The word horsepower was introduced
by James Watt, the inventor of the steam engine in about
1775. Watt learned that "a strong horse could lift
150 pounds a height of 220 feet in 1 minute." One horsepower
is also commonly expressed as 550 pounds one foot in one
second or 33,000 pounds one foot in one minute. These are
just different ways of saying the same thing. Notice these
definitions include force (pounds), distance (feet), and
time, (minute, second). A horse could hold weight in a static
position but this would not be considered horsepower, it
would be similar to what we call torque. Adding time and
distance to a static force (or to torque) results in horsepower.
RPM, revolutions (distance) per minute (time), is today's
equivalent of time and distance. Back to horses; imagine
a horse raising coal out of a coal mine. A horse exerting
one horsepower could raise 550 pounds of coal one foot every
second.
Here is an example of another way horsepower could be directly
measured. Say you have a horse hitched to a plow. In the
hitch is a spring scale (like a fish scale). The horse pulls
the plow one foot every second and you see 550 pounds on
the scale. That horse would be generating one horsepower.
We see horsepower can be directly measured. However there
is a problem directly measuring horsepower of modern day
internal combustion engines because they produce rotary
motion not linear motion, and unless the engine is geared
down, the speed at which they do work (time and distance
or RPM) is too great for practical direct measurement of
horsepower. It seems logical then that the solution was
to directly measure torque (rotational force eventually
expressed in pounds at one foot radius) and RPM (time and
distance, i.e. distance in circumference at the one foot
radius) and from these calculate horsepower. Torque and
RPM are easily measured directly. Early dynamometers used
a brake device to load the engine. A torque arm was attached
to this brake's stator. The brake's rotor was coupled to
the engine's crankshaft. A spring scale or other measuring
device connected the torque arm to the stationary fixture
holding the engine and brake. During a test the brake's
application loaded the engine. Torque and engine rpm were
observed and recorded.
On modern day dynamometers horsepower is a calculated value.
It's important to remember the dyno measures torque and
rpm and then from these calculates horsepower. On the dyno
it takes more water flow to the water brake to increase
the load on the engine being tested. As the test engine's
torque rises more water flow is needed. As the test engine's
torque drops less water flow is needed. The dyno's water
brake does not respond to Horsepower. Major adjustments
to water flow are needed as an engine crosses its torque
peak but none are needed as it crosses its horsepower peak.
In other words the water flow to the brake during a dyno
test follows the engines torque curve and not its horsepower
curve. Torque is what twists the tire, prop, or pump. Horsepower
helps us understand an amount or quantity of torque. (Torque
+ time and distance)
Now, if we are measuring torque and RPM how can we calculate
horsepower? Where does the equation HP=TORQUE * RPM / 5252
come from? We will use Watts’s observation of one horsepower
as 150 pounds, 220 feet in one minute. First we need to
express 150 pounds of force as foot pounds torque.
• Pretend the force of 150 pounds is "applied"
tangentially to a one foot radius circle. This would be
150 foot pounds torque.
Next we need to express 220 feet in one minute as RPM.
• The circumference of a one foot radius circle is 6.283186
feet. ft. (Pi x diameter 3.141593 * 2 feet)
• The distance of 220 feet, divided by 6.283185 feet, gives
us a RPM of 35.014.
We are then talking about 150 pounds of force (150 foot
pounds torque), 35 RPM, and one horsepower.
Constant (X) = 150 ft.lbs. * 35.014 RPM / 1hp
35.014 * 150 / 1 = 5252.1
5252 is the constant.
So then hp = torque * RPM / 5252
Here is another
way;
Remember we know 150 foot pounds and 35.014 RPM = one horsepower
1hp is to 150 ft.lbs. * 35.014 RPM as X hp is to observed
ft.lbs.torque * observed RPM
Example; We dyno test and observe 400 ft.lbs. torque at
5000 RPM
1 hp is to 150 ft.lbs. * 35.014 RPM as X hp is to 400 ft.lbs.
* 5000 RPM
When we cross multiply X hp * (150 ft.lbs. * 35.014 RPM)
= 1hp * (400 ft.lbs. * 5000 RPM)
X hp * (5252 ft.lbs. RPM) = 1 hp * (2,000,000 ft.lbs. RPM)
Divide both sides by 5252 ft.lbs. RPM
X hp = 1 hp * 380.80
X hp = 380.80 hp
Horsepower = torque x rpm / 5252
Here's an interesting bit of trivia; below 5252 rpm any
engine's torque number will always be higher than its horsepower
number, and above 5252 rpm any engine's horsepower number
will always be higher than its torque number. At 5252 rpm
the horsepower and torque numbers will be exactly the same.
-Author unknown
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