Nitrogen-nitrogen
28
225.9
1,418
Carbon-oxygen
28
257.3
1,610
Hydrogen-hydrogen
2
104.2
9,118
Positronium-positronium
1/918.6
104
16,700,000
* Some of these element pairs do not exist as stable molecules, but can exist in a crystal lattice structure.
** We are using the support length of the graphite whisker as the standard of strength provided by the chemical bonds.
Examining the Table, we see that the hydrogen-hydrogen bond has by far the greatest potential strength. In this bond, every electron participates in the bonding process (each atom has only one!) and the hydrogen nucleus contains no neutrons, which offer added weight without adding anything to the possible strength. A substance that consisted of pure solid hydrogen could in principle have a support length of more than 9,000 kilometers—very similar to the Fictionite of Table 1.
Even this strength is very modest if we are willing to look at a rather more exotic composition for our cables. Positronium is an 'atom' consisting of an electron and a positron. The positron takes the place of the usual proton in the hydrogen atom, but it has a far smaller mass. Positronium has been made in the laboratory, but it is unstable with a very short lifetime. If, however, positronium could be stabilized against decay, perhaps by the application of intense electromagnetic fields, then the resulting positronium-positronium bond should have a strength comparable with that of the hydrogen-hydrogen bond, and a far smaller molecular weight. It will have a support length of 16,700,000 kilometers—the taper of a Beanstalk made from such a material would be unmeasurably small. This would be true even for a Beanstalk on Jupiter, where the strength requirement is higher than for any other planet of the Solar System.
The positronium cable is likely to remain unavailable to us for some time yet. Even the solid hydrogen cable offers us the practical problem that we don't know how to build it. Rather than insisting on any particular material for our Beanstalk, it is safer and more reasonable to make a less specific statement: the strength of materials available to us has been increasing steadily throughout history, with the most striking advance coming in this century. It seems plausible to look for at least an increase of another order of magnitude in strength in the next hundred years. Such an advance in materials technology would make the construction of a Beanstalk quite feasible by the middle of the next century, at least from the point of view of strength of materials. It could come far sooner.
Something with the properties of Fictionite would do very nicely. The taper ratio would be only 1.6, and a Beanstalk that was one meter in diameter at the lower end and of circular cross-section could support a load of nearly sixteen million tons.
WHERE TO BUILD THE BEANSTALK.
We have talked about what we will make the Beanstalk out of, but we have not discussed where we will find those materials. The answer to such a question is provided when we look at how we will build it.
For several reasons, the 'Tower of Babel' technique—start here on Earth and just build upwards—is not the way to go. The structure would be in compression, not tension, all the way up to beyond geostationary altitude, and we picked our material for its tensile strength. Worse still, structures in compression can buckle, which is a form of mechanical failure that does not apply to materials under tension.
Clearly, we will somehow begin at the top, with materials that we find up there. But where at the top? This is worth thinking about in more detail.
To a first approximation, the Earth is a sphere and its external gravity field is the same as that of a point mass. To a good second approximation, it is an oblate spheroid, with symmetry about the axis of rotation (the polar axis). The third order approximation gets much messier. Not only does the Earth "wobble" a bit about its axis of rotation, but there are fine inhomogeneities in the internal structure that show up as 'gravity anomalies' in the external gravitational field. These gravity anomalies are the deviations of the field from that which would be produced by a regular spheroid of revolution.
The anomalies are small—only a couple of milli-gals—but they are important. (In geodesy, a gal is not something that a male geodesist would like to snuggle up to; it is a unit of acceleration, equal to 1 centimeter per second per second. A milligal is a thousandth of that. Earth's surface gravity is about 980 gals. If the Earth's gravity field were to change by one milligal, you would weigh differently by about one four-hundredth of an ounce. Even a change of a full gal—a thousand milligals—would not be noticed.)
If we look at these small gravity anomalies in the region of the orbit of a geostationary satellite, we find that they give rise to local maxima and minima of the gravitational potential. Satellites in such orbits tend to 'drift' to where the potential has its nearest local maximum, and to oscillate about such a position. For this particular location (35,770 kilometers up, in the plane of the equator) these are the stable points of the gravitational field. At first sight, this looks like the best place to start to build your Beanstalk. You could put your source of materials there, and begin to extrude load-bearing cable up and down simultaneously, so as to keep a balance between the gravitational and centrifugal forces on the whole cable. Doing this, you might expect to be able to keep the cable Earth-stationary, always over the same fixed point of the surface.
Unfortunately, the gravitational potential is not so well-behaved. The positions of the stable points, the places where the potential has its local maxima, depend on the distance from the center of the Earth.
As you begin to extrude cable upwards and downwards, parts of the cable will move into regions where they are no longer at a local maximum of the potential. There will then be a strong tendency for the cable to "walk." It will begin to move steadily around the equator (and off the equator!), adjusting its position to the average of the gravity potential maxima encountered at all heights where a piece of the cable is present.
Such behavior is—at the very least—an annoyance. It means that you must allow for such motion in the design and construction, and you must tether the cable at the ground end when you have finished.
Such a tether is not a bad thing. We shall see later that it is an essential part of the Beanstalk design if we want a usable structure, one that can carry cargo and people up and down it. However, you can't tether the Stalk until you have finished building it. So we have still not answered the question, where do you do that construction? Remember, the geostationary location is full of other satellites—the communications satellites sit out there, and some of the weather satellites. It would be intolerable for the Beanstalk, half-built, to come drifting along through their lebensraum until it was finally long enough to tether.
What other options do we have? Well, there is the "bootstrap" method. In this, you fabricate a very thin Beanstalk, tether it, and use that to stop your main Beanstalk from wandering about during the construction.
My own favorite is more ambitious than a construction from geostationary orbit. You build all your Beanstalk well away from Earth, out at L-4 or L-5. When you have it all done, you fly it down. You arrange your timing so that the lower end arrives at a pre-prepared landing and tether site on the equator at the same time as the upper end makes a rendezvous with a ballast weight, way out beyond geostationary height. Once the Beanstalk has been tethered, the problem of a stable position for the orbit is not serious—it merely means that the Stalk doesn't follow the exact local vertical on the way up, because it tries to adapt to the mean gravity gradient all the way along its length.
Building the Stalk well away from Earth helps the problem of material supply. We certainly don't want to use Earth materials for construction, since getting them up there would be an enormous task. Fortunately, two of the promising substances that we found in the table of strong materials are graphite and silicon carbide
. Coincidentally, two of the main categories of asteroid are termed the carbonaceous and the silicaceous types. They can be the source of our raw materials.
The way to build the Beanstalk is now apparent. We fly a smallish (a couple of kilometers in diameter) asteroid in from the Asteroid Belt and settle it at L-4. We build a solar power satellite or a fusion plant out there, too, to provide the energy that we need. Then we fabricate the Beanstalk, the whole thing: load-bearing cable, superconducting power cables, and drive train (more on these in a moment). And we fly it on down to Earth.
The final descent speed need not be high. We can use the inertia of the whole length of the Stalk to slow the arrival of its lower end.
The demand on the raw material resources of Earth in this whole operation will be minimal.
USING THE BEANSTALK.
A couple of paragraphs back, I threw in reference to superconducting power cables and drive train. These are the key to making the Beanstalk useful. Let us look in more detail at the whole structure of the Stalk.
We will have a load-bearing cable, perhaps a couple of meters across at the lower end, stretching up from the equator to out past geosynchronous altitude. It will be tethered at its lower end to prevent it from moving about around the Earth. It will be strong enough to support a load of millions of tons. What else do we need to do to make it useful?
First, we will strengthen the tether, to make sure that it can stand a pull of many millions of tons without coming loose from Earth. Next, we will go out to the far end of the cable, and hang a really big ballast weight there. The ballast weight pulls outwards, so that the whole cable is now under an added tension, balancing the pull of the ballast against the tether down on Earth.
We really need that tension.
Why? Well, suppose that we want to send a million tons of cargo up the Beanstalk. The first thing we will do is hang it on the cable near the ground tether. If the tension down near the lower end is a couple of million tons, when we hang the cargo on the cable we simply reduce the upward force on the tether from two million tons to one million tons. The cargo itself is providing some of the downward pull needed to balance the upward tug of the ballast at the far end. The whole system is still stable.
But if we had used a smaller ballast weight, enough to give us a pull at the tether of only half a million tons, we would be in trouble. If we hang a million tons of cargo on the cable, it will pull the ballast weight downwards. There is just not enough ballast to provide the required upward pull. We must provide an initial ballast weight that is sufficient to give a tension more than any weight that we will ever try and send up the cable.
There is another advantage to a massive ballast weight. We can use a shorter cable. We can hang a really big ballast at, say, a hundred thousand kilometers out, and it will not be necessary to have more cable beyond that point. The ballast weight provides the upward pull that balances the downward pull of the cable below geostationary height. We have to be a little careful here. A ballast that has a mass of ten million tons will not be enough to allow you to raise a weight of ten million tons up from Earth. The ballast will not pull outwards as hard as the weight pulls downwards, unless it is out at a distance where the net outward acceleration due to combined centrifugal and gravitational forces is one gee. This requires that the ballast be more than 1.8 million kilometers out from Earth—far past the Moon's distance of 400,000 kilometers.
We conclude from this that the ballast will be a massive one. This is no real problem. After all, even a modest sized asteroid, a kilometer across, will mass anything up to a billion tons.
Once we have a taut cable, suitably anchored, we need a power source for the activities on the Beanstalk. We put a solar power satellite or a fusion plant out at the far end and run cables all the way down, attaching them to the main loadbearing cable. Superconducting cables make sense, but we will have to be sure that they are suitably insulated—near-Earth space isn't that cold. But perhaps by the time we build the Stalk we will have superconductors that operate up to higher critical temperatures. The ones available now remain superconductors only up to about 23 degrees Kelvin.
There is a fringe benefit to running cables down the Beanstalk. We can carry down power from space without worrying about the effects of microwave radiation on Earth—which is a serious worry with present solar power satellite designs.
Once we have the power cables installed, we can build the drive train, again attaching it to the load cable for its support. The easiest system for a drive train is probably a linear synchronous motor. The principles and the practice for that are well-established, which means it will all be off-the-shelf fixtures—except that we will want fifty to a hundred thousand kilometers of drive ladder. But remember, all this construction work will be done before we fly the Beanstalk in for a landing, and the abundant raw materials of the asteroid at L-4 will still be available to us.
Assuming that we drive cars up and down the Stalk at the uniform speed of 300 kilometers an hour, the journey up to synchronous altitude will take five days. That's a lot slower than a rocket, but it will be a lot more restful—and look at some of the other advantages.
First, we will have a completely non-polluting system, one that uses no reaction mass at all. This may appear a detail, until you look at the effects of frequent rocket launches on the delicate balance of the upper atmosphere and ionosphere of Earth.
Second, we will have a potentially energy-free system. Any energy that you use in the drive train in taking a mass up to synchronous height can in principle be recovered by making returning masses provide energy to the drive train as they descend to Earth. Even allowing for inevitable friction and energy conversion losses, a remarkably efficient system will be possible.
In some ways, the Stalk offers something even better than an energy-free system. When a mass begins its ascent from the surface of the Earth, it is moving with the speed of a point on the Earth's equator—a thousand miles an hour. When it reaches synchronous height, it will be travelling at 6,600 miles an hour. And if, from that point on, you let it "fall outwards" to the end of the Stalk, it will be launched on its way with a speed of more than 33,000 miles an hour, relative to the Earth. That's enough to throw it clear out of the Solar System.
Where did all the energy come from to speed up the mass?
The natural first answer might be, from the drive train. That is not the case. The energy comes from the rotational energy of the Earth itself. When you send a mass up the Beanstalk, you slow the Earth in its rotation by an infinitesimal amount, and when you send something back down, you speed it up a little. We don't need to worry about the effects on the planet, though. You'd have to take an awful lot of mass up there before you could make an appreciable effect on the rotation rate of Earth. The total rotational energy of Earth amounts to only about one thousandth of the planet's gravitational self-energy, but that is still an incredibly big number. We can use the Beanstalk without worrying about the effects that it will have on the Earth.
The converse of this is much less obvious. What about the effects of the Earth on the Beanstalk? Will we have to be worried about weather, earthquakes, and other natural events?
Earthquakes sound nasty. We certainly want the tether to be secure. If it came loose the whole Beanstalk would shoot off out into space, following the ballast. However, it is quite easy to protect ourselves. We simply arrange that the tether be held down by a mass that is itself a part of the lower end of the Stalk. Then the tether is provided by the simple weight of the bottom of the Beanstalk, and that will be a stable situation as long as the force at that point remains "down"—which will certainly be true unless something were to blow the whole Earth apart; in which case, we might expect to have other things to worry about.
Weather should be no problem. The Stalk presents so small a cross-sectional area compared with its strength that no storm we can imagine would trouble it. The same is true for perturbations from the gravity of the Sun and the Moon. Proper design
of the Stalk will avoid any resonance effects, in which the period of the forces on the structure might coincide with any of its natural vibration frequencies.
In fact, by far the biggest danger we can conceive of is a man-made one—sabotage. A bomb, exploding halfway up the Beanstalk, would create unimaginable havoc in both the upper and lower sections of the structure. That would be the thing against which all security measures would be designed.
WHEN CAN WE BUILD A BEANSTALK?
We need two things before we can go ahead with a Beanstalk construction project: a strong enough material, and an off-Earth source of supplies. Both of these ought to be available in the next fifty to one hundred years. The general superiority of Beanstalks to rockets is so great that I expect to see the prototype built by the year 2050.
I do not regard this estimate as very adventuresome. It is certainly less so than Orville Wright's statement, when in 1911 he startled the world by predicting that we would eventually have passenger air service between cities as much as a hundred miles apart.
Unless we blow ourselves up, bog down in the Prox-mire, or find some other way to begin the slide back to the technological Dark Ages, normal engineering progress will give us the tools that we need to build a Beanstalk, by the middle of the next century. The economic impetus to deploy those tools will be provided by a recognition of the value of the off-Earth energy and raw materials, and it will be with us long before then.
This discussion seems to me to be so much a part of an inevitable future that I feel obliged to speculate a little further, just to make the subject matter less pedestrian. Let us look further out.
Non-synchronous Beanstalks have already been proposed for the Earth. These are shorter Stalks, non-tethered, that move around the Earth in low orbits and dip their ends into Earth's atmosphere and back out again a few times a revolution. They are a delightful and new idea that was developed in detail in a 1977 paper by Hans Moravec. The logical next step is free-space Beanstalks. These are revolving about their own center of mass, and they can be used to provide momentum transfer to spacecraft. They thus form a handy way to move materials about the Solar System.
Vectors Page 19