I’ve never really been much of a fan of the space elevator concept. Not so much that it relies upon nearly magical levels of structural strength (though some new materials are strong enough – at least at small scale – to make the concept feasible), but because it is something of a snail for getting payloads into orbit. If your elevator can climb at a brisk 100 km/hour, and that would be a massive challenge, it will take the elevator about 358 hours to climb to geosynchronous… slightly over two weeks. That’s a couple days in the van Allen belts, so your elevator had better be highly shielded… which means the ratio of payload to climber will be minimal. And then your climber has to either be jettisoned, or it has to make the climb all the way back down. That will be probably several days, during which time you can’t send another climber back up. So you’re probably looking at a turnaround time of around three weeks per “flight.”
Turnaround time can be improved by not going all the way to GEO. Instead, go several thousand miles up, then throw the payload overboard. The higher up you go, the more tangential velocity you’ve have, and the closer to a circular orbit you’ll have. To get into an actual circular orbit, you’ll need to have an onboard propulsion system; the lower your ejection altitude, the more propulsive capability you’ll need. But while this’d speed up the elevator system, it’ll reduce effective payload by *a* *lot.*
Jettisoning a payload puts it into an elliptical orbit with the jettison point being apogee. Perigee rises as the elevator rises; at some point you’ll have an orbit where the perigee is something convenient like 400 km. So all you’ll need is enough propulsive capability to circularize at perigee. But since I can’t be bothered to do the actual math, it seems to me the apogee altitude will be quite high for the elevator, so it might only shave a relatively small fraction off the elevator trip time compared to going all the way to GEO.
Then there’s the problem of actually climbing. How? The cable might be a flat ribbon, millimeters thick by centimeters wide, or it might be actually cable-shaped. But the materials under consideration, graphene and diamond fiber and such, have a little problem: they are virtually frictionless. Run wheels on them all you like, you probably won’t get much traction. Adding a ribbed surface for traction, or adding magnetic materials so a maglev system can haul up the elevator, will add vast amounts of weight to the system.
This video points out some of the engineering issues with the concept: