[Diy_efi] ABS retrofit, many messages replied

[Perry Harrington]

This message is mainly regarding Mos' message and Eric Byrd's.

A brake bias valve is designed such that *when* a wheel locks up while braking,
it's the front wheel.

The reason for this is that it promotes directional stability.  If you lock up
the front before the rear, the car will travel in the same direction as
it was when the brakes locked.  This is understeer.

If the rear brakes lock before the front, the car loses directional stability
and swaps ends.  This is very prominent on vehicles with a large weight transfer
to the front under braking, or vehicles with a large disproportion in weight
distribution.

A stock late 80's Mustang gives a greate example of the first.  The rear suspension
on those cars was very softly sprung, with a lot of braking force in the front.
If you were to chance hitting the brakes abruptly (emergency) at high speed, the back
end of the car will nearly lift off the ground.  It is neccessary then to modulate
the brakes in order to prevent the car from swapping ends do to a large weight transfer.

A very good example of the second scenario is an 80's Dodge D50 or Mitsubishi pickup.
These trucks were very light and had almost no weight over the rear axle.  This
manifested itself in several manners, rear brake lockup and lack of traction on steep
surfaces.  This vehicle would always lock up the rear brakes in a brisk stop.  It
was very disconcerting as the front brakes were not great.

To address single axle ABS, the driven wheels are almost always the ones with ABS.
On FWD cars they put ABS on the front because the weight distribution sucks so bad
and only is worse under braking.  They effectively have to limit the applied
braking force in order to compensate for the small, cheap, crappy tires often
installed on such vehicles.

On RWD vechicles, ABS is almost exclusively found on the rear axle of pickup trucks just
for the reason I listed above.  Pickups are designed to carry weights that are a
significant fraction of their GVWR, thus they make the back end stiffly sprung and
light in order to cheaply carry loads.  They offset the design by installing ABS on
the rear axle only.

In inclimate weather this is no peace of mind, as the understeer phenomenon is very
present.

As to brake biasing, the vehicle's typical power is distributed 70/30, front biased.
The more bias you add to the rear, the more it is likely to lock up.

Thus if you biased the vehicle 70/30, an ideal vehicle with no weight transfer would
have both axles lock up.  If the same vehicle was biased 75/25 the front would lockup
and the rear would not.

Since there are few ideal vehicles (if at all), you must limit the pressure to the
rear brakes in order to prevent their lockup, or locking up before the fronts.  In
low friction coeffient situations you will likely lock both axles, but with normal
to high friction coefficients, the front will lock only.

VW has been installing a variable bias valve on their semi trailing rear axle FWD
vehicles for many years.  These cars have single, very large stamped steel "swaybar"
type trailing arm assembly with MacPherson struts.  There is a bias valve attached
to the body of the vehicle with the actuator rod connected to the trailing arm.
When the car experiences a large weight transfer the bias valve progressively limits
braking force to the rear axle, effectively preventing lockup.

As for the mechanics of weight transfer, here's a very simple model:

A tire has a given grip which is a function of it's friction coefficient and weight
applied to the tire.

Let's describe 2 tires:

The race tire has a coefficient of 1, meaning that 100% of the weight applied to the tire
can be transferred to grip.

The street tire has a coefficient of .85, meaning that 85% of the weight applied to the
tire can be transferred to grip.

This model only applies up to the maximum rating of the tire, let's give the race tire
a weight rating of 1500lbs and the street tire a rating of 1200lbs.

What this means is that the tire can see a vertical loading force of 1500 and 1200 lbs
respectively before overloading.

Our model car weighs 3000lbs.

If we take the ideal car that has a 50/50 weight distribution, you will see that the
race tire will sustain 1G on 2 tires and the street tires will sustain .68G on 2 tires.

This may confuse you at first, but there is more to come.

First, let's explain the ideal numbers:

Car weight			3000lbs
Weight per tire at rest:	750lbs
Maximum load per tire:		1500lbs(race)	1200lbs(street)
Friction coefficient:		1.00(race)	0.85(street)
Percentage of static grip:	50%(race)	73.5%(street)

When the car is loading the tires you must take into account the weight rating and
the friction coeffient as multipliers.  Your weight rating is the maximum vertical
load you can place on that tire, the friction coefficient is how much grip the tire
will generate at maximum load.

Grip is distributed in 2 axis, lateral and forward.  You can quickly determine how
much of a grip budget you have per tire by just doing the friction coefficient math
first, thus the race tire has a budget of 1500lbs and the street tire has a budget
of 1020lbs.  This is the useful grip you can expect from the tire at maximum load.

Thus with the race tire you have 750lbs lateral thrust and 750lbs forward thrust
available.  With the street tire you have 510lbs of lateral thrust and 510lbs of
forward thrust.

You can trade off these values all you want, but you cannot exceed your budget.

Weight transfer directly affects your budget, because weight gives you grip.  This
is where the friction coefficient comes in.

Say you are driving forward, but you only have 1700lbs on the rear tires, you will
only have 1*1700 or .85*1700 lbs of forward grip available.  This means that even
though your tires CAN generate more grip they aren't because there is not enough
weight transfer to cause them to generate maximum grip.

Take drag racing as example:  The ultimate ideal drag racer has 100% weight transfer
to the rear tires.  In our example that means 3000lbs on the rear axle.  With
100% weight transfer the race tires in our example will generate 1G of forward
thrust. The street tires will generate .68G of forward thrust before slipping, but
100% weight transfer will never occur because this would exceed your budget.

Now you must take into account that the friction coefficients of these tires are
based on a surface with a coefficient of 1.  On drag strips they can modify the
surface to increase the coefficient and thus the coefficient of the tire.  If you
doubled the coefficient of the surface, you double the coefficient of the tire.

This plays in both directions.  If you halve the surface coefficient, you halve the
tire coefficient.

This is where rain, snow, and ice come in.  This is also where weight transfer comes
in and why bias matters so much.

If your weight transfer were exactly the same for all surface coefficients, your
brake bias would be the same for all surfaces.  Unfortunately there is a problem.
Your weight transfer is determined by the friction coefficient of the surface.

If you apply your brakes on a surface coefficient half of normal, your weight transfer
will be less and thus generated grip of the tires.  Your tires need weight transfer
to develop grip, otherwise they will only have the grip they do at static weight.

This is why your brakes lock up when it's slippery outside.  Your brakes are generating
the same force, but the tires aren't and thus there is less weight transfer and less
grip.

The whole stumper in all this is:

Tire manufacturers as a general rule do not release friction coefficient information.  Thus
you do not know how much better a tire is.

You also cannot rely on treadwear ratings as they are not standard across manufacturers, only
within model lines.

What you can do is make some educated assumptions.  Race tires usually have a FC of around 1,
the more expensive, the higher the FC.  Street tires are similar.  The cheaper the tire, the
less the FC.  There are many factors in tire construction which influence the FC, so price
is a good starting point for estimating FC.

I hope this makes sense to everyone.  You can find similar material in books on race cars,
with nice pretty graphs.

--Perry

-- 
Perry Harrington			Data Acquisition & Instrumentation, Inc	
perry at dainst dot com					 http://www.dainst.com/

Those who would give up essential liberty to purchase a little temporary safety
deserve neither liberty or safety. Nor, are they likely to end up with either.
                             -- Benjamin Franklin

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