How do train wheels follow the rails?

Many railway vehicles have two wheels fixed to one axle, forming a wheelset. The wheels rotate together, yet the outer rail on a curve follows a longer route than the inner rail. The wheel surfaces that roll on the rails, called treads, help accommodate this difference.

The treads are shaped rather than perfectly cylindrical. A simple teaching shape is a shallow cone, wider toward the inside of each wheel. When the wheelset shifts sideways, the rail contacts can lie at different effective rolling radii. The wheel rolling on the larger radius travels farther in one turn even though both wheels complete the same number of turns.

In the ideal cone example, both centered radii are 450 millimeters. Moving the wheelset 10 millimeters to the right makes the right contact radius 450.5 millimeters and the left 449.5 millimeters. The resulting distance difference can help turn the wheelset. The exact contact radii of real wheels depend on the shapes of both the wheels and the rails.

Raised rims called flanges lie on the inside of the wheels. They can contact the inner rail sides and limit sideways movement, especially where tread geometry alone cannot accommodate a curve. Guidance is not a guarantee of automatic centering. Wheelsets can oscillate, and their stability also depends on suspension, speed, contact forces and track condition. Flanges do not make derailment impossible.