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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
dynomometer) 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? :-)


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 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 drivewheels 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 drivewheels 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 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 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 occuring 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 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 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 preceeding 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 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*." :-)
Thanks for your time.

Bruce


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