Here's yet another permutation of winch application...Gringletaube, please weigh in here. I'd been trusting the formula you cited but not sure what it's based on, so maybe that's the problem.
I'm looking at repurposing a winch taken from a scrapped 5-ton, by using it in a stationary configuration to haul stuff up a steep slope. In my case, the winch would be adapted to be driven by a variable-speed AC motor (really a 3-phase motor driven by a VFD, for those who want to know). So I'm looking to determine my line-pull with one possible motor candidate, which happens to be a 3HP/1750RPM model.
Reorganizing your formula to solve for torque:
Torque = (HP x 5252)/RPM
The HP is just 3 in this case, from my motor ID plate.
RPM (at drum, as per your example) would, at design RPM of the motor, be 1750/23 = 76RPM. (but note that RPM can go down to as low as zero, using the VFD, as well as maybe double the 1750 ID-plate rating, though I'd not do that for real).
Thus, at my AC motor's design RPM, I'd get a torque of (3 x 5252)/76 = 207 ft-lbs. So at the full (12") drum condition, I'd get only 207lbs of line pull? Seems intuitively wrong from a 3HP motor.
But playing with that version of the formula a little more, say I reduced the motor's RPM using the VFD (which will still give something close to rated HP because of the VFD electronics) - say I dropped the RPM by half. Per the formula, that'd mean I'd get TWICE the line-pull? Nah...can't be right. And of course, as I drop the RPM closer to zero, the line-pull would blow up to something astronomical.
I must be mis-using the formula - let me know what's up with that. Seems like it's only appropriate to use it to calculate the input HP vs any other variable, but that's not how formulas are supposed to work...
Thanks - Dave