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"Coning of wheels" is what allows a train to take a turn without slipping off its tracks.

When a car takes a turn, the outer wheel must turn more quickly than the inner wheel, because it travels a greater distance. In a car, this is accomplished by allowing the wheels on either side to turn at different rates. This is not a problem for the front wheels, which turn freely, but in the case of the back wheels, which are powered by the motor, it requires what is known as differential gearing.

But in the case of most trains, the wheels on the left are joined to the wheels on the right by solid steel axles. So how can the train take a turn, if the outer wheel must travel a further distance than the inner wheel?

The answer is that the wheels are beveled. That is, their edge is inclined, so that the outer edge of the wheel has a smaller radius than the inner edge.

So, if the tracks turn left, the right wheel shifts with respect to the rail and now turns on a bigger radius. Similarly, the left wheel turns on smaller radius. This way the right wheel can travel further than the left, even as they go around at the same rate.

A train wheel thus looks like the base of a cone, rather than like a cylinder. This is what is called "coning of wheels."

Notice also that if it were not for the coning of wheels, only the flange on the edge of the wheel would prevent the train from derailing. But this would mean that the flange would be repeatedly hitting the rail, causing constant noise, heat, sparks and wear of the tracks and the flange.

Instead, what happens is that if the wheels become displaced with respect to the tracks, the coning causes them to turn back inwards. Actually, at very high speeds the wheels will turn too far before starting to turn in the opposite direction to compensate, leading to a problem called "hunting oscillation." Overcoming this problem was the main step in the development of modern high-speed trains, such as operate today in Europe and Japan.

Theoretical physicist Richard Feynman gives an amusing oral account of how this "coning of wheels" works to keep the train on track and allow it to turn:

http://www.YouTube.com/watch?v=y7h4OtFDnYE

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