BondoBob said:
So energy ft lbs has nothing to do with it?
Energy has everything to do with it. It just isn't the simple equal and opposite that momentum is. But at the velocity of a recoiling gun, ft-lbs of recoil energy produces a good representation of felt recoil. If there were no powder mass involved (pretend the bullet is driven electromagnetically for the sake of taking powder out of it for the moment). If the gun weighed 300 times what the bullet weighs, in order to have momentum that was equal and oppositely directed from the gun, the bullet has to be going 300 times faster than the gun recoils. So let's give the bullet a velocity of 300 and the gun a velocity of 1. 1 squared is 1. 300 squared is 90,000. So the bullet will be going 300 times faster but the muzzle energy will be 90,000 times greater than the gun's recoil energy. This is the main reason the target on the receiving end of the bullet is damaged more than the shooter is. You can add-in greater area of distribution of the rifle butt plate as compared to the bullet nose, but that's a smaller factor than the energy difference.
Why is gun recoiling energy a good predictor of felt recoil? I like to give the example of an 5.6 ounce 100 mph baseball vs. a 2000 lb small car in neutral that is just barely rolling along a flat at a very sedate one quarter of an inch per second (about 1/6 of a mph). Both have the same momentum (mass times velocity). Now you put your hand out to stop the baseball and your other hand out to stop the car. Which one hurts more to do? The baseball's kinetic energy is about 117 ft-lbs. The car's kinetic energy is about 0.013 ft-lbs. That's an 8800:1 difference and that's about what it feels like because if you stop both of them over the same distance (say, a foot) you spend 8800 times more time stopping the car than you do the baseball, so it takes 8800 times less force to stop the car. And that's what you feel. The amount of force involved in taking the energy out of something.
So, when your gun has 900 times less energy than your bullet, it takes 900 times less force to stop it over the same distance. You don't actually do that, of course. You actually stop the bullet over a shorter distance (the recoil distance) than the target stops the bullet over (a deer thickness, for example), so you don't get the full 900 times less impact than the target, but it is significantly less.
Rocket effect can be very significant, especially in overbore cartridges where the powder charge weight approaches that of the bullet. This is because propellant gasses are less dense than lead or copper so when the bullet uncorks the muzzle, these lighter gases have the same pressure behind them that the bullet did at the muzzle, but that accelerates them to a higher velocity than the bullet, which is why shadow graphs of guns firing show a sphere of expanding gas out ahead of the bullet for a foot or so. Of course, it looses velocity fast as it works to push air out of the way, so that by the time it gets into that size range, the bullet is moving faster than the gas pressure front and catches back up and goes on to penetrate the front of the gas bubble and move on forward. But while that gas is at its highest speed near the muzzle, it creates a lot of thrust to the rear as it vents from the muzzle and that accelerates the gun further toward the shooter's shoulder. For some overbore cartridges like the 22-06, the recoil energy due to muzzle blast actually exceeds the recoil energy due to accelerating the bullet. What a muzzle brake does is vent much of that gas sideways so it doesn't contribute to recoil. This is why muzzle brakes do nothing to reduce recoil of cat sneeze loads, but reduce the recoil of full-house loads significantly. the former have very little left by way of muzzle pressure when they exit, but the latter have a lot of it, so the brake makes a very noticeable improvement there.
The v² relationship of velocity to kinetic energy also explains why pulling a rifle stock hard into your shoulder reduces felt recoil. The action adds your mass to the mass of the gun, and thus the highest possible recoil energy cannot be reached because your body mass is in the way of the gun achieving its maximum possible recoil velocity.