Recoil Control

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Recoil (often called knockback, kickback or simply kick) is the backward movement of a gun when it is discharged. In technical terms, the recoil momentum acquired by the gun exactly balances the forward momentum of the projectile and exhaust gases (ejecta), according to Newton’s third law, known as conservation of momentum. In hand-held small arms, the recoil momentum is transferred to the ground through the body of the shooter; while in heavier guns such as mounted machine guns or cannons, recoil momentum is transferred to the ground through the mount.

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 after the projectile exits the muzzle. 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. Gun chamber pressures and projectile acceleration forces are tremendous, on the order of tens of thousands of pounds per square inch and tens of thousands of times the acceleration of gravity (g’s), both necessary to launch the projectile at useful velocity during the very short travel distance of the barrel. However, the same pressures acting on the base of the projectile are acting on the rear face of the gun chamber, accelerating the gun rearward during firing. Practical weight gun mounts are typically not strong enough to withstand the maximum forces accelerating the projectile during the short time the projectile is in the barrel, typically only a few milliseconds. 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. 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. “Recoilless” guns, (recoilless rifle), also exist where much of the high pressure gas remaining in the barrel after projectile exit is vented rearward though a nozzle at the back of the chamber, creating a large counter-recoiling force sufficient to eliminate the need for heavy recoil mitigating buffers on the mount.

The same physics affecting recoil in mounted guns and cannons 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 recoil padding, individual pain tolerance, the weight of the firearm, and whether recoil buffering systems and muzzle brakes are employed. For this reason, establishing recoil safety standards for small arms remains challenging, in spite of the straight-forward physics involved
A change in momentum of a mass requires a force; according to Newton’s first law, known as the law of inertia, inertia simply being another term for mass. That force, applied to a mass, creates an acceleration, which when applied over time, changes the velocity of a mass. According to Newton’s second law, the law of momentum — changing the velocity of the mass changes its momentum, (mass multiplied by velocity). It is important to understand at this point that velocity is not simply speed. Velocity is the speed of a mass in a particular direction. In a very technical sense, speed is a scalar (mathematics), a magnitude, and velocity is a vector (physics), magnitude and direction. Newton’s third law, known as conservation of momentum, recognizes that changes in the motion of a mass, brought about by the application of forces and accelerations, does not occur in isolation; that is, other bodies of mass are found to be involved in directing those forces and accelerations. Furthermore, 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; hence, momentum of the system is conserved. This conservation of momentum is why gun recoil occurs in the opposite direction of bullet projection — the

A change in momentum of a mass requires a force; according to Newton’s first law, known as the law of inertia, inertia simply being another term for mass. That force, applied to a mass, creates an acceleration, which when applied over time, changes the velocity of a mass. According to Newton’s second law, the law of momentum — changing the velocity of the mass changes its momentum, (mass multiplied by velocity). It is important to understand at this point that velocity is not simply speed. Velocity is the speed of a mass in a particular direction. In a very technical sense, speed is a scalar (mathematics), a magnitude, and velocity is a vector (physics), magnitude and direction. Newton’s third law, known as conservation of momentum, recognizes that changes in the motion of a mass, brought about by the application of forces and accelerations, does not occur in isolation; that is, other bodies of mass are found to be involved in directing those forces and accelerations. Furthermore, 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; hence, 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 in the positive direction equals the mass times velocity of the gun in the negative direction. In summation, the total momentum of the system equals zero, surprisingly 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, and properly design recoil buffering systems to safely dissipate that momentum and energy, simply based on estimates of the projectile speed (and mass) coming out the barrel. 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.

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 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: Free-recoil, in which the time duration of the counter-recoil force is very much larger than the duration of the recoil force, and zero-recoil, in which the counter-recoil force matches the recoil force in magnitude and duration. Except for the case of zero-recoil, the counter-recoil force is smaller than the recoil force but lasts for a longer time. Since the recoil force and the counter-recoil force are not matched, the gun will move rearward, slowing down until it comes to rest. In the zero-recoil case, the two forces are matched and the gun will not move when fired. In most cases, a gun is very close to a free-recoil condition, since the recoil process generally lasts much longer than the time needed to move the ejecta down the barrel. An example of near zero-recoil would be a gun securely clamped to a massive or well-anchored table, or supported from behind by a massive wall. However, employing zero-recoil systems is often neither practical nor safe for the structure of the gun, as the recoil momentum must be absorbed directly through the very small distance of elastic deformation of the materials the gun and mount are made from, perhaps exceeding their strength limits. For example, placing the butt of a large caliber gun directly against a wall and pulling the trigger risks cracking both the gun stock and the surface of the wall.