>On car tires, shoes and other such items, having less of the material in contact with the surface underneath increases traction.
This is a faulty inference. Since most roads and walkways are fairly rough, having a knobby, textured surface in the soles of shoes or tyre treads tends to actually increase the area of contact, not decrease it. The same reason why shoes and tyres are made of highly flexible substances like rubber. This is because it makes the surface of the tread or sole more compliant or squishy. This brings more surface area into contact with the road or trail, not less, because it conforms to the surface in the same way that a soft mattress conforms to the bumpy surface of your body. Moreover, dirt or gravel particles will wedge themselves into the grooves and crevices, further increasing fraction. Such a design is more resistant to skidding in dirty, sandy, or gravelly conditions.
Most importantly, the grooves act as channels for water or oils which prevent a layer of water being trapped between the soles or tyre, and the surface of the road. This reduces the tendency for a phenomenon called “hydroplaning” wherein water acts to lubricate the road surface by formingba thin liquid film between the two, which drastically reducing traction. In cars this can have disastrous consequences during a downpour, by causing tires to skid and causing the car to lose all control. Grooves and channels in the tires act to spoil this tendency by provinibg a lower pressure flow path
All things being equal, however, racing tyres are often smooth, when they are used on clean, dry, mostly gravel and dirt free racetracks. The reasons why slick tyres offer a better grip in racing conditions is complex. It’s partially related to heat retention. During drag racing the drivers usually deliberately spin their rear tyres to heat them up to improve grip. Likewise if you mount a thermal imaging camera on a F-1 car, you can see the tires heat up during braking and turns. However using slicks on a wet racetrack would be very dangerous. Because racecars typically use oversized tires precisely to increase the contact surface are with the road. But this reduces the average ground pressure and makes hydroplaning much easier.
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