Does anyone know of a tabulation (spreadsheet or hardcopy) of the actual breech pressure and corresponding 'backward force' (kick) for long guns? Or a formula for calculating same?
There is no single formual for calculating pressure or recoil of black powder firearms that I am aware of. There are programs that can help, maybe, such as quick load, but have shown to produce errors, sometimes quite dramatically - in modern ctgs. when dealing with pressures. How they work with BP, I have no experience or idea.
The recoil formulas given in most loading manuals which utilize bullet weight, weight of rifle and the weight of propelling charge, give dramatic errors when used with black powder rifles, and even more so with black powder muzzleloaders. This is mostly due to the difference in energy per grain produced between BP charges compared to smokeless powder charges, along with the differences between individual rifles which can have a dramatic effect on the outcome.
For example, the loss of pressure at the breech is a consideration not taken into account. It is different, literally for every gun - different pressue seating the ball itself, on the powder charge will change the ballistics. Different patch thickness also makes a difference. Use of a wad makes a difference. A different nipple hole and shape, different vent diameter & shape will make a difference in ballistics, internal and external. What difference is made just by the different shape of the inner chamber in a vent, vs. just a drilled hole of the same shape - length of end-hole will have a difference. There are too many variables in our rifles, so I sincerely doubt a 'pat' formula would work well. Changing any of these can be shown on a simple chronograph to make a difference, thus the pressure and recoil will also be different.
On top of all of this, there are the different makes of black powder and granulations which will also all give different results to each other. Unlike modern ctg. guns, there are too many variations to be workable - maybe.