Recoil
Recoil (often called knockback, kickback or simply kick) is the rearward
Basics
Any launching system (weapon or not) generates recoil. However recoil only constitutes a problem in the field of artillery and firearms due to the magnitude of the forces at play. Gun chamber pressures and projectile acceleration forces are tremendous, on the order of tens to hundreds
This moves the gun rearward and generates the recoil momentum. This recoil momentum is the product of the mass and the acceleration of the projectile and propellant gasses combined, reversed: the projectile moves forward, the recoil is rearward. The heavier and the faster the projectile, the more recoil will be generated. The gun acquires a rearward velocity that is ratio of this momentum by the mass of the gun: the heavier the gun, the slower the rearward velocity. As an example, a 8 g (124 gr) bullet of 9×19mm Parabellum flying forward at 350 m/s muzzle speed generates a momentum to push a 0.8 kg pistol firing it at 3.5 m/s rearward, if unopposed by the shooter.
Countering recoil
In order to bring the rearward moving gun to a halt, the momentum acquired by the gun is dissipated by a forward-acting counter-recoil force applied to the gun over a period of time during and after the projectile exits the muzzle.. Practical weight gun mounts are typically not strong enough to withstand the maximum forces accelerating the gun during the short time the projectile is in the barrel. To mitigate these large recoil forces, recoil buffering mechanisms spread out the counter-recoiling force over a longer time, typically ten to a hundred times longer than the duration of the forces accelerating the projectile. This results in the required counter-recoiling force being proportionally lower, and easily absorbed by the gun mount.
To apply this counter-recoiling force, modern mounted guns may employ recoil buffering comprising springs and hydraulic recoil mechanisms, similar to shock-absorbing suspension on automobiles. Early cannons used systems of ropes along with rolling or sliding friction to provide forces to slow the recoiling cannon to a stop. Recoil buffering allows the maximum counter-recoil force to be lowered so that strength limitations of the gun mount are not exceeded.
Contribution of propellant gasses
Modern cannons also employ muzzle brakes very effectively to redirect some of the propellant gasses rearward after projectile exit. This provides a counter-recoiling force to the barrel, allowing the buffering system and gun mount to be more efficiently designed at even lower weight.
Propellant gases are even more tapped in
Hand-held guns
The same physics principles affecting recoil in mounted guns also applies to hand-held guns. However, the shooter's body assumes the role of gun mount, and must similarly dissipate the gun's recoiling momentum over a longer period of time than the bullet travel-time in the barrel, in order not to injure the shooter. Hands, arms and shoulders have considerable strength and elasticity for this purpose, up to certain practical limits. Nevertheless, "perceived" recoil limits vary from shooter to shooter, depending on body size, the use of
Physics: momentum, energy and impulse
There are two conservation laws at work when a gun is fired:
Momentum is simply mass multiplied by velocity. Velocity is speed in a particular direction (not just speed). In a very technical sense, speed is a
A change in momentum of a mass requires applying a force (this is Newton's laws of motion). In a firearm forces wildly change, so what matters is impulse: the change of momentum is equal to the impulse. The rapid change of velocity (acceleration) of the gun is a shock and will countered as if by a shock absorber.
Energy in firing a firearm comes in many forms (thermal, pressure) but for understanding recoil what matters is kinetic energy, which is half mass multiplied by squared speed. For the recoiling gun, this means that for a given rearward momentum, doubling the mass halves the speed and also halves the kinetic energy of the gun, making it easier to dissipate.
Momentum
If all the masses and velocities involved are accounted for, the vector sum, magnitude and direction, of the momentum of all the bodies involved does not change; that is, momentum of the system is conserved. This conservation of momentum is why gun recoil occurs in the opposite direction of bullet projection -- the mass times velocity of the projectile (gas included) in the positive direction equals the mass times velocity of the gun in the negative direction. In summation, the total momentum of the system (ammunition, gun and shooter/shooting platform)) equals zero just as it did before the trigger was pulled.
From a practical engineering perspective, therefore, through the mathematical application of conservation of momentum, it is possible to calculate a first approximation of a gun's recoil momentum and kinetic energy simply based on estimates of the projectile speed (and mass) coming out the barrel. And then to properly design recoil buffering systems to safely dissipate that momentum and energy. To confirm analytical calculations and estimates, once a prototype gun is manufactured, the projectile and gun recoil energy and momentum can be directly measured using a ballistic pendulum and ballistic chronograph.
The nature of the recoil process is determined by the force of the expanding gases in the barrel upon the gun (recoil force), which is equal and opposite to the force upon the ejecta. It is also determined by the counter-recoil force applied to the gun (e.g. an operator's hand or shoulder, or a mount). The recoil force only acts during the time that the ejecta are still in the barrel of the gun. The counter-recoil force is generally applied over a longer time period and adds forward momentum to the gun equal to the backward momentum supplied by the recoil force, in order to bring the gun to a halt. There are two special cases of counter recoil force:
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. Assuming a near free-recoil condition, and neglecting the gases ejected from the barrel, (an acceptable first estimate), then 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:
Since momentum of a body is defined as its mass multiplied by its velocity, we can rewrite the above equation as:
- 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
A force integrated over the time period during which it acts will yield the momentum supplied by that force. The counter-recoil force must supply enough momentum to the firearm to bring it to a halt. This means that:
where:
- is the counter-recoil force as a function of time (t)
- is duration of the counter-recoil force
A similar equation can be written for the recoil force on the firearm:
where:
- is the recoil force as a function of time (t)
- is duration of the recoil force
Assuming the forces are somewhat evenly spread out over their respective durations, the condition for free-recoil is , while for zero-recoil, .
Angular momentum
For a gun firing under free-recoil conditions, the force on the gun may not only force the gun backwards, but may also cause it to rotate about its center of mass or recoil mount. This is particularly true of older firearms, such as the classic
where is the perpendicular distance of the center of mass of the gun below the barrel axis, is the force on the gun due to the expanding gases, equal and opposite to the force on the bullet, is the moment of inertia of the gun about its center of mass, or its pivot point, and is the angle of rotation of the barrel axis "up" from its orientation at ignition (aim angle). The angular momentum of the gun is found by integrating this equation to obtain:
where is the angle above the aim angle at which the bullet leaves the barrel, is the time of travel of the bullet in the barrel (because of the acceleration the time is longer than : ) and L is the distance the bullet travels from its rest position to the tip of the barrel. The angle at which the bullet leaves the barrel above the aim angle is then given by:
Including the ejected gas
Before the projectile leaves the
The overall recoil applied to the firearm is equal and opposite to the total forward momentum of not only the projectile, but also the ejected gas. Likewise, the recoil energy given to the firearm is affected by the ejected gas. By conservation of mass, the mass of the ejected gas will be equal to the original mass of the propellant (assuming complete burning). As a rough approximation, the ejected gas can be considered to have an effective exit velocity of where is the muzzle velocity of the projectile and is approximately constant. The total momentum of the propellant and projectile will then be:
This expression should be substituted into the expression for projectile momentum in order to obtain a more accurate description of the recoil process. The effective velocity may be used in the energy equation as well, but since the value of α used is generally specified for the momentum equation, the energy values obtained may be less accurate. The value of the constant α is generally taken to lie between 1.25 and 1.75. It is mostly dependent upon the type of propellant used, but may depend slightly on other things such as the ratio of the length of the barrel to its radius.
Muzzle devices can reduce the recoil impulse by altering the pattern of gas expansion. For instance,
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" is going to be approached with trepidation, and the shooter may 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 may result in a miss. The shooter may also be physically injured by firing a weapon generating recoil in excess of what the body can safely absorb or restrain; perhaps getting hit in the eye by the rifle scope, hit in the forehead by a handgun as the elbow bends under the force, or soft tissue damage to the shoulder, wrist and hand; and these results vary for individuals. In addition, as pictured on the right, excessive recoil can create serious range safety concerns, if the shooter cannot adequately restrain the firearm in a down-range direction.
Perception of recoil is related to the deceleration the body provides against a recoiling gun, deceleration being a force that slows the velocity of the recoiling mass. Force applied over a distance is energy. The force that the body feels, therefore, is dissipating the kinetic energy of the recoiling gun mass. A heavier gun, that is a gun with more mass, will manifest lower recoil kinetic energy, and, generally, result in a lessened perception of recoil. Therefore, although determining the recoiling energy that must be dissipated through a counter-recoiling force is arrived at by conservation of momentum, kinetic energy of recoil is what is actually being restrained and dissipated. The ballistics analyst discovers this recoil kinetic energy through analysis of projectile momentum.
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 deceleration, and sharp recoil is spread over a shorter period of time, that is with a higher deceleration. Like pushing softer or harder on the brakes of a car, the driver feels less or more deceleration force being applied, over a longer or shorter distance to bring the car to a stop. However, for the human body to mechanically adjust recoil time, and hence length, to lessen felt recoil force is perhaps an impossible task. Other than employing less safe and less accurate practices, such as shooting from the hip, shoulder padding is a safe and effective mechanism that allows sharp recoiling to be lengthened into soft recoiling, as lower decelerating force is transmitted into the body over a slightly greater distance and time, and spread out over a slightly larger surface.
Keeping the above in mind, you can generally base the relative recoil of firearms by factoring in a small number of parameters: bullet momentum (weight times velocity), (note that momentum and impulse are interchangeable terms), and the weight of the firearm. Lowering momentum lowers recoil, all else being the same. Increasing the firearm weight also lowers recoil, again all else being the same. 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 22frame, using the empty weight of 1.43 lb (0.65 kg), the following was obtained:
- 9 mm Luger: Recoil impulse of 0.78 lbf·s (3.5 N·s); 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 lbf·s (4.7 N·s); 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 lbf·s (3.9 N·s); Recoil velocity of 19.73 ft/s (6.0 m/s); Recoil energy of 8.64 ft⋅lbf (11.7 J)
- In a Smith & 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 lbf·s (8.5 N·s); Recoil velocity of 19.69 ft/s (6.0 m/s); Recoil energy of 18.81 ft⋅lbf (25.5 J)
- In a Smith & 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 lbf·s (14.0 N·s); Recoil velocity of 28.91 ft/s (8.8 m/s); Recoil energy of 45.43 ft⋅lbf (61.6 J)
- In a Smith & 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 lbf·s (16.7 N·s); 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,
Mounted guns
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; systems were used to somewhat limit this movement (ropes, friction including brakes on wheels, slopes so that the recoil would force the gun uphill,...), but utterly preventing any movement would just have resulted in the mount breaking. As a result, guns had to be put back into firing position and carefully aimed again after each shot, dramatically slowing the firing rate. The modern quick-firing guns was made possible by the invention of a much more efficient device: the hydro-pneumatic recoil system. First developed by Wladimir Baranovsky in 1872–5 and adopted by the Russian army, then later in France, in the 75mm field gun of 1897, it is still the main device used by big guns nowadays.
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 shorter and smaller than the barrel mounted parallel to it. The cylinder contains a charge of compressed air that will act as a spring, 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 is returned forward to the firing position under the pressure of the compressed air. 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 placed).
Soft-recoil
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 state, 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;
Other devices
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.
See also
- Muzzle rise, a torque generated by recoil that tends to cause the muzzle to lift up and back
- Power factor, a ranking system used in practical shooting competitions to reward cartridges with more recoil.
- Recoil operation, the use of recoil force to cycle a weapon's action
- Ricochet, a projectile that rebounds, bounces or skips off a surface, potentially backwards toward the shooter
- Recoil buffer
- Muzzle brake
- Recoil pad
Notes
References
- ^ A Limited Performance Tradeoff Analysis of a Novel Closed-Breech, Shoulder-Fired Weapon System, 1992; Appendix: Recoil in Shoulder-Fired Weapons: A Review of the Literature, Robert J. Spine, US Army Human Engineering Laboratory, 1982
- ^ Randy Wakeman. "Controlling shotgun recoil". Chuck Hawks.
- ^ "Soft Recoil System" (PDF). Field Artillery Bulletin. April 1969. pp. 43–48.
External links
- Recoil Tutorial
- Recoil Calculator and summary of equations at JBM.