Originally Posted by
yappstar
You asked....
OK, if HP = RPM x TORQUE ÷ 5252, then where does the 5252 come from?
By definition, POWER = FORCE x DISTANCE ÷ TIME
Using an example above (not displayed here on PF), where a constant tangential force of 100 pounds was applied to the 12" handle rotating at 2000 RPM, we know the force involved, so to calculate power, we need the distance the handle travels per unit time, expressed as:
Power = 100 pounds x distance per minute
OK, how far does the crank handle move in one minute? First, determine the distance it moves in one revolution:
Distance per revolution = 2 x π x radius
Distance per revolution. = 2 x 3.1416 x 1 ft = 6.283 ft.
Now we know how far the crank moves in one revolution. How far does the crank move in one minute?
Distance per min. = 6.283 ft .per rev. x 2000 rev. per min. = 12,566 feet per minute
Now we know enough to calculate the power, defined as:
POWER = FORCE x DISTANCE ÷ TIME
so
Power = 100 lb x 12,566 ft. per minute = 1,256,600 ft-lb per minute
Great, but how about horsepower? Remember that one horsepower is defined as 33000 foot-pounds of work per minute. Therefore HP = POWER (ft-lb per min) ÷ 33,000. We have already calculated that the power being applied to the crank-wheel above is 1,256,600 ft-lb per minute.
How many HP is that?
HP = (1,256,600 ÷ 33,000) = 38.1 HP.
Now we combine some stuff we already know to produce the magic 5252. We already know that:
TORQUE = FORCE x RADIUS.
If we divide both sides of that equation by RADIUS, we get:
(a) FORCE = TORQUE ÷ RADIUS
Now, if distance per revolution = RADIUS x 2 x π, then
(b) distance per minute = RADIUS x 2 x π x RPM
We already know
(c) POWER = FORCE x DISTANCE per minute
So if you substitute the equivalent for force from equation (a) and distance per minute from equation (b) into equation (c), we get:
POWER = (TORQUE ÷ RADIUS) x (RPM x RADIUS x 2 x π)
Dividing both sides by 33,000 to find HP:
HP = TORQUE ÷ RADIUS x RPM x RADIUS x 2 x π ÷ 33,000
By reducing, we get
HP = TORQUE x RPM x 6.28 ÷ 33,000
Since
33,000 ÷ 6.2832 = 5252
Therefore
HP = TORQUE x RPM ÷ 5252
Note that at 5252 RPM, torque and HP are equal. At any RPM below 5252, the value of torque is always greater than the value of HP; Above 5252 RPM, the value of torque is always less than the value of HP.
I hope that makes some sense.