# Why are the train wheel coned shaped?

Have you ever noticed the wheels of a train? Are they normal shaped or different? The train’s wheels are not perfectly cylindrical, but slightly conical. In my opinion, The conical shape is a marvel of engineering that accomplished two major goals things, one is correcting the course of the train towards the center and second is helping the train to achieve the differential action. In this article, I will explain to you why train wheels are shaped slightly conical.

## Experiment with glued paper cups

To understand the first accomplishment, I did a simple experiment with glued paper cups as shown in fig 1a. When I rolled this set of glued paper cups on a track, they were moving perfectly straight. Even if I tried to give a small tilt for the cups at the beginning.they were still managing to move straight. I took another shaped glued paper cup with a different shape as shown in fig 1b. Now, what about this set? This was glued in the opposite way. When I rolled these cups on the same track, it was failing to move straight. Railway wheels use the first kind of conical shape.

This angle makes sure that the wheels never leave the track, but the question is why? This conical arrangement produces a self-centering force. To understand how, we need to understand the forces acting on the wheels. During a straight track movement the gravitational and reaction forces acting on the wheels as shown in fig 2. The reaction forces will always be perpendicular to the surface of the cone. When the wheels are centered, the horizontal components of these forces cancel each other out.

## Why are flanges on railway wheels are kept inside?

Now, assume that, due to some reason, the wheels have moved to the right as shown in fig 3a. One interesting thing happens to the train’s wheels when it moves along the axis. Did you notice? In this case, the whole train wheel set tilts. Along with this tilt, the normal forces also get tilted. If I do a force analysis in this right condition, I can see that there will be net force towards the left direction. This force will bring the wheels automatically to its center. As the wheels approach the center, the self-centering force will disappear. What a simple but brilliant technique to self-center the wheels. right? Flanges are fitted on both the sides of the wheels as an extra safety feature (refer fig 3b).

For fun, let’s assume that the train’s wheels are in the opposite angle as I have explained earlier (refer fig 1b). Here if I do the same force analysis during a right displacement, you can see the net force developed is again towards the right as shown in fig 4. This is why for this wheel geometry, the train wheels always get thrown out of the track.

## How do train wheels turn?

Now, let me explore the second reason for giving a conical shape to the wheels. With this conical shape, the engineers were able to achieve differential action. Suppose the train has to take a turn as shown in fig 5a. Here, the left wheel has to travel more distance than the right wheel. However, when the wheels are connected using a common shaft, how is one wheel able to travel more distance than the other wheel? Here’s where the conical shape comes into play. To accomplish this, turning the wheels will cause it to slightly slide towards the left. If you consider the contact point of the wheels, the left wheel has a higher radius than the right wheels. In short, for the same angle rotation, the left wheel will travel more distance and achieve differential action as shown in fig 5b.

Do you remember how to achieve differential action in cars? The engineers had to separate out the wheels and turn them under different speeds. Here, In the train, they achieved the differential action just by giving the wheels a conical shape. Interesting, right?

Of course, when the wheels slide towards left, it will produce a force automatically towards the right as I explained earlier. During a cornering situation, this force is provided to supply the centripetal force needed for the turn. Due to this, the wheels will not slide back to the center during the cornering.

That's all in this article. I hope you have learned why train wheels are conical instead of cylindrical.