Upward Bound: Space Elevators

## Transcript

The biggest danger of space elevators isn’t the risk of them falling down, it is the risk of homicidal insanity from sharing the trip with others for hours while listening to elevator music.

So today we are looking at Space Elevators, a concept sufficiently well-known it needs little introduction but one which at same time is plagued with misconceptions. Our goal is to dispel those misconceptions and look at the concept in detail. As part of our continuing look at systems for getting into space cheaper, easier, and safer we will also discuss some of the safety and cost issues associated with space elevators.

Space Elevators hit the public eye in a big way in the last decade or two but it is actually a pretty old idea. It got new life breathed into it with the discovery of certain super-strong materials in the last couple decades. The concept itself it pretty straight forward. If we built a very tall tower on the equator, one that reached up 22,000 miles or 36,000 kilometers above the ground, you could step off the top and not fall down. At that altitude the top of the tower is moving at the same speed as what is needed to orbit the Earth at that height. Just above the Earth a stable orbit is just a couple hours, and way out at the moon it is a whole month, at the point where an orbit takes a day the ground stays directly below, since it also turns once a day. That is why we call orbits at that height geostationary.

Now this is only true right above the equator and in a circular orbit. You can have a 24-hour circular orbit at any angle, but it won’t stay over the same spot on the ground, though it will pass over the same points each day at the same time. That is called a geosynchronous orbit, as it is still synchronized to the Earth’s spin but not stationary relative to the ground. If you watched such a satellite from the ground it would seem to bob north and south each day. You can also have an elliptical geocentric orbit, which would appear to trace a figure-8 in the sky each day and if it were tilted off the equator one of those lobes would be bigger than the other. So a geostationary orbit is specifically a circular orbit directly over the equator, which means any space elevator we want to build needs to be above the equator, though we will discuss a few tricks to getting around this later on, so that your elevator station down on the ground doesn’t have to be at the equator.

But the basic space elevator is simply that, a long rope or tether hung down from geostationary orbit. You could also build a tower up to that height, which was the original concept. This idea goes all the way back to the late 19th century, if not before, but at the time they were thinking of supertall buildings, and at that time the word skyscraper was just entering the lexicon and buildings were being constructed now that finally took the title for tallest building away from the Great Pyramid, which held the number one slot for five thousand years, barring a brief upset by the Lincoln Cathedral till its tower collapsed. Now, millennia later, we were routinely building taller. So it isn’t much of surprise that folks were considering even taller buildings not just scraping the sky but stretching far above it into the heavens. We’ve contemplated that notion all the way back to the Tower of Babel, but the advantage of structural steel was now letting us build tall much cheaper and safer.

On the other hand orbital mechanics have been known for many centuries. Folks didn’t think much about putting people into space then not because they didn’t understand orbits, but because we didn’t understand rockets and had no computers. You really need both to get an object into a stable orbit. Now there is no material that can handle the kinds of stress involved with building a tower that high, or a rope that long, not straight up and as wide at top and bottom. That’s an important point for later on though because until structural steel replaced load-bearing masonry, building tall was quite trick unless you went the route the pyramids did, which was to have very little interior space and just build much wider at the bottom. That pyramid never collapsed not because its engineers were such geniuses, though they probably were the best in the world at that time, but rather because it is almost entirely one big solid heap of stone that is wider at its base than at its peak.

Such an object works on compressive strength, how good a material is at being compressed, such as by stone being piled on top of it. When each layer is wider than the one above. it spreads that compression out, letting you go taller. Mountains, for instance, do not require much skill at engineering. So a cone or pyramid can be taller than a cylinder or rectangle made of the same material. Hypothetically there is no limit as to how tall you can build, if you can keep making the base wider, but obviously when you live on a spherical planet there are some limits in that regard. For a given material you can only build a column of it so tall before it collapse under its own weight, and by making the base wider than the top you can increase this limit.

The same applies to ropes, only they are stretched rather than compressed. How much tension they can handle before snapping is based on their tensile strength. We will discuss this more in a bit since that is what matters for modern space elevator concepts, but for the moment it is important to note that you can go longer by making it wider at the top than the bottom. Tapering it just like a pyramid or cone, only upside down. Now building something tens of thousands of kilometers tall when the tallest building wasn’t yet a kilometer tall and the tallest mountain isn’t even ten tall seemed pretty ludicrous. However, the opposite idea, relying on tensile rather than compressive strength, wasn’t even on the table till we discovered certain super-strong materials in recent years.

Ideas for building such a tower usually relied on a concept called active support which we will discuss in detail in future episodes but briefly is the idea that just as you can float a sheet of paper over a floor vent, you could float a platform up by bouncing things off the bottom, thus allowing even taller towers. The advantage of such a tower or tether though is obvious. Unlike a rocket, where you need to carry all your fuel with you, on such a tower you can run a power cable up it from a reactor on the ground, or solar panels in space, to supply energy to whatever is climbing the tower, presumably an elevator though in practice it might better be thought of as a train. And you can gain power when things are going down instead of up, so you are spending virtually no energy climbing up the tether and can get a lot of it back on the way down, losing some energy to transferring that power between the one going down and the one up.

Needless to say we have discovered some materials that have far higher tensile strength than anything we had back in the 19th century. Kevlar and Zylon far surpass steel cables in tensile strength, and carbon nanotubes and graphene far surpass them. Now any given material has what is called a breaking length or self-support length. This is how long that can be before it would snap under its own weight. For instance if we were standing on cliff 2 kilometers up with a spool of rope that had a breaking length of 1 kilometer, once we unspooled more than kilometer of it off the cliffside it would snap even though no one was climbing it. A good nylon rope can have a breaking length of several kilometers, and some metals can be a hundred kilometers or more and Kevlar and Zylon can do a few times better. But carbon nanotubes appear to be good to 5000 kilometers or more.

Now here is where the first big misconception comes in that causes many flawed objections to space elevators. Our elevator needs to be 36,000 kilometers high, so if carbon nanotubes can only do 5000, we’d seem to have a problem, 5000 is a lot less than 36,000 and we need more than too because we want to carry material up it. But there’s two problems with this objection. First, as I mentioned, you can extend length by tapering your tether to be wider at the top than the bottom. And second, breaking length is how long something can be when hanging in Earth’s Gravity. It’s higher on Mars, for instance, where the gravity is lower, and even higher on the Moon. Of course we’re not on the Moon or Mars, we are on Earth, but the cable is not. Or at least most of it is not. The higher up you go the weaker Earth’s gravity is.

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{\displaystyle a={\frac {GM}{r^{2}}}}
 For Geostationary:*r*=6371+35,900 km,*a*=0.223 m/s2=2.27% normal

For instance, up at 5000 kilometers above Earth, which has a radius of 6400 kilometers, gravity has dropped to just a under a third of what it is here on the ground, and the breaking length of a material is three times longer there, since everything weighs only a third of what it does down here. Out at geostationary orbit gravity is only a couple percent of what it is here and breaking lengths are almost 50 times longer. Second, we have the ability to taper the tether, making it wider at the top, which lets it hold up a longer length. So it doesn’t matter if something’s breaking length is lower than the distance to geostationary orbit, because by making it wider at the top than the bottom, by giving it a high taper ratio, we can increase that breaking length and it is further increased as gravity weakens from getting further from the planet.

Hypothetically any substance can be used for a space elevator with a high enough taper ratio, but as before when we were building up taller objects with wider bases this does have a practical limit. Now actually mass manufacturing something that’s operating at its maximum tensile strength, and essentially has few or no flaws, is another matter. Very expensive. Especially since you either need to fly it up there or build it up there and spool it down, and getting stuff into space is incredibly expensive. I mean that’s the whole reason we want to build this thing. The usual notion is that you would actually build it here. You’d start with a thin wire, as thin as you could make it, again wider at top than bottom but still very thin, and fly that up. That first one doesn’t necessarily need to be able to handle double its weight, if you can either manufacture the next cable up there from material brought up in smaller bits or join sections without creating a weakness.

These are massive things too. Even a thin string weighing a gram per meter on average would mass out at 36,000 kilograms, and probably couldn’t carry anything like that much mass as cargo. That’s a bit more than the Space Shuttle was designed to get into low orbit, and we need to go all the way to geostationary, so it would be either a very large launch or we’d have to find a way to join sections of tether together without introducing a weakness in it at the joins. They also don’t have to be circular tethers like rope, a ribbon would work fine too or other shapes, though you have to worry about wind on these things. There are a lot of forces acting on these besides just straight down gravity that can potentially cause some problems. Now you can build bigger, but by and large it makes more sense to build more of them instead. Better five or six cables right next to each other than one bigger cable of equal strength, and better another elevator elsewhere, servicing another region, than to just have a single elevator at some point on the equator.

This raises two other points though. Having cables at places other than the equator and where the top of the cable actually is, because it isn’t at geostationary. We should cover that first. The tether doesn’t end at geostationary orbit, it has to go at least a bit further up, either ending in a massive terminus station just above that or a very long length of cable. Left to itself an object at geostationary doesn't fall, but any point beneath that would, and it is generating weight pulling the spot at geostationary. You need an equal force pulling upward, and past geostationary the tether is pulling outward, as those segments are now moving faster than orbital speeds for that height.

A tether running out, say, another 17,000 kilometers, which would make it 60,000 kilometers from the center of the Earth, would be moving about 4.4 kilometers per second, while orbital speed there is just 2.4, so you’ve got an extra 2 kilometers a second of free speed to launch into interplanetary space with. That counterweight doesn’t have to be more tether running off for thousands of more kilometers, it could just be a big space station right over geostationary. It’s all about making sure the total force up and down at geostationary cancels out, this is sometimes inaccurately called the center of mass, but that’s not quite right in a non-uniform gravitational field. Anyway that station can be quite massive, even with tethers running higher up, because anything you build just a bit down and adjacent to it, also at geostationary, is going to float right there of its own accord, and you just connect to it. You could construct some fairly huge space stations there, more than big enough to make artificial spin-gravity viable.

That also means you can ferry up huge amounts of material for whatever you are doing up there. Fuel for ships, solar panels for power, and all the building material and equipment you want, though it still costs money to make such things and carry them up. It is still fairly expensive but down to the point that the equipment and salaries for those there will be the bigger chunk of your budget. So you could have huge stations with industry and drydocks and hotels up there, all given artificial gravity by spinning them.

Now by default you build your space elevators on the equator, probably on a floating platform in the sea. Geostationary is limited to a ring around the equator after all. This means that while space elevators are pretty awesome they would seem to limit you to having all your spaceports at the equator, whereas most of the nations with robust space programs are way north of the Equator, and they’d rather have their space ports near their cities. This is fixable though if your cables are decently stronger than the absolute minimum strength needed. Because again it is only the terminus station that needs to be above the equator, or rather the center of force of the tether. Now if we stuck one end of the tether at geostationary and the other down in, say, New York, we have a problem, the station is going to be pulled north and then go all out of orbit with problems to follow. But if we stuck another tether on the opposite side of the equator, say down in Santiago in Chile, that slightly off-center force of being a few thousand kilometers north and 36,000 kilometers up would be counterbalanced. Just like guy wires holding up a tower, only without the tower. You’d want to use at least three, more works too, and they don’t need to form an equilateral triangle or anything. You’d probably also want to have winches at top and bottom of the tethers to help keep the tension right for each and tweak that tension if it starts to drift.

You can also stick one of these right in the middle of a city, unlike airports or some of the other designs where they either have a big footprint on the ground or are so loud they make a plane sound quiet. These would be quite quiet. Not much visual effect either, such cables would be virtually invisible from any serious distance and while the pods climbing them would be bigger and probably have navigational lights on them, you’d otherwise have to be quite close to see the tether. I often have folks worry that some of these launch assist systems will ruin the night sky but no more than airplanes or satellites or skyscrapers.

Of course people also worry about them breaking and wrecking their city, or the planet. We might as well talk about that then. Can such a tether break? Yes of course, they can. I mean the stuff they are made out of is as tough as diamond but it’s not going to survive intentional sabotage of someone setting off a shaped charge or something on it. It is not easy though, you could chop at one with an axe all day long, stopping only to replace your broken axe heads, without accomplishing all that much.

But yes one can be damaged. Where it breaks is what actually matters but first let’s crush this idea it would cause mass carnage. One popular portrayal is that the broken tether would wrap around the equator flattening everything in sight. That’s very exaggerated, there’s not much reason to build these things individually thicker than an arm, if even that, just add more in parallel if you need them, and they are not crashing into the ground at hypersonic velocities. These are not thick cables, probably no thicker in most cases then a large electrical wire on a trunk line, and they won’t hit going much faster than one of those would if it fell, air will slow them. They’ll either burn up if the fell from high enough or slow to normal speeds before hitting, and very low speeds if they are ribbon shaped rather than cylindrical. So yeah, don’t stand underneath one or it will hurt or kill you, but you could also see it falling anyway.

We also have a device for slowing things in air called the parachute, and while we don’t want to add a lot of static weight to our elevator by installing parachutes at certain intervals, what makes a parachute heavy is the material it is made out of. Parachute threads and ropes have to be very strong, in terms of tensile strength. Conveniently if you are building space elevators you have the ability manufacture superlight materials with huge amounts of tensile strength. So you get much lighter parachutes and you could place them at intervals with charges designed to sever the cable into smaller bits. So they wouldn’t do much damage falling in the first place, but with some parachutes on them this can be further minimized.

Another important factor is where it breaks, and if it is anywhere inside our own atmosphere the cable is going to ripple up like a cut thread toward the station and then fall back down and dangle just over the atmosphere. You go in and repair it, and in practice you probably have a couple hundred kilometers of extra line up at the terminus station and can just lower it back to the ground station. The ten or twenty kilometers in the atmosphere will just fall down, straight down. I wouldn’t want to be in that station when it happened, but you’d probably have gantries and scaffolding around the base anyway. A decently sturdy roof should survive it and again parachutes are an option. So a lot depends on where the cut occurs.

The problem is that orbital speeds around Earth get lower as you get further away, but on our tether, it gets faster the higher up you are. Up at geostationary the tether is moving at exactly the orbital speed for that height. Just a bit above it, at the Terminus station, the orbital speed is a bit lower but the station is actually moving a bit faster. If you cut the tether below that the station would drift off to a higher orbit and would need to have some thrusters on it to instead drop to geostationary while repairs were underway, then boost back up. It might need to cut free the tether higher up too, the one whipping ships into interplanetary space. As to the tether, once cut, its individual bits are moving too slow for orbit, orbital speed is higher than up at geostationary but the tether below that isn’t even moving at that speed. So it will fall down. This is where the notion of it wrapping around the planet comes from, it is still moving faster than the equator, they have the same angular velocity but not linear velocity, same as the equator is faster than the polar regions. The higher up, the faster it is moving, so it will fall and wrap around the equator.

But as we saw, it isn’t ground damage and casualties we have to worry about, rather it is the folks on the tether. What happens to the people on the elevator when it snaps? We also have to consider what would happen if the climber falls off the cable for some reason. For the folks above 23,000 kilometers, they’re okay, they’ll fall gaining momentum and actually enter an elliptical orbit around the planet. Anything with lateral speed relative to a massive object will enter an orbit around it, it’s just that if that is too elliptical that orbital path will pass through the planet. Since those pods have to be airtight the people on them will be fine, so long as the air doesn’t run out, until someone can retrieve them. They’d have many hours if not days to be rescued, probably by shuttles from the Terminus station. We will talk about how you keep folks alive in such a pod or any other spaceship in a few weeks in an Episode appropriately called Life Support, because there’s a lot of misconceptions about that too.

For the folks below 23,000 kilometers things are actually a bit easier. They won’t go into orbit, since the planet is in the way, but if your pods are built for reentry and have parachutes on them they should be fine. I mean for a given value of fine. I’m pretty sure crashing thousands of kilometers down to the planet in a passenger car full of dozens of other terrified people is going to leave some serious psychological trauma even if physical injuries don’t occur. And that is long fall too, dropping from halfway up that tether is going to take a few hours. Gravity is weaker there so you aren’t accelerating as much at first. There’s a lot of things that could go wrong on that fall for people to worry about, and a lot of time for them to worry, so I am not going to try to minimize how awful those hours of falling will be even if you do survive.

When the cable snaps most pods won’t initially notice anything, if you have a string suspended from the ceiling holding a weight and cut that string, the string above the cut is going to snap upwards but that isn’t instantaneous. It seems like it to us because the string is short but on a long cable it will take quite a while for the wave to travel up the tether. This thing is thousands of kilometers long, so even if the wave is moving several kilometers a second it could be some minutes before your pod bucks. Plenty of time for the control station to notice the break and send the command to the pod to break off, some detonating bolts probably. A little bit of speed is handy too since you do not want to get lashed by a diamond hard cable whipping upwards like a rubber band, so giving yourself a few meters a second of delta-v is probably a good idea. So I don’t want to trivialize the dangers and risks, but they stack up pretty good compared to trains, planes, and automobiles. Our normal methods of traveling around the planet.

Speaking of that, these elevators are pretty good for that kind of travel too, not just getting up to geosynchronous orbit. You can jump off part way up and do a controlled fall to some other part of the planet, again you are moving too slow for orbit so you could jump off a tether from Los Angeles and fall to New York, ride up a bit higher and fall to London or Madrid. You’d want wings and thrusters for control and maneuvering but it’s a pretty fast and cheap method of travel around the planet. This is even easier if you are doing the multi-tether option, where several ground stations run up to a single terminus station, especially if those cables are meeting part way up. You could have an airport up there, assuming your tethers are strong enough to handle that kind of weight. If they are you can also consider running tethers sideways between two tethers. Which would be faster than riding all the way up to the terminus station then down another tether, or taking a shuttle from that terminus station to another tether. You could also drop off those lateral tethers too, an option also available to us when we look at certain launch loops later in the series. But that’s a key point, these elevators are handy for more than just space travel.

We should probably talk about speed on one of these elevators. That will depend a lot on how much power you have to spend, but the default trip is many hours. There are some tricks using some of the other systems we will look at in future episodes, essentially hybrid versions, that could make the trip faster, like shooting down a vacuum tube first and up a space tower that was also in a vacuum around that elevator to let you build up speed without air getting in your way. If you could pull off one gee of acceleration the whole way there, flipping midway through to decelerate, your trip would take an hour, faster than actually falling since again gravity is weaker up there. But even pulling 3 or 4 gees on the trip is only going to cut that trip time in half. Going that fast is rather energy wasteful but convenience is often worth that and it would also change your fall dynamics.

Okay, let’s talk cost. We obviously have to be pretty vague here. At the moment graphene, our presumed elevator material, costs about $100 a gram. That’s more than double the price of gold and remember our thread-thin starter tether massed about a kilogram per kilometer, or 36,000 kilograms, or 36 million grams, or 3.6 billion dollars. The launch costs for getting that up there are in that neighborhood too. A tether as thick as a pencil or finger would mass out at more like a 100 kilograms a kilometer, or 360 billion dollars, with similar costs for transport. That’s why it’s important to start with the small tether first, so you can take advantage of the cheaper launch cost that tether will provide for subsequent ones.

Now we expect the cost of graphene to get a lot cheaper as we get into mass production of it, it’s just carbon, preferably made of graphite which is more like a buck per kilogram, not a hundred bucks per gram. The real issue is making a single cable as one complete unflawed or mostly unflawed thing. And more importantly of doing that up in space. Once you get that first small tether up it might be strong enough to hold another tether of equal mass, but more likely it will only be able to hold a fraction of its own weight, so you bring up shipments of the stock material in small amounts along the starter tether and manufacture up there. Your first Terminus Station is going to basically be a big tether manufactory.

I’ve seen cost estimates as low as 6 billion and as high as 40 billion, and I’ve seen even higher plus I’m a pretty conservative person where such estimates are concerned so I tend to automatically double them, but that’s a very affordable cost even if we take the high end one of 40 billion and double it. Even pessimistically it drops the cost per kilogram of material moved to space to about $100, whereas it cost several thousand dollars a kilogram right now. So those savings stack up pretty quick especially if you are increasing the amount of stuff you are sending into space. Which you would be too. If you build it they will come, because there’s all sorts of scientific, commercial, and industrial applications to space we don’t use right now because of the cost to transport things to and from space. Lots of folks would pay five figures for a vacation up there and you could haul whole film crews up there for months at a time to film a science fiction movie or TV series in actual zero-gravity for a change.

So why haven’t we built one? Well first off the cost. To break even on such a thing, which will surely have maintenance costs too, you need to be transporting a lot more up into space than we do now. Second and most important, of course, we can’t actually build one just yet. We don’t mass produce graphene and certainly not as big long cables. We need a while to get to that kind of production scale and then we’ll need to take kilometer long chunks of it and stretch it and see what its actual tensile strength is in real terms, not just on paper. It works on paper but so do a lot of things that later fall apart in practical design. When we get to that point we can start coming up with specific designs and better estimates.

And it might turn out to be impossible. As mentioned earlier, graphene’s breaking length is a lot shorter than the necessary cable length, tapering, having it wider up top, and the diminishing gravity as you get higher, might be enough, but it will be close and when we start making cables out of the stuff the real-world breaking length of those might not be viable. On the other hand we might find something even better than graphene or carbon nanotubes. So space elevators aren’t guaranteed, at least not for Earth, they work just fine on anything with less gravity like Mars or the Moon, but they are promising and something we could easily see even twenty years from now. Too soon to say, but there’s lot of room for optimism.

It is also not our only option on the table, as we will see with sky hooks in two weeks even much shorter tethers can help a lot with getting into space, but as a I mentioned near the beginning this idea predates super-strong tensile materials. We can build tall towers instead, exact same dynamics only it requires an alternative to tensile strength, something we call active support, which we talk about in another episode too, and which opens just as many interesting doors as super-tensile materials. And we’ll be looking at a lot of those in the upcoming episodes. Next week though we will be looking at Quantum Computers, a topic that like Space Elevators has a lot of misconceptions about it, showing a lot of promise and also a lot of hype. We’ll clear away the noise next week. After that we will return to this series for a look at Skyhooks, then we’ll segue the week after that to discuss not getting into space but staying alive when you’re up there. For alerts when those and other episodes come out, make sure to subscribe to the channel. If you enjoyed this episode, please like it and share it with others, and join in the discussion down in the comments section or at the channel’s Facebook and Reddit groups, Science and Futurism with Isaac Arthur. Until next time, thanks for watching, and have a great week!

1. ↑ A few other cathedrals arguably held the title of tallest building until the Washington Monument firmly got it in 1884.
2. ↑ Aravind, P. K.. “The physics of the space elevator.” *American Journal of Physics* 75 (2007): 125-130.
3. ↑ Note that the *taper ratio* is Cross Sectional area at the top of the cable divided by the bottom, so one twice as wide at the top would have a 4:1 ratio, a 1.6:1 ratio is 26% wider at the top. So an imperfect tether designed to haul a lot of weight might need a taper ratio of 100:1 instead of 1.6. That would mean the cable was 10 times wider up top than at ground, and weighed and cost about 50 times more.
4. ↑ So you could build cities up there since they'd just be hanging next door at geostationary on their own. You can also do this trick backwards and have a tether stretching far away from Earth with its counterweight just under geostationary, letting you hurl ships away from Earth at huge speeds.
5. ↑ You always need at least one tether in the North and South Hemisphere, but you could have 6 in the north and 1 in the south, for instance.
6. ↑ Orbital speed assumes a circular orbit, an elliptical orbit is possible above 23,000 km.
7. ↑ Waves take time to move through any medium. So if you were playing Tug of War with a long enough rope the other team could have dropped it and gone off for lunch before it went slack on your end.
8. ↑ Tether Mass will vary a lot on taper ratio of course, 4:1 would seem on the plausible side of optimistic.
9. ↑ We do have a lot of tricks for keeping long cables almost as strong as the maximum theoretical, but flaws in joining segments can stack up.
10. ↑ Prototyping, R&D, maintenance costs, administration, etc could skyrocket price estimates.