Thank you for starting an interesting thread.
My father developed a formula for parabolic taper in a hydraulic cylinder for constant recoil force over a distance.
I figured out that recoil pads distribute recoil over time, area, and shape:
a) Time takes a thick pad to slow the rifle down slowly.
b) Area takes a tall wide pad.
c) Shape takes a pad soft enough to comply with the shoulder shape.
Pain threshold is ~ 20 psi on the skin. We need enough recoil pad to stay below 20 psi everywhere, and we can shoot all day.
The best I can do is the largest Limbsaver grind to fit, and then I do not grind it.
same image as below link