Horse-power is a certain specific rate of doing work, viz., 33,000 foot-pounds per minute. Hence, to find the horse-power that a shaft will transmit, we must first find the work done, and then relate it to the speed. Take, for example, the case of a pulley, the symbols being the same as before - namely, P = driving force at rim of pulley (lbs.); R = radius of pulley (inches); N = number of revolutions per minute; and H = horse-power. Then,
Work = fore© X distance = P X (2π RN) = H X 33,000 X 12; or, PR = 63,02511 / N. (54)
This is one of the most useful equations for calculations involving horse-power. By it the number of inch-pounds torsion for any horse-power can be at once ascertained.
It should be clearly noted, however, that in this equation the bending moment does not enter at all. Hence any shaft based in size on horse-power alone, is based on torsional moment alone, bendiug moment being entirely neglected. In many cases the bending moment is the controlling one as to limiting fiber stress introducing the element of speed as basis for assumption of a high or low working fiber stress.