JHL
Senior Member
I was clearing out some files and came accross this, I don`t know where it was previously posted but as the author makes reference to Vette`s for one of his examples and it raises some interesting points I thought you might have some comments.
J.
J.
Torque and Horsepower
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
dynamometer) 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, incidentally, 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 car land?
First of all, from a driver's perspective, torque, to use the vernacular, RULES
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 car land 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.
At The Drag strip
OK. 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 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 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
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 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
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
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 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 nitro methane), 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
