Dustbuster

OK...

Since there seems to be a bit of confusion about what torque and horsepower are and how they are determined, this might help (the important conclusions are at the bottom):

On modern day dynamometers horsepower is a calculated value. It's important to remember the dyno measures torque and rpm and then from these calculates horsepower. On the dyno it takes more water flow to the water brake to increase the load on the engine being tested (engine dyno's generally use this method. Unsure about wheel dyno's, but it's not relevant to the explanation). As the test engine's torque rises more water flow is needed. As the test engine's torque drops less water flow is needed. The dyno's water brake does not respond to horsepower. Major adjustments to water flow are needed as an engine crosses its torque peak but none are needed as it crosses its horsepower peak. In other words the water flow to the brake during a dyno test follows the engines torque curve and not its horsepower curve. Torque is what twists the tire, prop, or pump. Horsepower helps us understand an amount or quantity of torque. (Torque + time)

Here's an interesting bit of trivia; below 5252 rpm any engine's torque will always be higher than its horsepower, and above 5252 rpm any engine's horsepower will always be higher than its torque.

Horsepower = torque x rpm / 5252

Some history:
Horsepower was conceived by James Watt in 1775. Watt determined that one horse could lift 550 pounds one foot in one second. So imagine a horse raising coal out of a coal mine. A horse exerting one horsepower could raise 550 pounds of coal one foot every second. I've also read Watt learned that "a strong horse could lift 150 pounds a height of 220 feet in 1 minute."

If you do the math you see these numbers are expressing the same amount of work. Lifting 150 pounds, 220 feet, in one minute is the same as lifting 550 pounds, one foot, in one second. It is also the same is the same as lifting 33,000 pounds, one foot, in one minute. It can be expressed many different ways.

Here is a way this could be directly observed. Say you have a horse hitched to a plow. In the hitch is a spring scale (like a fish scale). The horse pulls the plow one foot every second and you see 550 pounds on the scale. That would be one horsepower.

So horsepower can be directly measured. However there is a problem directly measuring horsepower of modern day internal combustion engines because they produce rotary motion not linear motion. And unless the engine is geared down, the speed at which they do work (RPM) is too great for practical direct measurement of horsepower. It seems logical then that the solution was to directly measure torque (rotational force eventually expressed in pounds at one foot radius) and RPM (time and distance, i.e. distance in circumference at the one foot radius) and from these calculate horsepower. Torque and RPM are easily measured directly. Early dynamometers used a brake device to load the engine. A torque arm was attached to this brake's stator. The brake's rotor was coupled to the engine's crankshaft. A spring scale or other measuring device connected the torque arm to the stationary fixture holding the engine and brake. During a test the brake's application loaded the engine. Torque and engine rpm were observed and recorded.

Now if we are measuring torque and RPM how can we calculate horsepower? We will use Watts observation of one horsepower as 150 pounds, 220 feet in one minute. First we need express 150 pounds of force as foot pounds torque.

Pretend the force of 150 pounds is "applied" tangentially to a one foot radius circle. This would be 150 foot pounds torque.
Next we need to express 220 feet in one minute as RPM.

The circumference of a one foot radius circle is 6.283186 feet. ft. (Pi x diameter 3.141593 * 2 feet)
The distance of 220 feet, divided by 6.283185 feet, gives us a RPM of 35.014.
We are then talking about 150 pounds of force (150 foot pounds torque), 35 RPM, and one horsepower.

Constant (X) = 150 ft.lbs. * 35.014 RPM / 1hp

35.014 * 150 / 1 = 5252.1

5252 is the constant.

So then hp = torque * RPM / 5252

-----
Or, this formula, which is easier.
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Remember we know 150 foot pounds and 35.014 RPM = one horsepower

1hp is to 150 ft.lbs. * 35.014 RPM as X hp is to observed ft.lbs.torque * observed RPM

Example; We dyno test and observe 400 ft.lbs. torque at 5000 RPM

1 hp is to 150 ft.lbs. * 35.014 RPM as X hp is to 400 ft.lbs. * 5000 RPM

When we cross multiply X hp * (150 ft.lbs. * 35.014 RPM) = 1hp * (400 ft.lbs. * 5000 RPM)

X hp * (5252 ft.lbs. RPM) = 1 hp * (2,000,000 ft.lbs. RPM)

Divide both sides by 5252 ft.lbs. RPM

X hp = 1 hp * 380.80

X hp = 380.80 hp


Soooo....
* Maximum acceleration at any speed occurs at the HP peak.
* Maximum acceleration in any gear occurs at the torque peak
* HP = torque * RPM / 5252
* torque = HP * 5252 / RPM
* torque = HP at 5252 RPM


What does this all mean to us car-freaks?

First of all, from a driver's perspective, torque, 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. Therefore, horsepower isn't particularly meaningful from a driver's perspective.

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

Because, 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. 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.

It'll get explained how this works at the drag stip in part II.

NASA racer

this too...

if you read carefully, torque up-high is prefereable for speed but a car that makes torque down low (twisting force) will FEEL faster. That's how a car making torque down low can feel faster than a car that is faster from a driver's perspective.

996 is a good comparo to the S4...almost exactly the same torque but at 4600rpm instead of 1800rpm. Its up there where the shifts will never drop RPM below the peak in torque...due to HP, gearing and weight the 996 is faster even though the S4 "feels" faster.<ul><li><a href="http://www.seansa4page.com/resource/torquehp.html">http://www.seansa4page.com/resource/torquehp.html</a</li></ul>

Dustbuster

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 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


(((Numbers for 94 Integra LS/RS and GS-R

Engine Peak HP @ RPM Peak Torque @ RPM
------ ------------- -----------------
B18B 142 @ 6300 127 @ 5200
B18C 170 @ 7600 128 @ 6200

(sorry for the ricer explanation, but it's what data is on hand)

If you overlap the torque curve for B18B and B18C, you'll see that B18C's maximum torque (127 vs. 128 ft-lbs) is about the same as B18B, except B18C's torque curve just keeps on climbing, thus the much higher HP. B18B and B18C are quite similar, but not identical. Mostly notably the B18B has slightly longer stroke, which gives it the displacement of 1835 cc vs. B18C's 1797 cc. The stroke explains why the B18B has better low end, and it is also a factor why it revs slower and has lower redline than B18C.)))

The cars (Corvett) 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 turbocharging 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 seen 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 write-up. 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 nitromethane), 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 :-).

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*." All about torque, boys.
:-)

katana

Nice write up, but torque is expressed properly as lb/ft, not ft/lb.

BluLytNin

"Unobtanium"....nice! 8^)

KKelly

Max torque is at 4000+ and you will never drop below say 4500rpm if shifting near redline. It is quite easy to drive around town, you just don't have max torque from 1800rpm.

djillusion

<ul><li><a href="http://www.stanford.edu/~voloshin/lhowwhy.html">http://www.stanford.edu/~voloshin/lhowwhy.html</a></li></ul>

Dustbuster

I suppose we could further go down the line and debate the best (automobile) engine ever made...

That's a tough one.

I have a honda riding mower that is just marvelous... :-)

NASA racer

ironic because actually that 1800rpm torque is about perfect for street driving characteristics but not the ultimate for raw numbers. It's a credit to the design of the S4 that it's as fast as it is not only with the torque being in the "wrong" place but with the weight and driveline friction.

Dustbuster

That's a good one