How do you convert engine torque to horsepower?
I once met an engineering student of Naval Institute of Technology (that’s how I assess his “porma”) during one of my trips to the my beloved island. He was driving a modified Honda XRM 110. We had a chat and as promised, here’s the what I know about the above-mentioned topic.
Have you ever looked at the specs of an engine in a magazine and seen something like "this engine makes 300 pound-feet of torque at 4,000 RPM," and wondered how much power that was? How much horsepower are we talking about here? You can calculate how many foot-pounds of horsepower this engine produces using a common equation:
(Torque x Engine speed) / 5,252 = Horsepower
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."
Chances are you've heard about horsepower. Just about every car ad on TV mentions it, people talking about their cars bandy the word about and even most lawn mowers have a big sticker on them to tell you the horsepower rating.
But what is horsepower, and what does the horsepower rating mean in terms of performance? In this article, you'll learn exactly what horsepower is and how you can apply it to your everyday life.
The term horsepower was invented by the engineer James Watt. Watt lived from 1736 to 1819 and is most famous for his work on improving the performance of steam engines. We are also reminded of him every day when we talk about 60-watt light bulbs.
The story goes that Watt was working with ponies lifting coal at a coal mine, and he wanted a way to talk about the power available from one of these animals. He found that, on average, a mine pony could do 22,000 foot-pounds of work in a minute. He then increased that number by 50 percent and pegged the measurement of horsepower at 33,000 foot-pounds of work in one minute. It is that arbitrary unit of measure that has made its way down through the centuries and now appears on your car, your lawn mower, your chain saw and even in some cases your vacuum cleaner.
What horsepower means is this: In Watt's judgement, one horse can do 33,000 foot-pounds of work every minute. So, imagine a horse raising coal out of a coal mine as shown above. A horse exerting 1 horsepower can raise 330 pounds of coal 100 feet in a minute, or 33 pounds of coal 1,000 feet in one minute, or 1,000 pounds 33 feet in one minute. You can make up whatever combination of feet and pounds you like. As long as the product is 33,000 foot-pounds in one minute, you have a horsepower.
You can probably imagine that you would not want to load 33,000 pounds of coal in the bucket and ask the horse to move it 1 foot in a minute because the horse couldn't budge that big a load. You can probably also imagine that you would not want to put 1 pound of coal in the bucket and ask the horse to run 33,000 feet in one minute, since that translates into 375 miles per hour and horses can't run that fast. However, if you have read How a Block and Tackle Works, you know that with a block and tackle you can easily trade perceived weight for distance using an arrangement of pulleys. So you could create a block and tackle system that puts a comfortable amount of weight on the horse at a comfortable speed no matter how much weight is actually in the bucket.
Horsepower can be converted into other units as well. For example:
• 1 horsepower is equivalent to 746 watts. So if you took a 1-horsepower horse and put it on a treadmill, it could operate a generator producing a continuous 746 watts.
• 1 horsepower (over the course of an hour) is equivalent to 2,545 BTU (British thermal units). If you took that 746 watts and ran it through an electric heater for an hour, it would produce 2,545 BTU (where a BTU is the amount of energy needed to raise the temperature of 1 pound of water 1 degree F).
• One BTU is equal to 1,055 joules, or 252 gram-calories or 0.252 food Calories. Presumably, a horse producing 1 horsepower would burn 641 Calories in one hour if it were 100-percent efficient.
If you want to know the horsepower of an engine, you hook the engine up to a dynamometer. A dynamometer places a load on the engine and measures the amount of power that the engine can produce against the load.
You can get an idea of how a dynamometer works in the following way: Imagine that you turn on a car engine, put it in neutral and floor it. The engine would run so fast it would explode. That's no good, so on a dynamometer you apply a load to the floored engine and measure the load the engine can handle at different engine speeds. You might hook an engine to a dynamometer, floor it and use the dynamometer to apply enough of a load to the engine to keep it at, say, 7,000 rpm. You record how much load the engine can handle. Then you apply additional load to knock the engine speed down to 6,500 rpm and record the load there. Then you apply additional load to get it down to 6,000 rpm, and so on. You can do the same thing starting down at 500 or 1,000 rpm and working your way up. What dynamometers actually measure is torque (in pound-feet), and to convert torque to horsepower you simply multiply torque by rpm/5,252.
Imagine that you have a big socket wrench with a 2-foot-long handle on it, and you apply 50 pounds of force to that 2-foot handle. What you are doing is applying a torque, or turning force, of 100 pound-feet (50 pounds to a 2-foot-long handle) to the bolt. You could get the same 100 pound-feet of torque by applying 1 pound of force to the end of a 100-foot handle or 100 pounds of force to a 1-foot handle.
Similarly, if you attach a shaft to an engine, the engine can apply torque to the shaft. A dynamometer measures this torque. You can easily convert torque to horsepower by multiplying torque by rpm/5,252.
If you plot the horsepower versus the rpm values for the engine, what you end up with is a horsepower curve for the engine. A typical horsepower curve for a high-performance engine might look like this (this happens to be the curve for the 300-horsepower engine in the Mitsubishi 3000 twin-turbo):
What a graph like this points out is that any engine has a peak horsepower -- an rpm value at which the power available from the engine is at its maximum. An engine also has a peak torque at a specific rpm. You will often see this expressed in a brochure or a review in a magazine as "320 HP @ 6500 rpm, 290 lb-ft torque @ 5000 rpm" (the figures for the 1999 Shelby Series 1). When people say an engine has "lots of low-end torque," what they mean is that the peak torque occurs at a fairly low rpm value, like 2,000 or 3,000 rpm.
Another thing you can see from a car's horsepower curve is the place where the engine has maximum power. When you are trying to accelerate quickly, you want to try to keep the engine close to its maximum horsepower point on the curve. That is why you often downshift to accelerate -- by downshifting, you increase engine rpm, which typically moves you closer to the peak horsepower point on the curve. If you want to "launch" your car from a traffic light, you would typically rev the engine to get the engine right at its peak horsepower rpm and then release the clutch to dump maximum power to the tires.
Your explanation is basically right, however such theory are more explained well in any Internal Combustion Engine text books, assuming that lad is a Mechanical Engineering Student.
Last edited by Jeff; 10-24-2007 at 01:52 PM.
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