Have you ever thought about how trains stay on the tracks when they round corners? Trains typically have wheels that are connected together by a fixed axle, meaning that the wheels on both sides of the train always turn at the same speed. This can present problems when turning, because one wheel has to cover more distance than the other.

Most vehicles solve this problem by decoupling the wheels. In a car, for instance, the left and right wheels turn at different speeds when rounding corners. But that's impossible to do in a train, so how do locomotives stay on a bending rail? The above video by Numberphile explains.

Train wheels aren't perfect cylinders. They're beveled to make them wider on the inside. This means that when the train shifts left or right on the track, the diameter of the wheels can change. But because the wheels are connected by an axle, they still spin at the same rate. Effectively, this means that the wheels will travel different distances per revolution.

The wheel bevels are specifically designed so that when the train goes around a corner it stays on the tracks. The wheels that have to travel a greater distance have a greater diameter, and everything stays aligned. The end result is a train that stays on the tracks.

Source: Numberphile

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