There's been a certain amount of discussion about the concepts of horsepower and torque, how they relate to each other, and how they apply in terms of automobile performance. 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 :-)

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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.

James Watt (the same gent who did all that neat stuff with steam engines)
determined that the average horse 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: 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
rotational force, in 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.

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, 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 x 2
feet), and, incidentally, we have done 6.2832 foot-pounds of work.
Watt defined 33,000 foot-pounds of work per minute 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 x RPM
Horsepower =    --------------------
                                          5252

This is not a debatable item. This is the way it's done, period.

Now, what does all this mean in carland? From a driver's perspective,
torque, to use the vernacular, RULES :-). Any given car, in any given gear,
will accelerate at a rate that 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.

The Case for Horsepower

If torque is so important, why do we care about horsepower? 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 observed a while ago. This was a 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:

12 x 2600 / 5252 = 6 HP

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

At The Drag Strip

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 current
LT1 Corvette with the last of the L98 Corvettes, 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 restate the horsepower formula, we can begin
to discover exactly why the LT1 is faster:

                           Horsepower x 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. The ZR-1 actually pulls a
little harder than the LT1, although its torque advantage is softened
slightly by its extra weight. The real advantage, however, is that the ZR-1
pulls another 1500 rpm beyond 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. Suppose 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. (All of the moving parts would be made out of unobtanium).
:-)

If you raced a stock LT1 against this hypothetical 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 developed a computer simulation that models an LT1 Corvette in a
quarter mile pass, and it predicts a 13.38 second ET, at 104.5 mph. That's
close (actually a tiny bit conservative) to what a stock LT1 can do at
standard air density at a high traction drag strip, being powershifted.
However, our hypothetical modified car, pushing no harder than the stocker
(at peak torque) runs an 11.96, at 135.1 mph, all in first gear. It's also
making 900 hp, at 15,000 rpm.

Folks who are knowledgeable about drag racing know 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 modifications, 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.

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, but that is outside of the scope of this already massive document.

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 taller 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 versus car speed, the power peak is it. An example, yet again, of
the LT1 Corvette 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 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 versus 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

For the final-final point, 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 needed.

The Only Thing You Really Need to Know

It is better to make torque at high rpm than at low rpm, because you can
take advantage of gearing.