Just to be clear, you wouldn't actually run the flywheel in the opposite direction.. You'd take energy out of the flywheel versus putting it in?
0.5 x 29 tons x (50 mph)^2 to kWh
0.5 × 29 ton × (50 mi/
h)^2 -> kW·h = 2.01233 kW·h
So a Victoria line train at top speed has 2 kWh of kinetic energy.So it does seem feasible to do it either by installing battery packs connected to the tracks, or in the cars themselves. I wonder which would be better.
The only issue is that each third rail section is fed by its own set of independent rectifiers, and the third rail sections are not paralleled together. This means that if there's no other currently-accelerating train on the section of rail that you're on, it's just you and the rectifier substation -- and those rectifiers can't accept your regenerative braking current.
Adding inverter circuitry to the substations would introduce a path for energy flow to go from the DC third rails into the AC grid (opposite of the normal direction of flow, hence the term "reversible substation"). Since the AC grid is connected to all the rectifier substations and since there's many trains on the rail network, there'll always be a source for regenerative braking current that's dumped onto the AC bus.