The Mobius Loop Rollercoaster

Blackpool's most famous mathematical curiosity.


One of the famous rollercoaster rides at Blackpool Pleasure Beach is called 'The Grand National'.  Its name comes from the fact that two trains set off together on parallel tracks and then 'race' each other around the track to see which gets back to the starting station first. Here's a video of the ride which gives an idea of the experience: http://www.youtube.com/watch?v=9aw08LhxNIU

A plaque on the side of the ride declares that this is a 'Mobius Loop' rollercoaster, one of only three in the world.  If you can't remember a Mobius loop, it's what you get if you take a strip of paper and you twist one end by a half turn before joining it to the other.  The result is a 'one-sided' piece of paper.  Why one-sided?  Because if you were an ant with very muddy feet and you walked along the surface of the loop, you would leave your tracks along the entire surface before getting back to where you started.  In the same way, the Mobius loop has only one edge - if you run your finger along the edge, you have touched every part of edge of the paper by the time you get back to the start.

Now a key thing about Mobius strips is that they involve a twist, and the ant leaving its footprints at some point has to turn upside down, and will remain upside down when it returns to the starting position.  The Grand National ride, on the other hand, has no sections where you go upside down, not even a loop-the-loop. So how can it be called a Mobius Loop?

A clue is that if you start the ride on the left platform you end the ride on the right-hand platform, and vice versa.  So something strange has happened.  One way this swap could be achieved would be if the train on the left-hand track were to climb over a bridge while the other train goes beneath so that the trains swap sides.  From this point on, the trains ride in parallel right the way back to the starting platforms.  You can possibly imagine how this would make a Mobius loop by imagining that the two parallel rollercoaster tracks have a sheet of rubber joining them together.  This rubber would be flat for almost the entire ride.  However  at the point where one train went under the other, the rubber sheet would make a half twist.  It is this imaginary rubber sheet that is the Mobius loop.  The track represents the edge of the Mobius loop.

However, one track going up while the other goes down would be obvious for passengers to detect.  The reality is that the two tracks are always at the same level. [*spoiler alert*] The two tracks peel away from each other at the start of the ride, loop round and down, and ONE of the tracks passes under the station before joining the other track that doesn't.  It's all so subtle that few realise it has happened.  And what has been created is, as it happens, just as much a Mobius loop as the up-and-down switch I described before.

What it means is that there is actually only one continuous track on the Grand National, which doubles up on itself.  If you start on the left platform, then after doing one circuit you loop around to the right platform then on the next circuit you loop back to the left platform.   Clever - and mindbending - stuff.