[dremd]

Not sure why everyone doubts such basic physics.
Easy test.

You need
Scale (spring for measuring force),
Wooden block,
various bits of tire (my high school and college physics teachers both spent more time telling us no to cut ourselves on steel cords than the experiment),
String
Some surface to frag on (floor, table, pavement, etc)

Basic test, drag a mass along on the same surface with each tire type, cut tire piece in half repeat (with scrap tire on top of mass), cut the remaining piece in half repeat (again scrap on top).

The various sizes of tire represent the contact patch with different inflation pressures.
You will quickly realize that contact patch has extremely little to do with friction (traction)