Another tyre size thread - this time with physics

[bogan]

Read this explanation on the HawkGT site, looks like all the smartest people ride the mighty RC31s :yes:

Here goes:


Firstly, remember a math 'model' is just a simplification intended to facilitate easy calculations. All of those equations in textbooks are just such models. Sometimes they're good enough for what you're doing, and sometimes they're not.

Basically, the linear, physics 101 model of Friction = CoefficientofFric*NormalForce (Usualy written F = uN) - where the 'normal force' is the gravitational mass pushing down on the contact patch - has been shown by a variety of studies to be very limited in dealing with tires - and many other things.

The most famous model in use today is the Pacejka Tire model, which basically treats the tire road interface as a 'black box' which is too complicated to treat analytically. Other analytical treatments have shown this non-linear model more precisely, and basically speculate that a brief chemical bond forms between the road and the tire - thereby increasing friction.

But to show precisely the non-linear nature of tire road friction, the basic test is this:
Put a 10lb block on a 2x2" patch of rubber, and see how much force it takes to drag across the road. Then put the same 10lbs o a 3x3" patch of the same rubber, and measure how much force it takes to drag the the weight across the road.

Basically, if the physics friction model is right, the force will be the same. But because it is not correct - and I promise you engineers test this all the time - the force relationship is not linear & therfore more force will be required for a bigger contact patch.

This is precisely how tires are compared for grip - and furthermore precisely why wide tires have been preferred on race vehicles for decades.


and...


I think a lot of the machines you see with a smaller contact patch/smaller tires is more of an optimization - that is to say that the corner traction gains made by employing a bigger tire would be negated by the rotating mass of using a bigger tire. There is a lot of weight in a tire, and it is the largest radius on the wheel. In other words,you might gain an iota of corner speed, but then lose your ass trying to move that mass down the straight with a tiny engine.

As for tire heating, indeed we know that a heavier bike will put more heat into a tire, but this is caused by a number of factors: the carcass flex, and the added force necessarily required to change direction on a heavier bike. As you also know, at a certain temperature point, the tire chemistry degrades - in that too ho a tire becomes slippery. I will look for more information on this myself, because the whole chemical-mechanical grip thing is kindof the domain of tire designers.

A lighter bike can easily reach identical tire temperatures (to those of a heavier bike) by either: running lower air pressure - thereby inducing carcass flex or carrying more corner speed - thereby dissipating the same net energy as a big bike via F = mass*accel (integrated over time = energy)

It is 100% correct to say that twice the tire will not equal twice the traction (i.e. non linear relationship). The tire maximum friction is is usually given in terms of something called the slip-ratio. The slip ratio is the relative speed of a point on the tire over the point on the ground. As the tire under load starts to 'creep' over the ground (about to slip or spin) the tire responds with a given force - more creep = more force - up to a point.... after that point the tire force drops off dramatically (resulting in the slide we're all familiar with). This stretching of the tire across the ground is what we call grip, and a more compliant (softer) tire, acting over a larger area will create more.

I will work on finding some papers or overviews that are reasonable for you guys. Motorcycle tires are an even less studied subset of tire dynamics in general. A lot of work has been done on road tires, but comparatively little for off-road.

For anyone who is interested in motorcycle dynamics questions like this - and have maybe some math/physics skills to back it up - I highly recommend this book. It is by far the most thorough examination of the entire bike available:

http://www.amazon.com/Motorcycle-Dynamics-Second-Vittore-Cossalter/dp/1430308613 p37 on for this stuff

[avgas]

I am tired and dislike reading today.

so a quick scan told me this:
High pressure - quicker cornering
Low pressure - better grip

Bigger tyre - better grip
smaller tyre - better cornering

did I miss something?

[Jantar]

But to show precisely the non-linear nature of tire road friction, the basic test is this:
Put a 10lb block on a 2x2" patch of rubber, and see how much force it takes to drag across the road. Then put the same 10lbs o a 3x3" patch of the same rubber, and measure how much force it takes to drag the the weight across the road.

Basically, if the physics friction model is right, the force will be the same. But because it is not correct - and I promise you engineers test this all the time - the force relationship is not linear & therfore more force will be required for a bigger contact patch.

Here is a BIG error in assumtion. The assumption being that the CoF will be the same simply because it is the same materials that are being tested. However the CoF will not be the same for the two samples because the contact area is not the same. In this case the CoF for the larger sample is likely to be 2.25 times that of the smaller sample.

[Banditbandit]

I am tired and dislike reading today.

so a quick scan told me this:
High pressure - quicker cornering
Low pressure - better grip

Bigger tyre - better grip
smaller tyre - better cornering

did I miss something?

Mate .. you're doing well .. I read this bit ..."Firstly, remember a math 'model' is just a simplification intended to facilitate easy calculations." and thought Yeah OK ... I will follow this .

Then I read "CoefficientofFric*NormalForce (Usualy written F = uN) - where the 'normal force' is the gravitational mass pushing" and thought:

Fuck it ... I don't need to read this ... bored already ...

[bogan]

I am tired and dislike reading today.

so a quick scan told me this:
High pressure - quicker cornering
Low pressure - better grip

Bigger tyre - better grip
smaller tyre - better cornering

did I miss something?

bigger tyre is more rotational mass, so bad for acceleration, and if bigger tyre = better grip, doesn't it follow that you will be able to corner harder on it?


Here is a BIG error in assumtion. The assumption being that the CoF will be the same simply because it is the same materials that are being tested. However the CoF will not be the same for the two samples because the contact area is not the same. In this case the CoF for the larger sample is likely to be 2.25 times that of the smaller sample.

That is an example to disprove the assumption that those who subscribe to the simple physics friction model make. If you try such a test with things like wood or steel, iirc the force to move em is the same, but not for rubber. edit, also CoF is not a variable that changes with contact area.

[avgas]

doesn't it follow that you will be able to corner harder on it?

Nope - as you have counter rotational mass and rotational in both x-y and z planes (leaning).
Bikers usually call this "flickability" - meaning you can drop the bike into a corner quicker.

Also the reason why mini's turn better if they have skinny tiny tyres.

The whole "corner harder" thing is actually not just based on tyre size, but compound, balance, radius, form....... cornering harder does not actually mean cornering faster. But it is a shitload more fun.

[bogan]

Nope - as you have counter rotational mass and rotational in both x-y and z planes (leaning).
Bikers usually call this "flickability" - meaning you can drop the bike into a corner quicker.

Also the reason why mini's turn better if they have skinny tiny tyres.

The whole "corner harder" thing is actually not just based on tyre size, but compound, balance, radius, form....... cornering harder does not actually mean cornering faster. But it is a shitload more fun.

yeh harder was not the best choice of words, I meant with more lateral force, get that knee down a bit more...
to increase flickability, just design it so the crank spins opposite to the wheels :yes: I would suggest that other option, but there are enough worms in here without opeening another can :innocent:

[Ocean1]

If you try such a test with things like wood or steel, iirc the force to move em is the same, but not for rubber. edit, also CoF is not a variable that changes with contact area.

I remember sweating over COF equations relating to clamping forces required to hold various materials while machining. In real life it was a waste of time, empirical data is the only real way to establish that, and I’ve thrown enough bits of metal across the workshop to have a really good baseline of data.

Same applies to traction on bikes. Again, I’ve got a pretty good history of data explaining roughly where the limits of traction are. In the dirt. Not quite so keen on developing a data set explaining the finer limits of traction for a Michelin PP2CT on hotmix.