Re: ABS Stuff

[Scott Fisher <sefisher@cisco.com>]

DeWitt Harrison writes:

> I'm not as confident as you are that a locked up tire produces less
> friction than a "threshold" rolling tire. 

Maybe a simple demonstration (or at least a description of said simple
demonstration) will help you visualize what's going on.

Years ago, at one of the first competition driving classes I attended,
the instructor had cobbled up a neat little demo rig using a spring
scale, a board, and a weighted block of wood to which the scale was
attached.  

He'd pull the spring scale parallel to the board, in an attempt to drag
the weighted block down the board.  As he pulled, we saw the scale
register the side load at so many pounds (or ounces or grams or
whatever) on the scale.  He'd keep pulling until the weighted block
started to slide --

*at which point the indicator on the scale dropped to a lower figure.* 

You can do the same demo at home with a box, a rubber band, a ruler, and
your kitchen table.  Staple the rubber band to the box, align the ruler
at one end of the rubber band, and note how far the band needs to
stretch before the box starts sliding, versus how far it stays stretched
after the box starts sliding.

The obvious, visible, and unforgettable lesson to be drawn from this is
that static friction is higher than sliding friction.  We all saw it, in
a measurable and quantifiable demo.

The more *subtle* lesson, not always obvious or visible, is that tires
while rolling are exhibiting static friction, for the simple reason that
the contact patch is actually immobile (or very nearly so) with respect
to the road surface.  If you want the Bill Nye proof of that, drive
through a puddle, then get out and look at your tire tracks; you'll see
the imprint of your tread pattern, and not a blur of straight lines
(unless you goose the throttle so much that you spin the wheels coming
out of the puddle!)

Audi's own reasoning for disabling the ABS, back when they were
introducing ABS and quattro in the same cars, was that in certain
conditions (mainly loose snow and loose gravel/dirt), locking the wheels
let a wedge of the loose material build up under the fronts of the
tires, and this actually helped slow the car faster.  In effect, locked
wheels in gravel let the tires build their own wheel chocks.  Hard to do
on asphalt. 

> I admit that I have seen graphs of cornering force vs. slip angle 
> which show clearly that when you push a tire too hard in a turn, it 
> "lets go." But can we extrapolate that to straight line braking? I 
> don't know. 

Apples and oranges, or at least tangerines and oranges. Cornering force
is really a case of vector addition; you've only got a limited amount of
adhesion on each contact patch, the so-called "friction circle."  If you
try to add two acceleration vectors whose sum is outside the friction
circle, that's how a tire lets go.  (Vector addition, in this case, can
be modeled by making a parallelogram with the known vectors being the
two adjacent legs; the sum vector is the diagonal.)  ABS probably won't
do much for a car that's going to spin, or one that's going to plow off
course, because it's simply going too fast in a corner; ABS is limited
to managing the fore-and-aft vector alone, and it's possible (given the
right lateral acceleration) for the ABS to manage the rolling friction
within the linear threshold of the friction circle and still exceed the
circle's limits when you add a lateral acceleration.

So in the dual-vector case (which is more or less the same whether
you're cornering while braking or cornering while accelerating), you're
asking the contact patch to do more than it's physically capable of, and
it starts sliding because the sum of the two loads exceeds its limit of
adhesion.  In the locked-up braking case, you've moved the car from
static friction (which is higher) to sliding friction (which is lower).

I *will* say that understanding this and implementing it at 100%
efficiency, lap after lap, are two entirely different things; the last
time some dimbulb in a minivan poked out in front of me, I still slammed
on the (non-ABS) brakes and locked up at least one wheel, forgetting
everything I learned about threshold braking.  But the understanding of
what's actually going on down at the road surface will certainly help
make anyone a more engaged driver, which is what this is all about.

--Scott Fisher