Many here are aware of Neil Winston's work, which includes the only to my knowledge single blind sorta controlled study regarding the ability to perceive fast vs. slow powder recoil curve www.claytargettesting.com



As a victim of a State of Missouri public education, here's the non-deep thinking version.

1.Recoil is easily calculated: http://www.handloads.com/calc/recoil.asp

as is Recoil Velocity http://www.loadammo.com/Topics/August01.htm

2. Perceived or 'felt' recoil is almost impossible to define. Good science is reproducible and measurable and there is no 'pain-o-meter' because pain is entirely subjective. One can measure the difference in perceived pain OF an individual but not BETWEEN individuals. One person may rate the recoil of the same shell and gun as a 7 and the next a 4.
And perceived pain is highly variable and dependent on multiple external and internal physiologic factors ie. pain seems worse at night when there are fewer external stimuli. One's assessment of recoil when shooting a record Kudu vs.sighting in the .375 is entirely different. 'Felt' recoil may differ based on too much coffee that morning or too much alcohol the night before, fatigue, sleep deprivation, stress, or anxiety. And stock design/gun fit/muzzle jump contribute significantly.

But a smart guy is working on understanding, or at least quantifying, 'felt recoil'.
https://www.researchgate.net/publication/223811001_Measuring_felt_recoil_of_sporting_arms

And breaking news from 1897 wink

Sporting Guns and Gunpowders: Comprising a Selection from Reports of Experiments, and Other Articles Published in the “Field” Newspaper, Relative to Firearms and Explosives, Volumes 1-2, 1897
https://books.google.com/books?id=inQCAAAAYAAJ&pg=PA197
“Some Notes on Recoil”

https://books.google.com/books?id=inQCAAAAYAAJ&pg=PA254
It is a fundamental principle that action and re-action are equal and opposite; therefore, at the moment when the shot leaves the muzzle of the gun, the momentum (or weight x velocity) of the shot will be equal to the momentum of the gun. This is strictly true from the tune the shot first commences to move until it finally leaves the muzzle, but only up to that instant.
On no subject in connection with gunnery are there more erroneous ideas—superstitions one might almost call them—than on recoil. Many men will tell you that certain guns, with precisely the same ammunition, will give much more recoil than other guns of exactly the same weight. It will generally be found that these men are either novices in the art of shooting, or else they do not hold their guns properly up to the shoulder. Once and for all, it may be laid down that the recoil of guns, rifles, and arms of every description, from the smallest pistol to the heaviest piece of ordnance, proceeds from the same causes and depends upon the same elements.

https://books.google.com/books?id=inQCAAAAYAAJ&pg=PA266
“judging of the weight and nature of recoil by the feeling alone one is apt to be misled; for according to the state of bodily health at the time, so will be the sensation produced by a normal recoil…”