# Physics of Fiction

I got into a dispute with a team member over the connection of surface area and the force of friction. Basically he said that using two wheels instead of one (like on big trucks) would give the robot better traction. Other than the trivial weight distribution of the extra wheel, I said that it had absolutely no impact based on the equation for Friction (Friction = coeff * force normal). We both agreed instead of arguing that we would accept whatever response is given from this message… So any comments on this one?

I know there has been a recent thread on this (so you should search for it) but in short:

Theoretically there is no difference according to F=mu*N … ln actuality, adding more wheels will help you a little bit.

My suggestion is to try to get material or shape your wheels that can dig into the carpet a little. This is hard because I think I heard the rules on wheels are strict this year… But if you can come up with a way to legally add “cleats” to the wheels like soccer players use to dig into the ground, that will help you the most as far as traction is concerned… A lot moreso than adding wheels.

Also, do some experiments to find the answers you seek… we can theoreticize (i don’t think that’s a word…) this all you want but every wheel with every surface behaves differently. Emperical data is great in these types of cases.

• Patrick

Surface area does come into play with the materials we use because the surfaces can deform. When surfaces deform the meshing (and coefficient of friction) can change when the weight distribution is changed.

Simply put, more weight in a small area can cause the carpet to “flatten” which is why only 4 wheels with 30lbs of pressure each will not perform as well as, say, 6 wheels with 20lbs of pressure each.

I am not sure at what pressure the carpet fibers begin to “flatten”. This will need to be experimented with.

Technically, surface area does not directly affect the F = “mu” * “weight” equation. It does, however, change how the weight is distributed (pressure acting on the carpet… as long as the weight remains the same) and can change how the surfaces mesh, which is one factor in calculating the coefficient of friction (mu).