Space Elevators Face Wobble Problem

NewScientist is reporting that while the strength of the tether has long been considered the main problem in building a space elevator, a new study suggests that a dangerous wobbling problem may also be a serious obstacle. "Previous studies have noted that gravitational tugs from the Moon and Sun, as well as pressure from gusts of solar wind, would shake the tether. That could potentially make it veer into space traffic, including satellites and bits of space debris. A collision could cut the tether and wreck the space elevator."

Comments

Of course it's not easy

[TheCoders]

I don't think anybody really thought building a space elevator would be as simple as reeling out some cable and strapping on a cabin. There are a million complications, even before we get to solar winds or tidal pulls. How about something as simple as airplane traffic? Birds? Squirrels, for goodness sake!?

Plus a million things we haven't thought of, and won't think of until the product is built. When train tracks were first laid down, they were too close together, because nobody had heard of the Bernoulli effect. Trains were getting slammed against each-other by their own created air pressure. What did people do? They learned from it, and moved the tracks further apart. We take trains for granted, but they were not without their technological hurdles to overcome.

Of course something like a space elevator is not an easy accomplishment. Does that mean we shouldn't try?

What do you think?

Re:Of course it's not easy

[Gat0r30y]

Of course something like a space elevator is not an easy accomplishment. Does that mean we shouldn't try? I think we should and probably will at least give it a shot. Also, as you note, there are a LOT of complications. Complications I look forward to seeing innovative and cool solutions to. First and foremost though, we gotta get the material engineering issue solved, until we have a material which can withstand the forces involved, were stuck with regular elevators. Nanotubes look promising, and this gives us an excuse to invest in the research.

"I think" Engineering

[iamlucky13]

.But Perek says that may not be enough. "Previous proposals for a passive tether controlled from the ground do not seem stable to me," he told New Scientist. Anders Jorgensen of the New Mexico Institute of Mining and Technology in Socorro, US, who has previously studied the problem, agrees that stability is a concern for space elevators. But he says the new paper does not provide a quantitative analysis of the issue, and is not convinced that thrusters would be needed to stabilize the cables.

Basically, the problem has been noted before this Perek guy's paper, but not studied in any detail. Perek reiterates and perhaps expands upon the concern, but doesn't do any analysis to establish the actual likelihood of a problem. It's basically an opinion.

Atmospheric oscillations should be extremely well damped by drag. Oscillations due to gravity from the sun and moon may be a greater concern, because there is no drag, although including conductive paths in the cable may allow the earth's magnetic field to suitably damp the oscillations.

An IEEE article on the topic discussed the related issue of harmonics. If these oscillations propogate through the cable at a rate that syncs up well with the rotation of the earth, gravity of either the moon or sun may amplify them. The tensile component can be tuned by adjusted the mass and tensile stiffness of the cable, and even better, the mass of the counterweight, allowing you to tune it by changing the tension, like an incredibly huge guitar string. The will also be a pendulum like motion due to the fact that the earth is on a tilted axis. This seems to be the concern discussed in the article.

I personally am not at all convinced that oscillation of the cable alone (waves) is a problem due to it's low density, but oscillation of the combined cable and counterweight (pendulum) may be. If so, thrusters on the counterweight are much simpler to attach and refuel than they would be at intermediate altitudes on the cable.

wreck the elevator

[alta]

Looking at the sheer size of this, I'd say that 'wreck the elevator' is a major understatement. Look at all the other stuff that would be wrecked. I remember reading a Ben Bova book a while back where terrorists sabotaged an elevator. They went to the top and severed the connection to the counterweight. The rest of the thing toppled like a flimsy tree, wrapping itself 1/2 way around the earth. Yeah, scifi, but it could happen.

Re:wreck the elevator

[merreborn]

Actually, no. The rotation of the earth would cause the ribbon to wrap around the earth in an easterly direction

If what you propose were true, a pin balanced on its end would always fall over to the east as well, as would a perfectly symmetrical tree, or a falling skyscraper.

They don't, because all these things, a space elevator included, travel through space at the same speed as the earth's rotation. Why would it suddenly, magically lose that momentum, were it severed from its counterweight?

It's easier to postulate than actually engineer

[EmbeddedJanitor]

"I predict flying cars by year 2000^h^h^h^h2010^h^h^h^h2020". Prediction is the easy bit. Actually engineering a flying car or space elevator or whatever is the hard bit. There are a lot of very significant obstacles to overcome.

The old well worn bridge analogy: In theory it's pretty easy to built a bridge, but you need to only look at the Tacoma Narrows bridge to see that engineering a viable structure takes a bit more than str theory is prettSame deal with a space elevator. The theory is pretty straightforward, but the actual engineering to make a reliable structure is something else.

Re:Then why not a space escalator?

[sgage]

What's lacking is the unobtainium.

Your post is a statement of religious belief. This WILL happen, and that WILL happen. Why? Because you say so?

no, it would go east.

[F�an�ro]

Actually, no. The rotation of the earth would cause the ribbon to wrap around the earth in an easterly direction
If what you propose were true, a pin balanced on its end would always fall over to the east as well, as would a perfectly symmetrical tree, or a falling skyscraper.

There is no tipping or balancing involved here

The top of an intact space elevator in orbit would move eastwards, just like the ground under it does.
The top would move at a much greater speed than the ground, since it is further from the center of the earth and has to cover a greater distance for a full circle.

As any part of this elevator falls towards earth, it would keep its greater eastward speed and therefore overtake its anchor point quickly.

Re:Then why not a space escalator?

[SnowZero]

Less sense, actually. Trans-continental conveyors are at least technically possible. A space elevator violates basic physics, as people with more than two brain cells can easily see for themselves. One brief google brings up for example this post from 1995 which should give you all you need.

That's not an answer, that's another question, with plenty of unspecified assumptions which would let you come up with almost any answer you want. Lots of people have worked it out under various assumptions, and you get an answer requiring a cable with strength between 60-120 GPa. Scientists have measured carbon nanotube filaments which have a tensile strength in that range. We can't build an assembly (cable) that strong yet, but I wouldn't call that "violating laws of physics".

Requiring research beyond our current knowledge and capability is not the same as "impossible". The most you can say is that it's not possible within the current limits of materials known to materials science. Why don't you link to a *proof* that no material can have a higher tensile strength than carbon nanotubes, and a *proof* that it not possible to bond carbon nanotubes so that an assembly has >50% of the strength of the filament.

Re:Then why not a space escalator?

[Anonymous Coward]

I decided to undertake the challenge in the Usenet posting you linked to, which claims that a space elevator is physically impossible.

Because I'm an undergraduate, I'm going to try option (1). Because I'm not a very good undergraduate, I'm going to simplify things even further: I'll assume the elevator has a uniform width and density along its entire length. This assumption allows me to relate the mass element dm with the radius element dr easily: V = mass / density (I'll use rho from now on), so A * r = m / rho and therefore dm = A * rho * dr.

Now consider a mass element dm. Define "up" as positive. Since we're in a rotating frame of reference, the "centrifugal force" on dm is 0.5 * omega^2 * r * dm, where omega is the angular velocity of the Earth and r is the distance of dm from the centre of the Earth. The gravitational force on dm is -mu * dm / r^2, where mu = G * M = standard gravitational parameter. This gives a total force, in the absence of tensile forces of: (0.5 * omega^2 * r - mu / r^2) * dm.

Since dm = A * rho * dr, the total force can be expressed as (0.5 * omega^2 * r - mu / r^2) * A * rho * dr. Now I'm going to add in the tensile forces. In order to have a stable elevator, each mass element dm must have a zero net force. Since the most recent stated equation is not zero except at geostationary orbit, excess force will have to be transmitted through mass elements. Since forces are additive, I'm going to integrate from r_0 to r (where r_0 is the radius of the Earth) in order to obtain the excess force at radius r. Integration results in:

F_excess(r) = [0.25 * omega^2 * (r^2 - r_0^2) + mu * (1 / r - 1 / r_0)] * A * rho

Now for the key step. I'm going to set F_excess(r) to 0 and solve for r. If a solution exists, this means that there exists a length of elevator such that the net forces all cancel to 0 (ie. the excess force is completely cancelled out). Unfourtunately the equation is cubic in r, so solving the equation is cumbersome. I found this cubic solver which can make the process easier. Using:
a = 0.25 * omega^2 (approx. 1.32e-9 s^-2)
b = 0
c = -0.25 * omega^2 * r_0^2 - mu / r_0 (approx. -6.25e7 m^2 s^-2)
d = mu (approx. 3.99e14 m^3 s^-2)
I get three real answers. One of them is negative, which I discard as unphysical. Another corresponds to the radius of the Earth, which is valid but useless (it represents a zero-length elevator). The third answer is about 2.15e8 m, which is actually far beyond geostationary Earth orbit (approx. 4.22e7 m).

Using your example of a weight being swung round on a rope, you can swing a weight around as slowly as you want as long as you make the rope longer. The mistake you may be making is to forget that the magnitude of "centrifugal force" grows linearly as a function of radius, which will eventually beat gravity (which does not grow (in magnitude) as a function of radius).

Some fine print: I've assumed a spherical Earth. A constant width elevator is not an optimal design (unless you want to run it as a continuous loop) since the tensile forces are not uniform along its length. The elevator, as I've described, is unstable under loading but can be stabilised by extending it a bit further and fixing it to the ground.