing gun
A quick-firing gun is an artillery piece, typically a gun or howitzer, which has several characteristics which taken together mean the weapon can fire at a fast rate...

s is the hydro-pneumatic recoil system (first introduced in the French 75mm field gun of 1897
Canon de 75 modèle 1897
The French 75mm field gun was a quick-firing field artillery piece adopted in March 1898. Its official French designation was: Matériel de 75mm Mle 1897. It was commonly known as the French 75, simply the 75 and Soixante-Quinze .The French 75 is widely regarded as the first modern artillery piece...

). In this system, the barrel is mounted on rails on which it can recoil to the rear, and the recoil is taken up by a cylinder which is similar in operation to an automotive gas-charged shock absorber
Shock absorber
A shock absorber is a mechanical device designed to smooth out or damp shock impulse, and dissipate kinetic energy. It is a type of dashpot.-Nomenclature:...

, and is commonly visible as a cylinder mounted parallel to the barrel of the gun, but shorter and smaller than it. The cylinder contains a charge of compressed air, as well as hydraulic oil; in operation, the barrel's energy is taken up in compressing the air as the barrel recoils backward, then is dissipated via hydraulic damping as the barrel returns forward to the firing position. The recoil impulse is thus spread out over the time in which the barrel is compressing the air, rather than over the much narrower interval of time when the projectile is being fired. This greatly reduces the peak force conveyed to the mount (or to the ground on which the gun has been emplaced).

In a soft-recoil system, the spring (or air cylinder) that returns the barrel to the forward position starts out in a nearly fully compressed position, then the gun's barrel is released free to fly forward in the moment before firing; the charge is then ignited just as the barrel reaches the fully forward position. Since the barrel is still moving forward when the charge is ignited, about half of the recoil impulse is applied to stopping the forward motion of the barrel, while the other half is, as in the usual system, taken up in recompressing the spring. A latch then catches the barrel and holds it in the starting position. This roughly halves the energy that the spring needs to absorb, and also roughly halves the peak force conveyed to the mount, as compared to the usual system. However, the need to reliably achieve ignition at a single precise instant is a major practical difficulty with this system; and unlike the usual hydro-pneumatic system, soft-recoil systems do not easily deal with hangfires
Hang fire
Hang fire refers to an unexpected delay between the triggering of a firearm and the ignition of the propellant. This failure was common in firearm actions that relied on open primer pans, due to the poor or inconsistent quality of the powder. Modern weapons are susceptible, particularly if the...

 or misfire
Misfire
Misfire may refer to:* Misfire , the Transformers character* Misfire , an episode from That '70s Show* Misfiring behavior, in biology* An engine misfire, see catalytic converter* A song on Queen's album Sheer Heart Attack...

s. One of the early guns to use this system was the French 65 mm mle.1906
Canon de 65 M(montagne) modele 1906
The Canon de 65 M modele 1906 or was a French mountain gun which entered service with the regiments d'artillerie de montagne in 1906 and was one of the first soft-recoil guns in service. The carriage of the mle 1906 was hinged and could be broken down into four mule loads for transport...

; it was also used by the World War II British PIAT
PIAT
The Projector, Infantry, Anti Tank was a British hand-held anti-tank weapon developed during the Second World War. The PIAT was designed in 1942 in response to the British Army's need for a more effective infantry anti-tank weapon, and entered service in 1943.The PIAT was based on the spigot...

 man-portable anti-tank weapon.

Recoilless rifle
Recoilless rifle
A recoilless rifle or recoilless gun is a lightweight weapon that fires a heavier projectile than would be practical to fire from a recoiling weapon of comparable size. Technically, only devices that use a rifled barrel are recoilless rifles. Smoothbore variants are recoilless guns...

s and rocket launchers
Shoulder-launched missile weapon
A shoulder-fired missile, shoulder-launched missile or man-portable missile is a projectile fired at a target, small enough to be carried by a single person, and fired while held on one's shoulder...

 exhaust gas to the rear, balancing the recoil. They are used often as light anti-tank weapons. The Swedish-made Carl Gustav 84mm recoilless gun
Carl Gustav recoilless rifle
The Carl Gustav is the common name for the 84 mm man-portable reusable multi-role recoilless rifle produced by Saab Bofors Dynamics in Sweden...

 is such a weapon.

In machine guns following Hiram Maxim's design - e.g. the Vickers machine gun
Vickers machine gun
Not to be confused with the Vickers light machine gunThe Vickers machine gun or Vickers gun is a name primarily used to refer to the water-cooled .303 inch machine gun produced by Vickers Limited, originally for the British Army...

 - the recoil of the barrel is used to drive the feed mechanism.

Misconceptions about recoil

Hollywood depictions of firearm shooting victims being thrown through several feet backwards are inaccurate, although not for the often-cited reason of conservation of energy. Although energy must be conserved, this does not mean that the kinetic energy of the bullet must be equal to the recoil energy of the gun: in fact, it is many times greater. For example, a bullet fired from an M16 rifle has approximately 1763 Joules of kinetic energy as it leaves the muzzle, but the recoil energy of the gun is less than 7 Joules. Despite this imbalance, energy is still conserved because the total energy in the system before firing (the chemical energy stored in the propellant) is equal to the total energy after firing (the kinetic energy of the recoiling firearm, plus the kinetic energy of the bullet and other ejecta, plus the heat energy from the explosion). In order to work out the distribution of kinetic energy between the firearm and the bullet, it is necessary to use the law of conservation of momentum in combination with the law of conservation of energy.

The same reasoning applies when the bullet strikes a target. The bullet may have a kinetic energy in the hundreds or even thousands of joules, which in theory is enough to lift a person well off the ground. This energy, however, cannot be efficiently given to the target, because total momentum must be conserved, too. Approximately, only a fraction not larger than the inverse ratio of the masses can be transferred. The rest is spent in the deformation or shattering of the bullet (depending on bullet construction), damage to the target (depending on target construction), and heat dissipation. In other words, because the bullet strike on the target is an inelastic collision
Inelastic collision
An inelastic collision, in contrast to an elastic collision, is a collision in which kinetic energy is not conserved.In collisions of macroscopic bodies, some kinetic energy is turned into vibrational energy of the atoms, causing a heating effect, and the bodies are deformed.The molecules of a gas...

, a minority of the bullet energy is used to actually impart momentum to the target. This is why a ballistic pendulum
Ballistic pendulum
A ballistic pendulum is a device for measuring a bullet's momentum, from which it is possible to calculate the velocity and kinetic energy. Ballistic pendulums have been largely rendered obsolete by modern chronographs, which allow direct measurement of the projectile velocity.Although the...

 relies on conservation of bullet momentum and pendulum energy rather than conservation of bullet energy to determine bullet velocity; a bullet fired into a hanging block of wood or other material will spend much of its kinetic energy to create a hole in the wood and dissipate heat as friction as it slows to a stop.

Gunshot victims frequently do collapse when shot, which is usually due to psychological motives, a direct hit to the central nervous system, and/or massive blood loss (see stopping power
Stopping power
Stopping power is a colloquial term used to describe the ability of a firearm or other weapon to cause a penetrating ballistic injury to a target, human or animal, sufficient to incapacitate the target where it stands....

), and is not the result of the momentum of the bullet pushing them over.

See also

  • Ricochet
    Ricochet
    A ricochet is a rebound, bounce or skip off a surface, particularly in the case of a projectile. The possibility of ricochet is one of the reasons for the common firearms safety rule "Never shoot at a flat, hard surface."-Variables:...

    , a projectile that rebounds, bounces or skips off a surface, potentially backwards toward the shooter
  • Recoil buffer
    Recoil buffer
    A recoil buffer is a factory-installed or aftermarket component of firearms which serves to reduce the velocity and/or cushion the impact of recoilling parts of a firearm.-Design:...

  • Muzzle brake
    Muzzle brake
    Muzzle brakes and recoil compensators are devices that are fitted to the muzzle of a firearm or cannon to redirect propellant gases with the effect of countering both recoil of the gun and unwanted rising of the barrel during rapid fire...

The source of this article is wikipedia, the free encyclopedia.  The text of this article is licensed under the GFDL.
 
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