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The physical reasoning I suppose could be that more contact areas mean more and higher friction. But is there an actual formula or a more mathematical explanation?

Application for bicycling was my question

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Apologies for this, but is there a good example of the definition of a dubbed tire? I did a quick search and have a rough idea, but was wondering if there was a particular definition to understand what a dubbed tire is. – user11547 Feb 2 '13 at 17:13
@HalSwyers I'm learning it as we speak, I think it's safe to say that is has more contact surfaces than the so-called skinny tire. I'm no vehicle expert, just been wondering where it comes from to minimize the number of contact surfaces to get lower friction. – Dac Saunders Feb 2 '13 at 23:11
up vote 3 down vote accepted

For a rolling tyre the resistance (it's not really friction) is due to viscous losses in the rubber as the tyre is deformed.

If you take a piece of rubber and put work in to stretch it then get work out as it relaxes, the work you get back is less than the work you put in. The balance goes into heating the rubber. If the piece of rubber is part of a tyre, this loss of energy means you have to put energy in to keep your vehicle moving at a constant speed i.e. you have to apply a force. That force is what you feel as rolling resistance. If you touch your car tyres after you've driven the car you'll find they are warm because they've been heated by the losses within them.

The more the tyre deforms, the more energy is lost, and therefore the greater the resistance. So if you use a smooth tyre and pump it to a very hard pressure the rolling resistance will be low. If you use a knobbly tyre and run it at a low pressure the resistance will be high.

You ask if there's a way to describe this mathematically, and yes there is assuming you know the material properties of the rubber you're using. However you'd need to use a finite element analysis.

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I think with knobby tires, in addition to the increased deformation, there may also be a bit of friction. Knobby tires are generally designed so that the knobs move closer together at the contact point (to "grab" things being rolled over), and that would probably cause the knobs to rub laterally against the surface being rolled over. – freiheit Feb 18 '13 at 2:14
Note that there's an upper limit for how much increased tire pressure reduces rolling resistance that is lower the rougher the surface being rolled on is, due to vibration (energy lost to pushing the whole bike up over small bumps instead of only deforming the tire). – freiheit Feb 18 '13 at 2:15

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