How to calculate maximum altitude difference between metro stations?

For story purpose I am trying to design a mass transit system for a perfect city. Right ... maybe not so perfect, if you look carefully into the details, but actually the mass transit system is supposed to be highly efficient.

Nevertheless, the city is built from scratch with heavy inspiration from New Urbanism (mass transit, high buildings, mixed zoning, nice parks, very little cars). In RL the metro suburban rail system is able to waste even 45% of used energy for braking (and engineers hope to recover a small fraction for regenerative breaking). In RL there are also attempts to reduce wasted energy by working with slopes - after leaving the station the train goes down a bit to go up just before the next one, thus saving all this accelerating /decelerating stuff.

I want to go one step further - I want to position the stations clearly higher than the track, thus effectively no breaking would be needed. (Yeah, the metro would resemble a bit like a roller coaster, I know). The system would work perfectly, if all stations were on the same height, just a bit energy would be used to compensate for rolling and air friction. If the altitude difference would be minimal, then train would need to use energy only in this slightly uphill direction, while on the opposite, everything would be provided by gravity.

Is there any idea how to calculate (rule of thumb, whatever) what the maximum height difference between stations would be, under which such a system may indeed work?

The tech level is comparable to contemporary Earth.

(Clarification: I know that you have to include rolling friction, air friction, etc... The issue is just how to either find data to put into such a formula, or how to make a very rough adjustment based on some RL life example, to derive calculations, that would not make any engineer cry)

posted almost 7 years ago

Shadow1024‭

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