Computing Gun Recoil Forces

References:
Modern Land Combat by David Miller

Average Recoil force on a Gun Trunnion (Standard Units)

Force = (WeightProj * VelocityProj + WeightCharge * VelocityCharge)2 / (2 * g * WeightGun * LengthRecoil)

Equation Explained

Force = Force on the Trunnion (pounds)

WeightProj = Weight of Projectile (pounds)

WeightCharge = Weight of Propellant (pounds)

WeightGun = Weight of the recoiling mass (pounds)

VelocityProj = Muzzle velocity of projectile (ft/sec)

VelocityCharge = Escape Velocity of Propellant Gasses (ft/sec)

LengthRecoil = Length of Recoil (feet)

g = Acceleration due to gravity (32 ft/sec2)

EXAMPLE: A modern 120mm gun is firing a projectile massing 50 pounds at a muzzle velocity of 3,500 ft/sec, with a charge weight of 29.5 pounds and a propellant gas escape velocity of 4,700 ft/sec. The recoiling mass of the gun is 6,400 pounds, and the recoil length is one foot.

Force = (50 * 3,500 + 29.5 * 4,700)2 / (2 * 32 * 6,400 * 1)

These variables result in 240,177 pounds of force (or if translated into tons; 107.2 tons) on the gun trunnion.

Discussion on Recoil

There are several ways to reduce final recoil forces felt on the trunnion. They are:

Heavier Recoiling Masses: This is only truly feasible if the mass of the gun is not really a concern; like on a warship.

Muzzle Brakes: These can reduce felt forces on the trunnion; but at a price. They generate tremendous overpressure, and in some of the early tests with the Stryker Mobile Gun System when the gun was fired directly ahead, the overpressure from the muzzle brake was enough to shatter the driver's vision blocks. Infantry providing close support to the vehicle might also not like it when the gun fires. Additionally, they can kick up a large amount of dust when they fire, obscuring the target in your sights, or providing an easy location marker for the enemy.

Longer Recoil Strokes: These offer the best alternative out of the three for reducing recoil forces with acceptable tradeoffs. Their one disadvantage is that it becomes very hard to mount them in already existing weapon mounts without causing problems. For example, you might be able to add a few centimeters more of recoil length in a tank while not compromising safety for the loader, but adding significant amounts? Forget about it.

Also, as a rule of thumb, the maximum acceptable recoil force for vehicle mounted weapons is generally held to be about 1.5 times that of the vehicle's weight. For example, a 15-ton vehicle would be able to reliably accommodate a weapon with a recoil force of about 22.5 tons. Anything above that would cause unreliabilty issues, like the crew being shaken around badly, the vehicle having to deploy jacks to stabilize itself for left/right firing, or equipment on the vehicle breaking from recoil-induced stresses. This was a major issue with the M551 Sheridan tank and it's missile guidance equipment.