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Perhaps they should just put the stations on the top of an incline, then as the train enters the station the momentum would be converted to potential energy and back again as it leaves the station.



This is already done — originally (in the 19th century) so that seeping water didn't pool in the stations.


The Victoria line - the newest - is built with humpbacked stations exactly like you describe (where practical), and they save something like 16% on energy. But it's not really economically feasible to do that with the older tunnelled lines.


That was quite common in the days when locomotives were much weaker than they are now.




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