Horsepower is a unit of measurement that is commonly used to describe the power output
of mechanical equipment such as car engines, steam engines, and electric motors.
Power, in general, can be defined as the rate at which work is done, and it is typically
measured in watts, or joules of energy per second.
Take a 60-watt light bulb for instance, which requires 60 watts of power to operate.
The light bulb’s rate of energy consumption is 60 watts, which is to say that it will
use 60 joules of energy every second that it is turned on.
Just like the watt, horsepower also describes a rate of change of energy.
There are actually two common definitions of horsepower that are in use today, mechanical
horsepower (or imperial horsepower), and metric horsepower.
1 mechanical horsepower is equal to approximately 745.7 watts, while 1 metric horsepower is
equal to approximately 735.5 watts.
When somebody tells you how much horsepower their new sports car has, they are most likely
referring to mechanical horsepower, however the difference between mechanical horsepower
and metric horsepower is less than 2%.
The concept of horsepower was originally conceived in the early 1700’s as a way to measure
the power output of steam engines.
It became a useful marketing tool, as the horsepower of a new steam engine described
the number of draft horses that someone could replace by purchasing the new engine.
It was found that one draft horse could turn a mill wheel 144 times in one hour (or 2.4
times in one minute).
The wheel was 24 feet in diameter, and so the horse travelled about 181 feet every minute.
It was estimated that the horse could pull with a force of approximately180 lbs, and
so one horsepower was calculated as 32,572 lb-feet per minute.
This value was rounded up to 33,000 lb-feet per minute, which equates to 745.7 watts.
This was accepted as the definition of mechanical horsepower, and it is the same definition
that we use today.
So now we know what horsepower is and how we came to use it, but what if we wanted to
use a different animal to define a new unit of power?
Let’s take ducks for instance? Is it possible to measure the power output
of cars and other machines using ducks?
Well unfortunately it’s not really feasible to tie a whole bunch of ducks to a mill wheel
to see how fast they can spin it.
But what we can do instead is compare the rate of energy consumption of a duck to that
of a draft horse.
This will allow us to develop a relationship between duckpower and horsepower.
An animal’s rate of energy consumption is referred to as its metabolic rate, and in
the early 1930’s it was found that the metabolic rate of most animals is directly proportional
to the animal’s mass raised to the power of ¾.
This relationship was discovered by Max Kleiber's, and is known as Kleiber's law.
We can use Kleiber's law to convert horsepower to duckpower by taking the mass ratio of a
duck to a horse and raising it to the power of ¾.
Ducks typically have a mass between 1.6 and 3.5 lbs, and draft horses typically have a
mass between 1,400 and 2,000 lbs.
This gives an average mass ratio of 0.0015.
Raising this number to the power of ¾, we find that 1 duck-power is equal to approximately
0.00762 horsepower.
Or conversely, 1 horsepower is equal to approximately 131.2 duckpower.
This means that we can convert a known horsepower value to duckpower simply by multiplying the
value by 131.2.
For example, a 380-horsepower sports car will have a power output of about 50,000 duckpower.
This same concept can be used to define a unit of power using any other animal as well.
All you need to know is the average mass of the animal that you want to use.
For example, a male African bush elephant has an average mass of 13,228 lbs, and 1 elephant-power
can therefore be calculated as approximately 4.66 horsepower.
This means we can say that our 50,000 duckpower sports car from before also has a power output
of about 81.6 elephant-power. You can try these calculations for yourself,
and let us know what animal you would use for a new unit of power in the comments below.
Please send us a like if you enjoyed this video, and hit the subscribe button to stay
up to date with future content.