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Recoil
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Recoil, in common everyday language, is considered the backward kick or force produced by a gun when it is fired. In more precise scientific terms, this force is equal to the time derivative of the backward momentum resulting when a gun is fired.
The backward momentum is equal to the mass of the gun times reverse velocity.
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Recoil, in common everyday language, is considered the backward kick or force produced by a gun when it is fired. In more precise scientific terms, this force is equal to the time derivative of the backward momentum resulting when a gun is fired.
The backward momentum is equal to the mass of the gun times reverse velocity. This backward momentum is equal, by the law of conservation of momentum, to the forward momentum of the ejecta of the gun (the projectile(s), wad, sabot, propellant gasses, etc.). Provided that enough information is known about the mass and velocity of the ejecta, it is possible to calculate its momentum and thus the recoil. In practice, however, it is often easier simply to measure the recoil force directly, such as with a ballistic pendulum.
In most small arms, the force of the recoil is absorbed usually by the body of the shooter; in heavier guns such as mounted machine guns or cannons, the recoil is absorbed by a mounting system.
Recoil versus energy
Recoil is from the law of conservation of momentum. Energy is a quality of work that can be measured. When discussing recoil and energy it tends to be more understandable if one thinks of them separately. Recoil generally conveys an action with an equal and opposite reaction as a topic for discussion. Energy and that energy specific to recoiling firearms conveys "kick" as in what a shooter feels.
In the firearms lexicon, the energy of a recoiling firearm is called felt recoil, free recoil, 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.
In mathematics, the recoil and energy of a recoiling firearm are different as well. The recoil of a firearm, both large and small, is a function of the law conservation of momentum and can be stated mathematically as mf·vf = mp·vp from Newton's third law. The equation describes the recoil of a firearm and the user or gun-mount system in its entirety. The equal sign (=) represents the total thermodynamic energy held within the powder charge. "mf·vf" found on the left side of the equation represents the backwards motion of the firearm or firearm system. "mp·vp" found on the right of the equation represents the forward motion of the ejecta and projectile moving down the barrel, before either have left the barrel.
The energy of a recoiling firearm can be stated mathematically as Et=0.5·m·v²
from Newton's second law. This equation is known as the "classic statement" and yields a measurement of energy in joules (foot-pound force in non-SI units). The calculated energy is the amount of work that can be done by the recoiling firearm, firearm system, or a projectile because of their motion. When looking at the classic statement (Et=0.5·m·v²): the "Et" represents the translational kinetic energy of a recoiling firearm, firearm system, or ejacta and projectile's motion after the two exit the barrel. The "m" in the equation represents the mass of the firearm, firearm system, or ejecta and projectile. The "v²" in the equation represents the square of the velocity for the firearm or firearm system in backwards motion and the ejecta and projectile in forward motion; again after the two exits the barrel.
The difference between these two equations and events is that during recoil, m·v = m·v, a projectile has not left the barrel. When calculating the energy of a recoiling firearm, Et=0.5·m·v², the projectile has exited the barrel. Again, recoil is a principle of the law of conservation of momentum and the energy of a recoiling firearm, firearm system, or ejecta and projectile is a quality of work that can be measured
It can also be helpful to think of the energy of a recoiling firearm or firearm system as a byproduct of work being done to accelerate a projectile towards its target.
See physics of firearms 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 "kicks like a mule" 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 momentum associated with a particular gun. The total force of 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 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 , the following was obtained:
- 9 mm Luger: Recoil Impulse of .78 ms; Recoil Velocity of ; Recoil Energy of
- .357 SIG: Recoil Impulse of 1.06 ms; Recoil Velocity of ; Recoil Energy of
- .40 S&W: Recoil Impulse of .88 ms; Recoil Velocity of ; Recoil Energy of
- In a Smith and Wesson .44 Magnum with 7.5-inch barrel, with an empty weight of , the following was obtained:
- .44 Remington Magnum: Recoil Impulse of 1.91 ms; Recoil Velocity of ; Recoil Energy of
- In a Smith and Wesson 460 7.5-inch barrel, with an empty weight of , the following was obtained:
- .460 S&W Magnum: Recoil Impulse of 3.14 ms; Recoil Velocity of ; Recoil Energy of
- In a Smith and Wesson 500 4.5-inch barrel, with an empty weight of , the following was obtained:
- .500 S&W Magnum: Recoil Impulse of 3.76 ms; Recoil Velocity of ; Recoil Energy of
In addition to the overall mass of the gun, reciprocating parts of the gun will effect 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 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.
Dealing with recoil in mounted guns
A recoil system absorbs momentum, for example, by the barrel moving backwards. Cannons and such weapons without a recoil system roll several meters backwards when fired.
In a soft-recoil system, a gun's barrel is moved forward prior to shooting. As the barrel is forced backwards by the recoil force, the energy is reduced by friction, resulting in less of an overall "kick". One of the early guns to use this was the French 65 mm mle.1906; however, this method did not receive much attention until the 1970s.
In a mounted gun, a down-recoil system is when the barrel is forced down on a spring mechanism, and immediately springs back up to its original position. This modern system, since around 2003, can work so rapidly that it works with machine guns.
Recoilless rifles and rocket launchers exhaust gas to the rear, balancing the recoil. They are used often as light anti-tank weapons.
Misconceptions about recoil
Hollywood depictions of firearm victims being thrown through several feet backwards are inaccurate, although not for the often-cited reason of conservation of energy. Although the momentum possessed by a bullet as it leaves the muzzle of a gun is indeed equal to the recoil momentum of the gun (neglecting the momentum possessed by gas molecules and particles also leaving the muzzle), the kinetic energy of the bullet is many times greater than the recoil energy of the gun. For example, a bullet fired from an M16 rifle has approximately 1300 foot-pounds of kinetic energy as it leaves the muzzle, but the recoil energy of the gun is less than 5 foot-pounds. The reason mechanical energy is not conserved is because much more of the chemical energy released during powder combustion is transferred to the bullet than is transferred to the gun.
Thus, when a bullet strikes a target, it may have a kinetic energy in the hundreds or even thousands of foot-pounds, which in theory is enough to lift a person well off the ground. (A foot-pound is the energy required to lift a one-pound weight to a height one foot off the ground.) This energy, however, is largely 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, a minority of the bullet energy is used to actually impart momentum to the target. This is why a ballistic pendulum 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), and is not the result of the momentum of the bullet pushing them over.
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