Brachistochrone trains

The main advantage of trams over subways is that they're surface-running. This means that you don't get disoriented, you don't need to travel up and down, you can see destinations as you travel and you can find a route quickly by following the tracks.

Undergrounds, on the other hand, can run faster, avoid level junctions using flyovers, have longer trains due to the lack of intersection blocking and don't interrupt other vehicles and pedestrians on the surface.

Consider the possibility of combining surface running trams with underground trains. Have surface stations and surface running trams, but every few km provide a heavy rail station on the surface, ideally with cross platform transfers to trams. How could we do this? The heavy rail would drop down an incline (perhaps a cycloid/brachistochrone path) at the end of each platform, rising back up at the next station. The train would accelerate down and decelerate up, ideally removing almost all acceleration and jerk for the passengers. It's unlikely for there to be a feeling of weightlessness, given the shallowness of the slopes.

The underground portions would be in straight lines, so people knew which direction they were heading as they descended, corners instead would be provided only with surface running (although it's probably best to avoid corners altogether). The descending ramps could be covered over with garden beds, or buildings. We might even allow both trams and trains on these lines, allowing for considerably greater operating flexibility (tram-trains). Straight lines also minimise jolting on cornering and avoid the need for precise cornering speed control.