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post #1 of 3 (permalink) Old 07-19-2005, 04:56 AM Thread Starter
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Horsepower questions

The equation to find horsepower is (torque x rpm)/ 5252. Where at 5252 rpm the lines of the torque and hp are equal. Where did the number 5252 come from and who decided that this number was the one to use?
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post #2 of 3 (permalink) Old 07-19-2005, 07:12 AM
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Good question, I think this is scientifically referred to as a "fudge factor".
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post #3 of 3 (permalink) Old 07-19-2005, 08:18 AM
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The following is from howstuffworks.com



The engine that makes 300 pound-feet of torque at 4,000 RPM produces [(300 x 4,000) / 5,252] 228 horsepower at 4,000 RPM. But where does the number 5,252 come from?

To get from pound-feet of torque to horsepower, you need to go through a few conversions. The number 5,252 is the result of lumping several different conversion factors together into one number.

First, 1 horsepower is defined as 550 foot-pounds per second (read How Horsepower Works to find out how they got that number). The units of torque are pound-feet. So to get from torque to horsepower, you need the "per second" term. You get that by multiplying the torque by the engine speed.

But engine speed is normally referred to in revolutions per minute (RPM). Since we want a "per second," we need to convert RPMs to "something per second." The seconds are easy -- we just divide by 60 to get from minutes to seconds. Now what we need is a dimensionless unit for revolutions: a radian. A radian is actually a ratio of the length of an arc divided by the length of a radius, so the units of length cancel out and you're left with a dimensionless measure.

You can think of a revolution as a measurement of an angle. One revolution is 360 degrees of a circle. Since the circumference of a circle is (2 x pi x radius), there are 2-pi radians in a revolution. To convert revolutions per minute to radians per second, you multiply RPM by (2-pi/60), which equals 0.10472 radians per second. This gives us the "per second" we need to calculate horsepower.

Let's put this all together. We need to get to horsepower, which is 550 foot-pounds per second, using torque (pound-feet) and engine speed (RPM). If we divide the 550 foot-pounds by the 0.10472 radians per second (engine speed), we get 550/0.10472, which equals 5,252.

So if you multiply torque (in pound-feet) by engine speed (in RPM) and divide the product by 5,252, RPM is converted to "radians per second" and you can get from torque to horsepower -- from "pound-feet" to "foot-pounds per second."
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