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Friction, traction and surface area

Discussion in 'The Pub' started by Bravus, Mar 10, 2009.

  1. (apology 1: yes, more physics - those who don't like it should look away)

    (apology 2: I'm pretty sure this has been addressed here before)

    So, given that friction seems to be independent of surface area (since larger surface = lower pressure, smaller surface = higher pressure for the same mass) why do we use fat tyres with big contact patches?

    As far as I can tell the formulae for traction is also independent of surface area.

    So is it just about heat dissipation, and having a contact patch big enough to avoid things like sand on small parts of the area? Or....?

  2. I think the "friction is independant of surface area" tenet is wrong. The additional pressure on a smaller contact patch wouldn't make up for extra surface area.

  3. friction != pressure
  4. It seems to me that friction/traction would have to be linked to surface area, can you show us your formula?
  5. This one's a really tricky one.

    My limited understanding from car suspension textbooks (and even they seem to have a limited understanding) is to do with stresses overloading the tyre, causing the tyre carcass to squirm and distort, consuming grip.

    Lower profile tyres (and wider tyres, simularly) could reduce that effect...

    But if the tyre is too big then you create other issues (unsprung mass, having to twist a large contact patch to change direction, sidewalls too stiff, etc..) that eat up mechanical grip.

    I don't think there's an easy answer for it. Would be eager to see any references/texts people can offer on tyre grip theory. :)
  6. Easy solution - the coefficient of friction is an empirical measurement.
    So even though you may have two identical materials the friction between them will be dependent on things like contact area, temperature etc.

    Traction is simply the coefficient of friction (which ideally needs to be measured), multiplied by the force pushing down on the tyre (which can be calculated but can be complicated) - so contact area does certainly play a part.

    Edit: An interesting article on traction/acceleration (though it's for cars, not bikes unfortunately).
  7. Physics and basics engineering has it that friction is independent of area.

    BUT the ability of a material to absorb heat is dependent on area. So at the limit the friction capability of a tyre will be effected by area.

    I also once saw a theory on a dirty surface. i.e. particles between the two surfaces that could not be factored into the standard friction equation. the "dirty" equation did factor in area.

    I haven't been able to find it recently and it annoys me.
  8. Yeah if you get really into it friction is quite complex. I saw a paper recently which looked at the way insects are able to stick to walls, and found similarities in the behaviour of car tyres - partial liquification of the rubber which allows it to flow into microscopic imperfections in the road surface allowing it to grip better than the basic physics say it should.

    This is why coefficient of friction is something you measure, not calculate :).
  9. I don't agree with that. yes, area does not factor explicitly in the F = uR formula. BUT it is inherent in the u.

    the 'u' doesn't change in the 'coefficients lists' you see (e.g. Rubber has a coefficient of blah) because the density per unit volume of a single material object doesn't change, so any size of the material will exhibit the same coefficient.

    the same does not hold true for a multi-material object like a motorbike. i.e. the bigger the contact patch the higher the coefficient of friction.

    or at least, that's my take on it
  10. I'd imagine that a big contact patch with a low amount of force pushing on it (e.g. the weight of a motorcycle) allows you to run a soft tyre without needing a new one every five minutes.

    If we were running a skinny soft tyre with a narrow contact patch, the pressure would be quite high and so tyre life would be impractically short.
  11. First of all, contact area has NOTHING to do with tyre width! It is a product of vehicle mass and tyre pressure. Think about it.

    So why different sized tyres (width, profile and diameter)?

    Heat is a big one, and the capacity of a certain tyre to spread that heat with a greater usable area. You can compensate with harder compounds, or have reduced life. In fact I believe tyre life is one of the main reason superbikes and such run the larger tyres, they could run the lap times (probably better with improved turning) on smaller sizes but for not as long. Street tyres are a different story altogether, mostly for looks.

    Not a whole lot said about the coefficient of friction you'll notice, except implied with the overheating (especially locally i.e. instantaneously over very small area), when the rubber basically loses its normal properties. As for coefficient of friction changing with area, I'm certain it does, but we are mistaken thinking that tyre width equates to contact patch.
  12. Don't forget though that there is a difference between kinetic friction and static friction. Contact area has nothing to do with kinetic friction, but is important to static friction (or traction).
    It's static friction that allows power to be transferred from the wheel to the ground, so increasing the contact area allows more power to be transferred. Kinetic friction is only relevant if you lock the brakes.
  13. It's a shorthand, but if you take it to the extreme, a racing bicycle tyre dead flat is not going to have a bigger contact patch than a 180x17 tyre fully inflated... so width does have a *little* to do with contact patch.
  14. Dead flat means the bike is resting on the rim.... and you are comparing different pressures. :roll:

    For all *practical* purposes (I'm not even being an academic pedant here), the contact areas are identical for tyres in which an end user would be interested (cars, buses and bikes alike). There are exceptions to the rule, with particularly stiff sidewalls etc, but for the most part it is completely true. F=P*A. The contact patch increases and decreases with pressure, not tyres size.
  15. But tyre size has to determine the limit of the contact patch's size at lowest pressure, doesn't it?
  16. Yes, when it sits on the rim. Not very relevant wouldn't you say.
  17. But at the point before flat-to-rim (where the tyre is still usable), a larger tyrer should have a larger surface area value, should it not?
  18. Bravus is the teacher, perhaps he should get his head around it then explain.

    But, no.

    The only thing holding your tyres in shape is air pressure. This pressure is measured in units of force per area, eg, pounds per square inch (psi). If your bike is happily sitting there, not on the rims, it is because the pressure in your tyres, multiplied by the surface area of the contact patch, equals the mass of your bike. eg, your bike weighs 300 pound, and you've got 30psi in the tyres. Your contact patch will be a little less 10 square inches (5 at each end), given that the actual rigidity of the tyres supports a little weight.

    Explain to me, how a skinny tyre, fat tyre, 21" vs 17" tyre, with the same pressure, will have a different area contact patch. Different shape, yes, different area, no.
  19. Sometimes the rules of physics don't translate all that well into the real world. I think that's due to that not all bikes have been to uni.