Graph theory I think?

Solving the Börneplatz Problem

Last night, I blogged about an inefficient bit of track design at Börneplatz in Frankfurt. And to make it EVEN MORE exciting, I left… A CLIFFHANGER.

In case you forgot the thrilling tram junction diagrams.

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The Börneplatz Problem

This is a little maths problem I was thinking about on the tram back today.

Until recently, there were two tramlines running through the centre of Frankfurt, the 11 and the 12. The two lines follow the same track through the old town, then split at a major crossroads outside the Judengasse Museum, at a plaza called Börneplatz. Since it’s in a convenient location for various museums and things, Börneplatz is an obvious place for a tram stop. This is easy enough to set up; just put a set of platforms on the shared track leading up to the junction.

The blue line (straight on) is the 11, the yellow line (curving) is the 12. The white rectangles are the platforms.

Then Frankfurt Transport decided to open a new tram route, the 18. The 18 doesn’t share the same track as the 11 and the 12 through the old town. Instead, it comes in from the other side, using the same track as the 11 up to Börneplatz, and then switching and following the route of the 12. Continue reading