
Torque VS Horsepower
Drive a Seight and people are always saying things like 'Of course you don't
need horsepower in something like that because you have so much torque'.
The truth is that while good torque is useful for lazy overtaking on the road,
helps away from the start line in a drag race,
and means you don't have to pay quite so much attention to gear selection on a
race track, power to weight ratio is the most important determinant when it comes
to acceleration.
Here is an article written by Bruce Augenstein which explains all this far
more eloquently than I ever could:
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
*doubled* 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, and especially so 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. This is a key point. If you mess about with the formula, you can
see that, as long as torque values aren't dropping at a rate that is as
great or greater than the rise in rpm, horsepower will climb.
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 allfired 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. In
fact, gearing up (so as to increase the speed of the output), means that
you lose torque at the output in a proportional manner. That is, if you gear
up the output for twice the speed, you lose half the torque at the output,
and so on.
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 (one sixtieth of the direct torque), 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 262 pound feet of torque at 5000 rpm, or
it would be making 250 hp or more at that engine speed, and would be so
rated (262 foot pounds times 5000, over 5252 = 249 hp). If it were making
263 or more foot pounds of torque at 5000 rpm, it would be making 250 or
more hp, and Chevrolet would likely publish that peak figure and engine
speed. 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 464700 rpm, because more torque is available at the drive wheels
in the next gear at that point.
Note: This is a side point, but the optimum shift point for best
acceleration occurs at a time when the torque at the drive wheels in the
next gear just equals the torque at the drive wheels in the current gear.
You shift well above the power peak (and obviously way past the torque
peak), because the next gear gives you less mechanical advantage (less
torque multiplication) than the gear you're in. As an example, with a
3.00:1 first gear and a 2.00:1 second gear, you wouldn't want to shift
until the torque curve dropped by at least 33% from peak  and even then,
that would only be true assuming that you'd be *at* the torque peak in the
next gear. Otherwise, you'd shift even later. As a practical matter, this
usually means shifting at an engine speed of 10  15% above the power peak
with twovalve engines, and at the redline in fourvalve engines, or maybe
even the rev limiter :). If you know your torque curve and gearing, you
can plot this out yourself. If you do this, drop your onetwo shift point
24% from the calculated optimum, and by lesser amounts in subsequent
shifts, to account for flywheel effect. More on that later.
OK. Back to the hp vs torque comparison.
As we've said, the L98 has dropped way off on torque by 5000 rpm, but on
the other hand, the LT1 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
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 ZR1 Vette. Same deal, only in
reverse. The ZR1 actually pulls a little harder than the LT1, although
its torque advantage (385 foot pounds at 5200 rpm) is softened somewhat by
its extra weight. The real advantage, however, is that the ZR1 has another
1500 rpm in hand at the point where the LT1 has to shift.
There are numerous examples of this phenomenon. The Integra GSR, 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 highrpm 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 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. It doesn't pull any harder, but it sure as hell pulls longer.
Per the formula, it's also making *900* hp, at 15,000 rpm (315 foot pounds
times 15000, over 5252).
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 selfrespecting
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 600 or more 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 finaldrive 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 difficulty with such aggressive gearing would be that it would
introduce really massive polar moments of inertia (flywheel effect), and
that rather complex topic is best addressed through a document of its own,
though I'll take an abbreviated poke at it in the next several paragraphs.
Suffice it to say that rotating objects tend to resist either acceleration
or deceleration, and engine components are no exception. Gearing up (by
either selecting first gear, or in fact tripling the final drive ratio, as
we've done with the Vette) means that the engine and other rotating
components have to speed up by a greater amount for every mph the vehicle
gains, so more energy is expended in accelerating these items to gain a
given amount of speed, and thus less energy is available to actually belt
you in the back.
As an example of how flywheel effect dampens performance, my old '85 Vette
would pull .50 Gs at peak torque in its 1.91 second gear (measured with a
Vericom). With a 2.88 first gear, one would expect it to pull around .75
Gs (2.88 over 1.91 = 1.51, times .50 Gs = .75 Gs). It would actually pull
a peak of .66 Gs in first gear. The difference can be attributed to a tad
more tire slip (maybe sucking up .01 G at most) and the fact that first
gear is marginally less efficient than second in most transmissions,
thereby sucking up another .01 G (or less), but the main reason that first
won't pull as hard as you'd expect (in *any* car) is that the engine uses
more energy accelerating itself in first than in second (to gain the same
amount of speed), so you get less energy at the drive wheels. This is why
you adjust calculated shift points downward, since the actual torque
available at the drive wheels is always reduced a bit from what you would
calculate it to be, compared to the next higher gear. Flywheel effect
goes up as the square of the gearing, which is one reason why the onetwo
shift point is affected the most.
In the example I used of the 900 hp LT1 using 10.35 gears, the car would
drop into the nines for a quarter mile, but in so doing, the trap speed
would climb to about 148 mph, because the car is essentially putting more
average power to the track with the stiffer gearing. However, drag race
nuts are snickering again, because any selfrespecting car that can get to
148 mph in a quarter mile ought to be able to do this somewhere in the mid
eight second bracket.
The reason this fantasy car doesn't get into the eights is that, in order
to get it to effectively use its power, we had to gear it so stiffly that
flywheel effect took a major toll from its relatively paltry 340 foot
pounds of torque, and since flywheel effect is most pronounced in the
lower gears, elapsed times suffer, while trap speeds are affected less.
You can see why drag racers think torque is what wins races. It isn't
strictly true, but high rpm, low torque (as opposed to lower rpm, high
torque) cars are at a disadvantage in a drag race as long as overall power
to weight is similar, because they either only start getting effective
somewhere down track (thus crippling elapsed times), or they suffer greater
flywheel effect if you gear them aggressively enough to create high torque
at the drive wheels (thus crippling elapsed times).
What's really needed in a drag race is high torque (for that massive belt in
the back) *and* high horsepower (extending the torque curve), so you can
take advantage of gearing.
Of course, looking for top speeds, it's a simpler story......
At The Bonneville Salt Flats
Looking at top speed, horsepower absolutely wins, 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*. Remember,
there isn't any flywheel effect at top speed because you're not
accelerating.
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 regear 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. (This is another reason why you *must* be at least at the
power peak (or higher in most cases) before you shift to the next gear.)
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 finalfinal 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*." 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 :).
Thanks for your time.
Bruce
© Bruce Augenstein
Last updated on Sep 24th 1998
