#### JHL

##### Senior Member

J.

Torque and Horsepower

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 . I've posted a subset of this note in another string, but

felt it deserved to be dealt with as a separate topic. This is meant to be a

primer on the subject, which may lead to serious discussion that fleshes out

this and other subtopics that will inevitably need to be addressed.

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 foot pounds 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.

Awhile 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 foot pounds per second, or 33,000

foot pounds per minute, for an eight hour shift, more or less. He then published

those observations, and stated that 33,000 foot pounds per minute of work was

equivalent to the power of one horse, or, one horsepower.

Everybody else said OK.

For purposes of this discussion, we need to measure units of force from rotating

objects such as crankshafts, so we'll use terms which define a *twisting* force,

such as foot pounds of 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. What we actually measure (on a

dynamometer) is torque, expressed in foot pounds (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 foot pounds of work.

OK. Remember Watt? He said that 33,000 foot pounds of work per minute was

equivalent to one horsepower. If we divide the 6.2832 foot pounds of work we've

done per revolution of that weight into 33,000 foot pounds, we come up with the

fact that one foot pound of torque at 5252 rpm is equal to 33,000 foot pounds

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 foot pounds 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 foot pounds 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 pushback 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?

Fine. Can we go on, now?

The Case For Horsepower

OK. If torque is so all-fired important, why do we care about horsepower?

Because (to quote a friend), "It is 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 awhile ago. This was a pretty massive wheel (built a

couple of hundred years ago), rotating lazily on a shaft which 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(!) foot pounds 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 mph for the

average car, and, in order to go faster, we'd need to gear it up. To get to 60

mph would require gearing the wheel up enough so that it would be effectively

making a little over 43 foot pounds of torque at the output, which is not only a

relatively small amount, it's less than what the average car would need 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

OK. 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 current LT1 Corvette 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

LT1 300 @ 5000 340 @ 3600

The cars are geared identically, and car weights are within a few pounds, so

it's a good comparison.

First, 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 LT1 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 LT1 is

faster. Here's another slice at that formula:

Horsepower * 5252

Torque = -----------------

RPM

If we plug some numbers in, we can see that the L98 is making 328 foot pounds of

torque at its power peak (250 hp @ 4000), and we can 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 LT1 is fairly happy making 315 pound feet at 5000 rpm,

and is happy right up to its mid 5s redline.

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 LT1 has a wider, flatter curve

(again pretty much by definition, looking at the figures). From somewhere in the

mid range and up, however, the LT1 would begin to pull away. Where the L98 has

to shift to second (and throw away torque multiplication for speed), the LT1

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 LT1,

by definition, has an advantage.

Another example would be the LT1 against the ZR-1. Same deal, only in reverse.

The ZR-1 actually pulls a little harder than the LT1, although its torque

advantage is softened somewhat by its extra weight. The real advantage, however,

is that the ZR-1 has another 1500 rpm in hand at the point where the LT1 has to

shift.

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

LT1 engine so that it still makes peak torque of 340 foot pounds 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.

OK, 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 LT1 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'd 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 LT1 Vette in a quarter mile pass,

and it predicts a 13.38 second ET, at 104.5 mph. That's pretty close (actually a

tiny bit conservative) to what a stock LT1 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, of course. It doesn't pull any

harder, but it sure as hell pulls longer . It's also making *900* hp, at

15,000 rpm.

Of course, folks who are knowledgeable about drag racing are now openly

snickering, because they've read the preceding paragraph, and it occurs to them

that any self respecting car that can get to 135 mph in a quarter mile will just

naturally be doing this in less than ten seconds. Of course that's true, but I

remind these same folks that any self-respecting engine that propels a Vette

into the nines is also making a whole bunch more than 340 foot pounds of torque.

That does bring up another point, though. Essentially, a more "real" Corvette

running 135 mph in a quarter mile (maybe a mega big block) might be making

700-800 foot pounds of torque, and thus it would pull a whole bunch harder than

my paper tiger would. It would need slicks and other modifications in order to

turn that torque into forward motion, but it would also get from here to way

over there a bunch quicker.

On the other hand, as long as we're making quarter mile passes with fantasy

engines, if we put a 10.35:1 final-drive gear (3.45 is stock) in our fantasy

LT1, with slicks and other chassis mods, we'd be in the nines just as easily as

the big block would, and thus save face . The mechanical advantage of such a

nonsensical rear gear would allow our combination to pull just as hard as the

big block, plus we'd get to do all that gear banging and such that real racers

do, and finish in fourth gear, as God intends.

The only modification to the preceding paragraph would be the polar moments of

inertia (flywheel effect) argument brought about by such a stiff rear gear, and

that argument is outside of the scope of this already massive document. Another

time, maybe, if you can stand it .

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

thus have more effective torque *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*. An example, yet again, of the

LT1 Vette will illustrate this. If you take it up to its torque peak (3600 rpm)

in a gear, it will generate some level of torque (340 foot pounds times whatever

overall gearing) at the drive wheels, which is the best it will do in that gear

(meaning, that's where it is pulling hardest in that gear).

However, if you re-gear the car so it is operating at the power peak (5000 rpm)

*at the same car speed*, it will deliver more torque to the drive wheels,

because you'll need to gear it up by nearly 39% (5000/3600), while engine torque

has only dropped by a little over 7% (315/340). You'll net a 29% gain in drive

wheel torque at the power peak vs. the torque peak, at a given car speed.

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, theoretical "best" top speed will always occur when a given vehicle

is operating at its power peak.

"Modernizing" The 18th Century

OK. For the final-final point (Really. I Promise.), what if we ditched that

water wheel, and bolted an LT1 in its place? Now, no LT1 is going to be making

over 2600 foot pounds of torque (except possibly for a single, glorious instant,

running on nitro methane), but, assuming we needed 12 rpm for an input to the

mill, we could run the LT1 at 5000 rpm (where it's making 315 foot pounds of

torque), and gear it down to a 12 rpm output. Result? We'd have over *131,000*

foot pounds of torque to play with. We could probably twist the whole flour mill

around the input shaft, if we needed to .