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Tuesday, January 12, 2010


I have had an original idea, at least I haven't seen it anywhere else. I cannot say that I understand the engineering well enough to be certain it is feasible but here goes. I welcome comments.

It has always been assumed that a Space Elevator would have to go from a geosynchronous satellite exactly to the equator because if the ground base were off the equator it would exert a force which, however slight, would be unbalanced by any counter force, on the orbiting satellite. In particular I said that though Ascension Island would make a good conventional spaceport being 7.5 degrees south of the equator would make it impractical.

However assume 2 cables from the same orbiting station - each going to the same longitude but one to the northern & one to the southern hemispheres. Then each exercises a countervailing pressure balancing the other, the triangle is stable & so is the orbiting satellite.

There would be some lateral stress on the cable & it would have to be a bit longer but because Geopstationary is 22,300 miles up the angle is very narrow. Therefore the lateral stresses are very small & as Pythagoras proved the extension of length minor.

Here are some examples:

Ascension Island cable length (root 22,300^2 + 500^2) is 22,306 miles.

New York (41 degrees = 2500 miles north) cable length (root {22300 + 400)^2 +2500^2) is 22,837 miles. (I have added 400 miles to account for New York being, due to the curvature of the Earth, "lower" than the equator)

Glasgow (56 degrees & 3,400 miles north) cable length (root (22300 + 700)^2 + (3400^2) is 23,250 miles.

North pole (4000 miles north) has cable length (root {22300 + 4000(^2 + 4000^2) of 26,600 miles.

In fact such is the distance to geosynchronous orbit that the angle to a non-equatorial spot is tiny & the main extension is just because any non equatorial spot is "lower" towards the Earth's axis than a point on the equator. Even if we assume the difficulty & expense of a cable going up with the cube of its length the increase in cost is trivial compared with the advantage of being able to ship to orbit directly, by "cable car" from any major city on the planet.

Note that I do not propose this for the first Elevator - lets keep everything as simple as possible. However once 1 elevator exists shipping up enough material to build another cable is very much easier & cheaper & their growth can be exponential. If they doubled annually then in a decade we would have 1,000 cables or 500 pairs connecting directly to the 500 biggest cities in the northern hemisphere & a lot of very small places in the southern.

Note that in the interview with Dr Brad Edwards of Black Line Ascension he said that the base of an Elevator would need to be mobile at sea because it would have to be regularly moved to avoid other orbiting objects. However with an angled Elevator there are lateral forces acting & it might be possible, either by using placement of lifts to bend the cable a few metres to the side or by letting out or in a little more cable for the same effect to keep a fixed tether site. I have neither the mathematical knowledge nor the understanding of the qualities of the materials to know if this is possible or practical but I put the idea up.

I can even imagine enough spare capacity to use them to take suborbital craft up 1,000 miles & let them glide to anywhere in the world, though this, even though it takes little energy, may not be cost effective.

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Surely an effective station-keeping system for the satellite would be a cheaper alternative.
I think Prof. Bolonkin did something like this
which linked an Earth pole (rotation, you know) with a point on the Moon.

The trouble with all this is a non-shortest path requires yet stronger materials when we are already pressed to produce 60 gpa materials (actually 6 right now, but you get the idea--)

No problem if--
Actually, if that be true-- deliverably true-- [buckeytubes able to build a Space Elevator now] than even 20pct of that strength-- at a reasonable price-- could make flight to orbit possible another way, and 40 pct of that strength would make lunar flights (one way) cheap as a light airplane.

For that reason I see the final stage space elevator as something done in the more distant future-- NOT because it cant be done but because the materials will enable good enough substitutes for it in the interim. Eventually, though, old fogies will demand riding an elevator rather than catching a flight.

Throughput rate is the key to payback.
Hi Neil, there's no reason why in theory this idea wouldn't work. We considered it for the Mars Society Scotland's book project "Building the Martian Nation."

Essentially we were faced with the problem of a potential strike on the Martain space elevator by the moon Phobos. One of our solutions was to use this idea, I calculated that in order to permanently avoid Phobos the north and south anchor terminals would have to be displaced from the equator by at least 6 degrees either side.

We figured that once we had dropped the cables at the equator we'd play out some more slack and then move them by rail to the terminals. Provided that the motors move along the rail at the same speed north and south, and that they were anchored to the track, it should probably work.

As it happened we eventually went for a different idea of having just one cable. In this idea we'd still have the track going north and south and we'd anchor it to the little motor but we would use computers to run the cable up and down the track in such a manner as to avoid the cable ever hitting phobos. If calculated right you should only have to deal with very low amplitude oscillations as you're not avoiding the full orbital range of phobos' inclination but only its diameter on each pass. Note that the terminal would not need to be in motion constantly but could be moved in short burts.

Both ideas should in principle work but we felt that it would be easier and also use less resources
just to go for the single cable moving terminal idea.
It just occurred to me, that with a hypothetical Clarke Belt like in the novel 3001,
four huge space elevators spaced around the Earth's Equator connected by a spaceport ring in geostationary orbit.

What you would have would look like a cosmic maypole connected to a ring in geostationary
I think you are correct here regarding this type of elevator on Earth. It would certainly seem much more advantagous if you're connecting cables to cities. On Mars the north and south terminals might one day develop into cities but at the outset it could just mean extra resource expenditure.

Its an interesting concept, it will be interesting to see how this develops
Not clear why you think people thought you had to put it in geosynch orbit. You can tether a space elevator with a single cable from anywhere (possibly the pole would be difficult, but potentially even there). The weight on the end of the string keeps the cable taught, and the weight of course has to be further out than geosynch orbit, but there is really no need for 2 cables. The major problem as other commentors have observed is in getting a cable strong enough to reach that lon without breaking under its own weight.
A cable which hit the equator at the Geo point would be unbalanced - the bit at the top being south of the equator & having a lateral force pushing it northwards & that in the north (assuming that is where it is tethered) having a southward lateral force. I was assuming these forces would weaken it & set up various lateral movements but am not certain.

A tether longer than geo & off the equator at the end could not be used to catapult material futher out because dropping it would certainly produce a strong lateral force which would vibrate along the length of the structure.
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