# Graphene space elevator possible?

I just read this story on MIT working on industrial scale, km^2 sheet production of graphene.

A quick check of Wikipedia on graphene and Wikipedia on space elevator tells me

Measurements have shown that graphene has a breaking strength 200 times greater than steel, with a tensile strength of 130 GPa (19,000,000 psi)

and

The largest holdup to Edwards' proposed design is the technological limit of the tether material. His calculations call for a fiber composed of epoxy-bonded carbon nanotubes with a minimal tensile strength of 130 GPa (19 million psi) (including a safety factor of 2)

Does this mean we may soon actually have the material for a space elevator?

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A decent terrestrial space elevator could be built with a material with a tensile strength of 50 Gigapascals (including a decent safety factor), so this material may suffice.

Note that there is no prospect of having one 100,000 km nanotube - they would actually be much shorter (maybe 10 cm) and held together by the much weaker inter-tube molecular bonds (if the strings are long enough, they will bond together billions of times where they touch; if there are enough such contact points, the inter-tube bond can be as strong as you want.

Graphene uses the same carbon-carbon bond as the nanotubes for strength, so it would not surprise me if graphene could be used to create strong tethers. I think that what is really holding the terrestrial space elevator back is the lack of money for elevator-focused R&D on string materials. There is really no other market for these materials, and other uses (such as bullet-proof vests) are not close enough to

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The other things holding back research on beanstalks as such are the mind-boggling cost of such a project and the fact that they essential kill the entire satellite based space infrastructure out past geostationary orbit, and don't offer any compensation in terms of polar observation. It's a big hit. –  dmckee Sep 24 '11 at 23:37
Well, for the "no other market" argument; the article says it's 100 times more electrically conductive than copper and can transmit data 10 times faster than fiber optics. Both uses call for long sheets of graphene. In addition, MIT is actually working on it. –  JollyJoker Sep 25 '11 at 11:23
@lurscher: It might pay for itself, but it wouldn't get build because for the foreseeable future trying to build it would bankrupt the whole planet. The fool things has to be built from geostationary orbit (oh, you can build a tower on a mountain, but that's chump change), which means getting gigatons there in the first place (we wouldn't lift them all, of course we'd bring them from the asteroids or some such). The short version is: it can't be done until we have pretty easy access to space. Chicken and egg problem. –  dmckee Sep 26 '11 at 16:45
@dmckee: Huh? Yes, putting 100 tons in geostationary orbit is expensive. But it didn't bankrupt the whole planet the last time we put 100 tons (a little at a time) into geostationary orbit. Since humans have already done it once, the evidence seems to indicate that putting 100 tons into geostationary orbit is feasible. –  David Cary Sep 28 '11 at 2:42
@JollyJoker Your idea to build a 44 ton ribbon that can lift 1 ton is like proposing to build the Sears Tower with no engineering margin, at all. Quality control of the manufacturing will swamp these other strength limits - limits that have been obtained from microscopic quantities or from theoretical calcs using chemical bond strength. If we should ever become advanced enough to build 44 tons of material with such a finely controlled micro-structure, we will certainly have no need for a space elevator. Even a bulkier ribbon would require technology that makes the elevator itself obsolete. –  Alan Rominger Sep 30 '11 at 16:48

The real economics will come into play via electricity. Space based solar transmitting electricity down graphene cables solves our energy crisis basically forever. Once you build the first cable, building more is an order of magnitude cheaper. Once you make that initial investment, the solar farms become trivial, although it will take years if not decades to get them up and running. Inexhaustible, utterly green energy that can be scaled virtually limitlessly- thats the gamechanger for the human race.

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I like the optimism, but it might be tempered a bit; people made similar statements about nuclear power. There is wear and tear on any system, meteors and space debris will necessitate occasional replacement. The replacements will have to be manufactured from mined materials and transported so the system is not entirely green. There are also safety risks; the occasional accidental aeroplane collision with a cable and the potential for terrorism cannot be ignored. –  AdamRedwine Sep 30 '11 at 16:27
I'll put aside the problems with space based solar for a moment, the lifting mechanisms, and I'll even put aside the glaring idea-crushing problem with the minimum payload size. Wait, we also have to put aside the fact that we've never built a 4,000 mile HVDC line. Provided that we build this, what will be the linear density of the power transmission line from GEO to Earth be? –  Alan Rominger Sep 30 '11 at 16:38
@zassounotsukushi, couldnt the electricity be transmitted inside the tube as a stream of electrons(not in a metal just in a vacuum, ie cathode rays, and therefore no resistance?) –  Jonathan. Oct 3 '11 at 6:39
@Jonathan You'd need a vacuum tube for the part in the atmosphere, but since that's a small fraction of the length, it might not weigh the elevator down prohibitively. The bigger question is the charge return. If electrons are being sent down to Earth at high voltage, what positive charge is being sent up? Simple superconducting HVDC lines would seem more promising, since low temperature is (relatively) easy, although radiation damage is still a problem. –  Alan Rominger Oct 3 '11 at 14:01
Could the electrons be sent down the nanotubes? (where there are no particles?) –  Jonathan. Oct 3 '11 at 14:59

Most proposed designs of the space elevator are such that the whole structure is under tensile stress from the ground anchor point. In these designs, there are stress limits that constraint the material properties of the ribbon. The calculations (based on geosynchronous height of earth) point to that 130 GPa figure.

There is potentially another design approach in which there is no stress limit required in any point in the structure. In this case, the tensile stress is entirely from the geo synchronous orbit holding up the structure against its weight (rather than the earth holding it up against centrifugal force). You only need to make sure the whole structure is at equilibrium, so the center of mass stay roughly at GEO. So, you start at GEO, and start each level one at a time. after finishing each level, you adjust your center of mass to stay at equilibrium. Then you proceed to build the next level below the previous one, until you reach ground.

In order to the upper levels to be able to hold the weight of the lower ones, the structure will follow a exponential pattern of joints. If whole elevator structure will have $N$ levels, the ground level (Level 0) will have one link. the next level (Level 1) will have $k$ links, which all sustain the weight from level 0 link. Level 2 links will have $k^2$ links, which sustain each of the $k$ links of the level 1 links. The last level will have $k^N$ links.

So at GEO, the stress is the whole weight of the structure by the cross section area of all links. the area grows as $k^N$ while the weight of the whole structure grows as $\frac{1-k^{N+1}}{1-k}$. So asymptotically the stress as GEO stays under parameter control.

The benefit of this approach is that you even can make the whole structure with normal materials (no stress limit required). Of course the tensile strength of the material chosen still affect the number of links and levels required to make the structure sustain its own weight.

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This doesn't make sense to me. The stress at the point where it touches the ground is negligible compared to the ripping stress encountered GEO, which is the maximum stress (evidenced by true weightlessness at that point). If there is little or no stress at the point of contact with Earth it doesn't change the material requirements. You could make it out of steel, a 1 ton payload will still take a trillion tons of steel, and again, I believe this is before engineering margins are applied! You pattern may initially work, but we should run out of steel without much of the distance spanned. –  Alan Rominger Sep 30 '11 at 18:58
why you think there is ripping stress at GEO? stress is force(weight) by area. the area is proportional to $k^N$. The weight grows as $\frac{1-k^{N+1}}{1-k}$, i hope that clears your doubts –  lurscher Sep 30 '11 at 19:03
I agree that it is expensive, and the engineering challenges are significant, but the material of the structure is NOT one of them, at least with this design –  lurscher Sep 30 '11 at 19:27
The force at GEO is just the maximum. It's also a little more complicated than just using $k$ times the last stage material for the next stage because the apparent acceleration (and the force) isn't linear. What you say works for piling up blocks or stacking paperweights on Earth. For the distance the space elevator spans, it's much more nonlinear, meaning the length of the stages change or they don't follow a geometric multiplier. The typically referenced designs for the space elevator are already optimized and have ridiculous material requirements. –  Alan Rominger Sep 30 '11 at 19:53

@lurscher of course I understand it's from GEO, the fact that GEO is the net zero apparent acceleration point is the reason it would be "unfurled" from GEO. If your point behind the stages is that it could be carried up in segments, then yes, no one ever argued otherwise. The only thing your $k^N$ mathematics shows is that it could theoretically be made with any material, regardless of its specific strength. This is true for any compression structure as well. There is still a practical problem if the approach results in needing trillions of tons of material.

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agreed. in this sense, maybe its overall cheaper to use $10^7$ Tons of, i don't know, steel bars, than to use $10^{4}$ of carbon nanotube unobtainium (or can we say, notyetavailablaintium?) –  lurscher Oct 4 '11 at 20:28
@lurscher lol, I was meaning to write this as a comment, but oh well. What you say about steel over concrete may be true, it all depends on the tradeoffs. The high strength/weight materials are very appealing b/c of the exponential nature of material needs. But it's important to stress that it's not just price, but energy, that is needed for every stage. Manufacture requires energy just like lifting to GEO does. One way or the other, we are limited in the energy society has access to, and one can categorically dismiss an idea by proving it requires too much energy. –  Alan Rominger Oct 5 '11 at 18:18