The Geometry of Railway Geometric Overthrow Revisited Using Computer Algebra Methods

There are size standards for railway coaches and freight wagons in order to allow trains to pass from one railway line or even network to another. The maximum size and shape of the rolling stock is denoted gauge. On curves, vehicles sweep a larger path than on straight track. We shall focus on the geometric overthrow of the different kind of rolling stock (the geometric overthrow is that part of the vehicle element offset which is due to the track curve). We shall detail the influence of the kind of vehicle (two axles, classic bogies, shared bogies or Talgo vehicles) in the geometric overthrow. The computations can be easily carried out with a computer algebra system such as Maple and some curious results are obtained (for instance, a negative value (!) is obtained for Talgo coaches).