We often hear the term horsepower as a measurement of power. Power is the rate at which work is done. Work is a force applied over a distance. Work lets us do things like lifting loads, moving objects and in general, just making things operate. You can do the same amount of work quickly or slowly. Whether you lift 50 pounds of sand 6 feet high a shovel-full at a time or you grab the entire 50 pound sack and lift it in 2 seconds to the 6 foot height, you are still doing exactly 300 foot-pounds of work. Since power is the rate at which work is done, the more time it takes to do the work the less power is being applied.

When the steam engine began to do the work of horses in the mines during the early 1800's, the mine owners began to ask how many horses an engine would replace. James Watt, who made steam engines, figured out a mathematical way to equate horses to engine power. So, the term horsepower was invented. Watt measured the capability of a big horse to pull a load and found it could pull at 150-pounds while walking at 2.5 miles per hour. This works out to 33,000 foot-pounds per minute, or 550 foot-pounds per second.

A device was then invented to measure an engine's horsepower. It is called a Prony brake.  It is attached with a pulley block system and spring balance to the rotating shaft of the engine to measure the output of the engine. The speed of the engine is also recorded and with this information we can calculate horsepower using this equation:

Horsepower = (Force ´ 2p ´ Radius ´ RPM) / 33,000

This equation can be simplified by dividing 2p into both terms, which will give you:

Horsepower = ( Force ´ Radius ´ RPM) / 5,250

Where

Force = the scale reading from the spring balance attached via the pulley block spring balance system to the engine shaft.

Radius = the distance from the center of the engine's shaft to the spring balance arm. It is called the radius or torque arm.

RPM = the engine speed in revolutions per minute.

A steam engine is connected to a Prony brake, and when tested and gives this data:

Scale reads 250 pounds
Radius arm is 3 feet
Speed in RPM is 1,000

What is this engine's horsepower?

Horsepower = (250 ´ 3 ´ 1,000) / 5,250 = 142.9 horsepower

A steam engine is rated at 200 horsepower. The radius arm on the Prony brake horsepower tester is 4 feet. The indicated force is 400 pounds. At what speed is the horsepower rating based upon (another way of saying it is---At what speed does the engine achieve its rated horsepower?)

Possible answers:

656 RPM
1,380 RPM
2,625 RPM

Bonus Information:

Force, work, and power can be expressed also in units other than pounds, foot-pounds, and horsepower. Scientists and engineers prefer metric units, and in scientific work, the unit of work is one joule per second. A joule is roughly 0.75 of one foot-pound. The name given to this one-joule-per-second unit is the watt, in honor of James Watt.

The term watt is most often applied to electricity, but in the big scheme of physics, energy is interchangeable. The watt is really a mechanical unit, though much smaller than one horsepower. One horsepower is the equivalent of 746 watts. So, you can use watts to calculate horsepower and vice-versa.