[1] has rolling resistances for railways and cars on roads, which are almost an order of magnitude apart.

Intuitively, I'd expect that once the train has accelerated, it will keep its momentum very nicely, and (if electric) can easily return energy if it does need to slow down.

I can't find a real-world coasting distance for a train on level track, only reports during accidents/near misses -- 5km under emergency braking on a slight downhill slope, for one! [2]

[1] https://en.wikipedia.org/wiki/Rolling_resistance [2] https://www.gov.uk/government/uploads/system/uploads/attachm...

Rolling resistance is roughly constant with speed, so it's unimportant for efficiency. The main driver of changes of efficiency with speed is aerodynamic drag, because that increases with the square of the speed. Trains presumably have very low aerodynamic drag because they're long and thin.

The calculation is straight forward. The coefficient given for rolling resistance is 0.0004 for rail which means that .0004W is the frictional resistance of the track. Given a train going at velocity v then the train is accelerated by friction at a rate of -.0004W/m (F=ma so a=F/m) which is equal to -.0004g (W=mg).

Then to stop it will take t = v/.0004g which means that you will travel vt/2 in that time.

For example, if a train is cruising along at 30 mph (44 fps) then it takes 44 ft/s / .0004(32.2 ft/s^2) = 3416 seconds to stop which means that the train travels 14.2 miles under ideal conditions.