Recoil

This article is about backward momentum produced in firearms when fired. For other uses, see Recoil (disambiguation).

An early naval cannon, which is allowed to roll backwards slightly when fired.

Recoil (often called kickback or simply kick) is the backward momentum of a gun 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, the momentum is transferred to the ground through the body of the shooter; while in heavier guns such as mounted machine guns or cannons, the momentum is transferred to the ground through a mounting system.

A change in momentum results in a force, which according to Newton's second law is equal to the time derivative of the momentum of the gun. The momentum is equal to the mass of the gun multiplied by its velocity. 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 or ballistic chronograph.

Recoil: momentum, energy and impulse

Momentum

There are two conservation laws at work when a gun is fired: conservation of momentum and conservation of energy. Recoil is explained by the law of conservation of momentum, and so it is easier to discuss it separately from energy.

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:

$p_{f}+p_{p}=0\,$

where $p_{f}\,$ is the momentum of the firearm and $p_{p}\,$ 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:

$m_{f}\times v_{f}=m_{p}\times v_{p}$

where:

$m_{f}\,$ is the mass of the firearm

$v_{f}\,$ is the velocity of the firearm immediately after firing

$m_{p}\,$ is the mass of the projectile

$v_{p}\,$ is the velocity of the projectile immediately after firing

Energy

A consideration of energy leads to a different equation. From Newton's second law, the energy of a moving body due to its motion can be stated mathematically from the translational kinetic energy as:

$E_{t}={\frac {1}{2}}m\times v^{2}$

where:

$m\,$ is the mass of the firearm system, or ejecta and projectile after leaving the barrel

$v\,$ is its velocity

This equation is known as the "classic statement" and yields a measurement of energy in joules (or foot-pound force in non-SI units). $E_{t}\,$ 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, 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 $I_{r}\,$ of a small arm can be roughly described as:

$I_{r}=V_{0}\cdot m_{p}+1{.}75V_{0}\cdot c$

Where:

$V_{0}\,$ is the muzzle velocity

$m_{p}\,$ is the mass of the projectile

$c\,$ 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 for a more detailed discussion.

Perception of recoil

Recoil while firing Smith & Wesson Model 500 revolver

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" 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 (0.65 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 (17.0 J)
  • .40 S&W: Recoil impulse of 0.88 ms; Recoil velocity of 19.73 ft/s (6.0 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 (1.417 kg), the following was obtained:
  • .44 Remington Magnum: Recoil impulse of 1.91 ms; Recoil velocity of 19.69 ft/s (6.0 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 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

Recoilless designs allow larger and faster projectiles to be shoulder-launched.

A recoil system absorbs recoil energy, reducing the peak force that is conveyed to whatever the gun is mounted on. Old-fashioned cannons without a recoil system roll several meters backwards when fired. The usual recoil system in modern quick-firing guns is the hydro-pneumatic recoil system (first introduced in the French 75mm field gun of 1897). 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, 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 or misfires. One of the early guns to use this system was the French 65 mm mle.1906; it was also used by the World War II British PIAT man-portable anti-tank weapon.

Recoilless rifles and rocket launchers 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 is such a weapon.

In machine guns following Hiram Maxim's design - e.g. the Vickers machine gun - 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, 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.

See also

• Ricochet, a projectile that rebounds, bounces or skips off a surface, potentially backwards toward the shooter
• Recoil buffer
• Muzzle brake

References

Notes

External links

• Recoil Tutorial