| It occurred to me that, although a significant subset of this post has
been up on the Vettenet home page for at least a year, I forgot to post
it here. If you can stand it, this is the more complete answer regarding
horsepower and torque. Corrections and comments cheerfully received.
Horsepower and Torque - A Primer
--------------------------------
OK. Here's the deal, in moderately plain language.
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 all-fired important, why do we care about
horsepower?
Because (to quote Eric Goehl), "It's 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 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 the new
peak figure. 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.
(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 way above the torque peak, and typically well past the
power peak, because the next gear gives you less mechanical advantage
(less torque multiplication) than the gear you're in. This usually
means shifting at an engine speed of 10 - 15% above the power peak with
two-valve engines, and at the redline in four-valve engines, or maybe
the rev limiter :-). Any later than the optimum point and the
decreasing torque in the current gear means you are at a disadvantage
compared to being in the next gear, but any earlier means that you'll
give up drive wheel torque, even if you're at the engine's torque peak
in the next gear.)
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 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 Vette. Same deal,
only in reverse. The ZR-1 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
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 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 :-). Of course, 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
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 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 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 rather massive 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) 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 operating example, measured with a Vericom, my old '85 Vette
would pull .50 Gs at peak torque in its 1.91 second gear. 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 or .02G) 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
than you would expect.
As a by the way, that means that what I said about shift points awhile
back needs to be modified a tad for flywheel effect, since actual
available drive wheel torque is lessened a bit from what you'd expect
while accelerating in the lower gear. As a practical matter, one might
drop the one-two shift point by 5% from the calculated optimum, and
less than that in subsequent shifts.
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 (in the computer model), 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 self-respecting 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.
Sigh.
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 flywheel effect is most
pronounced in the lower gears, so 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 cars are at a disadvantage in a
drag race (as opposed to lower rpm, high torque cars) as long as
overall power to weight is similar. This is 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 off the
line (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 different 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 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's 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
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