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BRIDGES

A COMMENTARY BY DOUG MEYER

Monday February 5th, 2007
Torque - The question you didn't ask
I've been seeing quite a bit of discussion about torque and horsepower in the Bikeland ZX-12 and 14 forums lately. It seems to me that there are some basic misconceptions on this topic. Maybe I can help a little. Let's start with a question- "Why do the horsepower and torque curves of an engine always cross at 5252 RPM." A good question, but maybe one you've never asked yourself, based on a fact that you may not have been aware of. But it is a truth. If you plot the horsepower and torque curves of any engine, the curves will always cross at 5252 rpm. Assuming, of course that the engine will reach 5252 rpm, and assuming that the curves are plotted on the same X/Y scale. Unfortunately, in order to answer this one I'm going to have to get into a little math. I'm a card carrying "math a-phobe" and I hate this stuff as much as you (probably more) but I think I can make it relatively painless..

I was doing a little reading the other night preparing to write this column about the relationship between horsepower and torque and as I looked at a copy of "THE INTERNAL COMBUSTION ENGINE IN THEORY AND PRACTICE" by Charles F. Taylor, I was struck by what little reference there was to the topic of "horsepower". Horsepower, after all, is what we all apparently seek. We all want to know how much we can get, how much the other guy gets, and how can we get more! How can this most scholarly journal of engine design spend so few pages on such an important subject? The answer is that horsepower really isn't what the engine produces. It produces torque. Torque is what you feel. Torque is what turns the wheels. Torque is what lifts the front end in those long wonderful wheelies and torque is what engine builders really want to find when they design, fiddle and adjust. Horsepower is a measure of what you can do with that torque. Horsepower is the result of a calculation that takes the measured torque of an engine multiplied by time. Torque is a measure of force and horsepower is a measure of work. Work is what the force accomplishes as it is applied over time and distance. Torque is, by definition, the product of a force applied in a rotational motion or twisting force. Remember, there need not be motion for a force to exist. A good example of this is the torque exerted when you try and loosen a very tight nut. As you are pulling on the wrench you are exerting a force, but not until the nut moves has this torque resulted in work. If the wrench is one foot long and you are exerting a force of 50 pounds on the end, you are exerting 50 pound/feet of torque on the nut. The distance from the center to the point where the force is applied is called the moment arm. Now, visualize an engine with a flywheel whose diameter is one foot, and on this flywheel you hang a one-pound weight from the circumference of the flywheel. Then we arrange for this engine to make one power producing stroke from this position and when this happens, the engine produces sufficient force to lift this one-pound weight one foot. We would have seen a force of one foot/pound of work done by the crankshaft. But even though this force might have been applied, it was only when the weight moved (an event which took some amount of time) was work performed, and only then was the measure we call "horsepower" created. Horsepower was defined in the 17th century by James Watt (of steam engine fame) as the amount of work that one horse can (theoretically) produce. His definition of one horsepower was and is the amount of power necessary to lift 33,000 pounds one foot in one minute. He apparently observed that a horse could exert a pull of 150 pounds while moving at 2 1/2 miles per hour. This works out to 33,000 foot pounds per minute (550 ft/lb. per second). I don't know how he got the horse to do that, but that's what he decided to call it. In case you're curious, one horsepower is also 745 "Watts" of electrical energy

To determine the measure of horsepower produced by internal combustion engines the standard calculation is Torque x RPM divided by 5252. Torque is the force, RPM is the amount of time spent applying the force (revs PER MINUTE). Measured torque times RPM only gives force applied over time though, not "horsepower". To get horsepower a further calculation is necessary, one that incorporates the distance and the 5252 is the distance factor.

Let's go back to the flywheel. When the flywheel turns, it produces torque through its' entire revolution. Now, order to measure this force we have to have it act on something at some distance (radius) from the center of its rotation (it doesn't matter where). The moment arm is this radius and of course the time is the RPM. So, the work done (horsepower) is the product of the force (foot/lb.) times the distance traveled in one revolution which is the circumference of the circle (whose radius has become the length of the arm), times the number of times per minute this distance is traveled (RPM). This is convenient, because Watt's horsepower was determined to be 33,000 foot-pounds per minute. I hate to do this, but here I have to resort to showing the actual math. I can't think of any other way. It looks like this:

Force X Circumference X RPM
Horsepower= 33,000

You might remember from high school that the circumference of a circle is computed by the formula 2 Pi times the radius. You can then simplify the above by dividing both the top and bottom by 2 Pi (God help me, I've become my eighth grade math teacher!) and because 33,000 divided by 6.2832 = 5252, it then looks like this:


Force X Radius X RPM
Horsepower= 5252

Or: Torque x RPM
5252

At 5252 RPM, this number appears both above and below the dividing line. Because of this, 5252 rpm is where the horsepower and torque curves will always cross. (You have 5252 (rpm) divided by 5252 (foot-pounds per minute) which is a number (5252) divided by itself which equals 1. And since 1 times any number is the same number, at 5252 RPM all you have left is Horsepower = Torque.

That's not very exiting unfortunately, since the answer to the question has less to do with engines than grade school math.

The term brake horsepower or BHP comes from the device that was developed to measure horsepower, the Prony Brake. The Prony brake was predecessor to modern dynamometers that absorbed the power output of an engine and directed that output to a point that it could be measured. A band of friction material was wrapped around the rotating output of an engine. This band was then tightened as the throttle was opened and a specific RPM was maintained. At the point that the throttle was fully open and any further tightening of the band would slow the engine down, maximum power was being developed. The band had a beam attached to it that acted on a scale. The length of the beam was the arm and the scale measured the force. The resulting readout on the scale was the indicated torque. The above described calculations then gave indicated BHP.

If an engine were to run at a constant RPM, and it had been designed to run ONLY at that rpm, to produce it's maximum twisting force (torque) at that rpm, that rpm would then yield the maximum (and only) horsepower of the engine. Spin it faster and the power production would cease, spin it slower and the power would also cease. But, in the real world engines are designed to run through a range of speeds, to accelerate from low speeds to higher speeds.

Because they are designed to operate through a range, they necessarily work better at some central "band" of rpm. This is the region of "best torque" and the highest point is called "peak torque". As the engine is operated at an rpm less or more than it's optimum point of torque production, the horsepower will vary. This is primarily due to changes in "volumetric efficiency" or the tendency for the airflow into the cylinder to vary with RPM and to be best in a particular range. If the torque was constant and the rpm was increased, the horsepower would continue to increase. But there comes a point at which the increase in the rpm can't make up for the decrease in the torque due to the lessening of the engine's efficiency (it's moving away from the point at which it "works" best-peak torque). The point at which this happens is "peak power". Keep increasing the rpm and horsepower falls off because the torque is falling. Remember, the power is the result of torque times the rpm. If there is no torque, all the rpm in the world won't give you any power. This is why one of the most sought after characteristics of an engine is a broad torque curve. More torque kept higher in the rpm range gives more horsepower. So, what we're actually saying when we say an engine has a lot of horsepower is "It produces a lot of torque at a high rpm". The horsepower number is really just a way of quantifying this with one number. Having said all that, I still like the idea of horsepower. We learn from the time we're little- big numbers are better, and as far as I'm concerned, when it comes to horsepower you can never have too big a number. Next column, I'm going to talk about the relationship between stroke length and torque. I bet it is NOT what you think it is.



Posted by Doug @ 13:57  -  Permalink  -  4 Comments  -  0 Trackbacks

Comments

“I’ve been seeing quite a bit of discussion about torque and horsepower … It seems to me that there are some basic misconceptions on this topic. Maybe I can help a little.”

People who don’t really understand this stuff always begin their articles this way.

“Let’s start with a question- “Why do the horsepower and torque curves of an engine always cross at 5252 RPM.” … If you plot the horsepower and torque curves of any engine, the curves will always cross at 5252 rpm.”

Let’s start by getting one thing straight. “Horsepower” is not a physical entity. It is a unit of measure used to represent power. What you said isn’t true. If I represent torque in something other than ft-lb, the engine speed where torque and power take on the same numerical value, will not be 5252 rpm. That value is merely an artifact of using English units of measure for torque and power.

“I was doing a little reading the other night preparing to write this column about the relationship between horsepower and torque and as I looked at a copy of “THE INTERNAL COMBUSTION ENGINE IN THEORY AND PRACTICE” by Charles F. Taylor, I was struck by what little reference there was to the topic of “horsepower”.”

That’s because horsepower is merely a unit of measure. Maybe you should have looked up the relationship between torque and power instead.

“Horsepower, after all, is what we all apparently seek. We all want to know how much we can get, how much the other guy gets, and how can we get more! How can this most scholarly journal of engine design spend so few pages on such an important subject? The answer is that horsepower really isn’t what the engine produces. It produces torque. Torque is what you feel. Torque is what turns the wheels. Torque is what lifts the front end in those long wonderful wheelies and torque is what engine builders really want to find when they design, fiddle and adjust. Horsepower is a measure of what you can do with that torque. Horsepower is the result of a calculation that takes the measured torque of an engine multiplied by time.”

WRONG! WRONG! WRONG! WRONG! WRONG! This is utter nonsense. There does not exist any objective, meaningful, rational basis for claiming that torque is what the engine produces, as opposed to power. Claims of this sort are utter nonsense, and exist outside of the orthodoxy of physical science. The orthodoxy of physical science cares only about notions that can be expressed analytically and verified experimentally. Any notion that doesn’t satisfy that criteria is just prattle. You cannot devise an experiment to prove that an engine produces torque instead of power! What you wrote here is utter crap. Engine torque tells you how much work the engine performs over any specific interval of crankshaft rotation. Acceleration at any time is proportional at any time to the instantaneous rate at which work is being performed, which rate may be deduced from the product of engine torque and engine speed. Wheel torque, at a given wheel speed, is proportional to power, and depends just as much on engine speed as it depends on engine torque.


“Torque is, by definition, the product of a force applied in a rotational motion or twisting force.”

That is ridiculous.

“… Then we arrange for this engine to make one power producing stroke from this position and when this happens, the engine produces sufficient force to lift this one-pound weight one foot.”

It does not make sense to talk of the force sufficient to move an object a specific distance.

“To determine the measure of horsepower produced by internal combustion engines the standard calculation is Torque x RPM divided by 5252. Torque is the force, RPM is the amount of time spent applying the force (revs PER MINUTE). Measured torque times RPM only gives force applied over time though, not “horsepower”. To get horsepower a further calculation is necessary, one that incorporates the distance and the 5252 is the distance factor.”

THIS IS UTTER NONSENSE! RPM is not a measure of time. RPM is a measure of the rate at with angular distance is covered, i.e., a measure of angular distance divided by time. Torque multiplied by engine speed does in fact yield the power, just not in units of horsepower. The additional operation that you have to perform only performs a change of unit of measure. To say that that is needed in order to incorporate distance, and that 5252 is a distance factor, is preposterous. I have never heard such nonsense in my entire life.

“The moment arm is this radius and of course the time is the RPM.”

Time is the RPM? What planet did you come from?

“So, the work done (horsepower) is the product of the force (foot/lb.) times the distance traveled in one revolution which is the circumference of the circle (whose radius has become the length of the arm), times the number of times per minute this distance is traveled (RPM).”

NO! NO! NO! Power is not the work done! Power is the rate at which work is being done at some instant in time! If you multiply torque and angular distance, you get work, and if you multiply torque and angular velocity, you get power! You’ve turned the whole thing into an incoherent mess!

“Force X Circumference X RPM
Horsepower= 33,000”

Your attempt to use equations to explain this is offensive to me! You are a clueless boob! What possessed you to do this?

“That’s not very exiting unfortunately, since the answer to the question has less to do with engines than grade school math.”

NO, NO, NO! You boob! IT HAS ONLY TO DO WITH THE FACT THAT WHEN YOU USE ENGLISH UNITS OF MEASURE, YOU END UP MULTIPLYING POWER MEASURED IN FT-LB/MIN BY 33,000 AND THEN DIVIDING BY TWICE PI IN ORDER TO CONVERT IT TO UNITS OF HORSEPOWER, AND 33,000 DIVIDED BY TWICE PI HAPPENS TO BE APPROXIMATELY 5252.

“Because they are designed to operate through a range, they necessarily work better at some central “band” of rpm. This is the region of “best torque” and the highest point is called “peak torque”.”

Good God Almighty! If you want to maximize acceleration, you have to operate the engine at the engine speed that yields the greatest power, not the greatest torque!

“So, what we’re actually saying when we say an engine has a lot of horsepower is “It produces a lot of torque at a high rpm”. The horsepower number is really just a way of quantifying this with one number.”

That is absurd. When we say that an engine produces a lot of power, what we are saying is that it is capable of performing work at a high instantaneous rate. At any time, acceleration and wheel torque are both proportional to the instantaneous rate at which the engine is performing work. Engine torque reveals the amount of work that the engine performs over any specific interval of crankshaft rotation, and you can deduce the instantaneous rate at which the engine is performing work, by multiplying the engine torque by the engine speed!

From kaiser soze on 2007-03-14 21:49  -  Permalink


Doug-- Great article! IDisregard Kaiser's comments. The guy obviously doesn't have any class.

I would appreciate an article dealing with gearing for Bonneville.... how to achieve maximum top speed through gearing. This should incorporate when the change the front spocket and when to change the rear one.

Thanks--
From flyboy on 2007-05-21 04:12  -  Permalink


Hmmm.... should I listen to Doug Meyer, mechanical expert, or kaizer who is a professional barber....

Mechanic or barber... tough call on this one! NOT!
From fish_antlers on 2007-06-18 16:24  -  Permalink


Barber or not, and subtle or not, kaiser makes some valid points.

In general terms:
Power = force x velocity or torque x angular velocity or work/time
Velocity = distance/time
Work = force x distance or torque x angular distance

I agree with Doug that a lot of discussions about torque and power assume that the two properties are independent and deal with low- and high-RPM, respectively (e.g., I'm building a torque motor for towing).

Mechanically speaking, it sound as though Doug and kaiser both have something to contribute.
From tcchin on 2007-07-13 16:23  -  Permalink


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THE AUTHOR


Doug Meyer has been working with race engines professionally and as a hobby for the past 45 years. He has built engines for everything from dragbikes and cars to outboard race boats, from the famous Can-Am sports cars and an F-1 car to motorcycle streamliners. He spent many years as a professional race team member and engine builder. Everything from nitrous to nitro, Doug's had his hands in it. He has set 16 Bonneville speed records...
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