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Basically, with treads, you have more surface area of contact.
So what would that do to you? Well, you have more surface area to take advantage of frictional force, and you won't be pushing as hard on each square inch of carpet your robot drive on.
I don't think using treads will necessary give you more traction. I think this because I believe if you wrap the same tread material around wheels, you will get the same traction.
Say team 45's chain tread with metal pieces digging into the ground, and team 159's wheels with similar metal pieces attach all around the wheel digging into the ground. I don't think there is a lot of difference.
As for being pushed on the side, you do have more side area on your treads to resist against the push, but the resistance should be the same with wheels with similar material wrap around them. With the same pushing force from another robot, that pushing force will spread through out the tread, or concentrate on the 4 wheels. Tread have more surface area to resist, but less force per surface area... Wheels have fewer surfaces to resist, but more force per surface area... They should both come out to be the same...
So, do treads give out a false sense of more traction, because in general the material for treads has better coefficient of friction than normal wheels?
Or, is there some special physics behind treads that help it gain traction over wheels with the same material wrap around it?
By the way, I also believe that it is more important to think about traction and friction of the material you use, rather than thinking about wheels vs. treads.
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