# Why are the wheels of railway trains such a strange shape

(ORDO NEWS) — The next time a subway or commuter train pulls into a station, take a closer look at its large metal wheels.

You will notice that instead of being perfect cylinders, their sides diverge at a slight angle. This is not a factory defect, but a thoughtful engineering design choice that allows the train to turn smoothly without flying off the rails.

On Numberphile’s mathematics and science channel, Tadashi Takeda, Director of Mathematics Research at Trinity Hall, Cambridge, uses two sets of plastic cups held together with duct tape to show the difference between stability and instability of railway axles.

When the tops of the glasses are fastened together, they can roll along parallel paths without deviating or falling over on their side. However, if you fasten them at the base, they will always take a little sideways until they finally go out of the way.

As the glasses are turned to the left or right, their diameter changes on both sides, resulting in a peculiar pair of linked wheels of different sizes. But the version where the cups are held together by the vertices corrects itself as it moves, which gives it stability.

As Takeda explains, it is this property of the wheels that keeps the train on the track during turns. The outer rail is actually physically longer than the inner one, which in the case of two perfectly cylindrical wheels would require them to rotate at different speeds, which is very problematic to implement in practice.

To solve this problem, the engineers designed the wheels to be tapered so that they could sway from side to side in real time as the train turned.

On the one hand, the contact area becomes larger, which allows them to remain on the outer track, and on the other hand, it is shortened, which is optimal for the inner track.

Everything happens automatically thanks to centrifugal forces that push the train outward as it rounds a corner, which means it doesn’t need any extra support.

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