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Engine Power - Torque Vs HP

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Horsepower and Torque (In-Depth)

Date: Sun, 31 Jan 1999 17:19:12 -0500

From: Bruce Augenstein <Bruce.Augenstein@digital.com>

Subject: Horsepower and Torque - a Primer (part 1)

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 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 on a standard dynomometer. What we

actually measure 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, incidently, 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 carland?

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?

(part two follows)

------------------------------

Date: Sun, 31 Jan 1999 17:19:24 -0500

From: Bruce Augenstein <Bruce.Augenstein@digital.com>

Subject: Horsepower and Torque - a Primer (part 2)

The Case For Horsepower

OK. If torque is so all-fired important (and feels so good), 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 carland 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. If you

remember your junior high school physics 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 foot pounds

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

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 Dragstrip

OK. Back to carland, 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 LT1 Corvette (built from 1992

through 1996) with the last of the L98 Vettes, built in 1991. I'm sorry to

mention the "C" word amongst this august group, but there just isn't a

better example to use. 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 very nearly identical,

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 give up some torque

multiplication for speed, a la the waterwheel), 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.

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. (part three follows)

------------------------------

Date: Sun, 31 Jan 1999 17:19:34 -0500

From: Bruce Augenstein <Bruce.Augenstein@digital.com>

Subject: Horsepower and Torque - a Primer (part 3)

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 powershifted. 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 preceeding 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 Corvette 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 rotational

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*. A BMW

example will 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 foot pounds of torque thrown at

them at 57 mph (225 foot pounds, times the third gear ratio of 1.66:1, times

the final drive ratio of 3.15:1), so the car will bang you back very nicely

at that point, thank you very much.

However, if you were to regear 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 foot pounds of torque at that

point(240 times 5252, divided by 6000), but if you do the arithmetic (210

foot pounds, times 1.66, times the 4.45), you can see that you are now

getting 1551 foot pounds 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, 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 a 3 liter E36 M3 engine in its place? Now, no 3

liter BMW is going to be making over 2600 foot pounds of torque (except

possibly for a single, glorious instant, running on nitromethane), but,

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 foot pounds of torque), and gear

it down to a 12 rpm output, using a 500:1 gear set. Result? We'd have

*105,000* foot pounds of torque to play with. We could probably twist the

whole flour mill around the input shaft, if we needed to .

The Only Thing You Really Need to Know

Repeat after me. "It is better to make torque at high rpm than at low rpm,

because you can take advantage of *gearing*."