Recoil - Recoil: Momentum, Energy and Impulse - Energy

Energy

A consideration of energy leads to a different equation. From Newton's second law, the energy of a moving body due to its motion can be stated mathematically from the translational kinetic energy as:

where:

is the translational kinetic energy

is the mass of the body

is its velocity

is its momentum (mv)

This equation is known as the "classic statement" and yields a measurement of energy in joules (or foot-pound force in non-SI units). is the amount of work that can be done by the recoiling firearm, firearm system, or projectile because of its motion, and is also called the translational kinetic energy. In the firearms lexicon, the energy of a recoiling firearm is called felt recoil, free recoil, and recoil energy. This same energy from a projectile in motion is called: muzzle energy, bullet energy, remaining energy. The energy of the projectile at the point of impact is known as the down range energy or impact energy and generally will be slightly smaller than the muzzle energy due to wind resistance acting upon the projectile.

Again assuming free-recoil conditions and assuming all forward momentum is due to the projectile, the energy of the projectile will be and the energy of the firearm due to recoil will be . Since, by Newton's third law, it follows that the ratios of the energies is given by:

The mass of the firearm is generally much greater than the projectile mass which means that most of the kinetic energy produced by the firing of the firearm is given to the projectile. For example, a rifle weighing 5 pounds firing a 150 grain bullet, the recoil energy will be only 0.43 percent of the total kinetic energy developed. In the case of zero-recoil, the firearm will gain no energy, and the energy of the projectile will be increased by 0.43 percent over that of the free-recoil case.

The recoil energy is generally absorbed by the mechanism which produces the counter-recoil force, and is dissipated as heat. For a hand-held firearm, the energy is absorbed by the shooter's body, creating a small amount of heat. For the naval cannon from the figure above, it will roll backwards and the recoil energy will be mostly absorbed by the friction forces in the wheel axles and between the wheel and the ship deck and this energy is again converted to heat.