A list of variables are at the bottom of this page.
The forward momentum (sometimes written as impulse), that of the bullet and powder charge are given by
Because momentum is conserved, this is equal to the rearward momentum of the firearm:
We can set these two equations equal to each other and solve for the velocity of the firearm, yielding
Once the velocity is found, the recoil energy can be found by solving
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
The constant 32.2 is the acceleration due to gravity, g, and is used to convert weight to mass:
The free recoil velocity can now be found
And the free recoil energy is given by
M_{B} | Bullet mass | V_{B} | Bullet velocity |
M_{C} | Charge mass | V_{C} | Charge velocity |
M_{F} | Firearm mass | V_{F} | Firearm velocity |
E_{F} | Firearm energy | g | Acceleration due to gravity |