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# Mathematics in the Rail Industry

Tonight we had the first of the East Midland’s branch of the IMA evening talks. David Worsley, from Network Rail (and a Visiting Lecturer at Newcastle University) was talking about mathematics in the rail industry.

It was a very engaging, entertaining and informative whistle-stop tour of the various mathematics used in the rail industry.

He started by talking about the forces on rail bridges before moving on to talk about the cant of a track. I had never considered the fact that if rail track bends were not banked then the outside track would experience greater wear than the inside track resulting in a need for an earlier replacement. This, as well as the desire for passengers to experience little centrifugal force explains why a cant is put in on the bends. The cant would be perfect if, in the picture below, $$a l_j$$ was zero. However each piece of track has many different trains running over it at different speeds so selecting the optimal cant is an interesting optimisation problem.

Seeing a table showing how the Department for Transport values the time of people commuting by various means

If you are a passenger in a taxi your time is worth more than anyone else.
The discussion concerning strategic optimisation and  the planning of the HS2 route through the midlands was very interesting as it is an issue that is local to us.

If you fancy checking out the talk there is a video here