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.

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 *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.

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.

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

Because (to quote
a friend), "It’s 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.

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 driver’s
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 story…

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*.
I’ll 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 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 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.

At this point, if
you’re getting the picture that work over time is synonymous with *speed*, and as speed increases, so does
the need for *power*, you’ve 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. It’s 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?
That’s *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, you’ll
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
isn’t everything. Horsepower can be fun at antique velocities, as well…

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.

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: "It’s 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