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I have just read most of the lively discussion about the StopTech balance chart and brake bias. Sorry we have been too busy to properly answer all the questions generated. James Walker has written a great new article that I hope will answer many of your questions about brake bias. James Walker will follow this thread and answer questions for Stoptech--Bob Lee

Here is the link<ul><li><a href="http://www.stoptech.com/whitepapers/brakebiasandperformance.htm">Link to StopTech white paper on brake bias and performance</a></li></ul>

ryoung

James Walker states "Perfect brake bias is obtained when the front-to-rear balance of the brake system exactly matches the front-to-rear weight balance of the vehicle".

The real world performance of tires throws a wrinkle into this. The available grip of a tire (whether cornering or braking) is almost, but not quite, proportional to the load on the tire. The coefficient of friction between tire and road is <b>not</b> constant; and if you double the load on a tire, the available grip does <b>not</b> double. This is actually the main reason that changing springs, sway bars, or shock damping affects the balance of a car; but back to braking ...

At 0.95g deceleration, optimum braking of my S8 occurs with a brake bias of 2.23:1, but the front/rear load "bias" at that same 0.95g is 3.62:1. That's a huge difference, and it's a result of the fact the heavily loaded front tires have much less lb of grip per lb of vertical load than the lightly loaded rear tires. See <A HREF="https://forums.audiworld.com/a8/msgs/36145.phtml">Load Distribution Revisited</a>.

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

And thanks for the White Paper. Stoptech has gone a long way toward removing the mythology from braking systems.

VonK :: Retired

Amen!!!. :-) Also why wider treads stick better (lower contact patch stress).

ryoung

Wider tires front and rear increase rear bias (higher deceleration limit)

Wider rear tires only increase rear bias

and the converse for narrower tires

[BTW: I'd be embarrassed to admit how many years it took for me to understand why wider tires grip better. Just changing the shape of a contact patch from long and narrow to short and wide improves the pressure distribution under the contact patch itself, even when both contact patches are the same size. As you said, reducing the amount that a contact patch has to wrap around the circumference lowers the contact patch stress.]

VonK :: Retired

---&gt; in terms of (pounds of contact load)/(square inch of contact area). One more reason why ever larger tire diameters are sought to increase the patch <b>length</b> as well as the width, until unsprung weight becomes prohibitive.

I'd be interested in your opinion as to why F1 uses such high aspect ratio tires when racing sports cars seem to go the other way.

Harald

ryoung

Last year I read an interview with a Bridgestone F1 race tire engineer, and he said that the optimum wheels for F1 would be 18" in the front and 20" in the rear versus the current 13" front and rear. He also said, though, that he didn't think that F1 drivers could drive an entire race at the higher cornering g's with the quicker response to steering input that would result.

The larger wheels would also provide room for better brakes, as if 4+ g's of deceleration wasn't enough.

StopTech Support

Thanks for taking the time to read and comment on our paper. In direct response to your proposed correction, there are multiple factors at play which both support and simulatneously negate the effect of tire sensitivity to normal force loading.

1. In the region of stable tire slip (all partial braking events before the tire reaches its friction (mu) peak), tire normal force sensitivity is a non-issue. In other words, driving around town under typical decleration levels (and in fact under all deceleration levels up to the point of ABS control) optimum bias is truly independent of tire loading characteristics.

Of course, tire normal force loading will indeed impact the force vs deceleration relationship under these conditions, but, if I can quote myself "Perfect brake bias is obtained when the front-to-rear balance of the brake system exactly matches the front-to-rear weight balance of the vehicle" is 100% accurate for all non-limit braking events.

2. For the discussion of limit braking (those events where the tire is operating at or near its mu peak) there are many, many factors at play which can effect the optimum bias. Naturally, tire load sensitivity can effect the ability of a tire to sustain a given level of braking torque, but other factors as well can effect such a change in performance:

- speed of the vehicle
- angular velocity and resultant inertia of the rotating wheel end components
- tire temperature rise throughout the braking event
- rate of force build-up at the contact patch
- rate of body pitching
- suspension tuning (specifically front damper bump valving and rear damper rebound valving)
- dynamic toe and camber effects during suspension compression (front) and rebound (rear)
- and on and on...

In order to craft a white paper for all to appreciate, we had to draw a line in the technical sand where we could focus on the topic at hand while assuming consistent characteristics for these additional factors.

So yes, tire normal force loading under limit braking maneuvers can influence the optimum bias, but the material that we present is completely valid under the conditions we specify, and even with this additional factor our fundamental analysis is sound.

That said, because we deal with these extraneous factors every day, we are well aware of these effects and optimize every one for every application we develop. How? Real-world testing.

While one could certainly develop a math model to simulate all of these twenty-some-odd degrees of freedom in the bias relationship, models are only so good. There is no substitute for a real-world confirmation of perfect bias, and at StopTech we take that last step to ensure that what our models predict works in the field. Note that it is not uncommon to find that our predicted sizing is off by a touch when we get to the test track. This is expected, and we can experiment with alternate components in order to dial-in that last 5% of optimum bias to account for these other factors (such as normal force sensitivity).

That's what makes us different. You have the confidence that even though there are multiple compounding factors in the bias equation, we test our stuff. Every application. Period.

Finally, while longitudinal tractive effort coefficients might change dramatically on a winged race car, in the real world on real cars the effect of normal force loading during weight transfer is actually not a very significant factor. In fact, because the fronts gain weight as the rears remove weight, the end effect is a slight forward shift in bias, as the rears will gain effective work capability faster than the fronts will lose effective work capability. Compared to the reduction in absolute normal force, however, this is a secondary effect which is usually only addressed during final testing and fine tuning.

Thanks again for your input. Here at StopTech we are simply trying to educate as much as possible, as we believe firmly that once you, the potential consumer, have a firm grasp of the fundamentals of braking systems our products and testing techniques will sell themselves.

JWJr

StopTech Support

Thanks for the question. Let's address this question in three distinct phases.

1. During all braking up to the point of EBD intervention (light braking), the bias is dicatated by weight distribution and brake torque ratio. EBD cannot effect bias before enough rear slip is present to warrant EBD intervention.

The end effect of this situation is that while stability is not a concern (this is light braking after all), bias also influences brake pad life. In other words, a system which is heavily front biased will experience premature front pad wear. Just the opposite will be true for a system which is heavily rear biased.

2. During medium braking, a system which is heavily front biased will delay the activation of EBD because the front wheels will be building torque more rapidly than the rear wheels. However, if a system is heavily rear biased, EBD will activate earlier than it would with an optimized system. While stability will be maintained, the system is simply acting as a band-aid for a poor design. In extreme cases, the driver may receive excessive audible and tactile feedback if EBD now has to enter modes which require the release of rear wheel pressure (an undesirable mode of EBD operation).

3. Under full ABS conrol (maximum braking) it is possible that the effects of poor bias (either too much front or rear) can be masked by the closed-loop nature of the control. However, nothing is guaranteed, and without testing it is not possible to know if the ABS is capable of effectively controlling the mismatched hardware.

Naturally, the ill-effects of poor bias under light and medium braking will still be there, but arguably in full-tilt ABS, the system has the best shot of making the vehicle function in a reasonable fashion. As the saying goes "Even a blind squirrel finds a nut every now and then."

Thanks again for your question.

JWJr

s4what?

Great stuff - I printed every article

StopTech Support

Thanks for your comments, but your additional statement are actually stated incorrectly.

1. A wider rear tire will allow the rear tires to react to more braking torque before the point of instability. This effectively increases front bias (rears slip later).

2. A narrower rear tire will allow the rear tires to react to less braking torque before the point of instability. This effectively increases rear bias (rears slip earlier).

It is true (as the original article delineates) that increasing the overall deceleration limit of the vehicle also increases rear bias (more weight transfer). Therefore, some of the benefit of a wider rear tire (which on its own increases front bias) may allow for a slightly higher overal vehicle deceleration (which on its own increases rear bias), so as you can see the two factors are diametrically opposed. However, since most vehicles are not rear biased to begin with, the front tires are the limiting factor for ultimate deceleration. Under these conditions a wider rear tire will not allow for a higher overall deceleration limit and will only serve to increase front bias.

JWJr