Fellow still-awake SOL'ers,
Some responses have come in from my Torque-Power posting. They covered a
range of reactions... boring, great, huh?, yeah...but?, how do they do that?
Etccccc.
Here are a few further comments. (No! Not again!! AAAaaaaiiiighh...)
[First, a diversion.]
I was trying to avoid the issue of engine design. Torque itself is largely
the straightforward physics of cylinder pressure acting against the surface
of the pistons producing a force, which torques the driveshaft via the lever
arm of the crankshaft, whose length is half the stroke. At any given time,
the distribution of pistons is such that some are pushing and some aren't,
and the torquing is at some average (rms, maybe) crank angle other than the
ideal 90 degrees, etc., and there must be some time averaging, so the exact
proportionality constants will be kludgey, ...but... We can see from this
that torque will be linear with average (or maximum) cylinder pressure,
piston surface area, and crank-throw length. The product of piston surface
area and crank-throw length (along with random factors of pi and 2) is the
volume per cylinder. Perhaps there will be some different time distribution
if we rearrange the same displacement into different numbers of cylinders,
but if we keep the number of cylinders constant, the torque is linear (more
or less) with total volume. (Whew!) Given that, the only way to get more
power is to make it spin faster while still maintaining torque. Since power
is torque x rpm, if you increase rpm and the power will go up as long as the
factional increase in rpm is more than any fractional decrease in torque.
Yes, I know...you can also increase the (time average of) cylinder pressures
(which aren't at all constant during combustion). The limits to maximum
cylinder pressure are bearing loading and just how much air+fuel you can ram
into the cylinder during induction (and if you are concerned about emissions,
how complete your combustion will be and how well you can maintain ideal
stoichemistry). With exhaust-scavenging and ram-tuning (or forced-breathing
i.e. turbo- or super-charging) and with increased thermal efficiency (i.e.
inter-cooler), you can squeeze more air in and increase the pressures. This
is what I meant by breathing, and it is usually limited by technology, and in
racing, the rules. By the way, higher compression allows for both greather
exhaust scavenging and more thermal efficiency, but it too is limited, mostly
by the fuel quality and other combustion parameters.
Since torque is limited, how do we make it spin faster? Mostly make it breathe
as well at high rpms as it does at low. Also necessary is that it be able to
stand the higher rpms before it blows up from internal stress. In general,
high and low rpm breathing are different beasts, requiring both different cam
timing and different induction-tuning lengths for exhaust and intake, so you
have to choose your tradeoffs. As for mechanical limits to rpm, in a pushrod
engine, the limit is usually valve train, but with ohc, the limits may be
bearing loads (crank, con-rod, or wrist-pin). If you alter the bore/stroke
ratio while keeping the volume constant, you change all the bearing loads, but
also change the breathing and thermal behavior. In general, a large bore,
short stroke lets you spin faster, but not necessarily. If you choose to
go with more cylinders too, decreasing the size of each, then it is more
complicated still, but smaller pistons present lower bearing loads than big
ones. Finally, as Akkana pointed out, the width of the torque (or power) band
may change, and that is important. So even if you get more power, the total
over all rpms may go down. In a top-speed run, maximum power is important,
but in an always-changing-speed race, the off-peak power may be more important.
Finally, at high rpms, engine friction and the resonance of the air inside
the block become very important, especially with 12,000rpm ranges that F-1
engines run today. But this doesn't apply to our LBC's, does it?
[And now back to our regularly scheduled, but boring, power discussion. For a
quick summary, just skip to the end!]
I hope to keep this short... There was one important point I was trying to
make. Torque is indeed what accelerates you, but with the gearbox, you can
have all the torque you want!!! Period. You pay the price of having the
wheels spinning slower, but by golly, you can get torque. Ignoring the issue
of peak vs. non-peak, if the engine can generate torque, it isn't very good
unless it does so at a useful rpm. If another engine generates only 2/3 as
much torque, but does so at 3 times the rpm(!), we could gear it down by
a factor of 3, and the torque coming out of the gearbox would be twice as
great! And while travelling at the same speed. So you see, torque is not the
answer, power is. But are there any limitations to this model? Well, yes.
There are two of them. Consider two engines with identical torque (or power)
curves. Now for one of them, scale up the horizontal axis by some factor, oh,
say x2, and scale down the vertical axis by the same factor. These two
engines still produce the same peak power. In fact, they still have the same
effective power curve widths since the normalized shape of the modified curve
did not change. But one now has twice the peak torque of the other, and both
peak torque and peak power occur at half the rpm. Both engines will give the
same top speed. But even if they had identical snap-throttle response (not
necessarily a consequence of same-shape power curves), they would not be able
to accelerate the same car equally. The high-rev'er, low-torque'er would have
to accelerate *itself* (and all driveline components upstream of the gearbox)
more than the high-torque'er, low-rev'er. In fact, the dynamic load of the
engine itself would be twice as great for that reason. The only way it could
possibly be made to accelerate as well would be for its flywheel (and other
upstream-from-the-gearbox components, including the engine itself) to have only
half the moment of inertia. This is just one limitation to the model in the
preceding paragrah, and was the main point of my earlier posting. It does not
apply to a non-dynamic situation, i.e. when the car is not (or is just barely)
accelerating, as is the case near top speed. And it applies less if the gear
is higher so that the dynamic load of the car is higher compared to the engine
(also the case when approaching top speed).
The second limitation is just that in practice, when you *choose* to tune an
engine for higher rpm, you usually *don't* end up with the same normalized
shape of the the power curve. It may get fractionally wider or it may get
fractionally narrower. As Akkana suggested, this is important when you are
always changing speeds and thus run over a broad range of rpms. If you are
tuning for top end, you can presumably adjust your gearing to put you right
at peak power when it is most critical, but in a race, this won't help. The
ability to choose a gear closer to peak power is important, and is the real
reason for wanting more gears in your gearbox (or a CVT). Given production
gearboxes with a fixed number of speeds but with some freedom to tune the
engine, you may find it better to widen the power (or torque) curve at the
expense of peak power, peak torque, or peak both. If the wider power band is
obtained at a lower rpm, then you win *twice* to help offset any decrease in
peak power. (On the other hand, if you can switch to more gears, more narrowly
spaced, you can *afford* to have a narrower power band.)
So, in quick summary:
1. Power and torque are *not* the same. People who say torque is the key are
missing half of the physics, and more importantly, are implictly assuming a
useable rpm for that torque. That rpm is rarely mentioned but is *critical*.
2. If the *curves* of power or torque vs. rpm are given, they express the
same info in different ways, so, yes, one implies the other.
3. *Peak* power is only part of the equation, applicable only to top speed,
and then only if you have the right gear. The width of the power curve is
important whenever you run a broad range of rpm (i.e. during any acceleration).
4. Equal *power* (not torque, and whether at peak or not) can be geared to
produce equal torque at the wheels, for the same wheel speed. It is torque at
the wheels that both produces acceleration and overcomes wind drag.
5. Gearing down from higher rpms to give more torque carries the liability of
higher dynamic load of the engine itself. Given a choice of two equal-power
engines, the lower-rpm one will perform better, and this is more of a factor in
lower gears. Tuning for lower-rpm may be worth a small loss in peak power, and
especially so if it also means a wider power band.
6. Given a fixed displacement, peak (or average) torque is fixed (more or less
and especially with a fixed piston configuration). So with fixed displacement,
more power is most obtainable via more rpms, the limit of which is either
engine breathing (also affecting cylinder pressures) or mechanical stresses.
(Whew! again)
Jim
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