Horsepower and Torque a Primer
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 pound feet 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 pound feet per
second, or 33,000 pound feet per minute. He then published those
observations, and stated that 33,000 pound feet per minute of work was
equivalent to the power of one horse, or, one horsepower.
Everybody else said okay.
For purposes of this discussion, we need to measure units of force from
rotating objects such as crankshafts, so we'll use terms that define a
twisting force, such as 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 pound feet (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 pound feet of
work.
Okay. Remember Watt? He said that 33,000 pound feet of work per minute was
equivalent to one horsepower. If we divide the 6.2832 pound feet of work
we've done per revolution of that weight into 33,000 pound feet, we come up
with the fact that one foot pound of torque at 5252 rpm is equal to 33,000
pound feet 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 pound feet per minute), and so on.
Therefore, the following formula applies for calculating horsepower from a
torque measurement:
Horsepower = torque * rpm/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. 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 pound feet 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 push back 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? Okay. Now that we're all on the same wavelength (and I hope you
didn't get a ticket or anything), we can go on.
The Case for Horsepower
So if torque is so all-fired important (and feels so good), why do we care
about horsepower?
Because (to quote a friend), "Its 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 a while ago. This was a pretty massive
wheel (built a couple of hundred years ago), rotating lazily on a shaft
that 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(!) pound feet 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 mile per
hour for the average car, and, in order to go faster, we'd need to gear it
up. If you remember your junior high school science class 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 pound feet 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 needs 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
Now 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 LT-1 Corvette (built from 1992
through 1996) 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
LT-1 .....300 @ 5000 ..............340 @ 3600
The cars are essentially identical (drive trains, tires, etc.) except for
the engine change, so it's an excellent comparison.
From a drivers perspective, 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 LT-1 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 LT-1 is faster. Here's another slice at
that torque and horsepower calculation:
Torque = (Horsepower * 5252) / RPM
Plugging some numbers in, we can see that the L98 is making 328 pound feet
of torque at its power peak (250 hp @ 4000). We can also 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 LT-1 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 red line.
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 LT-1 has a
wider, flatter curve (again pretty much by definition, looking at the
figures). From somewhere in the mid-range and up, however, the LT-1 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 LT-1 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 LT-1,
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.
A final example of this requires your imagination. Figure that we can tweak
an LT-1 engine so that it still makes peak torque of 340 pound feet 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. Okay, 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 LT-1 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 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 LT-1 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 LT-1 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,
naturally. It doesn't pull any harder, but it sure as heck pulls longer.
It's also making 900 hp, at 15,000 rpm.
Of course, looking at top speeds, it's a simpler story
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 have more effective torque (and thus more thrust) 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. Ill use
a BMW example to 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 pound feet of
torque thrown at them at 57 mph (225 pound feet, 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 re-gear 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 pound feet of torque at that
point (240 times 5252, divided by 6000). However, doing the arithmetic (210
pound feet, times 1.66, times 4.45), you can see that you are now getting
1551 pound feet 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, you get the best possible acceleration at any given speed
when the engine is at its power peak, and, theoretical "best" top speed
will always occur when a given vehicle is operating at its power peak.
Force, Work and Time
At this point, if youre getting the picture that work over time is
synonymous with speed, and as speed increases, so does the need for power,
youve got it.
Think about this. Early on, we made the point that 300 pound feet of torque
at 2000 rpm will belt the driver in the back just as hard as 300 pound feet
at 4000 rpm in the same gear - yet horsepower will be double at 4000. Now
we need to look at it the other way: You NEED double the horsepower if you
want to be belted in the back just as hard at twice the speed. As soon as
you factor speed into the equation, horsepower is the thing we need to use
as a measurement. Its a direct measure of the work being done, as opposed
to a direct measure of force. Torque determines the belt in the back
capability, and horsepower determines the speed at which you can enjoy that
capability. Do you want to be belted in the back when you step on the loud
pedal from a dead stop? Thats torque. The water wheel will deliver that,
in spades. Do you want to be belted in the back in fourth gear at 100 down
the pit straight at Watkins Glen? You need horsepower. In fact, ignoring
wind and rolling resistance, youll need exactly 100 times the horsepower
if you want to be belted in the back just as hard at 100 miles per hour as
that water wheel belted you up to one mile per hour.
Of course, speed isnt everything. Horsepower can be fun at antique
velocities, as well...
"Modernizing" The 18th Century
Okay. 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 pound feet of torque (except
possibly for a single, glorious instant, running on nitromethane). However,
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 pound feet of torque), and gear
it down to a 12 rpm output, using a 500:1 gear set. Result? We'd have
*105,000* pound feet of torque to play with. We could probably twist the
entire flour mill around the input shaft, if we needed to.
The Only Thing You Really Need to Know
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?
Repeat after me: "Its better to make torque at high rpm than at low rpm,
because you can take advantage of gearing."
arty:
