All the above is concerned with the velocity of the gun's recoil, which tells us very little about the actual force, or more correctly, the energy of the recoil.
The energy of the recoil is calculated by use of the formula
The kinetic energy (KE) of the recoil, or the recoil energy, gives us a much clearer picture of the actual forces involved.
The recoil energy of a weapon and, for that matter, the kinetic energy of a bullet are calculated in exactly the same way and are measured in foot pound (or joule in the metric system). This force can be expressed in two ways: (i) 1 ft/lb is the energy necessary to lift a 1 lb weight 1 ft off the ground or (ii) the force of 1 lb being dropped from a height of 1 ft.
If we consider the same weapon as used in the calculation for recoil velocity, that is, a 2 lb 0.38" Special calibre revolver firing a 158 gr bullet at 860 ft/s with a calculated recoil velocity of 9.7 ft/s, then we have
As mentioned earlier, the weight of the propellant charge, multiplied by one and a half, should be added to the total weight of the bullet. The propellant charge for a 158 gr 0.38" Special calibre cartridge would be 3.6 gr, which would be 5"! for the above equation. Substituting this into the above equation would give a final figure for the recoil energy of 3.15 ft/lb.
From the above, it can be seen that the weight of the weapon has a very great influence on the recoil energy. If the weight of the weapon is reduced to 1 lb, then the recoil velocity is 20.0 ft/s and the recoil energy is 6.3 ft/lb.
In simple terms, the recoil velocity is the factor which makes a gun unpleasant to shoot. The higher the recoil velocity, the greater the discomfort. In 1929 Textbook of Small Arms (HMSO, 1929), the figure of 15 ft/s was given as the highest recommended recoil velocity of a rifle. Above this figure, 'gun headache' would be experienced.
The recoil energy is what gives the push to the shoulder and the muzzle lift to a handgun; it is expressed in foot pound and has the same magnitude as the kinetic energy of the bullet.
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