A comment to an answer to a question about Mars missions stated that using Starship to launch mass to orbit would be cheaper than a space elevator. I didn't imagine that. I know that space elevators are speculative, including their predicted cost; additionally, the Starship operating cost will depend on the actual re-usability and required maintenance, if it ever succeeds in the first place.
But still: Is that plausible?
Short answer The price of Starship is definitely going to make things cheaper, but a space elevator still is cheaper than Starship is - atleast in the long run.
Long answer It is a bit hard to compare the price of Starship to a space elevators just because a space elevator hasn’t been built and there are different types of space elevators. Lets look at the price Starship first.
The price of Starship is hard to say since it is not regularly flying payloads into orbit yet (that might soon change). Right now the price range is pretty large going anywhere from 300 - 400$/kg to only about 20 dollars per kg into LEO.
A space elevator would carry cargo all the way to GEO, not LEO. Unfortunately I couldn’t find any number about the price of Starship to GEO, but Elon musk did say in a presentation at Starbase that it will take about 10 Starships to refuel a single Starship in LEO. So I will just multiply the price to GEO by ten. However, this might not be actual price of a Starship to GEO and since it does not need as much fuel as going to the moon, SpaceX might not send up 10 tankers to fuel 1 Starship going to GEO.
The price a space elevator might be expensive to set it up, assuming the space elevator is similar to the Edwards proposal is estimated to cost about 40 billion dollars (The 6B was the cost of part of the space elevator, but the whole thing is much more) Also many comments mentioned below, 6 billion dollars is a quite optimistic price, while in reality it will probably be one or two magnitudes more. The price of Starbase has been about 3 billion dollars so far, but more money is being invested, so that is not the final price.
So setting up Starship is most likely cheaper, but there is the possibility that it might not be because 3 Billion dollars is not the full price.
However, that price is only for the short term. The long term looks different. Using a space elevator to carry cargo into GEO is much cheaper than using a rocket. It is thought that a space elevator could lower the price to only about 5 dollars/kg to GEO. Unfortunately, there are also maintenance costs and energy costs so the price can easily reach a couple hundred dollars per kilo, but that is still cheaper than Starship because Starship can only get about one kilo per a couple hundred kilos into LEO, not GEO.
This means that in the long run, a space elevator is cheaper than Starship, but setting it up will probably be more expensive.
Bradley C. Edwards at NIAC published a detailed study of space elevators in 2000 that resulted in energy costs alone of \$220/kg. This is an easy order of magnitude above the aspirational operating costs for Starship. Even if Starship just matches the operating cost per launch of Falcon 9 (despite not expending any hardware and having much simpler recovery logistics), that still works out to launch costs of \$100/kg. Further consider that the space elevator requires revolutionary advances in material science, and if actually achieved, such advances would help further decrease the cost of rocket launch as well.
Beyond the energy costs, a space elevator has strict limits on payload mass and volume and number of ascending payloads the elevator can handle at a given time. It can only easily access equatorial orbits, and the further away from geostationary those orbits are, the smaller the effective payload it can handle, the remainder being propellant for adjusting the payload's orbit later. Scarcity would make elevator time more expensive, and the need to lift propellant and tugs for positioning will further increase the effective costs of using the elevator.
Reusable rocket systems like Starship are far more logistically flexible and scalable. There is no need to schedule launches around other vehicles in flight or the kinetic state of a giant piece of infrastructure. Capacity can be increased almost arbitrarily by performing launches in parallel, and payloads can be delivered directly to non-equatorial orbits of a wide range of altitudes. A space elevator also entails a prolonged crawl through the radiation belts, which a rocket launch can easily avoid, making the rocket a far preferable way to launch personnel.
To counter a claim made elsewhere: a space elevator is not an electrodynamic tether. The overriding concern with its material selection will be material strength, not conductivity, and an electrodynamic tether additionally needs to make good electrical contact with the plasma of the thermosphere at its end while being insulated along its length. This insulation and the plasma contactors required to make electrical contact without damaging the cable would make the tether far too heavy to use as a space elevator.
Additionally, the space elevator is geostationary, and where the thermospheric plasma is densest and the magnetic field the strongest, it is barely moving any faster through Earth's magnetic field than the ground it is attached to. Even a good conductor stretched along that portion would be little better as an energy source than the ground-side power distribution grid.
Chemical Rockets don't stand a chance.
The energy cost to hit geostationary orbit is about 72 MJ per kg. The rocket equation for a 3 km/s exhaust rocket means only 30% of the expended energy is used to lift the payload (including the craft holding it), the rest is wasted accelerating fuel and lifting it.
Edwards wrote a paper describing the economics of a space elevator using near future materials science - specifically carbon sheets or nanotubes - as that is our barrier at this point. (Everything else is "just" engineering).
It calculated a 2% efficiency for the power transfer of electrical to optical laser transmission, back to electrical and turned to kinetic to life the transport up the elevator. This was using 2000 era tech - our lasers and solar panels have gotten significantly more efficient since then, and pulling off 30% is not at all a problem today.
So using today's power transfer tech, a rocket has to have 100% efficiency in converting electricity to fuel to match an elevator. And I assumed the staging sections have 0 mass. This both isn't true, and also means there is nowhere to improve.
The space elevator meanwhile could continue to improve power transfer to the lifter from my current assumption of 30% using 2023 technology.
The actual cost of making a space elevator, and maintaining one once built, means that this is just the limit of using it over the long term.
But, over a long term, space elevators win thermodynamically. And because it takes a LOT of energy lift things to space, getting costs down to that energy level means it remains expensive.
You can get cheap power for 3.6 cents per kWh or 0.01\$/MJ: so 0.72\$ per kg at thermodynamic limit, or 2.2\$ per kg at space elevator energy costs using modern laser power beaming.
Nobody is talking about Dragon hitting these numbers. The most extreme brags I have heard are "one day 20\$ to LEO". Current prices are about 1500\$/kg.
But, be aware we cannot build the material for the cable at the scales required at this point. So, actually building a working space elevator is, of course, not possible.
Space elevator to LEO still needs chemical rockets
Space elevator designs rely on the cable following the surface of the Earth, being anchored to a counterweight above GEO orbit. At low-Earth orbit altitudes, the tangential speed is only about 0.5 km/s. To get into LEO, you need about 8 km/s tangential speed.
The potential energy of lifting up 1000 km to LEO is 10 MJ/kg. The kinetic energy to get to LEO orbital speed is 32 MJ/kg.
It appears that optimal way to LEO using a space elevator would be to lift the payload higher and release it into an orbit that intersects LEO tangentially at its perigee. For 1000 km altitude LEO, this would mean a release at about 15 000 km altitude. To circularize the orbit needs about 2 km/s delta-V retrograde burn.
This is much less than the 8 km/s delta-V needed for a LEO launch using only chemical rockets. But you still need the rocket, so combined with the operational costs and investment of the space elevator, it may not be cost effective.
Space elevator, if it works, is very effective for getting to GEO
When a mass rises up the cable, it simultaneously gains tangential velocity and reaches the necessary orbital speed 3 km/s at GEO without needing any chemical power. The total energy needed would be about 100 MJ/kg. At current wholesale price of electricity of around 50 USD/MWh, this would give a lower bound of 1 USD/kg. On top of this you would have any maintenance costs and depreciation of the investment.
The launch price of a space elevator would be dominated by the initial investment, which we have no way to accurately estimate. Once operating, it is bound to be cheaper than chemical rockets, unless there is significant maintenance costs due to e.g. cable wear.
Short answer:
For Earth-based space elevator, Starship wins. Simply because Space Elevator, while endearing idea, is still about technical readiness level 1, while Starship is about TRL 6 already (with high likelyhood of reaching TRL 7 in first half of 2024). So one can't really say if Earth Space Elevator is actually doable with current technologies, much less would it be economical.
Longer answer:
Even Falcon 9 (or even any other spacecraft) wins, as the Space Elevator is simply way too unrealistic for current technology even if everything was to be made perfectly up to the theoretical limits and all risks (some were mentioned like: Lightnings, Meteors, LEO objects, Wind, Atomic Oxygen, EM fields, Radiation Damage, Induced Oscillations etc) were minimized. And some risks (like war, sabotage, cargo malfunction problems, unknown factors etc) were not accounted for at all.
Add to that the basically any failure leads to complete and utter failure of whole Space Elevator project and all invested funds (as opposed to even catastrophic failure of any single Starship, which would end up being relatively cheap and minor annoyance). Also, rebuilding the cable after its failure would also take not just huge amount of money, but also many years to rebuild from scratch, as opposed to few months for new Starship (of which you'd have several ready in reserve anyway - so no time delays).
In other words Edward's work sounds like very wishful thinking, to say the least. 5 Stars for enthusiasm, but only 2 for reality check. And it is one of more realistic suggestions available.
Just on nanotube cable production: "No defects in the cable are allowed.", "The length of the finished cable is to be 91,000 km", "Production time for each cable must be no more than one year and it must be possible to make up to 100 in parallel" etc.
So the prerequisite to even think about that is to be able to build some 9 million kilometers of perfect carbon nanotube cables in one year on a budget of (admittedly in his own words "Still difficult to estimate") about 5 billion dollars?
That sounds very unrealistic to me, especially considering we likely don't even have the tech to produce carbon nanotubes of required quality, much less at that price (unless I'm miscalculating, that works out at about $0.50 per meter of 8cm wide [on average, it tapers from 11.5cm to 5cm] perfect quality carbon nanotube woven cable)
And considering other estimates (khm SLS), I'd suggest adding at least one or two zeros after that $70B estimate to get more realistic value.
And then there is the issue of risk by putting all your eggs in one basket. Even if the price of basket happens to be lower, that is extremely risky. And there is the issue that you don't actually want to launch all spaceships from same location in space, and you don't want same orbit for them, which means you (even with space elevator) still have to have chemical rockets to put you in desired orbit, which adds to the costs.
Don't get me wrong. I'd love to see Space Elevator, and it remains a possibility on say Moon (where the problems, risks, costs and especially technology challenges would be much lower). Several decades after using Moon Space Elevator is as mundane and as risk-free as taking a airplane today, we might consider building Mars Space Elevator, and many decades after that we might even consider possibility of building Earth one.
But even in my most optimistic mode, I'm not seeing even the possibility (of extremely simple, by comparison to Earth-based one) Moon Space Elevator before the last quarter of this century (we'll be lucky if we manage to have constantly manned moon base station significantly before mid-century, and you'd most likely need at least thriving industrial moon city to warrant considering investing in Moon space elevator)
In the some distant theoretical sci-fi future, sure, some Earth Space Elevator design might be more viable than using chemical rockets. But at the moment I'm not seeing it at all.
About the costs
When it was written in 2000, it was estimated that "Getting to space is very expensive: millions for the launch of a small payload to low-
Earth orbit", and that the Space Elevator might cost on the order of $40 billion. Note that it is over $70B in 2023 dollars.
Also, note that the market has changed significantly. What did on Space Shuttle cost $54,500/kg to get to LEO, it only cost $2,720/kg on Falcon9 in 2018. And the prices continue to fall, reaching $1,500/kg in 2023. Starship promises to drop that price by another order of magnitude when fully operational, with aspirational two orders of magnitude in the longer run (!!).
So, even if Space Elevator might've made economical sense (if one was willing to disregard all the risks and operational issues and only look at estimated costs savings) in year 2000 with hopes to break-even after 10 or so years of operation (as the paper seems to suggests), it is quite unlikely that it would still be able to compete on price basis after huge costs drops in 2023 chemical rockets launches -- much less after estimated 2030 prices.
