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Underneath the track is a tube with fins wrapped around it in a helix. Like with a screw. There is a slot between the rails.
Instead of long subway trains, each 'car' is big enough to hold eight people sitting in a semicircle, opposite a slide door The cars are connected the the screw thread via a pair
of wheels that grip it either side.
This has two effects:
1. The headway can be very low
2. The speed of the cars can be changed by varying the angle of the screw thread to the screw.
The stations are similar to today's stations, exept there are a continous stream of cars passing through. The cars don't stop, but slow to just under a walking pace as they enter a station. The slide doors open, and people can get on and off.
No waiting times, and your trip is in peace without stinky old men and obnoxious litle kids rubbing up against you.