Tire Tread - Why are there so many tires with direction arrows?

In road tires, a tread with a rolling direction generally provides a slight reduction in rolling resistance. In addition to this, aesthetic considerations can also be important. Off road, rolling direction is far more important, as the tread ensures optimum connection between the tire and the ground. The rear wheel transmits the driving force and the front wheel transmits the braking and steering forces. Driving and braking forces operate in different directions so this is why certain tires are fitted in opposite rolling directions when used as front and rear tires. There are also treads without a specified rolling direction.  more