Common Sense Counterfactuals - Tire Width

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multisync
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Common Sense Counterfactuals - Tire Width

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this was posted on another forum recently:

"Did you know that the width of a tire has no effect on a car's ability to stick to the road on turns or on accelerating or breaking?"


Does the panel agree?

NewtonMeter
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Re: Common Sense Counterfactuals - Tire Width

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I'm gonna take a flyer and say he/she cited coulomb friction as the source of their argument, yes? Namely, the friction force being directly proportional to the frictional coefficient and the normal force acting on the body?

Though correct, it's not the only source of the grip from a tyre. There's a shearing component at play as well in generating tyre grip. Let's call it the "digging in" component - think of offroad tyres/applications for a very graphic example. And that component does have a surface area term in it - thus brining tyre width into the equation.
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Tim.Wright
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Re: Common Sense Counterfactuals - Tire Width

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Like Newtonmeter said, if tyres operated purely as linear coulomb friction devices then yes its true.

In reality, tyre grip is horribly non linear and is a function of many things which include tyre width.

So the original statement is complete crap. Where did you read it?

Tim
Not the engineer at Force India

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Ciro Pabón
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Re: Common Sense Counterfactuals - Tire Width

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Well, I adhere to Tim opinion: what you read is plainly wrong.

Summary: if the width is not important, why slicks? You could use rain tyres and get the same grip. So, get a grip... ha, ha.

Now, one of my legendary short posts. I disagree with Tim in one thing: it's not "horribly" non-linear, it's beautifully non-linear. What's going to be horrible is this post, because of its length, but I honestly think that any aspiring racer in the XXI century should know this. In short, the best graph I could make of the data available to me is this one:

Image

Why? Well, kep reading.

The weight of the car is not the only thing that limits the adherence, but the interlocking and sticking you get between tires and asphalt. If you could develop a perfect interlocking (think of a "funicular" with gears) you would, in theory, get infinite "friction factor". Same consideration applies if you could develop perfect "stickiness" between the asphalt and the tire. This is not as farfetched as you could think, there are new materials based on gecko's feet that help to develop this "microeffect" of fractal grip.

In the end, friend, F1 and dragster tires "work" mainly by adhesion. Therefore, slicks.

I give some links again:

Why Tires Grip The Road: New Theory Reduces Testing
..dry-weather tires in Formula One racing ... exude resins and actually even out irregularities in the asphalt, thus considerably improving the area of contact... Racing tires are literally sucked dry.
As you can imagine, the wider the tyre, the largest the amount of fluid the tyre "sweats".

So, what you try to do with a racing tyre is to "fill" the spaces among the irregularities in asphalt. There is a new theory, some years old by now, that has completely superseded Coulomb's. If you wish, read here.

Elastoplastic Contact between Randomly Rough Surfaces

As, in my experience, NOBODY follows links around here, there you have my explanation. I do not doubt many people will point out my errors... sigh. 8)

Essentially, what Bo Persson (blessed be his soul!) proved is that if you see the asphalt as a fractal surface (remember fractals?) the area of contact between tyre and asphalt increases proportional to the force you put on the tyre. This image shows how small is the real contact area under regular loads:

Image

There are several "modes" of developing friction, from an "interlocking" mode to a "sticky" mode. The interlocking works at macroscopic scales, the stickiness work at molecular scales.

This means that the tyre "grabs" the small rocks in the asphalt and also "sticks" to the smooth parts of the tarmac. In the following image, which I also repost, the "interlocking" occurs when you see the tyre at the 5 mm level (macrotexture) while the "stickiness" happens at the microtexture level.

Image

Therefore, the references to the "physics of smooth bodies" don't apply: the smoother the surface, the more adhesion you can develop by chemical, electrostatic or even dispersive or diffusive mechanisms (and less macroscopical interlocking or "mechanical adhesion"), which are the five mechanisms developed to explain adhesion.

There is an optimal asphalt-and-rubber texture where the sum of the five modes of adhesion reach a maximum.

Finally, slip angle is what makes the tyre grip. An infinitely narrow tyre has no slip angle... This is the image from "The Racing and High-Performance Tire", that shows how slip angle works. For the non mathematically inclined, the idea is that a tyre works by twisting. So, a wider tyre has a more "gentle" twisting, so the erosion (wear) is smaller.

Image

So, why are not infinitely wide tyres used in racing?

Well, the problem is aerodynamic, as you can imagine. So, the width of a tyre is a compromise between the aerodynamic drag you "pay" and the "stick" rewards you get from a wider tyre.

What are the rationals? Here you have a "small" history of tribology.

The first known theory of friction was written by Leonardo Da Vinci around 1450. He studied a lot of things about friction, including wear, bearing materials, plain bearings, lubrication systems, gears, screw-jacks, and rolling-element bearings. Almost two centuries before Amontons' Laws of Friction were introduced, he had discovered them.

Unfortunately his writings were lost and unread for two centuries. After Leonardo, the first guy (and almost the last...) to explain friction was Amonton, around 1650. He rediscovered Leonardo's principles of:

- friction proportional to weight and
- friction independent of the area of contact

Coulomb, around 1750, introduced the idea of:

- kinetic friction independent of speed of displacement

These three laws can be summarized in this graph, which, unfortunately is most of what the majority of people learn about friction:

Some engineering courses never go beyond this graph. Sad.
Image

Then after another century, Reynolds (and a russian guy whose name I cannot remember) came up with an equation (unchanged since 1880 or so) of:

- friction in fluids proportional to sliding velocity and bulk viscosity and inversely proportional to thickness of film

A few years later Stribeck (not sure about the name) came up with the Stribeck curve that explains that when the film is very thin, Reynolds equation fails. He stated that:

- the area enlarges because the contact surface deforms elastically and the film, with a larger area, can support the weight.


Then, after 50 years (we're getting some speed here... ), Hardy, around 1920, came up with the idea of very thin films like this:

- asperities coming in contact, breaking and then reacting chemically with the lubricant, thus creating a tenacious layer of lubricant and small chips of material that supports the weight and prevents further wear (I swear I'm not making this up... ).

Hardy findings about films inspired some people to try to understand what happens in dry friction. Finally, a few years later, a guy named (I think) Bowden came up with the concept of friction by adhesion. Another guy called Desangulier in Coulomb's time had the same idea but nobody heard him because of Aumonton 2nd law (friction independent of area), so people devoted to purely geometric explanations (interlocking of asperities). Bowden discovered that Tim is right and:

- friction is created by adhesion of solids because of electric charges.

It might sound incredible, but asperities in solids deform above a critical shear strength, which depends on the adhesive forces of the two surfaces in contact. That adhesive force, the one that "crushes" the asperities, is created by electric charges.

Yes, I know, it sounds like science fiction, but I'm dead serious. The relationship with the load is not lineal but is, as showed in the first graph of this "summary": ;)

F = L^2/3 (that is, friction is proportional to load elevated to two thirds)


The inconsistence with Aumonton's first law (friction proportional to load) is explained because the real contact area varies under load. Why nobody noticed in five centuries beats me.

Once electronic force microscopes were developed, around 1950, Bowden (and Desangulier) were vindicated, because measurements were precise enough to validate their theory. Thus, Tim is right. That's most of what I know about friction. and you can stop reading now.

If someone is interested in visualize (that's what distinguishes engineers!) what's going on, please, come with me for a couple more paragraphs and imagine what happens if you become really tiny: your weight decreases as the cube of your height does (a person half as tall, half as wide and half as deep, weighs eight times less!), right? However, if you're half as tall, your surface is only one quarter of the original one. For example, let me tell the story about Gauss famous observation on the size of things.

Gauss teacher told the class (in primary school, according to legend) that the Universe could grow slowly to one million times its actual size and nobody would notice. Gauss answered that it was not true, because all the picture frames would fall from the walls. Their weight would increase to the cube, but the area of the strings holding the pictures would increase to the square and they would not be resistant enough to hold the pictures to the walls. Incidentally, that's why ants and spiders have such thin legs and elephants have sturdy ones, but I digress.

So, if you're a really small asperity, you have a very large surface compared with your weight. If your ten thousand times (2^13) smaller than a person (around 0.2 mm), your weight/surface relationship is 10.000 times larger (I think). Persons are taller than wider: this means that electric charges migrate to the pointy parts (by electromagnetic laws: that's why lightning rods are pointy). Like this:

Small clay particle with positive electric charges in the pointy parts
Image

Thus, any point in a microscopic asperity of the tyre (charged positively) adheres to the sides of the microscopic asperities of the track (charged negatively). Its weight is ridiculously small compared with the surface, thus the electric forces are immense compared with gravitational forces at these scales. Tyres adhere to asphalt by electricity. QED.

Finally, in the last ten years friction has been explained by quantum theory. In the improbable case that someone is interested in "The Master Equation" of friction, there you go: http://www.sbfisica.org.br/bjp/files/v27_214.pdf

Friction Quantum Theory Master Equation. If someone can explain it in simple terms, be my guest!
Image

As usual, sorry for going OOT and sorry for the length of the post.. perhaps someone will read al this voluntarily! On the other hand, my poor students have no choice.
Last edited by Ciro Pabón on 11 Jan 2011, 20:08, edited 2 times in total.
Ciro

Dragonfly
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Re: Common Sense Counterfactuals - Tire Width

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I am not an engineer
... but read to the end.
=D> :)
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strad
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Re: Common Sense Counterfactuals - Tire Width

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I don't think I need to add to the discussion of contact patch size...What you've read is wrong.
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Dragonfly
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Re: Common Sense Counterfactuals - Tire Width

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Does not matter much to me, I am not a physicist, neither an automobile professional. I simply like the style Ciro uses to write and represent his view :)
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humble sabot
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Re: Common Sense Counterfactuals - Tire Width

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glad i refreshed before i posted. i didn't have quite as much to add before and now i know all sorts of new stuff, thanks!

I can't speak for anyone else but i'm going to read the links too!


what i was going to add actually is the accepted wisdom that your contact patch size is weight dependent and not as much tyre dependent, this is probably the real source of the claim you heard.
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Ciro Pabón
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Re: Common Sense Counterfactuals - Tire Width

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Well, yeah, that's the accepted wisdom. It works when you try to measure patch size in this way:

Image

However, this previous picture alone (a "thought exercise" I use in class) shows you that the linear relationship cannot increase infinitely, ain't it? ;)

You have a "maximum absolute patch", when the "ultraelastic, unbreakable" tyre I'm showing in that picture, touches the asphalt completely and becomes perfectly flat under an infinite load... thus, even in that there is no linearity, but I digress (again!).

However, what Mr. Persson showed is that this isn't true at the microscopic level. If you were small enough, or if you had enough powerful vision (like the one fans ask from race marshalls, ha, ha) you would see something like this (sorry for using the same image):

Image

That's why the real patch size, that is, not a measure of the "flat" area of the tyre but the actual contact surface, made of many small points where the tyre is supported by the small irregularities in the asphalt, increases with load.

Of course, if your tyre is softer, this real patch size is larger.

This explains why dragsters have frictions coefficients (calculated by Coulomb's law) that are twice the one of your regular car. The actual surface of contact is twice the size of the one of your car, something that can be very easily proved (just calculate how large is the friction factor to go from 0 to 400 mph in 400 meters, using school equations for accelerated movement and you'll get around 2.2. My car tyres have 1.3, tops).

In reality, friction is not a simple phenomena. It is in fact very complex and you need complex equations to describe it. I find marvelous that these equations have been discovered in my life time, barely 10 years ago... more or less at the same time that Ferrari started to win every race with Schumacher. Coincidence? I don't think so.

For example, if you make supersmooth surfaces and put them in contact you can develop forces that are enormous. This contradicts conventional wisdom explanations of Coulomb's law and it is called a cold weld (in vacuum, no contaminants, that is, polished surfaces AND mirror like surfaces).

Thus, a softer tyre, one with a "true" patch that is larger, has a larger grip than the puny tyres I have in my normal car.

Incidentally, cold welding is what produces gold nuggets... believe it or not. For the people I see in this thread, you might like also to read about magnetic welding: you use a powerful magnetic field and a powerful "blow" to weld surfaces together. Incidentally, that's how classic katana swords are made, by hammering two different steels together, by powerful blows... We call it forging. Read here: http://en.wikipedia.org/wiki/Magnetic_pulse_welding or here: http://en.wikipedia.org/wiki/Explosion_welding

This proves that the patch you see is not the true patch... Once you make materials to come close enough, the electric Van Der Waals forces weld them together. That's one of the mechanisms that explain tyre wear, like this:

It is the cold welding of rubber to asphalt what explains tyre wear
Image

We should write something called "Friction for the old or the wise" instead of the "Friction for dummies" articles I read once in a while in the Net. ;)

Sorry again for the "runaway post"...
Ciro

multisync
multisync
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Re: Common Sense Counterfactuals - Tire Width

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Difficult to say anything past "Thanks" :D

riff_raff
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Re: Common Sense Counterfactuals - Tire Width

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Ciro,

You forgot to consider the aero lift created by spinning tires on an open wheel car.

In purely theoretical terms, if the tires were made incredibly wide, at some point the lift created by these spinning cylinders would exceed the combined weight and aero downforce of the chassis. Thus the car would lose contact with the track and there would be no tractive force produced by the tires.

So that would seem to be one possible limit to increasing tire width.....

riff_raff

ps. I'm just having fun, so save the snide responses.
"Q: How do you make a small fortune in racing?
A: Start with a large one!"

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flynfrog
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Re: Common Sense Counterfactuals - Tire Width

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there is the problem of having to wide of a tire that you cant get heat into them quick enough.

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747heavy
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Re: Common Sense Counterfactuals - Tire Width

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maybe this makes for some interesting reading for some.
some measurements taken from Avon F3000 tires

http://performancesimulations.com/fact- ... ires-1.htm
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strad
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Re: Common Sense Counterfactuals - Tire Width

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So as a drag racer I don't really need those two foot wide slicks? WRONG!
To achieve anything, you must be prepared to dabble on the boundary of disaster.”
Sir Stirling Moss

buzzmatrix
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Re: Common Sense Counterfactuals - Tire Width

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Wow cold welding is amazing !! Science never fails to impress :o . Ciron , what would i give to sit in your class man !!!