Q: I’m aware that the recoil energy of any cartridge is reduced in direct proportion to the increase in the weight of the rifle, so long as the bullet weight and muzzle velocity remain the same. And if the recoil is known for a certain load in a rifle weighing 6lb, then the recoil of the same load fired in an 8lb rifle will be about three-quarters of what it was. But what is the effect on recoil velocity and energy with different loads and bullet weights? Is there a formula for calculating these things?
A: If the weight of the rifle and the muzzle velocity remain the same, the recoil energy will vary directly with the square of the sum of bullet weight plus powder charge. Take, for example, a 6lb rifle giving 3000fps with a 100gn bullet and 40gn of powder. If the same velocity is obtained with an 80gn bullet and 30gn of powder, the recoil of the new load will be as 110 squared is to 140 squared, or as 12,100 is to 19,600 and recoil will be 62 percent of what it was before. Changes in velocity, all else remaining equal, will result in changes of the velocities involved. Thus, if the velocity is cut in half, the recoil energy would be cut to one-quarter, provided bullet weight and powder charge were the same as before. To calculate recoil velocity, take the bullet weight and add to it one and three-quarter times the weight of powder charge (the extra 3/4 being to compensate for the fact that the powder gases leave the muzzle faster than the bullet does) and multiply by the muzzle velocity. Now divide by the weight of the gun in pounds, and also by the figure 7000, which is to compensate for the fact that the bullet weight and weight of powder charge are in grains instead of pounds. The result is the velocity in feet-per-second with which the rifle recoils. The recoil energy is obtained with the formula where half the MV is squared, and where V is the recoil velocity and M is the mass of the rifle (mass being weight in pounds divided by the acceleration of gravity, 32.2). Square the velocity of the recoil, multiply it by the weight of the gun, and divide by twice the acceleration of gravity, or 64.4. The result is the energy in foot-pounds with which the rifle moves to the rear.