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An Explanation of Horsepower
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This specifically pertains to SAE (Society of Automotive Engineers) Horsepower, used in the United States. The principles still apply to metric horsepower used elsewhere, just the numbers are different.
What is horsepower? It is among the most misunderstood of concepts. In a famous quote that is often repeated, Enzo Ferrari once said, "Horsepower sells cars. Torque wins races." Dare I say... he is actually wrong.
From a physics standpoint an engine produces only two measurables that matter, torque and RPM (revolutions per minute).
A long time ago somebody determined that a horse can pull 33,000 lbs one foot per minute. It wasn't *exactly* 33,000 pounds, but close enough. It obviously depends on the horse, friction, and countless other variables, but for the purpose of a uniform unit of measure it is determined that 1 horsepower = the amount of work needed to move 33,000 pounds 1 foot per minute. Or....
HP = Weight (in pounds) x Speed (In fpm) ÷ 33,000
If you double the weight, or if you move the same amount of weight twice the distance, you double the horsepower.
66,000 x 1 ÷ 33,000 = 2 Horsepower
33,000 x 2 ÷ 33,000 = 2 Horsepower
So how does this translate to measuring horsepower in an engine? Like vanilla horsepower it's a calculated number, but there's no weight being moved a linear distance. In this case the torque being produced by the engine represent weight: 1 ft.lb of torque represents 1 pound of weight being moved. For speed it's a little more complicated. Each revolution is considered to be a linear distance equal to a 1 foot pulley moving in a complete circle. In simple terms, the circumference of a 2 foot diameter circle diameter: π x diameter = about 6.28 feet, so one revolution of your engine is considered to be traveling a distance of 6.28 feet. So at 3000 RPM the linear speed is 3000×6.28 feet per minute.
Ergo:
SAE HP = Torque x RPM (6.28) / 33,000
This can be simplified. What you do to one side of a fraction you can do to the other and it remains equal. Divide both sides by 6.28.
SAE HP = Torque x RPM ÷ 5252
Ever notice on a (non-metric) dyno horsepower and torque always cross at 5252 RPM? That's why.
You can only produce more horsepower by spinning the engine faster, or by increasing the torque.
Through gearing automobiles make trade offs between torque (acceleration) and speed, sacrificing one to get more of the other. That's why in first gear you accelerate the fastest but your top speed is the lowest, and the opposite is true for 6th gear.
An engine that produces a modest amount of torque but spins really fast has more speed to sacrifice and convert into wheel torque. It also can build up more speed before the driver must upshift, sacrificing torque to the wheels.