recoil calculator

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.

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