A common equation used when analyzing car engines is Power=(Torque x RPM)/5252 w

Question

A common equation used when analyzing car engines is Power=(Torque x RPM)/5252 where power is measured in horsepower (hp), torque is measured in ft lbf and RPM is the rate at which the shaft spins. Derive this equation. In particular, justify the number 5252. Hint: for simplicity, imagine a one foot radius crankshaft being pushed with one pound of force. Then the torque on it is t=rF=1 ft lbf. Calculate the amount of work done by this pound of force traveling a distance of 2r. Supposing that this occurs once every minute, so that RPM=1 rev/min, you can calculate the power=work/time. Finally, convert from ft lbf to hp.

Explanation / Answer

Here ,

1 ft.lbf = 1.3558 N.m

1 hp = 745.7 w

1 rpm = 0.1591 rad/s

Now , as

Power = torque * angular speed

Power = (force * distance)/time

Power = (1 lb.2pi * 1 feet)/60

power = 1 lb.ft . RPM/(9.55)

converting power to hp

Power = 1 lb.ft . RPM/(9.55 * 745.7)

Power = 1 lb.ft . RPM/(9.55 * 745.7/1.3558)

Power = 1 lb.ft . RPM/5252

hence , we get the term 5252 in denominator

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