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Torque vs. HP - VERY interesting commentary.

F

Fiddler's Gold

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I posted this on the C4 forum but I thought everyone over here would like to see it. It is a fabulous explanation of torque vs. hp in both commonplace and "carland" terminology. Also offers a great rundown of the basics and some applicable info for vette engines. (originally from Bimmer group I believe)

HTH,
The Fiddler
Andy

Engine Power - Torque Vs HP
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Horsepower and Torque (In-Depth)
Date: Sun, 31 Jan 1999 17:19:12 -0500
From: Bruce Augenstein <Bruce.Augenstein@digital.com>
Subject: Horsepower and Torque - a Primer (part 1)

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.

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 on a standard dynomometer. What we
actually measure 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? :)
(part two follows)

------------------------------

Date: Sun, 31 Jan 1999 17:19:24 -0500
From: Bruce Augenstein <Bruce.Augenstein@digital.com>
Subject: Horsepower and Torque - a Primer (part 2)

The Case For Horsepower

OK. If torque is so all-fired important (and feels so good), 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 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. If you
remember your junior high school physics 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 foot pounds
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
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 LT1 Corvette (built from 1992
through 1996) with the last of the L98 Vettes, built in 1991. I'm sorry to
mention the "C" word amongst this august group, but there just isn't a
better example to use. 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 very nearly identical,
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 give up some torque
multiplication for speed, a la the waterwheel), 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.

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. (part three follows)

------------------------------

Date: Sun, 31 Jan 1999 17:19:34 -0500
From: Bruce Augenstein <Bruce.Augenstein@digital.com>
Subject: Horsepower and Torque - a Primer (part 3)

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 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 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 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 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 preceding paragraph would be the rotational
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*. A BMW
example will 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 foot pounds of torque thrown at
them at 57 mph (225 foot pounds, 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 regear 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 foot pounds of torque at that
point(240 times 5252, divided by 6000), but if you do the arithmetic (210
foot pounds, times 1.66, times the 4.45), you can see that you are now
getting 1551 foot pounds 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, 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 a 3 liter E36 M3 engine in its place? Now, no 3
liter BMW 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 BMW
engine at 6000 rpm (where it's making 210 foot pounds of torque), and gear
it down to a 12 rpm output, using a 500:1 gear set. Result? We'd have
*105,000* 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*."
 

Rob

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