Horsepower and Torque Ė a Primer

 

There's been a certain amount of discussion, in this and other files, about the concepts of horsepower and torque, how they relate to each other, and how they apply in terms of automobile performance. I have observed that, although nearly everyone participating has a passion for automobiles, there is a huge variance in knowledge. It's clear that a bunch of folks have strong opinions (about this topic, and other things), but that has generally led to more heat than light, if you get my drift. This is meant to be a primer on the subject.

 

OK. Here's the deal, in moderately plain English.

 

Force, Work and Time

 

If you have a one-pound weight bolted to the floor, and try to lift it with one pound of force (or 10, or 50 pounds), you will have applied force and exerted energy, but no work will have been done. If you unbolt the weight, and apply a force sufficient to lift the weight one foot, then one foot-pound of work will have been done. If that event takes a minute to accomplish, then you will be doing work at the rate of one foot-pound per minute. If it takes one second to accomplish the task, then work will be done at the rate of 60 pound feet per minute, and so on.

 

In order to apply these measurements to automobiles and their performance (whether you're speaking of torque, horsepower, newton meters, watts, or any other terms), you need to address the three variables of force, work and time.

 

A while back, a gentleman by the name of Watt (the same gent who did all that neat stuff with steam engines) made some observations, and concluded that the average horse of the time could lift a 550 pound weight one foot in one second, thereby performing work at the rate of 550 pound feet per second, or 33,000 pound feet per minute. He then published those observations, and stated that 33,000 pound feet per minute of work was equivalent to the power of one horse, or, one horsepower.

 

Everybody else said okay.

 

For purposes of this discussion, we need to measure units of force from rotating objects such as crankshafts, so we'll use terms that define a twisting force, such as torque. A foot-pound of torque is the twisting force necessary to support a one-pound weight on a weightless horizontal bar, one foot from the fulcrum.

 

Now, it's important to understand that nobody on the planet ever actually measures horsepower from a running engine on a standard dynomometer. What we actually measure is torque, expressed in pound feet (in the U.S.), and then we calculate actual horsepower by converting the twisting force of torque into the work units of horsepower.

 

Visualize that one-pound weight we mentioned, one foot from the fulcrum on its weightless bar. If we rotate that weight for one full revolution against a one-pound resistance, we have moved it a total of 6.2832 feet (Pi * a two foot circle), and, incidentally, we have done 6.2832 pound feet of work.

 

Okay. Remember Watt? He said that 33,000 pound feet of work per minute was equivalent to one horsepower. If we divide the 6.2832 pound feet of work we've done per revolution of that weight into 33,000 pound feet, we come up with the fact that one foot pound of torque at 5252 rpm is equal to 33,000 pound feet per minute of work, and is the equivalent of one horsepower. If we only move that weight at the rate of 2626 rpm, it's the equivalent of 1/2 horsepower (16,500 pound feet per minute), and so on.

 

 

 

Therefore, the following formula applies for calculating horsepower from a torque measurement:

 

 

††††††††††††††††††††††††††††††† ††† Torque * RPM

††††††† Horsepower††††† =†††††† ------------

†††††††††††††††††††††††††††††††††††††††††††† 5252

 

 

This is not a debatable item. It's the way it's done. Period.

 

The Case for Torque

 

Now, what does all this mean in car land?

 

First of all, from a driver's perspective, torque, to use the vernacular, RULES. Any given car, in any given gear, will accelerate at a rate that exactly matches its torque curve (allowing for increased air and rolling resistance as speeds climb). Another way of saying this is that a car will accelerate hardest at its torque peak in any given gear, and will not accelerate as hard below that peak, or above it. Torque is the only thing that a driver feels, and horsepower is just sort of an esoteric measurement in that context. 300 pound feet of torque will accelerate you just as hard at 2000 rpm as it would if you were making that torque at 4000 rpm in the same gear, yet, per the formula, the horsepower would be *double* at 4000 rpm. Therefore, horsepower isn't particularly meaningful from a driver's perspective, and the two numbers only get friendly at 5252 rpm, where horsepower and torque always come out the same.

 

In contrast to a torque curve (and the matching push back into your seat), horsepower rises rapidly with rpm, especially when torque values are also climbing. Horsepower will continue to climb, however, until well past the torque peak, and will continue to rise as engine speed climbs, until the torque curve really begins to plummet, faster than engine rpm is rising. However, as I said, horsepower has nothing to do with what a driver feels.

 

You don't believe all this?

 

Fine. Take your non-turbo car (turbo lag muddles the results) to its torque peak in first gear, and punch it. Notice the belt in the back? Now take it to the power peak, and punch it. Notice that the belt in the back is a bit weaker? Okay. Now that we're all on the same wavelength (and I hope you didn't get a ticket or anything), we can go on.

 

The Case for Horsepower

 

So if torque is so all-fired important (and feels so good), why do we care about horsepower?

 

Because (to quote a friend), "Itís better to make torque at high rpm than at low rpm, because you can take advantage of gearing

 

For an extreme example of this, I'll leave car land for a moment, and describe a waterwheel I got to watch a while ago. This was a pretty massive wheel (built a couple of hundred years ago), rotating lazily on a shaft that was connected to the works inside a flour mill. Working some things out from what the people in the mill said, I was able to determine that the wheel typically generated about 2600(!) pound feet of torque. I had clocked its speed, and determined that it was rotating at about 12 rpm. If we hooked that wheel to, say, the drive wheels of a car, that car would go from zero to twelve rpm in a flash, and the waterwheel would hardly notice.

 

On the other hand, twelve rpm of the drive wheels is around one mile per hour for the average car, and, in order to go faster, we'd need to gear it up. If you remember your junior high school science class and the topic of simple machines, you'll remember that to gear something up or down gives you linear increases in speed with linear decreases in force, or vice versa. To get to 60 miles per hour would require gearing the output from the wheel up by 60 times, enough so that it would be effectively making a little over 43 pound feet of torque at the output (one sixtieth of the wheel's direct torque). This is not only a relatively small amount; it's less than what the average car needs in order to actually get to 60. Applying the conversion formula gives us the facts on this. Twelve times twenty six hundred, over five thousand two hundred fifty two gives us:

 

6 HP.

 

OOPS. Now we see the rest of the story. While it's clearly true that the water wheel can exert a bunch of force, its power (ability to do work over time) is severely limited.

 

At the Drag Strip

 

Now back to car land, and some examples of how horsepower makes a major difference in how fast a car can accelerate, in spite of what torque on your backside tells you.

 

A very good example would be to compare the LT-1 Corvette (built from 1992 through 1996) with the last of the L98 Vettes, built in 1991. Figures as follows:

 

††††††† Engine††††††††† ††††††† Peak HP @ RPM†† ††††††† Peak Torque @ RPM

††††††† ---------†††††††††† ††††††† -----------------------†† ††††††††† -----------------------------

††††††††† L98†††††††††††††††††† 250 @ 4000†††††††††††††††††† 340 @ 3200

††††††††† LT-1††††††††††††††††††† 300 @ 5000†††††††††††††††††† 340 @ 3600

 

The cars are essentially identical (drive trains, tires, etc.) except for the engine change, so it's an excellent comparison.

 

From a driverís perspective, each car will push you back in the seat (the fun factor) with the same authority - at least at or near peak torque in each gear. One will tend to feel about as fast as the other to the driver, but the LT-1 will actually be significantly faster than the L98, even though it won't pull any harder. If we mess about with the formula, we can begin to discover exactly why the LT-1 is faster. Here's another slice at that torque and horsepower calculation:

 

†††††††††††††††††††††††††††††††† Horsepower * 5252

††††††††††††††† Torque=†††††† -----------------

†††††††††††††††††††††††††††††††††††††††††† RPM

 

Plugging some numbers in, we can see that the L98 is making 328 pound feet of torque at its power peak (250 hp @ 4000). We can also infer that it cannot be making any more than 263 pound feet of torque at 5000 rpm, or it would be making more than 250 hp at that engine speed, and would be so rated. In actuality, the L98 is probably making no more than around 210 pound feet or so at 5000 rpm, and anybody who owns one would shift it at around 46-4700 rpm, because more torque is available at the drive wheels in the next gear at that point. On the other hand, the LT-1 is fairly happy making 315 pound feet at 5000 rpm (300 hp times 5252, over 5000), and is happy right up to its mid 5s red line.

 

So, in a drag race, the cars would launch more or less together. The L98 might have a slight advantage due to its peak torque occurring a little earlier in the rev range, but that is debatable, since the LT-1 has a wider, flatter curve (again pretty much by definition, looking at the figures). From somewhere in the mid-range and up, however, the LT-1 would begin to pull away. Where the L98 has to shift to second (and give up some torque multiplication for speed, a la the waterwheel), the LT-1 still has around another 1000 rpm to go in first, and thus begins to widen its lead, more and more as the speeds climb. As long as the revs are high, the LT-1, by definition, has an advantage.

 

There are numerous examples of this phenomenon. The Integra GS-R, for instance, is faster than the garden variety Integra, not because it pulls particularly harder (it doesn't), but because it pulls longer. It doesn't feel particularly faster, but it is.

 

A final example of this requires your imagination. Figure that we can tweak an LT-1 engine so that it still makes peak torque of 340 pound feet at 3600 rpm, but, instead of the curve dropping off to 315 pound feet at 5000, we extend the torque curve so much that it doesn't fall off to 315 pound feet until 15000 rpm. Okay, so we'd need to have virtually all the moving parts made out of unobtanium, and some sort of turbo charging on demand that would make enough high-rpm boost to keep the curve from falling, but hey, bear with me.

 

If you raced a stock LT-1 with this car, they would launch together, but, somewhere around the 60-foot point, the stocker would begin to fade, and would have to grab second gear shortly thereafter. Not long after that, you'd see in your mirror that the stocker has grabbed third, and not too long after that, it would get fourth, but you wouldn't be able to see that due to the distance between you as you crossed the line, still in first gear, and pulling like crazy.

 

I've got a computer simulation that models an LT-1 Vette in a quarter mile pass, and it predicts a 13.38 second ET, at 104.5 mph. That's pretty close (actually a bit conservative) to what a stock LT-1 can do at 100% air density at a high traction drag strip, being power shifted. However, our modified car, while belting the driver in the back no harder than the stocker (at peak torque) does an 11.96, at 135.1 mph - all in first gear, naturally. It doesn't pull any harder, but it sure as heck pulls longer. It's also making 900 hp, at 15,000 rpm.

 

Of course, looking at top speeds, it's a simpler storyÖ

At the Bonneville Salt Flats

 

Looking at top speed, horsepower wins again, in the sense that making more torque at high rpm means you can use a stiffer gear for any given car speed, and have more effective torque (and thus more thrust) at the drive wheels.

 

Finally, operating at the power peak means you are doing the absolute best you can at any given car speed, measuring torque at the drive wheels. I know I said that acceleration follows the torque curve in any given gear, but if you factor in gearing vs. car speed, the power peak is it. Iíll use a BMW example to illustrate this:

 

At the 4250 rpm torque peak, a 3-liter E36 M3 is doing about 57 mph in third gear, and, as mentioned previously, it will pull the hardest in that gear at that speed when you floor it, discounting wind and rolling resistance. In point of fact (and ignoring both drive train power losses and rotational inertia), the rear wheels are getting 1177 pound feet of torque thrown at them at 57 mph (225 pound feet, times the third gear ratio of 1.66:1, times the final drive ratio of3.15:1), so the car will bang you back very nicely at that point, thank you very much.

 

However, if you were to re-gear the car so that it is at its power peak at 57 mph, you'd have to change the final drive ratio to approximately 4.45:1. With that final drive ratio installed, you'd be at 6000 rpm in third gear, where the engine is making 240 hp. Going back to our trusty formula, you can ascertain that the engine is down to 210 pound feet of torque at that point (240 times 5252, divided by 6000). However, doing the arithmetic (210 pound feet, times 1.66, times 4.45), you can see that you are now getting 1551 pound feet of torque at the rear wheels, making for a nearly 32% more satisfying belt in the back.

 

Any other rpm (other than the power peak) at a given car speed will net you a lower torque value at the drive wheels. This would be true of any car on the planet, so, you get the best possible acceleration at any given speed when the engine is at its power peak, and, theoretical "best" top speed will always occur when a given vehicle is operating at its power peak.

 

Force, Work and Time

 

At this point, if youíre getting the picture that work over time is synonymous with speed, and as speed increases, so does the need for power, youíve got it.

†††

Think about this. Early on, we made the point that 300 pound feet of torque at 2000 rpm will belt the driver in the back just as hard as 300 pound feet at 4000 rpm in the same gear - yet horsepower will be double at 4000. Now we need to look at it the other way: You need double the horsepower if you want to be belted in the back just as hard at twice the speed. As soon as you factor speed into the equation, horsepower is the thing we need to use as a measurement. Itís a direct measure of the work being done, as opposed to a direct measure of force. Torque determines the belt in the back capability, and horsepower determines the speed at which you can enjoy that capability. Do you want to be belted in the back when you step on the loud pedal from a dead stop? Thatís torque. The water wheel will deliver that, in spades. Do you want to be belted in the back in fourth gear at 100 down the pit straight at Watkins Glen? You need horsepower. In fact, ignoring wind and rolling resistance, youíll need exactly 100 times the horsepower if you want to be belted in the back just as hard at 100 miles per hour as that water wheel belted you up to one mile per hour.

Of course, speed isnít everything. Horsepower can be fun at antique velocities, as wellÖ

 

"Modernizing" The 18th Century

 

Okay. For the final-final point (Really. I Promise.), what if we ditched that water wheel, and bolted a 3 liter E36 M3 engine in its place? Now, no 3-liter BMW is going to be making over 2600 pound feet of torque (except possibly for a single, glorious instant, running on nitromethane). However, assuming we needed 12 rpm for an input to the mill, we could run the BMW engine at 6000 rpm (where it's making 210 pound feet of torque), and gear it down to a 12 rpm output, using a 500:1 gear set. Result? We'd have *105,000* pound feet of torque to play with. We could probably twist the entire flour mill around the input shaft, if we needed to.

The Only Thing You Really Need to Know

 

For any given level of torque, making it at a higher rpm means you increase horsepower - and now we all know just exactly what that means, don't we? Repeat after me: "Itís better to make torque at high rpm than at low rpm, because you can take advantage of gearing."

 

Thanks for your time.

 

 

This article was written by Bruce Augenstein and is presented with his permission on LS2.com