Recoil

A list of variables are at the bottom of this page.

Recoil Velocity

The forward momentum (sometimes written as impulse), that of the bullet and powder charge are given by

M_F = M_B*V_B + M_C*V_C

Because momentum is conserved, this is equal to the rearward momentum of the firearm:

M_R = M_F*V_F

We can set these two equations equal to each other and solve for the velocity of the firearm, yielding

V_F = (M_B*V_B + M_C*V_C)/M_F

Recoil Energy

Once the velocity is found, the recoil energy can be found by solving

E_F = 1/2 M_F V_F²

Example

Assume a seven pound rifle using 40 grains of powder to shoot a 168 grain bullet at 2700 feet/sec. First find the mass of the bullet, charge and rifle

M_B = 168 gr/(32.2 f/s²*7000 gr/lb) = 0.000745 slugs (unit of mass) M_C = 40 gr/(32.2 f/s²*7000 gr/lb) = 0.000177 slugs M_F = 7 lb/(32.2 f/s²) = 0.217 slugs

The constant 32.2 is the acceleration due to gravity, g, and is used to convert weight to mass:

Mass = Weight/g

The free recoil velocity can now be found

V_F = (0.000745 slugs * 2700 f/s + 0.000177 slugs * 4700 f/s)/(0.217 slugs) = 13.1 f/s

And the free recoil energy is given by

E_F = 0.5 * 0.217 slugs * (13.1 f/s)² = 18.6 ft•lbs

Variables

MB	Bullet mass	VB	Bullet velocity
MC	Charge mass	VC	Charge velocity
MF	Firearm mass	VF	Firearm velocity
EF	Firearm energy	g	Acceleration due to gravity