Remember saw a formula couple years ago to calculate recoil. Apparently my Google Foo sucks and can't find it. Believe used bullet weight, velocity, gun weight, etc. Anyone know what I'm talking about.
F=MA; where F= force, M=mass, and A=acceleration.
Furthermore, KE= (1/2)MV^2; where V= velocity.
We can calculate the velocity of the rifle from the steady state equation below;
M(rifle)*V(rifle, initial) + M(projectile)*V(Projectile, initial) + M(powder)*V(Powder, initial) = M(rifle)*V(rifle, final) + M(projectile)*V(Projectile, final) + M(powder)*V(Powder, final)
Recognizing that the initial velocities of all components of the system are 0, we can reorganize the equation as below;
V(rifle, final) = -(M(projectile)*V(Projectile, final) + M(powder)*V(Powder, final)) / (M(rifle))
The (-) is a function of the bullet and other "ejecta" moving in one direction while the rifle is moving in the opposite direction.
Note that; given an equivalent bullet weight, bullet velocity, powder charge, and rifle weight, the recoil velocity of the rifle will be the same regardless of the cartridge used. Further, the recoil energy of the rifle will be equivalent- regardless of the cartridge used. But, what we cannot easily calculate- with high school physics- is the acceleration of the rifle to that final velocity. We do know, however, that the acceleration of the rifle will take exactly the same amount of time as it takes for the ejecta to traverse and exit the barrel. After measuring that number, we can divide the final rifle velocity by the total "acceleration time" to empirically derive the rate of acceleration.
The difference between the 338 weatherby mag and the 375 H&H (if there be an actual difference in recoil metrics) is the
acceleration of the rifle. The acceleration of the rifle is the missing variable in the Force equation.
Beyond that, "felt recoil" is very much a function of rifle fit/form, and the body composition of the shooter. My 400 lb uncle will have a very different felt recoil experience, as compared to my 160 lb frame- all else being equal.
And, adding a muzzle device that slows/redirects the expanding gasses as they exit the bore render the above equations invalid- or at least not easily applicable.