Common Sense Counterfactuals - Tire Width

[roost89]

What I read previous to reading this (I've read all of what you wrote Ciro but whether it all made sense is another story ) states:

The actual grip that a tyre can generate is dictated by the coefficient of friction of the rubber compound used in the tyre. The higher the coefficient, the more grip which can be generated. The relation that is used is called Amonton's Law

Which makes sense, at least in my head

It carries on:

So, if you increase the weight on the tyre, then the frictional force will increase as well, in proportion to the increase in weight on the tyre - but the coefficient of friction will remain the same. The level of grip of the tyre (forgetting about suspension niceties - we are only discussing tyres here) is totally dictated by the coefficient of grip of the tyre and the weight acting on it - not the area of the contact between the tyre and the road.

It goes on to state that the reason wider tyres are better is, that they allow for greater heat control, as there's a greater area for cooling. So wider tyres can use a softer rubber which in turn allows for a greater friction coefficient and more grip, without overheating and ruining the rubber.

Is the article correct in what it says? (I'm know not of what makes tyres great)

[marekk]

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

http://performancesimulations.com/fact- ... ires-1.htm

I'm slightly surprised, how many people writing about tires (author of this article included) seem to don't have basic understanding how this pneumatic system works.
An example - a F1 tire (26" diameter,13" width, on 13" rim) has an area (rim included) of approximately 2400 sq-inch. If you inflate it to 28 psi gauge, resulting total load on tire's and rim's structure is 67,200 lbs.
How can one expect, that increasing load on this system from 67,200 + 600 lbs to 67,200 + 1200 lbs will result in two times increase in geometrical deformation (patch area)?

[marekk]

Ciro, as usual, did a great work to teach us one thing: it's a way more complex then one could expect.
In fact, this car to road interface is the most complex of all vehicle dynamics influencing systems.
Aerodynamics, thermodynamics processes in combustion engine, not to mention simple mechanics of Newtonian forces - it's peace of cake compared to this one.
We have geometry change, aerodynamics, energy transfer, mechanical (Newtonian) forces, coulomb forces, chemical reactions between rubber and tarmac, histeresis (as most of them change in respect to his history), nonlinearity, not to mention, that all of these phenomenas depend nonlinear on each other.

Than we use coefficient's. In physics, if you are forced to use some coefficient simply states that you failed to know how the thing realy works. So you have to discover through experminets the value of this one. But this coefficient is not a constant. It changes with pressure, temperature, tarmac (and his history), compound (and his history)...

And even this one mentioned by riff_raff about considering lift generation by rotating wheel - you can't ignore it, for F1 car with wheels rotating at 50 rps it will create in free flow 40-50 pounds of lift (direction will be down in this case).

I'm afraid, the best answer to thread's question is that it has very little to do with common sense - you just have to take these datasheets to start with and then to investigate on your own.

[FW17]

That was a great write-up.

I have a question which is off topic from the title but somewhat related.

The dry weather tyres have always been bald or broken with some square grooves. While the purpose of the tyres have primarily been mechanical grip, an aero element has never been incorporated into its design. F1 tyres contribute to a majority of the drag of the car, something which is a constant factor over the years.

Sports which uses a ball has been continually been developing over the years either to increase or decrease drag and lift. Since some of the elements are similar to the aero of a tyre, can improvements to the aero of a tyre be done?

Will addition of dimples on the tyre surface reduce the drag of the tyre?

[myurr]

It's not actually true that tyres haven't been designed with aero in mind before. On of the defining differences between the Michelins and Bridgestones during the tyre war was that Bridgestone went for a tyre with more rounded shoulders (thus a smaller contact patch) in order to work better with Ferrari's aero solution. Michelin went for out and out grip with a much squarer shoulder.

[Richard]

How can one expect, that increasing load on this system from 67,200 + 600 lbs to 67,200 + 1200 lbs will result in two times increase in geometrical deformation (patch area)?

This is explained by equilibrium of the external forces.

You have a tyre with an external force applied from the car weight of x, and the reaction from the ground also equals x. The force to the ground is applied by 28psi over an area of contact patch. The contact patch must equal force/pressure.

So you are wondering what happens to the other 67,200lbs? That total force is actually applied as hoop stress, it balances itself out. It just goes round and round without any bearing on the external forces. When you hold a car tyre you only feel the gravity load, you can't feel the total 67,200lb.

If some of that 67,200lb was used to apply a force to the ground, there'd be no equilibrium and the tyre would fly through the air.

[marekk]

richard_leeds,

agreed 100%.
But my point was rather, how can one expect that patch area will change equally (or even linearly) with applied load, in a nonlinear (geometry, elasticity of rubber, cord and used fabrics), highly preloaded system.
Knowing all relevant data we are able do build more or less accurate numerical models of this system, but there will never be a simple equation like patch_area=load*some_coefficient.

[marekk]

That was a great write-up.

I have a question which is off topic from the title but somewhat related.

The dry weather tyres have always been bald or broken with some square grooves. While the purpose of the tyres have primarily been mechanical grip, an aero element has never been incorporated into its design. F1 tyres contribute to a majority of the drag of the car, something which is a constant factor over the years.

Sports which uses a ball has been continually been developing over the years either to increase or decrease drag and lift. Since some of the elements are similar to the aero of a tyre, can improvements to the aero of a tyre be done?

Will addition of dimples on the tyre surface reduce the drag of the tyre?

I think yes.
You can add dimples (or better lateral grooves) on tire tread and decrease drag (both shape and induced by rotating tire) - but you loose grip. And since current F1 is grip limited, i doubt this package will perform better. It wiil also negatively influence tire's durability.
What can be (and currently is) done, is to route flow around tires as good as you can, and to generate some vortices (turbulences) in tire-facing flows, to minimize boundary layers buildup/separation related drag.

[Richard]

marekk - the contact patch has to be linear because the only way to transfer vertical force to the ground is via 28psi.

This is based on a number of assumptions, including constant tyre pressure. Also that the tyre is acting predominantly as a pneumatic structure and rigidity of the tyre carcass is not significant, a deflated flat road is very flat and floppy so we can see that it works as a pneumatic structure. Those are probably valid assumptions for us mortals, but I imagine F1 tyre engineers spend significant time worrying about varying temperature, pressure & stiffness.

[marekk]

marekk - the contact patch has to be linear because the only way to transfer vertical force to the ground is via 28psi.

This is based on a number of assumptions, including constant tyre pressure. Also that the tyre is acting predominantly as a pneumatic structure and rigidity of the tyre carcass is not significant, a deflated flat road is very flat and floppy so we can see that it works as a pneumatic structure. Those are probably valid assumptions for us mortals, but I imagine F1 tyre engineers spend significant time worrying about varying temperature, pressure & stiffness.

Agree, but only if we assume additionally constant pressure between tire and tarmac across perfectly square contact patch area.
I think, in our cruel physical world this is one assumption to far:


Regarding temperature - that's probably the most often used excuse from F1 drivers: "i can't get any heat in my tires"

[Ciro Pabón]

F1 tires are used at a pressure of 1.1 bar, that is, 15 psi, not 28.

[Richard]

Agree, but only if we assume additionally constant pressure between tire and tarmac across perfectly square contact patch area.

Who said square?

[marekk]

Agree, but only if we assume additionally constant pressure between tire and tarmac across perfectly square contact patch area.

Who said square?

This article linked by 747heavy, which my comment was about, mentioned something like: Patch_Area = Patch_Width * Patch_Length.

[rjsa]

Here's what boing thinks about pressure and patch area:

The tire contact area for any aircraft tire is calculated by dividing the single wheel load
by the tire inflation pressure.

http://www.boeing.com/assets/pdf/commer ... ctarea.pdf

[WhiteBlue]

To assume tyre pressure is equal to contact patch pressure you must simplify the mechanical model and make assumptions. The mechanical model would be the piece of tyre that is immediately above the oval contact patch. That piece of the tyre is in balance of three forces.
1. The area of the contact patch times the tyre pressure
2. The integral of the local contact pressure over the contact patch (assuming contact pressure is not locally constant)
3. The vertical component of the force around the edge of the contact patch in the tyre construction
So the first assumption is that internal forces around the edge of the tyre patch are negligible. The second is that pre inflation value is also negligible. It would make a difference if you inflate to 50 psi or 12 psi when you compare the load pressure with the pre inflation pressure.

747 aircraft and F1 tyre may be a bit different in application and load bearing. In aircraft the load is so huge that you may be able to neglect the forces transmitted through the carcass and the pre inflation pressure which exists without any load. If you go to a strict mechanical model as shown above those influences exist and may not always be negligible. Perhaps if you are familiar with the circumstances of the F1 application you can neglect them but that is not a valid assumption per se.
If we look at tyre with very high pre load and very small contact patch like a road racing bicycle all those assumptions may be a bit too much.