Watt's first steam engine was to move water out of mines, which previously had been done with draft horses turning pumps. So it was logical to relate the work his steam engine could do to the work a horse could do. The horse plodded around a circular path, pulling at right angle on a 12 foot lever projecting from a capstan at the center of the circle. The capstan, in turn, was geared to operate the pump. Watt estimated that the horse pulled with a force of 180 pounds. The circle it followed had a circumference of 2 times π times a radius of 12 feet or 75.4 feet. The horse could make 144 trips around the circle an hour; and 144 divided by 60 results in 2.4 trips per minute, for a speed of 2.4 times 75.4 feet or about 181 feet per minute. To convert the demonstration of the horse’s ability into measurable leverage, or what is known as torque, Watt multiplied 180 pounds times 181 feet per minute obtaining 32,580 pounds-feet per minute. He rounded that figure to 33,000 pounds-feet per minute or 33,000 divided by 60 which is 550 pounds-feet per second, which became the norm for one (1.0) horsepower. Many of his contemporaries doubted his comparison, not so much because of the math, but because they believed he was being too generous to the ability of the horse! His engine would do this work all day, while a horse under this kind of effort would last an hour or two at the most. Watt’s draft horse generated force around a circumference of a circle, due to the lever on the capstan. An engine does the opposite; it delivers force at the output end of the crankshaft. Imagine it turns a one-foot lever attached at right angles to the crankshaft. As the crank rotates, the free end of the lever will follow a circle with a one-foot radius. In order to convert the rotational force into horsepower, you need to know the distance the free end of the lever moves in one revolution. The answer of course is 2 times π times a radius of 1 feet or 6.28 feet. Therefore, the total distance the free end of the lever will go in one minute is 6.28 feet times the Revolutions per Minute or RPM of the engine. Multiplying the total torque (pounds-feet or foot-pounds) output of the engine by distance traveled by the free end of the lever in one minute, and divided by Watt’s pounds-feet per minute per horsepower number will yield horsepower: Horsepower = (6.28 x RPM x Torque) / 33,000

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