Space Elevator or Space Sling?

Liosse de Velishaf said:

I’m working on a near-future sf project involving space elevators, and one of the things I’d really like to know about is what would happen if you cut the cable? Well, yeah, it’d fall probably, but what would happen to the counterweight? Would it stay in orbit? (Seems unlikely.) Or fall? Or fly off into space? Anyone with some thoughts?

That said, what are some good books that involve space elevators? Don’t necessarily have to be near-future, but they do need to have an elevator (or similar structure) playing a reasonably large role in the plot. Like KSR’s Mars Trilogy, for instance.

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Didn't the Reds cut down the space elevator in Red Mars? And it was drastically destructive. I just read another book in which the space elevator was cut as an act of terrorism. *squeezes brain really hard to remember* Oh yah! "Annals of the Heechee" by Fred Pohl, the 4th book in the Gateway series. Terrible title, great book.

The weight at the top is PAST the geostationary point to keep stress in the cable. If the cable were cut the weight (and the top portion of the cable) would move away from Earth. I'm not sure at what rate - the weight/cable might be in an elliptical orbit with the original position at perigee. This could be "interesting" in that the cable could over time take out several geostationary satellites.

If the cable is cut at maybe a few hundred feet above its Earth tether or below, I'd guess it would just stand up on its own strength. Higher and it would of course fall over, and the higher it's cut, the more problems it could cause on the ground where it falls. Since it's tethered at the Equator where there may be low population, even a hundred miles of the cable might only cause problems at and around the base where people, buildings and shipping docks all related to the elevator would be.

The first two novels on space elevators/skyhooks were Author C. Clarke's "The Fountains of Paradise:"
http://en.wikipedia.org/wiki/The_Fountains_of_Paradise
and Charles Sheffield's "The Web Between The Worlds:"
http://en.wikipedia.org/wiki/Charles_Sheffield

His novel The Web Between the Worlds, featuring the construction of a space elevator, was published almost simultaneously with Arthur C. Clarke's novel about that very same subject, The Fountains of Paradise, a coincidence that amused them both.

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Sheffield's novel uses another neat device, rotating (end-over-end) cables in orbit around Earth and other planets. It's complicated to describe, but it allows low-energy transfers between planets using conservation of momentum in the rotation of the cables, and some very careful timing of incoming craft for one of the ends of the cable to catch the moving ship.

These novels were seminal works using the space elevator (each author thought he was the first), so it's of course a major part of both novels.

If those two and others' suggestions isn't enough reading, there's this:
http://en.wikipedia.org/wiki/Space_elevators_in_fiction

Liosse de Velishaf said:

I’m working on a near-future sf project involving space elevators, and one of the things I’d really like to know about is what would happen if you cut the cable? Well, yeah, it’d fall probably, but what would happen to the counterweight? Would it stay in orbit? (Seems unlikely.) Or fall? Or fly off into space? Anyone with some thoughts?

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The result would depend on where the elevator was cut and how balanced it was. If it was given little tension by extending farther into space than necessary to balance it and it was cut near the ground, then it might just sit there. If it had more tension then it is more likely that it would fly offinto space. If it was cut far out, then the loose section would simply become a satellite.

That said, what are some good books that involve space elevators? Don’t necessarily have to be near-future, but they do need to have an elevator (or similar structure) playing a reasonably large role in the plot. Like KSR’s Mars Trilogy, for instance.

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The Fountains of Paradise by Arthur C. Clarke

There is something that I read that gave the technical details, but I don't remember where, unless that was in FOP.

Space elevators. What a great idea. How nearly impossible to implement.

Even Clarke admitted the probability of ever building a working one on Earth was extremely remote. Even given his quasi-magical molecular fiber. First there is the problem of the right location (at the equator somewhere), and the weather. Habitable planets have weather, and y'know? you don't really need to wait around for the terrorists to cut the cable...next summer's hurricane will do the trick for you.

It wouldnt fall if it was cut up high, but the top part would be "thrown" away from the earth.

If it was cut low, the bottom part would fall, but the rest would float into orbit, depends entirely on the center of mass.

Was it Clarke who used the shafts made from diamond mined on Jupiter?

EG

Liosse de Velishaf said:

That said, what are some good books that involve space elevators? Don’t necessarily have to be near-future, but they do need to have an elevator (or similar structure) playing a reasonably large role in the plot. Like KSR’s Mars Trilogy, for instance.

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Not a large role, but there's the Nairobi Beanstalk in Heinlein's 'Friday."

I've been playing around with having such a thing in my next WIP. It's such a cool concept.

Clarke envisioned a ribbon made of nano-carbon fibers: one molecule thick, amazingly strong. (The nuclear force is vastly stronger than is gravity. YOu can prove this by picking something up. If gravity was stronger than the nuclear force, it'd tear the something out of your hand, ripping it to shreds as it fell to the surface. Of course, it'd do that to you, too...)

The proposals currently in the works for space elevators use similar technology--ribbons--along which crawl machines that carry cargo up and down. As far as I know, there is no substance available, currently, that can withstand the tensile forces in such a ribbon.

To think of the space elevator as using a rigid shaft might be fun, but highly unrealistic.

I'll have to go upstairs and check, but I thought ACC used iron whiskers in epoxy in his earlier work for super-strong cables.

If you really want some interesting technical details, check out Robert L. Forward's "Indistinguishable from Magic", where all kinds of outre concepts like space elevators are discussed at the medium tech level.

A space elevator begins with a satellite at GeoSynch extending mass in either direction, with the intent of keeping the center of gravity at GeoSynch. The tidal stresses keep the ribbon straight, there is no need to have a counterweight keeping tension on the cable. If CG should wander away from Geosynch, then the elevator is in trouble, as the cable is now dragging the whole elevator along. In fact, the ribbon will size differently throughout the 22300km length, being thichest the highest up, and being smallest on the ground.

This is all from memory. I would consult Dr. Forward, who really does a great job with it all.

Liosse de Velishaf said:

Yeah, I’m aware of the material issues. I’m considering some other form of lift, but a space elevator seems best. I need something to kill a few people and do a reasonable amount of property damage. If necessary I can come up with excuses for having such a high population density around the elevator.

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As is usually good advice about such things (and I believe you have given some of it yourself), just make the story work. Science Fiction isn't about "does it really work" so much as it is about "if it could work, what are the consequences?".

The stresses on the connection (ribbon) between the geosynchronous satellite and the ground, as well as between the satellite and the departure station are almost entirely tension. There is no bending, no shear. I see no reason to change the cross-sectional dimension of the anywhere other than to make it easier to fasten to whatever it's fastened to. There are all sorts of issues about those connections that to discuss would take up books of space.

But those connection points are the weakest link, as it were, and most ripe for sabotage. Consider the following: The ground station is conveniently located at the equator (beneath the geosynchronous point), on a mountain top (in an attempt to lift the station above the worst weather). AC Clarke had problems with finding such a location on Earth--he said in his end notes to Fountains of Paradise that he "moved" Sri Lanka south a few hundred miles to accomodate the plot.

Perhaps your elevator engineers have devised a system to "weather proof" the ground station, and your saboteurs do something to that. And maybe also fiddle with the connection mechanism. The resulting exposure to weather and weakened connection could cause the catastrophic failure you desire. If the elevator "shaft" is a meter-wide ribbon and the wind catches it just right, there could be harmonic vibrations (think: Tacoma Narrows Bridge) that would tear things violently apart. Depending on how many folks are hanging out there, you could have a considerable death toll. As for property damage, it's a no brainer: the damn elevator's systems are incredibly expensive. And, if commerce is the reason for its existance, you have those losses as well, while the elevator is out of commission.

Alastair Reynolds includes a space elevator in his novel Chasm City. It's not a major plot point, but it does have its cable cut. Might be worth a look.
Plus, Alastair Reynolds writes great books, so it's worth a look anyway.

Cross-sectional changes are desirable to accomodate changes in tension along the cable. Consider: one mile Earthward from the geosynch point, that section of cable is carrying the other 22,299 miles. That would be your largest cross section. The smallest cross section would be at connection to the Earth, and at the departure station. THe stress there would, oddly enough, be zero.

The track carrying the elevator cars is another matter - it should be a constant crossection.

As for sabotage, severing the connection with the ground would do little. The cable is under zero tension, theoretically. In reality, they would have it under just enough tension to keep the elevator tracks rigid and in tension at max load. Of far more concern are other kinds of sabotage, like elevator cars detonating halfway up, where a cut cable will plummet back to earth.

Weather, even a hurricane right over the cable, is of small moment given the overall stresses on the cable. There is a wind load, to be sure, but it operates only on the lowest 10 miles of cable, where it is of thinnest cross section and lowest stress.

No, the greatest problem will be the orbital debris, nearly all of which is travellign below geosynchronous orbit. Somehow, during construction, the debris issue must be addressed. One scheme that would work post-construction would be some way of 'twanging' the cable so that it moves horizontally to dodge the debris. This would lead to an interesting scene where the car full of people accelerates laterally as the twang goes past.

BillPatt said:

Cross-sectional changes are desirable to accomodate changes in tension along the cable. Consider: one mile Earthward from the geosynch point, that section of cable is carrying the other 22,299 miles. That would be your largest cross section. The smallest cross section would be at connection to the Earth, and at the departure station. THe stress there would, oddly enough, be zero.

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If this were true, then all cables carrying sky lift chairs, suspension bridges, towing cars, and so on, would have varying cross sections. This is just not the case. For a structural member to work in tension, it must transfer the tensile stresses from one end to the other! Distance doesn't magically reduce the stress to zero. But I imagine there are engineers who wish that were true!

The track carrying the elevator cars is another matter - it should be a constant crossection.

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Yes.

As for sabotage, severing the connection with the ground would do little. The cable is under zero tension, theoretically. In reality, they would have it under just enough tension to keep the elevator tracks rigid and in tension at max load. Of far more concern are other kinds of sabotage, like elevator cars detonating halfway up, where a cut cable will plummet back to earth.

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First there is no tension, then there is?

Weather, even a hurricane right over the cable, is of small moment given the overall stresses on the cable. There is a wind load, to be sure, but it operates only on the lowest 10 miles of cable, where it is of thinnest cross section and lowest stress.

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Given that the cable is in delicate equlibrium (balancing gravity and centripetal forces), that the bulk of the cable is in vacuum with only angular momentum acting on it (until you add the elevator car, that is) that 10 miles of atmosphere is highly significant. But I am curious. Other than tensile strain in the cable, what other "overall stresses" are there?

No, the greatest problem will be the orbital debris, nearly all of which is travellign below geosynchronous orbit. Somehow, during construction, the debris issue must be addressed. One scheme that would work post-construction would be some way of 'twanging' the cable so that it moves horizontally to dodge the debris. This would lead to an interesting scene where the car full of people accelerates laterally as the twang goes past.

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Yes, regarding orbital debris. But if you're going to invest billions to build the thing in the first place, you will invest several millions to clear any debris that may impact the cable. If you can "twang" a cable (like a guitar, or harp string, eh?) then that cable has tension in it. And the act of "twanging" adds tensile forces to the cable. The only way you get something flexible--like a cable--stiff enough to carry additional loads, is to put it in tension.

Look: if you have a structure shaped like this: )-----O-----° [where ")" is Earth, the "O" is in geostationary orbit, the ----- on each side are the cables (22,236 miles long each), and "°" is the reason for the thing in the first place: the departure station. Assuming the mass of the station is negligible with respect to the whole assembly, the entire structure is 44,472 miles long. That's immense.

Let's assume we can build a 22,236-mile-long cable out of oh, say, steel, like one of the two main cables of the Golden Gate Bridge. The wire that makes up those cables is about .196 inches in diameter or 0.03 square inches. There are 27,572 strands in each resulting in a net cross sectional area of 830 square inches (5.76 square feet). One of the Golden Gate Bridge main cables is designed to carry, in addition to its own weight, one ton live load per foot on just the 4200-foot main span.

The length of the cable from Earth to the geostationary satellite is almost 28 thousand times as long. And there's no tension in that? The mind boggles.

Let's ignore the dead load weight of the material (> half a million tons), AND the live load weight it's meant to carry (~8400 tons) and assume that the diameter needs to expand proportionately to the distance. That would require a steel cable with a cross sectional area of 161,280 square feet. Just one half of the space elevator cable would contain more than 676,259,021 cubic feet of steel. That's a volume the size of a football field almost six miles high!

Obviously, I've made some wild assumptions. But I think you'll agree that the design of a space elevator is far from trivial. There are indeed immense stresses in such a structure and they are in a very delicate balance. You disrupt that balance to an extent by fastening one end of it to the ground. Measures must be taken to offset that disruption. And removing one of those measures will result in catastrophe.

PThom,

Dr. Forward does a far better job at this than I do, I really recommend that you read his Indistinguishable From Magic. However, here's the precis.

When I first read Fountains of Paradise, I was under the distinct impression that the cables were just like suspension bridge cables. They carried a load from the center of the span to anchorages. Given that SB cables are fixed at both ends, every point along the cable is in approximately equal tension, given that the dead load is constant. Therefore, the cross section is constant. It is tempting to think of a skyhook as a cable swinging a really big rock overhead, like a sling. That image is appealing, but mistaken.

The baffling thing about skyhook cables is that in a dead load situation, tension varies from zero to max all along the cable. Consider the beginning of construction for the skyhook. The cable is, oh, one mile long. At the free end, the tension is necessarily zero - it isn't connected to anything. The end connected to the geosynch center of gravity is carrying the tidal forces of the mile of cable, otherwise, the cable would float away. And when that cable is 100 miles long, the free end is still at zero, while the anchored end is under tension. And so on, all the way down to the surface of the Earth. Given that the tensile force is a direct result of the amount of material 'hung' from geosynch, it only makes sense to pare down the cross section to match the stress caused by the material below you.

There comes a point where the end of the cable is just touching the Earth. The end is still at zero tension even after you fix it to the ground. In that state, should you run a car full of water up the cable, it will actually pull the cable downward slightly. Since you can't push a rope, the real effect is that the location of zero tension moves up the cable. Do it often enough, and these fatigue cycles will break your ribbon. So, you overextend the outbound station a little, to put the entire system in more tension.

There are other stresses operating on the ribbon. The Moon acts to pull the skyhook backwards in orbit, then straight up, then forward. These induce bending moments (what a moment arm!) in the cable, so that it flexes slightly in its terminal connection. The skyhook must be constructed along the Equator, but the Equator is tilted 22.5 degrees with respect to the ecliptic. On the equinox, the sun's gravity is coaxial with the skyhook, on other days it acts at some angle to it. At sunrise and sunset, the gravity is acting at right angles to the skyhook, noon and midnight, straight up and down. Then there's the nutation of the geosynch anchor and the terminal station. And so forth.

As for the twang, you can demonstrate that by hanging a rope from your finger. At your finger, there is no doubt that the rope is under tension, and twangable. But the wave dies out at the end of the rope, as there is no tension at the free end. That is another reason why you'd want to add more tension to the system - so you could twang it. So hang a bottle of water to the free end of your rope and notice that the twang actually returns along the rope.

This stuff is fascinating, wouldn't you agree? Now, I am going to do a little Forward reading. I do not believe that the terminal station is at 44k miles out. I seem to remember something really ridiculous, like ten times that number. But I will have to look that up, so don't fire me up yet.

Do not forget, the cable will go through etreme expansion and contractions each day and to a degree during various season as it is heated by the sun, cooled by cloud cover, or rain, etc, etc, etc. Temperatures play a very big role in how all materials react.

In construction, we have to take this into account while bolting plates together for buildings and bridges. There has to be wiggle room for expansion and contraction and we are not even talking about objects as large or as long as a space elevator would have to have to be successful. Hell, I am still trying to figure how you get the lift capabilities to get the cable from point a to point b and beyound.

For me, as a kid, I loved reading this stuff in SciFi...because I did not know better. Today, Scifi is harder for me to accept because I am more aware of the limitations of what science and engineering can and can not do.

Yes, the tension measured at the end of a cable connected only at the other end, is zero. But that changes immediately once you connect that free end.

As for the twang business, there is Liosse's devastation right there. The wave induced by the impact load winds up whipping the free end of the rope around. Your analogy of the water bottle on the rope is a bit over the top. A more in-scale analogy would be to hang a flea on the end of a mile-long piece of sewing thread attached at the other end to a golf ball. (Of course, there would have to be another flea on another bit of string going out of the golf ball in the opposite direction). The mass of the flea isn't about to do much at all to dampen the wave induced in the system by a grape hitting the thread. That wave will stop at the golf ball and be returned, but it will just wind up whipping the flea all to hell and gone.

Whatever mass may be suspended from the Earthside cable MUST be mached by a similar mass on the spaceside cable, so that the center of mass is always at the geosynchronous altitude. In other words, you don't get to ride up from Earth unless someone (or something) is coming down from space.

I guess the notion for the space elevator is that there has to be something along the lines of a Greyhound bus station at the Earthbound end of the thing. But it occurs to me that isn't a requirement. Since the arrangement of a cable extending away from both sides of the geostationary mass is stable (balanced) it will remain in this attitude:
(E) -----O----- due to tidal forces. Why not, then, extend the Earthward cable to the ground? Leave it in the stratosphere, and put the bus station there:
(E) °-----O-----°
It isn't trivial to fly cargo up into the stratosphere, but it's certainly easier to do that than to lift the load entirely out of the Earth's gravity well. Which is the reason for the elevator in the first place.

As for the distance, I got the number from (guess where?) Wikipedia. In the article on geostationary orbits. The larger number, Bill, that you may be thinking of, is the semi-major axis of the orbit, or the distance from the center of Earth, not the surface.

The other issues you mention, forces applied to the system by the moon and such, are also addressed in that article:

While a geostationary orbit should hold a satellite in fixed position above the equator, orbital perturbations, such as by the Moon and from the fact that the Earth is not an exact sphere cause slow but steady drift away from the geostationary location. Satellites correct for these effects with station-keeping maneuvers.

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Fortunately, the elevator can service the satellite, providing replacement thruster propellants for station-keeping.

Pthom said:

Yes, the tension measured at the end of a cable connected only at the other end, is zero. But that changes immediately once you connect that free end.

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In the absense of an applied load, the formerly free end will still be in zero tension. Unlike a suspension bridge cable, the skyhook cable is dangling from an anchor in geosynch. The other end is stressed by the weight of the entire cable. So the tension varies with the amount of cable below you.

Pthom said:

As for the twang business...

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The purpose of the twang is to move the cable out of the way of the incoming debris. When SkyHook Control senses an incoming piece of debris, it induces a rapid horizontal movement, a "twang", which propagates along the cable, arriving in time to move the cable out of the way of the incoming object.

All of my posts have been from memory of many discussions of this topic I have read from Clarke, Forward, Niven, and others. I finally repaired to my library, dug out Forward's Indistinguishable From Magic. Page 62 of the paperback:

Eventually, the lower end of the cable would reach the ground (or the top of some convenient near-equatorial mountain) 36,000 kilometers below. At that time, the outgoing cable would be 110,000 kilometers long. The outgoing cable has to be longer than the Earth-reaching cable because of the way the gravity forces and centrifugal forces vary with distance.
[...]
The bottom end of the long cable can now be anchored to the ground so it doesn't blow around in the winds, and a large counterweight (a small asteroid) would be attached to the outer tip. The counterweight, like a stone in a giant sling, would keep the cable under moderate tension to help keep it straight.
[...]

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On page 66, he refers to The Fountains of Paradise, where Clarke discusses how to vibrate the cable to avoid space debris. In fact, he uses the word "twang". I'd have to see if Clarke was the first to use that word in this context.

IMHO, yo stop the twang, you move the lower end rapidly sideways at the time that the impulse arrives. You then slowly return the lower end to the zero position, load up the elevator, and resume service.

As for the stratospheric terminal, I wonder if that is a cheaper solution. I don't think it would be. Loading cargo onto an elevator car, then using the solar panels 36,000 km away to power it may well be cheaper than running a blimp up to, oh, 20km up, then manhandling a cargo transfer off the blimp, onto the bobbing terminal floor, then into the elevator car. And up that high, everyone would be in at least a helmet and electical coveralls.

Still, if it is a cheaper solution, someone would do it.

BillPatt said:

Still, if it is a cheaper solution, someone would do it.

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And, no doubt, someone will. But cheaper is relative, methinks, when it comes to constructing something as immense as the space elevator.

I've always wondered about space elevators.

What if the moon was the anchor, and the earth bound station was free hanging up in our atmosphere. Like we just land planes in it and load the elevator.

a station that size, high enough to miss mountains would probably be pretty big, and have some force if it were to come crashing down.

The advantages (in my mind) would be that you could use multiple anchors, and for construction attach the elevator at the moon and lower it to the earth bound area to build the station.

On the other hand, cables are expensive to get into space. Maybe we could run a thin lead back from the moon to run the heavier ones up.

And now I'm starting to drift.

Because the Moon moves around relative to the surface of Earth, your lower station would move too...really really fast. Assuming it was even possible (which is a giant leap of the imagination), the environment on that station would be worse than the worst hurricane ever.

In order for your scheme to have a remote possibility of working, the station would have to be entirely outside the atmosphere. Then, of course, you'd still have the problem of getting your cargo up there. And that's the exact problem of getting cargo up to the ISS or Hubble.

Question withdrawn thanks to the power of Google.

As you were.