If you account for various inefficiencies like taking it slow in the lower atmosphere Ant whatnot, it still should be in the matter of hours. So totally feasible and even comfortable.
This means that half-way after 58 minutes, the climber is traveling at 0.3 * 9.81 m/s² * 60 * 58 ~= 10.2 km/s ~= 36,720 km/h (!!!) relative to the cable. A tiny imperfection or wobble is going to make the climber crash into the cable, destroying both.
A climber with a mass of 10 tonnes requires 10^4 kg * 1.3 * 9.81 m/s² ~= 127.5 kN of force to accelerate at 1.3 g. At the ~56 minute mark, the climber reaches a speed of ~9,888 m/s. This means it requires a power output of 127.5 kN * 9888 m/s = 1.26 GW (!!!) to achieve this acceleration, plus overhead for the power electronics and transmission. Even at a voltage of 1 kV, that's around 1,500,000 A (!!!) of current that you have to transmit and invert.
If you have a way to reliably transfer that amount of power without touching the cable which is moving at 10 km/s relative speed, or with touching but without immediately melting the cable or the collector, let me know :-)
> So totally feasible
lol no
A maglev train is several centimeters from the rail; if someone made the carbon nanostructures (the only known material strong enough are atomically precise carbon nanotubes or graphene, but the entire length has to be atomically precise you can't splice together the shorter tubes we can build today) this badly wrong, the cable didn't survive construction.
> Even at a voltage of 1 kV, that's around 1,500,000 A
Why on earth would you do one kilovolt? We already have megavolt powerlines. That reduces the current needed to 1500 A. 1500 A on a powerline is… by necessity, standard for a power station.
We even already have superconductor cables and tapes that do 1500 A, they're a few square millimeters cross section.
No maglev train I ever heard of travels at 36,000 km/h. This is about two orders of magnitude faster.
> We already have megavolt powerlines.
That's transmission over long distances, but you need to handle and transform all that power in a relatively small enclosure. Have you seen the length of isolators on high-voltage powerlines? What do you think is going to happen to your circuit if you have an electrical potential difference of 1 MV over a few centimeters?
Yes, you can handle large voltages with the right power electronics, but you need the space to do so. For comparison, light rail typically uses around 1 kV, while mainline trains use something like 15 kV. But a train is also 10 to 100 times as heavy as the 10t climber in my calculation, so you need to multiply the power (and therefore the electric current) by 10 to 100 as well.
From what I've seen nobody currently directly launches more than 4.9 tons direct to GEO (Vulcan Centaur VC4). Starship is supposed do 27 to GTO (not GEO) when finished, but it's not finished.
If a space elevator lasts long enough to amortise the construction costs (nobody knows, what with them not being buildable yet), they would represent an improvement on launch costs relative to current methods, even if you were limited to 10 tons at a time and each GEO being a 2 hour trip.
