Tyre load, area of contact, and pressure

[Ciro Pabón]

Shredcheddar last post is the most beautiful I've seen in years... finally, we're getting "collectively" close. Thanks, man.

[Jersey Tom]

The part about wheel rate as compared to the spring rate in an F1 car is actually correct; the two are roughly comparable.

According to what source?

[Gecko]

I can't really disclose this, but it comes straight from the horse's mouth, so to say. Otherwise, Race Car Vehicle Dynamics by Millikens says a similar thing, although the information in there is somewhat obsolete.

[riff_raff]

Shredcheddar,

That post looks like a lot of work. Very ambitious of you.

You begin your post by outlining classical Hertzian theory. But it does not really apply to rolling rubber tires, since Hertzian contact assumes statically loaded and purely elastic bodies. A rolling elastomer tire structure, preloaded (or strained) by a compressible fluid volume, is a much more complex beast. The elastomer is subject to hysteresis effects and the gas volume suffers losses due to imperfect compression/expansion processes.

Theoretically, infinitely elastic bodies in pure rolling contact is a perfectly efficient process. But even very rigid (ie. metallic) bodies with sliding contact produce friction losses, and these losses are not linear. There is a big change in friction as the contact condition transitions from boundary contact, to mixed regime contact, to elastohyrodynamic conditions, to full hydrodynamic conditions. These different Mu values all occur without a change in the Fn value. To answer your question regarding the difference between losses incurred in elastomer bodies in rolling contact versus rigid metallic bodies in rolling contact, rubber tires operate under the principle of traction and rigid bodies operate under the principles of friction. As I noted in my previous post, rubber tires have a "traction" coefficient, and rigid bodies would have a "friction" coefficient. As you noted, Mu=tau/sigma only applies for static friction conditions. Once you transition to sliding contact, "friction" coefficient is mostly a function of the shear forces present at the fluid boundary interface. "Traction" coefficient is a function of the shear forces present to overcome the micro-level interaction of the asperities of the rubber tire tread and asphalt road surface.

Hydrodynamic friction coefficient is governed by Newtonian fluid mechanics. As you have noted, traction effects are more likely governed by Van Der Waal's effects.

What we really need here is a physics expert. I'm just a piker who barely made it through high school. Surfing, drinking and chasing girls was more important to me when I was 18, than a college education. So take what I say with a grain of salt!

Regards,
Terry

[Shredcheddar]

Thanks for clarifying and making that distinction, Riff Raff. Perhaps I am attempting to find a link between two behaviors that should not really be considered related. (That is to say, the idea that rolling rubber tire friction explicitly shares any characteristics with classical Coulomb friction).

I plan to maybe do a little more reading on the subject this summer, and come back to all the tire theory after next semester (fluid dynamics) with perhaps a little more background and insight.

In the meantime, I'll be wishing I was a physics expert.

[Shredcheddar]

Another thing... I should say, thank you Terry, and that before you clarified the distinction for me, I thought your seemingly too-simple post was quite out of character.

Cheers, to knowledge.

*Holds up imaginary pint*

[PlatinumZealot]

Good posts.. =D>

I like info like this.. but i never try to remember it until i actually encounter a problem that needs it. Keep my brain comfortable. LOL

[xpensive]

When I understand that tyre-friction is a little more complicated that the classic F = N times Mu thing, can anyone give a "area-number" for a "Mu equivalent" on a heated-up F1 tyre?

It just struck me that such a number could be most useful in another thread. Thanks, n sminkle.

[Shredcheddar]

After going back and skimming some of the previous posts, I think the goal of this thought exercise should be clarified.

We are aware that a tyre's force capability at a given load can be expressed using a traction coefficient (NOT a friction coefficient). This is simply the normalized force capacity for a given slip angle for a given load.

However, this traction coefficient is a function of load (tyre load sensitivity). So, if we go through an investigative process, we can arrive at specific parameters that vary with load and try to express how they work, or research them individually.

Why is traction coefficient a function of load?
- Certain tyre parameters change with load: real contact area, apparent contact area, static loaded radius, contact patch shape, tire temperature, etc.
- How do these tyre parameters effect traction coefficient?

To answer this question, we investigate these areas to figure out how they change with load, as well as how much of an effect they have on traction coefficient and the relative importance of each phenomenon. We prefer to do this theoretically! We're looking for a scientific explanation, and eventually, a more precise model!

Research and books have informed us that primarily three of the things above effect traction coefficient: real contact area, contact patch shape, and tire temperature.

Tyre temperature is not as simple or easily controlled of a variable, so we will eliminate it from our discussion. If we focus on geometric properties, we're left investigating how real contact area and contact patch shape change with load.

Since contact patch shape is more or less specific to a particular tire and its construction, we would like to look at real contact area. In other words, real contact area is the most pure function of load for geometric properties! Bo Persson apparently has a model that attempts to predict tire behavior, and all he needs to collect the necessary input data is a small square of the rubber compound. That is the kind of elegance we are striving for!

So the Hertz equation gets us on the right path. Now we must figure out its usefulness and continue to trek on.

[Belatti]

When I understand that tyre-friction is a little more complicated that the classic F = N times Mu thing, can anyone give a "area-number" for a "Mu equivalent" on a heated-up F1 tyre?

It just struck me that such a number could be most useful in another thread. Thanks, n sminkle.

EDIT: we both would like to know that number. My bet was a "global" 10%

[xpensive]

In situations like these, it is often useful to turn to extreme cases for advise.

Thinking a Top fuel dragster with what, 8000 Hp?
At 320 km/h, when the wheel-spin has stopped and the power is say 5000kW (6800 Hp), the one meter diameter wheels are at 1700 Rpm, meaning a wheel-torque of a monster 28 000 Nm, resulting in a traction-force of 56 000 Nm.
If the combined vertical load on the rear wheels is 2 tons, this calls for a "traction coefficient" (thanks, shred) of almost three.
And obviously, with a coefficient of less than one, they would have very little use for all that power?

[The_Man]

Here is the most important part:

"Because adhesive forces in rubber friction arise in the real areas of contact, can be replaced by , the adhesive force developed between the two solids; and is replaced by , the adhesional constant for the two surfaces in contact. - Analyzing Friction

Thus,

Here I assume that the is the adhesive force.
So which direction is this force in?
I would think it is the force holding the 2 surfaces together so it is in the direction normal tot he road. Therefore the adhesive foce must be added to the normal force in the equation



I'm just doing this analysis intuitively without much knowledge about rubber friction, but to me it seems logical.

[Jersey Tom]

Here is the most important part:

"Because adhesive forces in rubber friction arise in the real areas of contact, can be replaced by , the adhesive force developed between the two solids; and is replaced by , the adhesional constant for the two surfaces in contact. - Analyzing Friction

Thus,

Here I assume that the is the adhesive force.
So which direction is this force in?
I would think it is the force holding the 2 surfaces together so it is in the direction normal tot he road. Therefore the adhesive foce must be added to the normal force in the equation



I'm just doing this analysis intuitively without much knowledge about rubber friction, but to me it seems logical.

Adhesion doesn't change normal load. I'd think of it as a shear capacity in the ground plane.

[fastback33]

In tune to win, Carroll Smith goes into great detail with what is happening to the tires as more pressure is added to them and how things like downforce are adding more grip, as well as nearly how everything else affects them. I would highly suggest reading it.

[Shredcheddar]

An excellent book indeed, fastback. It's sitting two feet away from my desk at the moment; I've read it.

I must say though, that Smith explains more of what is happening to the tyres and their resultant grip as a function of load, but not precisely why or how. That's what the goal of this thread was... to take the good information covered in most vehicle dynamics texts and explore its mechanisms more deeply, and dare I say with a more scientific (or investigative) approach, rather than pragmatic.