There are many, older, proposals for pneumatic subway systems - sealed tunnels with tightly fitting but unpowered tubular trains, and massive, stationary air pumps to pressurise or depressurise sections of tunnel. The resulting pressure differences drive the train forward. Passenger access requires
airlocks at the platforms.
Other visionaries proposed evacuated tunnels, so that high-speed trains (powered by whatever means) could progress free of wind resistance.
Hereforth I intend to adapt the previous "Non-stop underground" ideas - a constant-rate train with detaching carriages - to a pneumatic system.
The train is analogous to a computing "stack". [kindachewy]'s system [linked] is a [correction] LIFO stack (last in, first out).
Instead, let this be a FIFO stack (first in, first off). New carriages attach to the front of the train, and the rear carriage is jettisoned to stop at the station.
Admittedly, only usable in driverless or drive by wire systems, but this way there is no need for a separate tunnel or track to accelerate the departing carriage, and decelerate the arriving one. The departing carriage can accelerate to the required speed as the main train approaches, and drop the rear carriage as it passes.
Carriages are constantly cycled from the front to the rear of the stack. This allows carriages to be diverted from the system for maintenance as required, while the "stack" itself - being only a notional, ephemeral grouping of real objects - remains in motion 24/7/365.25
In addition, passenger in the newly adjoined carriage need not rush to find another seat before their carriage detaches - they can wait until closer to their destination.
Imagine the section of track both before and after each station is a linear electromagnetic motor. Connect the two, and energy captured by braking the arriving carriage can automatically be transferred to the departing carriage, minus losses. This would also provide a level of failsafe to prevent a high speed train from colliding with a carriage which has failed to leave the platform.
Something similar could probably be achieved with air pressure - viz:
As the train approaches the station, an automated marker beacon signals the rear carriage to detach.
The resulting system is a group of three freely moving pistons:
1/ the front (departure) carriage
2/the train, and
3/ the rear (arrival) carriage.
There are thus two pneumatic chambers:
a/ between the departure carriage and the train, and
b/ between the recently jettisoned arrival carriage and the train.
Designs differ from this point forward, depending upon the underlying design and driving power of the transit system. For example, a pneumatic system (air moving relative to tunnel, stationary relative to train) is different from an otherwise-driven system where the air is free to rush around the train.
The departing carriage is currently stationary. The rapidly approaching train creates an air ram behind it, which pushes it up to docking speed.
What we want is to:
z/ control this acceleration for passenger comfort, by
y/ bleeding air from chamber a/ at a controlled rate, and
x/ feeding the air back to chamber b/ to air-brake the arriving carriage.
We do this by a series of flap valves and pipes which transfer air from in front of the train to behind it.
I have been trying to nut out the exact arrangement of pipes and valves to achieve the required effect. I keep thinking I almost have it, but then lose my thread.