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
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
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
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.