Formula for friction


The formula for friction (f) or what we call traction is

=Mu x n  

Where =

  • f = friction
  • Mu = Coefficient of friction (Cf)
  • n = normal down force = weight or mass. 

Notice that the size of the surface area is not in this formula.

Cf is determined by the two materials rubbing together such as the tire & the pavement, its unit of measurement is g.  For street tires this value could be anywhere from 0.80g to 1.50g on good dry pavement.  A good race and good racing pavement can develop a Cf of 1.50g or more.  The normal down force is the weight or the mass of the bike on the tire.  

f = Cf x weight or again f =Mu x n

For example using round numbers, we will look at friction using the known Pounds per square inch (Psi).  If you have one hundred pounds on one square inch of rubber then you have

 (Psi=100lbs ÷ 1) = 100Psi 

For the actual friction value you will have,

f=Psi x area or f=100Psi x 1.0 Sq in =100

But, if you take the same one hundred pounds and put it on two square inches of rubber then you have

(Psi=100lbs ÷2i) = 50Psi 

For the actual friction value you will have,

f=Psi x area or f=50Psi x 2.0 Sq in=100

If total weight on the tire remains the same then, as the surface area increases the Psi decreases.  So in conclusion increasing the surface area of a tire in and of itself will not increase the friction level.

On the other hand the size of the tire contact surface area will come into play when you start to calculate in mechanical stresses on the contact patch.  If the surface area is too small for the mass or power of the bike, the tire will mechanically tear and shred resulting in premature and excessive tire spin or slide.  If the contact area is too big then the compound will not be able to come to the correct operating temperature and not develop the max coefficient of friction and result in premature and excessive tire spin or slide. 

In conclusion

The right size tire will give you the best performance.  Over-sizing or under-sizing can have a negative effect on the performance of the tire.  But a small change in the size, from a change in BP, will have no effect on traction available.