A geometric science project from Science Buddies

Key Concepts Physics Engineering Geometry Centrifugal force

Introduction Have you ever watched a train roll by? If so, you might have wondered how the train is able to stay on its tracks. The secret lies in the train's wheels. Although they seem cylindrical at first glance, when looking more closely you will notice that they have a slightly semi-conical shape. (Of course, never get close to a working train!) This special geometry is what keeps trains on the tracks. In this activity you will put different wheel shapes to the test to find out why the conical wheel is superior to other designs.

Background The wheels on each side of a train car are connected with a metal rod called an axle. This axle keeps the two train wheels moving together, both turning at the same speed when the train is moving.

This construction is great for straight tracks. But when a train needs to go around a bend the fact that both wheels are always rotating at the same rate can become a problem. The outside of a curve is slightly longer than the inside, so the wheel on the outside rail actually needs to cover more distance than the wheel on the inside rail. You can demonstrate this by drawing a train track—consisting of the two rails—with a turn on a piece of paper. Take a measuring tape (or string and ruler) and measure the length of each line. The outside line of the track should be longer than the inside line. But how can one wheel cover more distance than the other one if they both are rotating at the same rate?

This is where the wheels' geometry comes in. To help the wheels stay on the track their shape is usually slightly conical. This means that the inside of the wheel has a larger circumference than the outside of the wheel. (They also have a flange, or raised edge, on the inner side to prevent the train from falling off the tracks.) When a train with slanted wheels turns, centrifugal force pushes the outside wheel to the larger part of the cone and pushes the inside wheel to the smaller part of the cone. As a result when a train is turning it is momentarily running on wheels that are effectively two different sizes. As the outside wheel's circumference becomes larger it is able to travel a greater distance even though it rotates at the same rate as the smaller inside wheel. The train successfully stays on the tracks! In this activity you will test for yourself how train wheel shapes impact their ability to stay on track.

Observations and Results The different cup setups represent different train wheel shape possibilities. Both cup setups represent a set of slanted train wheels, but the direction in which the wheels are slanted was exactly the opposite. Whereas in the first setup the outer side of the wheel had the larger diameter, it was the reverse in the second cup setup. The wheel design makes a huge difference in how the wheels behave on a track, as you likely observed.

It was probably difficult to keep the first cup assembly on the track. It should have derailed almost every time before it reached the end of the track. No matter how you placed the cups they probably usually fell off the track. This assembly only stays on the track if it is perfectly centered. But this is almost impossible to accomplish. As soon as the setup is slightly off-center it will derail on its way down the slope. When you off-centered the assembly to the left the part of the cup that is sitting on the left rail had a smaller circumference than the part of the cup that is sitting on the right rail. Thus the left wheel of the train was smaller than the right wheel of the train. As a result the whole assembly probably turned even farther to the left—in the direction of the smaller circumference wheel and eventually fell off the tracks. The opposite was probably the case if you off-centered the assembly to the right.

The second setup, however, should have stayed on the track—even if you off-centered it. When you off-centered this setup to the left the part of the cup that was sitting on the left rail became larger than the part of the cup that was sitting on the right rail. In this case the left wheel of the train was larger than the right wheel of the train. As a result the assembly probably turned right and corrected its position closer to the center of the track. Whenever this wheel setup became off-centered it automatically corrected its course toward the center, which makes it a very stable system.

This same principle you observed on the incline also helps the wheels stay on track when a train is turning. As the wheel sizes change when the train is pushed sideways during a turn the outside wheel (which becomes larger) is able to move a greater distance than the inside wheel (which becomes smaller). This way the outside wheel can cover more distance while rotating at the same rate.

More to Explore How Do Train Wheels Turn? from Science ABC The Science of How Trains Turn Without Falling Off the Tracks, from Popular Mechanics Rolling Race, from Scientific American STEM Activities for Kids, from Science Buddies

This activity brought to you in partnership with Science Buddies

Josh Fischman, Tanya Lewis and Jeffery DelViscio

John Fialka and E&E News

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