Horsepower and Torque - a Primer (part 2)

[Bruce Augenstein <Bruce.Augenstein@xxxxxxxxxxx>]

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*." 

Thanks for your time. 

Bruce

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