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- Maximum
acceleration at any speed occurs at the HP peak.
- Maximum acceleration in any gear occurs at the torque peak
- HP = torque * RPM / 5252
- torque = HP * 5252 / RPM
- torque = HP at 5252 RPM
HP is not measured directly, it is simply calculated from torque.
However the HP to torque formula is useful to figure out how much torque
the engine is making at peak HP. I wish when the car magazines do a road
test they would include the torque and HP graph, gear ratios vs speed, 0
to top speed table in every 10 miles with G (acceleration) values...
etc.]
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 sub-topics 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.
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 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 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 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 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 |
[Numbers for 94 Integra LS/RS and GS-R]
| Engine |
Peak HP @ RPM |
Peak Torque @ RPM |
| B18B |
142 @ 6300 |
127 @ 5200 |
| B18C |
170 @ 7600 |
128 @ 6200 |
If you overlap the torque curve for B18B and B18C, you'll see that
B18C's maximum torque (127 vs. 128 ft-lbs) is about the same as B18B,
except B18C's torque curve just keeps on climbing, thus the much higher
HP. B18B and B18C are quite similar, but not identical. Mostly notably
the B18B has slightly longer stroke, which gives it the displacement of
1835 cc vs. B18C's 1797 cc. The stroke explains why the B18B has better
low end, and it is also a factor why it revs slower and has lower
redline than B18C. Monitor YAHP for an article that will talk about the
basic relationship between bore and stroke. - Frank]
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, theLT1
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
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 :-). 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 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 :-). 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 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*. :-)
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