Recoil of any load in a given shotgun is proportional to shot mass and velocity (squared) alone.
Interesting. I'll have to think on that. Feels like it breaks conservation, but my memory of physics has been trumped by books before.Recoil is a momentum balance, MV = MV, no squared term.
You can use the momentum balance to figure recoil velocity and then calculate recoil energy, but that is nowhere near shot energy.
Momentum is a vector quantity, momentum of shot going north is equal to momentum of gun kicking south.
Energy is conserved but it is not a vector quantity, it appears in various forms from the stressed molecular bonds of the gunpowder to the kinetic energy of the shot, to deformation of the target, everything trickling down to heat.