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Is it possible for a space elevator not to just reach speeds of a few hundred km/h, but much faster. Since in the future, people might want to go up to GEO to maybe work there and come back home on the same day. Using a typically proposed space elevator which slowly climbs up a 36 000 km long rope, possibly made of carbon nanotube, will take too long. In many sci-fi, space elevators are shown to take multiple days to reach the top. On Excel I made a few graphs showing how many days it would take to reach the top of a space elevator going a only a few hundred km/h.

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Even if the elevator were going around the speed of a commercial airliner, it would still take about 2 days to reach the top. So I was wondering how fast a space elevator could send people up.

If a space elevator could constantly accelerate in one direction and then once it is half way, start to decelerate, the time it would take, depends on how fast it is accelerating.

enter image description here

With a constant acceleration, the time it will take went from a couple of days to only about an hour at 1g acceleration. However, it doesn't make that much sense to accelerate it even faster because the time saved starts to become less, while the g force exponentially increase. At about 4g it will only take about half an hour. Imagine being in 4g for 30 min, ouch.

There is an issue though and that is the peak velocity (when the elevator is half way there and starts to decelerate) is quite high, even at 1g.

enter image description here

At about 1g acceleration the space elevator will travel at about 18km/s peak. That is nearly twice the orbital velocity a satellite has in LEO. A space elevator could possibly use rockets to reach that velocity, but the whole point of a space elevator is to make spaceflight cheaper and using rockets just misses the whole point of a space elevator in the first place. Maybe a maglev track could be used to accelerate the elevator to those velocities, but that would have to be a pretty long track (36 000km). Maybe something similar to a hyperloop would work, but that also faces similar challenges the maglev track would face.

Question: Has there been any studies to what could be used to get a space elevator to these velocities and if so what has been proposed?

For clarification:

  • The proposal should be reusable and practical. By practical I mean that having an elevator makes sense. If the elevator is powered by some onboard propulsion and then has to slow down again, just doesn’t make the elevator worth having. Just use the onboard propulsion instead.

  • I would consider an elevator powered by rocket impractical because there is no point of the elevator. Just use the rockets instead. An expectation would be if somehow the elevator powers the rockets

  • The type of things I am looking for is some type of other method of going up the elevator quickly. Maybe a magnetic track. Or maybe a rope which quickly pulls the elevator up. My question is what kind of proposals are there of a very fast space elevator

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  • $\begingroup$ I want to go to Paris every day for lunch. Just because I'd like to doesn't mean somebody will give me the means to do so. $\endgroup$
    – Jon Custer
    Jan 3 at 18:18
  • $\begingroup$ @JonCuster good point, but 100 years ago it would have been crazy to go to Paris in under an hour. Now there is a train which connects England and Paris and it is possible to travel to Paris in under an hour. So I was looking at the same application for spaceflight. $\endgroup$ Jan 3 at 18:29
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    $\begingroup$ Anyway, I don't think going to GEO and back every day is a reasonable goal given the distance involved. The whole point of a space elevator is to lift mass in an energy-efficient way, not doing it fast. You want fast, use a rocket. $\endgroup$ Jan 3 at 19:43
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    $\begingroup$ @DarthPseudonym, rockets can be used, but would not be great. Rule of thumb is that if you want to get twice the speed, you need a rocket 4 times the size. So if the peak velocity is 2 twice that of an orbital satellite and then you also need to slow down, that means you need a rocket that is four times as fast. Which would be 16 times the size of a regular orbital rocket. This is not fully accurate depiction, but it gives the idea that a rocket wouldn’t be great in this scenario. Also if the elevator is meant to be cheap, a big bulky rocket doesn’t meet the requirements. $\endgroup$ Jan 3 at 21:29
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    $\begingroup$ But that's exactly my point. You're basically complaining that a train doesn't go as fast as an airliner. They're two tools that do different things. A space elevator is for lifting huge amounts of mass on a shockingly small energy budget, like a train. That's the whole point of the thing. The price of going faster is giving up efficiency. $\endgroup$ Jan 3 at 22:04

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This is a challenge to write an answer for because a space elevator on earth may prove to be outside physics, so most detailed designs have focused on just the thread itself, with payloads as low as 100kg and speeds as low as walking pace.

Certainly if writing a fiction you can describe a vertical vacuum tunnel with cars traveling at least as fast as terrestrial maglev trains. This however involves much more complex structures than anything with detailed design work and will still involve rocket levels of energy, even if in electrical form (though a space elevator can fit a lot of solar panels on the sides).

Since the cost of building the first space elevator is directly related to total mass lifted most studies have trimmed things to some sort of tapered ribbon, that is climbed by mechanically gripping from both sides. The designs need to handle the taper and be self powered, leading to competitions such as this.

Which leads to travel times of weeks or longer. Adding something as simple as power rails to a drive the cars adds hundreds of tonnes of metal that then needs thousands of tonnes of additional thread to support so is normally discounted.

Where the mass of the moving car is massively larger than the local suspension thread there are additional obstacles to fast movement due to Coriolis force and other effects that add up over the thousands of km of vertical travel that mean even going down may be speed limited below 100kmh.

All of these mean that a first generation space elevator will be a very bare bones project, unsuitable for moving people and possibly marginal for moving cargo (low payload capacity on thread, and each payload on thread for extended time). Having built a space elevator it is in theory possible to scale up arbitrarily to handle desired travel speeds and payload masses, though more massive elevators increase the safety issues.

In summary, there are many ways that a high speed space elevator could operate, but there are no serious studies since all of them require a space elevator many magnitudes heavier than currently being considered.

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Terms

To set up this answer let's first define some terms...

Climber - The vehicle that carries the cargo up the tether.

Track - A non-loadbearing part of the tether that the climber engages with. The track may distribute power from a ground-based power plant. It could even include an electromagnetic linear motor generator.

Power

The per-climber power ($P$) requirement will be a function of acceleration ($a$), velocity ($v$), position, and climber plus payload mass ($m$). $F=ma$ and $P=Fv$ so $P=mva$.

$a$ is a function of position too, as it includes not only the acceleration that increases or decreases the upward velocity of the climber but also the difference between the pull of gravity and the inertial force due to the Earth's spin.

Increasing either $a$ or $v$ will require more $P$. Increasing $P$ leads to an increase in either: a) the climber's mass, $m$, leading to even more $P$, b) the track's mass, leading to a more expensive tether, or c) both.

For example, the power needed for a 5000 kg climber traveling up at 100 m/s with an acceleration 2x9.8 $m/s^2$ is

$$P=(5000 kg)(100 m/s)(2)(9.8 m/s^2)/1,000,000 = 9.8MW$$

For reference, a 10MW power transformer looks like this... enter image description here

.. and a 10 MW electric motor looks like this... enter image description here

At first blush, even for these relatively modest speeds and accelerations, it appears that it might be quite challenging to engineer a climber with a payload ratio greater than zero.

Energy

The difference in kinetic and potential energy between 1 kg on the ground and 1 kg in GEO is roughly 58 MJ, which is about 1.80 USD worth of electricity (assuming electricity is 10 cents/kWh). It seems like travel to GEO in a space elevator will be cheap. However, after factoring in payload ratio and energy efficiency and after adding the cost of servicing the debt on the capital cost of the tether, the cost-per-kg will go up considerably.

Approaches

There are a few ways that various space elevator proponents contemplate powering the space elevator climber.

Wires in the Cable

This idea involves embedding high-voltage power transmission lines in the tether and using brushes or an inductive coupling mechanism to draw power from those transmission lines to power the climber.

The first problem with this approach is weight. If you embed metal wires, those wires will change the overall strength-to-weight ratio (that is, the specific strength) of the tethers. This causes the mass (and thus the cost) of the tether to increase.

Some people have proposed that the tether can be made from both conductive and insulating super-materials such as carbon nanotubes for the conductors and boron nitride nanotubes for the insulators. But, carbon nanotubes do not conduct electricity well so I'm skeptical of this idea.

The second problem is ohmic losses, which will affect efficiency.

Even with a good conductor such as aluminum, the ohmic losses over these distances will be very high, which means that power transmission efficiency will be low, which means that per-kg cost will be high.

This approach could become viable if a room-temperature superconducting material with extremely high tensile strength were invented. But until then, let's look at some other ideas.

Linear Motor/Generator in the Tether

This concept would both lower the overall specific strength of the tether and suffer from low efficiency due to ohmic losses in the transmission lines.

Beamed power

There are two ways of beaming power that I've seen proposed by space elevator enthusiasts. The first is microwaves and the second is lasers. If the end-to-end efficiency of these power-beaming technologies were even close to the efficiency of transmission lines, we might see some applications of wireless power technology in our electric grids - but we don't. The reality is that the efficiency of these technologies over such distances is very, very low. So low, in fact, that the energy-cost-per-kg would be more expensive than just launching payloads with rockets.

Onboard Power

With this approach, the energy is stored in the climber, converted to electricity, and the electricity is used to power electric motors that lift the climber. As with rockets, the faster and higher you want to go the more energy you need. The more energy you need, the more fuel or batteries you need, and the heavier the climber becomes. It is a vicious cycle that can ultimately be captured by the space elevator's equivalent of the rocket equation.

Possibly a nuclear power plant could defeat the exponential nature of the "Climber Equation". However, if we want to generate 10 MW of power we would need ten 1 MW micronuclear reactors like the proposed micro-reactor shown below.

enter image description here A 1 MW micronuclear reactor concept from Radiant Nuclear

Solar Collectors

With today's technologies, a 10 MW solar collector would be too large for a climber with a 5000 kg total mass budget. (See image below) enter image description here

10 MW Shamsuna solar plant in Jordan

Of course, I haven't covered every possibility here, but hopefully, this helps illustrate that the problem of engineering the climber could be as significant as the problem of manufacturing and maintaining affordable defect-free super materials for the space elevator's tether.

Let me leave you with one final thought...

Space Infrastructure is still a great idea, just keep in mind that space elevators were conceived back in the 1970s (if not earlier) as a solution to rockets. Engineers realized early on that the tether material was a major problem. They side-stepped it in 1982 by coming up with the Orbital Ring concept. Soon after, the orbital ring idea was further improved upon with the introduction of the Launch Loop. Since then newer and potentially even better ideas have been published.

Many of the newer ideas do reference both the launch loop and the orbital ring as prior work, so by searching for papers and articles containing those terms you are likely to discover some of the most recent, and more interesting, space infrastructure concepts.

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