The Physics Of High-Speed Trains

While the accident in Spain is certainly a tragedy, it is also an opportunity to examine the physics involved for us to understand a bit more of a possible cause of the accident. This article in The New Yorker has a simple enough description of it that anyone without any mathematics or science degree can understand. It tries to explain why there is speed requirement or limit of curved tracks.

One of those forces is centrifugal (“to flee from the center”) force, the inertia that makes a body on a curved path want to continue outward in a straight line. It’s what keeps passengers in their seats on a looping roller coaster and throws unsecured kids off carousels. Centrifugal force is a function of the square of the train’s velocity divided by the radius of the curve; the smaller and tighter the curve, or the faster the train, the greater the centrifugal force. As it increases, more and more of the weight of the train is transferred to the wheels on the outermost edge of the track, something even the best-built trains have trouble coping with. That’s where the concepts of minimum curve radius and super-elevation, or banking, come in.

Banked curves, in which the outer edge of the track is higher than the inner edge, balance the load on the train’s suspension. Since gravity pulls a train downward and centrifugal force pulls it outward, a track banked at just the right angle can spread the forces more evenly between a train’s inner and outer wheels, and help to keep it on the track.

But banking the tracks isn’t a cure-all—a passenger train can tilt only so far before people fall out of their seats. So the minimum curve radius comes into play. Imagine that a curved portion of track is actually running along the outer edge of a large circle. How big must that circle be to insure that a train’s centrifugal force can be managed with only a reasonable amount of banking? 

It is interesting to note that this is the type of question that we deal with in first year intro physics.

Zz.