When is a space elevator not a space elevator?

Canadian space and defense company Thoth Technology has recently announced plans for a "Space Elevator".  The idea is to use pressurized Kevlar to build a tower 15 kilometers high (nearly twice as high as Mount Everest), complete with hotel and observation decks, and to launch and land space planes using a rooftop runway.  It's an ambitious project, to say the least, but I wouldn't call it a space elevator -- thus the they-said-it-I-didn't quotation marks.

The term space elevator usually refers to a structure built around a very long cable with one end attached to a counterweight somewhere beyond about 36,000 kilometers above the surface of the Earth.  The cable remains taut due to centrifugal force*.  Vehicles called climbers move up and down the structure, delivering payloads into space.

We're not even close to being able to build such a thing.  The main reason is that the cable would be under far more tension than any commercially available material can withstand (it's not theoretically impossible, just not practical with current technology).  Assuming we clear that hurdle, actually building the thing would still be a major piece of engineering.

How would a space elevator work in practice?  Since a space elevator cable is pulled taut by its counterweight, and it's rotating in sync with the Earth's rotation, the higher up you go, the faster that bit of the elevator is moving relative to the ground, since the higher you go the more distance you have to cover every 24 hours.  As a climber goes up the elevator, it will feel a slight force pushing it in the direction the cable is moving (technically a Coriolis force).  This is the force of the cable keeping the climber moving with it, ever so slightly faster for each meter you move farther out from Earth.

In order to put something into orbit it's not enough simply to lift it out of the atmosphere.  If you took a payload up a space elevator to an altitude of 200km, a typical distance for a low Earth orbit, and let it go, it would fall back to the ground.  At that height, the payload would start with a forward motion relative to the ground of around 50 km/h -- a typical speed limit for residential streets -- and lose most or all of it to wind resistance on the way down.  To go into orbit, it would need a forward motion of more like 28,000 km/h.  As Randall Munroe says, getting to space is easy. The problem is staying there.

To go faster you have to go higher, but fortunately you also need less speed to go into orbit as you get further from the Earth -- the Moon orbits at less than 4000 km/h, for example.  By the time a climber got to about 36,000 kilometers, not much less distance than going around the world, it would finally have enough speed (about 11,000 km/h at that point) that a payload would stay in orbit if released.

Orbits at this distance are geosynchronous (geosync for short), meaning the orbiting object is in sync with the Earth's rotation.  If they're also at the equator, which a space elevator would have to be, they're geostationary, meaning they always stay over the same point on the equator.  Otherwise they will appear to move north and south over the course of the day, but stay at roughly the same longitude.

From the point of view of someone on the elevator at geosync, the payload would just appear to stay where it was, at least for a bit.  In real life, it would tend to drift away over time due to factors like the gravity of the Moon and the Earth's not being a perfect sphere.  For basically the same reason, an object on the cable at this point would experience zero g (again neglecting secondary effects).  Points below would experience a pull toward Earth, however slight, and points above would experience a pull away from Earth.

Where does that leave us with Thoth's structure?

A 15km tower is nowhere near high enough to function as a space elevator.  The advantage to launching from there is not the difference in speed between the ground and the top, which would amount to a moderate walking pace, but being above about 90% of the atmosphere.  That's certainly helpful, but not enough to neglect the atmosphere entirely.  To do that, you would need to be somewhere above the Kármán line, somewhat arbitrarily defined as 100km, though the Wikipedia article asserts that 160km is the lowest point at which you can complete an orbit without further propulsion.

In other words, Thoth's structure doesn't even reach into space, or even a tenth of the way for the purposes of launching things into orbit.

While Thoth's structure might be still useful in launching thanks to bypassing much of the atmosphere, landing, on the other hand, seems a bit of a stretch.  If you're leaving low Earth orbit, you'll have to get rid of that 28,000 km/h somehow.  You could use rockets, the same as you used to get into orbit, but that means more fuel -- not just twice as much but a bunch more, because the extra fuel is just dead weight on the way up and you'll need more fuel to compensate for that.  And more fuel for that extra fuel, and so forth.

This is why actual reentry uses the Earth's atmosphere to turn kinetic energy (energy of motion) into heat.  If you're going to do that, you might as well go all the way to the ground, where you can have a nice big runway, safety crews and other amenities if you're a spaceplane, or at least your choice of an ocean or a large expanse of open ground to aim for if you're not.

Of course, if you have an actual space elevator, you can re-attach to the elevator at geosync and let the climber spill your kinetic energy gradually on the way down, neglecting the not-so-small matter of moving from your current orbit back to the elevator, matching speed, not just location.  But that's not what Thoth is proposing.

So the whole "space elevator" thing is marketing hype.  Is there anything left after you account for that?  Well, maybe.  It depends on the numbers.

The Really Tall Tower idea still has some value, I think.  Actually building it would turn up all kinds of interesting issues in building tall structures, from how to build a stable structure about 20 times taller than the current record holder to the logistics of supporting a crew well above the Everest death zone to even just getting materials to a construction site 15km up in the air.  At the end, though, you'd at least have a unique hotel property and, depending on how much load that inflated Kevlar can take, potentially a whole lot of residential and office space, though most of it will need to be pressurized.

Do you have a space elevator?  No.

Do you have a compelling value proposition for someone wanting to put things in orbit in a world where ground-launched rockets are pretty much the only game in town?  I really don't know enough to say, but my guess is that it would be better if the business model didn't depend on that happening.



(*) If you prefer, feel free to recast this in terms of centripetal force.  You'll get the same vectors, just with different names.