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The question What is a “space elevator”? describes two key points about the length of a space elevator: equatorial geosynchronous orbit at 22,245 miles (35,800 km) above mean sea level, and an additional 22,245 miles for counter balance.

The question Benefit of sling shot effect with a space elevator talks about launching from the far/upper end of the elevator.

Space elevators are not uncommon in science fiction. In a story I was just reading, travel time to the launch point was greater then a week; that seems overly slow. For the two main points, what would impact travel time from Earth and what would be reasonable travel times to expect?

  1. Stop at Geosynchronous orbit
  2. Release/Launch point (not sure if you would need to stop here, or just keep going)
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  • $\begingroup$ GEO is about 36,000 km above surface. As with ordinary elevators, you should count with waiting times. One at a time and not too much mass. If anything goes wrong anywhere, all space travel is canceled until further notice. It is a very centralized and sensitive launch system. $\endgroup$ – LocalFluff Oct 14 '14 at 12:23
  • $\begingroup$ The answer you link to gives incorrect info. Without a counterweight, tether above would need to be much longer than 22,245 miles. $\endgroup$ – HopDavid Oct 14 '14 at 14:44
  • $\begingroup$ Why the assumption of 22,245 miles for a counterbalance? If the mass were large enough, the distance from "geosynchronous" altitude to the counterbalance could be a lot shorter than that. $\endgroup$ – Anthony X Feb 16 '15 at 2:57
  • $\begingroup$ @AnthonyX A worthy question, why don't you ask it? $\endgroup$ – James Jenkins Feb 16 '15 at 11:23
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For a first order estimate, we can use Wikipedia's list of vehicle speed records. Let's look at ground vehicles, ignoring rocket-powered vehicles (which sort of defeats the point of using an elevator). For wheel driven vehicles, the speed records seems to be around 750 km/h (I'm rounding a bit). For maglev rail vehicles, the record is close to 600 km/h.

To geosynchronous orbit (double time to release point):

$$\text{35,800 km / 750 km/hr = 47.7 hrs = 1.99 days}$$ $$\text{35,800 km / 600 km/hr = 59.67 hrs = 2.49 days}$$

Now, it's quite likely that your space elevator isn't going to try out for any speed records, so your travel times could realistically be greater than this. So using a slower car, a week or more to the release points seems plausible. On the other hand, if high-speed were a priority, and the power was available, there's no reason they couldn't be made to go faster with the proper engineering.

For one thing, this simple estimate doesn't account for the fact that there will be no air resistance to fight against once you leave the atmosphere, which means that you won't be fighting against terminal velocity if you go too fast. Although, if any part of your car is in contact with the cable/rail, there will still be friction and heating limits in terms of how fast you can go.

Edit: Wikipedia references a technical paper, Space Elevator Dynamic Response to In-Transit Climbers (direct link to pdf), by David Lang, which simulates the stresses and oscillations in the cable of a space elevator. For simulation purposes, it assumes two different values of climber speed: a "nominal" case being 200 km/hr, and a "fast" case of 400 km/hr. These are both slower than my estimates above, but are of a similar order of magnitude (and considerably less than the values used in ForgeMonkey's answer).

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    $\begingroup$ David Lang's and your estimates sound in the right ball park. Conventional lifters climb by use of friction on the tether. Going from 0 to 4000 mph in 60 seconds would indeed be "burning rubber". The friction from ForgeMonkey's scenario would indeed put some wear and tear on the elevator (not to mention the coriolis force). $\endgroup$ – HopDavid Oct 15 '14 at 3:55
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Assuming energy transmission isn't an issue (and any society that has the technology to build a space elevator probably won't have problems with throwing insane amount of energy about) and ignoring other engineering problems the limiting factor becomes the acceleration that humans can tolerate.

Let's say we want to keep the acceleration around what it is for astronauts today: about 3-4 g. So to make the maths easy let’s say we're going to accelerate, relative to the cable of the elevator, at 3 g.

At liftoff the passengers would experience 4 g, our 3 g + Earth's. So we accelerate up until we reach halfway (17,900 km), and then accelerate in the opposite direction until we arrive at GEO.

Plugging in the equations of motion gives us:

$$s=ut+\frac{at^2}{2}$$

$$17,900,000 = 15\text{ t}^2$$

$t=1,092\text{ s}$ (approx) to get halfway so twice that, 2,184 seconds or about 36 minutes to go from the surface to GEO.

Now let's take a VERY rough stab at the energy requirements. Let's say our elevator masses 20 tonnes or 20,000 kg.

Completely ignoring the effects of Earth's gravity or atmospheric resistance (maybe someone with more time can add these), finding the force required to sustain the acceleration:

$$F=ma=20,000*30 = 600,000\text{ N}$$

Over a distance to give work: 600,000 N over 36,000,000 m gives 21,600,000,000,000 Joules.

If that work is done in 36 minutes:

$$\text{21,600,000,000,000 Joules / 36 minutes = 10 Gigawatts}$$

Or about the total power output of Scotland.

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    $\begingroup$ I suspect that 3-4 g's wouldn't be the typical acceleration. I suspect that 1 g of acceleration would be the more typical value, if not less than that... $\endgroup$ – PearsonArtPhoto Oct 14 '14 at 19:25
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    $\begingroup$ For what it's worth, at an acceleration of 3G your speed when you reached the half-way point would be ~16 km/s, or Mach 46.8 $\endgroup$ – Andrew Coonce Oct 14 '14 at 20:00
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    $\begingroup$ I know, it's a bit ridiculous really. If you can accelerate at 3 g for 36 minutes, you probably don't need an elevator to make space access easy. $\endgroup$ – ForgeMonkey Oct 14 '14 at 20:29
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    $\begingroup$ Where's all this energy come from? How's it transmitted to the lifters? If the lifters carry their own energy source that is extra mass that adds to stress but not tensile strength of the tether. This notion of lifters having access to huge amounts of energy is absurd. $\endgroup$ – HopDavid Oct 15 '14 at 3:30
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    $\begingroup$ And with huge accelerations, you would be exerting huge coriolis force on the tether (this is in addition to already enormous stress from gravity). Evidently you're thinking of an elevator made of scrith, not bucky tubes. $\endgroup$ – HopDavid Oct 15 '14 at 3:34
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That just depends on how much energy you put in. If the elevator is heavy, it may not be trivial to transport the energy to it (say, by microwaves). If you need a week to GEO, it means you're traveling at 60 m/s (216 km/h or 134 mph). That sounds reasonably fast to me, but who knows how efficient and light microwave antennae will become in the future, or what way future space people will have to transmit power.

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  • $\begingroup$ So you mean microwaves to transmit power, which will then be used to climb via contact with the ribbon? Because if the microwave transmitted momentum itself, that would sort of defeat the entire point. $\endgroup$ – AlanSE Oct 14 '14 at 14:21
  • $\begingroup$ I meant the former. How else would you transfer the power? Taking fuel with you would defeat the purpose of the space elevator, because you would still be bound by the Tsiolkovsky-equation. $\endgroup$ – Rikki-Tikki-Tavi Oct 14 '14 at 15:53
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    $\begingroup$ @Rikki-Tikki-Tavi Even if you had to take fuel with you, you would still be able to do much better than a rocket if you could pull/push yourself up the ribbon rather than having to bring along reaction mass to throw behind you. But I agree, it makes the most sense to transmit the power via microwaves or laser. $\endgroup$ – pericynthion Oct 14 '14 at 21:29
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One of the possible configurations of the Space Elevator is a gigantic rotating loop, going around a (very large) pulley at the Earth's surface and hanging out into space well beyond GEO. A vehicle would grab onto the ribbon just past the pulley and be lifted up to wherever it wanted to go, with no need for power other than life support. I did a rough design in which I assumed the loop would be traveling at 300 m/s -- just under Mach 1 to avoid "breaking the sound barrier" problems in the atmosphere. At that speed the vehicle would arrive at GEO in about 33 hours.

Note that this configuration requires very strong ribbon materials, as the ribbon cannot taper.

This is an important question because the Space Elevator transits the Van Allen radiation belts. Passengers have to get through them very quickly (as the Apollo astronauts did) or be inside heavy shielding.

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  • $\begingroup$ Van Allen radiation is a potential problem but even if a space elevator could only be used for cargo and humans were transported by faster and more expensive rockets it would greatly reduce the cost of exploring space. As an example NASA's reference mission to Mars is ~400 tons for 6 astronauts. A system where 380+ tons is sent by elevator and then a small manned capsule is launched and docked to the spacecraft could still cut the overall lift cost by 95%+. $\endgroup$ – Gerald Davis Sep 19 '15 at 16:00
  • $\begingroup$ Agreed, but with a 20-ton payload capacity, it would probably be possible to send one or two astronauts up at a time on the SE inside a lot of water and polyethylene shielding. A slow, uncomfortable ride, but still immensely cheaper (and safer) than rockets, and the shielding material will be reusable at GEO. $\endgroup$ – Bob Munck Sep 20 '15 at 18:07
  • $\begingroup$ For getting them back down, I suggest a rotating tether (bolo) to throw a small re-entry vehicle through the radiation belts down to LEO. It's both very expensive and unnecessary to use the SE to go down. $\endgroup$ – Bob Munck Sep 20 '15 at 18:14
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I was trying to flesh this out on my site. You should start about 100km at the surface, then once the atmosphere goes away, accelerate at about 1 gravity until you reach about 10000km/hour. That's too fast if the climber actually touches the elevator, but maglev might be able to do it. At 10000km/hour it would take about four hours. You could power it all by having a pair of elevators, one going up the other going down, and have heavier stuff (from mining asteroids) going down and doing regenerative braking. Speeding up as it climbs means the payload is more spread out over the elevator, so the elevator has to support less weight overall than if cargo moved at a uniform speed.

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    $\begingroup$ Welcome to Space SE! It seems the external link you've provided is not reachable. You might want to correct it. Regards. $\endgroup$ – Boosted Nub Dec 7 '18 at 7:41

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