Recoil does not enter into these two formulas. Recoil is based on the weight of the total charge (including powder, wads & shot) & the velocity of the load against the weight of the gun. It does not always even mean a higher Chamber pressure, Chamber pressure is controlled to a large extent by the burning rate of the powder.
Remember, it is absolutely necessary to look at the total pressure curve. To push the same shot load to the same velocity from a smaller bore takes a "Total" pressure that is higher in proportion to the square of their bore diameters. This follows all well known Scientific Principals.
The main point of this post is that I have fumed for a few weeks over an attempt to make me look like an Ignorant Hill-Billy who did not know what I was talking about when I said all was not equal when firing the same shot load from two different sizes of bores, with the formula F = MA cited to prove it. Well F = MA is a correct formula BUT is not the whole story by any means. The F = PA formula is equally Correct & Scientific & shows how that force is obtained in the different bores.
The weight of the shot per square inch to be moved, coupled with higher pressure, shows why deformation is more likely the longer the shot charge is in the bore.
