This is the the most common formula:
HP = RPM x TORQUE ÷ 5252
(Copied from the Internet)
By definition,
POWER = FORCE x DISTANCE ÷ TIME (as explained above under the
POWER heading)
Using the example in Figure 2 above, 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
Swell, 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 we plug 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 greater than the value of HP; Above 5252 RPM, the value of torque is less than the value of HP.
Karsten
(If your eyesight is good enough to see it - sorry can't find a bigger version.)
How is the GF liking the night rides?
