Black powder loads usually create MORE recoil than a smokeless load producing the same velocity. This was evident in a 12 bore SxS I worked with.
The black powder load produced what felt like twice the recoil of the smokeless load. So, the formulae is not transferable between the powder types.
I was shooting round ball with a 7 dram charge. The equivalent velocity in smokeless powder was a pussycat to shoot. The BP load just about turned
me around first shot. Braces, it only turned me slightly sideways. With smokeless loads, I was easily able to make fast right and lefts on a plate at 100
meters. With the BP loads, no way. The gun was light 7 1/2 pounds, which exacerbated the recoil of the black powder loads.