M3 shift points, Mr. Collie's flywheel, etc.

[Bruce Augenstein <Bruce.Augenstein@xxxxxxxxxxx>]

OK, I know I'm seriously off topic here (meaning it's not about book
purchases, elections or erams), but I figure what the heck, I'll write about
something technical.

Awhile back, a gentleman named Luis Marques went to considerable time and
trouble to post figures and graphics that demonstrate optimal shift points
on a 3.2 liter M3, stock, and after being sharked. His page is still up and
available at: http://www.geocities.com/MotorCity/Speedway/6172/m3shift.html

Not wanting to peak too early on this :-), I haven't gotten around to
responding until now, but the thing is, those shift points are incorrect. I
intend no flame here, and the data is accurate as far as it goes, but it
completely ignores rotational inertia in the engine and drivetrain.
Rotational inertia is measured in slugs (swear to God), and if you look it
up in an engineering text, you'll see that there's a *square* in the
formula. Why does that matter? Because you dramatically increase the effect
as you try and more rapidly accelerate rotational speed. On an automobile,
rotational inertia (sometimes referred to as "flywheel effect") is highest
in first gear, and drops off significantly as you go up through the gears.
The effect is often expressed in terms of additional vehicle weight, so a
car will have an apparent or dynamic weight (as far as the powerplant is
concerned) that is much greater than the actual weight measured as sitting
on a scale.

If you've stuck it out to this point, let me offer an example.

In three recent passes with a Vericom on board (same stretch of level road,
same technique, within a few minutes of each other, etc.), my 3 liter M3
showed an average peak acceleration of .463 G in second gear (at peak
torque, obviously). The G peaks were measured at .465, .462 and .463 G,
first to last.

In *first* gear (same stretch of road, same day and approximate time as the
second gear runs, etc.,etc.), the car pulled an average acceleration peak of
.644 G, averaged from three runs at .649, .638 and .646 G.

So what?

OK, here's what. According to BMW, my car has a first gear ratio of 4.20:1,
and a second gear ratio of 2.49:1. Assuming truth in BMW publishing :-), the
car should've been able to pull .781 G in first gear, based on the .463 G
average obtained in second. (The .781 figure is from multiplying the second
gear results by a ratio of 4.20/2.49.)

In fact, if I had tested the car on a chassis dyno at, say, a static 4250
rpm (peak torque), the car would've demonstrated a drive wheel force
differential that would very closely approximate the difference in gear
ratios between first and second gears. There would be slightly more wheel
slip in first gear, and first gear is generally slightly less efficient than
second gear by a percent or so, but this is small potatoes. Drive wheel
torque would vary, as I said, pretty much equal to the difference in gear
ratios.

So why the discrepancy in acceleration values?

The shortfall of about 17.5% out on the road (.644 observed over .781
theoretical) is due almost entirely to rotational inertia - "flywheel
effect", which only comes about when you are accelerating (or, in fact,
decelerating). In first gear, that M3 gains about 189 engine rpm for each
mile per hour gained, while in second, it's down to 112 rpm. It takes energy
to accelerate these rotating parts, and this energy is then unavailable to
accelerate the car. The parts affected are basically every rotating thingy
forward of the transmission tailshaft. This obviously includes the engine,
flywheel and all engine driven accessories, as well as the clutch, pressure
plate, transmission input shaft, various gear clusters, etc.

OK, so what in hell does this have to do with shift points?

Well, the first gear acceleration force and wheel power curves in Mr.
Marques' graphs should only be about 82.5% as tall as they are depicted,
compared with the second gear force and wheel power curves. That, in turn,
means the optimum one-two shift point is well under the 7150 rpm that Mr.
Marques has calculated it to be - assuming 3.0 and 3.2 liter M3s have
roughly similar rotating inertia values, which is a relatively safe bet.
I'll let him recalculate, if he cares to, but as a rule of thumb, if you
know your torque curve and gear ratios and want to use that data to
determine optimum shift points, either go out and get a Vericom (or
whatever) to revise your calculated shift points, or just drop the
calculated one-two shift point by around 5% for most cars. The two-three
shift point should drop around two to three percent and the three-four shift
point will typically be dropped around one percent, or even left alone.

One might drop the calculated shift points by even a bit more on many German
cars, since they appear to have flywheels rescued from old tugboats :-).

I've measured acceleration rates in first and second gears on many, many
cars over the years, and there is always a significant loss in first gear
acceleration values, based on an "expected" acceleration rate derived from
second gear actuals. The discrepancy varies on every car, but it's always
there, and it's always significant.

OK. If you've stuck it out this far without having done a snoring faceplant
into the keyboard, what about Mr. Collie's flywheel?

Well, a flywheel's main job (other than being a convenient place to hang a
starter and clutch) is to resist acceleration or deceleration. By design, it
has high rotational inertia, and it smoothes out the engine acceleration
from each power pulse and engine deceleration between power pulses, making
for a smoother drive. Of course, it also resists acceleration when that is
what you wish to do, with your right foot mashed to the floor, and your
right leg trembling from the effort. It does this especially in first gear,
as I've mentioned about rotating inertia way back at the beginning of this
epic tome.

As a result of the flywheel change, Mr. Collie's car would be noticeably
quicker in first gear, less noticeably quicker in second gear, barely (or
even not) noticeably in third, and probably impossible to measure any
difference in fourth or fifth. The change in each gear would be constant
from idle to red line. That is to say, a change in rotational inertia values
will not change the shape of the power curve being delivered to the drive
wheels in any given gear - only the height of that curve.

The reduction in rotational inertia would also mean that the optimum one-two
shift point in Mr. Collie's M3 will be higher than it would be in my M3.

OK, there's more, but thankfully, I've gotten enough of this stuff off my
chest to make me happy for the moment. You may now return to the key topics
of book purchases, elections or erams. :-)

Thanks for your time.

Bruce      

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