-OvO-

it's not worth doing if it's not a bolt-on -- for any significant investment I'd be just as far ahead to sell the A8 and buy an S8 instead.

randy's comments about tires being the limiting factor made sense. I'm sure I'm not running very sticky rubber - though I don't think I've ever activated the ABS on clean dry pavement either. Honestly, I think the ABS makes my stopping distances *longer* in the snow, though I've never tried to conduct a controlled experiment.

ryoung

Snow that piles up in front of a wheel that isn't rotating can often slow the car better than an ABS controlled wheel that keeps turning. The same can occur on gravel roads. The only problem is that without ABS in these cases, you lose steering when the front tires stop rotating. Actually, maintaining steering is probably the biggest advantage of ABS whether the road is wet, dry, or snow/ice covered.

ryoung

The 100% mechanical Citroen system you describe is an elegant solution. How does Audi do this with electronics?

With the A8/S8, the optimum brake bias is as low as 1.5:1 at low deceleration g's (such as on ice) to as high as 2.23:1 with maximum braking on clean dry roads. An accelerometer hidden away somewhere measuring deceleration g's would make a satisfactory sensor, but then how is brake bias actually changed? I guess this brings us back to your original question. :-)

I suppose that the ABS system could reduce braking on the front wheels when braking at low deceleration g's, but then we should feel ABS pulsation in all routine stops.

ttuling

A model year 2002 Saab press release at http://www.saabnet.com/tsn/models/2002/pr9.html says
<blockquote>This ABS system also incorporates improved electronic brake-force distribution (EBD) that works during hard braking before ABS activation. It correctly balances the friction available at each axle with the braking forces being applied. The system is controlled by the integrated ABS controller, which compares the rear-wheel slip with the front as a reference point. As soon as significant differences are detected, pressure to the rear hydraulic system is modulated to provide the most balanced effect without operating the electric ABS pump, so the driver is unaware of the adjustments taking place.</blockquote>
A European Toyota TSB at http://techdoc.toyota-europe.com/pdfs_TSB/CP5003_0_1.pdf covers Bosch EBD (or maybe a later version because it seems to have a place to put the released fluid between the master cylinder and the caliper) says
<blockquote>According to the slipping condition of the rear wheels Skid Control ECU control the pressure holding and the pressure reduction valves in order to adjust the fluid pressure in the rear brake callipers.</blockquote>
This is consistent with EBD not running the ABS pump and vibrating the pedal, which it can get away with so long as it doesn't want to rebuild rear brake pressure. And that wouldn't be likely because if the weight is transferring back onto the rear wheels, it's probably because the driver reduced pressure on the pedal.

For all this to work, the car is probably set up to have something like the 1.5:1 bias with stock pads. Supporting this, the owner's manual says
<blockquote>If both warning lights (ABS and BRAKE warning lights) come on at the same time, the rear wheels could lock up first under hard braking. [You could crash. Get it fixed. Drive slowly.]</blockquote>
The service manual says something similar. I suppose a fault which could trigger only the ABS light would have to do with the ABS pump for reapplying brakes.

So that's EBD -- I think. If I hear solenoid activity without the pump running or pedal pulsing, especially under firm braking on a dry road, I'd suspect it's EBD. Going to pay more attention now. Too bad we can't log ABS activity with VAG-COM.

Tom

ryoung

Assuming that the front and rear calipers see the same hydraulic pressure, the brake bias is ...

2.45 for the stock S8
2.30 with my Alcon/Stasis street set-up
2.35 with my Alcon/Stasis track set-up
2.23 optimum for maximum braking

I'm not sure what to say. At least with the S8, since the initial 2.45 brake bias doesn't allow any room to modulate (lower) the hydraulic pressure to the rear calipers, I'm having trouble imagining how EBD could work.

BTW: With this <a href="http://pws.prserv.net/usinet.Young/BrakeBiasCalculator.html">Brake Bias Calculator</a>, the values in the "Bold" fields will be calculated.

Also fwiw, this Stoptech chart shows that ~2.85 is the stock brake bias for an S4, and that the optimum brake bias is a range 2.2-2.8 (though I don't understand how the "optimum" could be a range).

<img src="http://www.stoptech.com/tech_info/img/brakebias_7.jpg">

ttuling

That's a nice online weight transfer calculator. I tried it out for a D2 A8L with HP 2 front brakes. The numbers stumped me for a while. I pulled the ABS valves' fuse and locked up the rear wheels twice when braking hard in an empty parking lot.

It turns out that a 4000 lb car with a 60:40 weight balance, a CG 22 inches high, and a 118 in wheelbase gets to 3:1 under 0.8 g braking. So say the force diagram and math at http://www.miata.net/sport/Physics/01-Weight-Transfer.html, which look okay to me, though they don't account for any lowering of the CG during braking whether by front squat or rear brakes pulling on the ends of softly sprung trailing arms (not an A8 phenomenon). I'll be interested to hear if you think this math is valid.

If the CG were 10% lower, it would take 10% more braking to reach 3:1.

That it could get so far away from 60:40 surprised me.

Tom

ryoung

What brake bias did you calculate for the A8L with HP2 front brakes?

In my load transfer calculations, I also make the assumption that these heights remain constant under braking, acceleration, and cornering. In the xls spreadsheet, I get 3.0:1 when I plugged in 0.8g of deceleration, a 118" wheelbase, and a 22" cg height; and also 3.0:1 with 0.88 g and a 20" cg height. Since I'm using essentially the same math as the miata.net link, I suspect the 0.1 difference is the result of rounding errors.

Note, though, that this front:rear load distribution is not the optimum brake bias. The friction force generated by a tire during braking does NOT increase in direct proportion to vertical load. The coefficient of friction of the front tires decreases slightly as load increases, and the cf of the rear tires increases. This reduces the 3.0:1 ratio of load distribution to a 2.2:1 optimum brake bias.

BTW: This coefficient of friction deviation from theoretical, though small, has a huge effect on a car's performance and explains a whole bunch of stuff.

1. How swaybars affect cornering balance

2. Why nose-heavy cars understeer

3. Why race cars run on slicks

4. Why wider tires increase grip

5. Why lighter cars corner at higher g's

6. Why a wider track increases cornering g's

7. Why lowering the center of gravity improves braking and cornering

8. Why max braking g's exceed max cornering g's

My spreadsheet in <a href="https://forums.audiworld.com/a8/msgs/36145.phtml">Weight Distribution Revisited</a> uses the formula shown at the bottom of this chart to convert load distribution to brake bias.

<img src="http://pictureposter.audiworld.com/17157/tiregrip.jpg">

ttuling

The calculator returned 2.49 for the A8 with HP2 front brakes. I used the larger rear cylinder diameter of the two in the Bentley manual.

Now I'm wondering if rear wheel lockup with ABS/EBD disabled happens because of some extra, temporary forward weight transfer when the rotation around the pitch axis ends following abrupt brake application. Or is something else likely to be a bigger factor?

Where did the grip/load curve come from? It varies for what -- tire compound, geometry, inflation pressure? (I suspect it's not universal because I have a hard time imagining 1000 lb on my bicycle tires.)

Thanks for this discussion. It has led me to think that the rear brakes are usually underutilized, and that ABS-like vibrations when braking strongly though not abruptly do indeed reflect tire limitations (like you said) rather than any built-in rearward brake bias. But I wish I could easily confirm that with a log of which ABS valves are operating.

Tom

ryoung

The data in my chart was the average of data taken from charts in "Going Faster" by Danny Sullivan and from an article in the July '03 edition of "Racecar Engineering" -- they agreed surprisingly well. The black line is actual, the coefficient of friction between the tire and road drops as load increases. The blue line would be the theoretically constant cf of 1.0. The formula in the chart is just an Excel polynomial curve fit of the data that I then used to determine "Available Grip" in the spreadsheet in "Weight Distribution Revisited".

Neither "Going Faster" or "Racecar Engineering" gave any details at all on the tire. I just used the data as-is and was moderately surprised when it seemed to predict the actual cornering and braking performance of the S8.

And you're right ... This has been an interesting dscussion. Thanks.