By definition, POWER = FORCE x DISTANCE ÷ TIME
Using the example where a constant tangential force of 100 pounds is applied to the rotating handle at a 6" radius, we know the force, so to calculate power, we need the distance the handle travels per unit time.
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 pi x radius
DISTANCE = 2 x 3.1416 x 1 ft = 6.283 ft. per revolution.
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 60 rev. per min.
= 377 feet per minute
Now we know enough to calculate the power:
POWER = FORCE x DISTANCE ÷ TIME
so
Power = 100 lb. x 377 ft. per minute
or
Power = 100 x 377 = 37,700 ft-lb per minute
You already know that one HORSEPOWER is defined as 33000 foot-pounds of work per minute. Therefore,
HP = POWER (ft-lb per min) ÷ 33,000
So the power being applied to the crank-wheel above is 37,700 ft-lb per minute, or 1.14 HP (37,700 ÷ 33,000).
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 by RADIUS, we get:
FORCE = TORQUE ÷ RADIUS (a)
Now, if DISTANCE per revolution = RADIUS x 2 x pi
then DISTANCE per minute = RADIUS x 2 x pi x RPM (b)
We already know POWER = FORCE x DISTANCE per minute (c)
so if we plug the equivalent for FORCE from (a) and distance per minute from (b) into (c), we get:
POWER = (TORQUE ÷ RADIUS) x (RPM x RADIUS x 2 x pi)
Dividing both sides by 33,000 to find HP,
HP = TORQUE ÷ RADIUS x RPM x RADIUS x 2 x pi ÷ 33,000
By reducing, we get
HP = TORQUE x RPM x 6.28 ÷ 33,000
Since
6.2832 ÷ 33000 = 1 ÷ 5252
thus
HP = TORQUE x RPM ÷ 5252
wheres my point??!!