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# Gravity Arch

A circular series of floating keystones
 (+13, -2) [vote for, against]

Theoretically, you could suspend a very large number of keystones around an entire planet if they were positioned in a ring at the right height. The angle on the keystones would probably be very small.

Maybe they would support a roadway. If positioned at the right altitude, it could be used to anchor satellites, although they don't need anchoring. It could be a bike path or a monorail track.

You might need international treaties to make sure no one messes up a part of it, or else the whole thing will fall down. It would be a pain for shipping if it were too low, but it would probably be high enough to not hit the highlands and mountains.

Maybe this would work better on a moon or an asteroid. You could make it a spherical arch, suspending a thin bubble of keystones around a gravity well of any kind. The trick would be to balance it so that one portion doesn't begin to get closer to the well over time, and thus experience more pull, and get closer until the arch broke. The breaking itself would be worth modeling in Comsol Multiphysics or some other computer physics program.

Even if it isn't very useful, it would still be worth building. I would be satisfied just doing the limbo.

Roche limit http://en.wikipedia.org/wiki/Roche_limit
May not be relevant, but illustrates how different distances affect forces. [baconbrain, Mar 30 2008]

Vernon's version of this Idea. Earth-Space_20Web
Basically, it solves both the endless suspension bridge problem and the endless arch bridge problem by balancing their strengths against each other's weaknesses. [Vernon, Mar 31 2008]

(?) Building a Stupa http://www.pinemtnb.../BuildingAStupa.htm
Make a meshed stone dome. [baconbrain, Mar 31 2008]

Ringworld http://www.orionwor...aching_Dawn_600.jpg
[ldischler, Mar 31 2008]

LIGO http://www.amnh.org/sciencebulletins/
Gravity wave observatory [2 fries shy of a happy meal, Apr 26 2009]

 — MaxwellBuchanan, Mar 30 2008

 Thought not. OK, let's try.

 First, let's assume that the ring is made of granite, and has a cross section of 1m x 1m (for the sake of argument).

 There are lots of ways to calculate the compressive forces in an arch, but we can go for a simple approximation. Suppose we consider the two stones on opposite sides of the equator. If they vanished, then the two half-rings (north and south) would collapse upon eachother.

 So, the equatorial stones are supporting the weight of a half-ring. What is that weight?

 Well, first of all, we can't just use the mass of half the ring, because gravity is directed towards the centre of the earth. In other words, the parts of the ring *very close* to the equator are not contributing significantly to the north- south force, whereas the parts very close to the north or south pole are contributing almost fully.

 As a reasonable guess, therefore, we can assume that the effective mass of each half-ring, in terms of loading on the equatorial blocks, is roughly two- thirds of its actual mass. So, what is the mass of a half-ring?

 Well, a half-ring has a cross-section of one square metre, and a length of 20,000km or 2x10^7m. Hence, each half-ring has a volume of 2x10^7 cubic metres, and (given the density of granite at 2.75g/cc), a mass of about 5x10^13 grams. As noted, we can take about 2/3rds as being the effective load placed on the equatorial blocks and, since there are two such blocks, the compressive load on each equatorial block will be about 2x10^13g, or about 2x10^11 N/m^2.

 The compressive strength of granite is about 2x10^8N/m^2.

 So, this will only really work if you can find a material 1000 times stronger (in compression) than granite. Of course, you could opt for a less dense material, but you're still looking for a strength/ density ratio 1000 times better than granite.

Bonne chance, pain-au-salsa.
 — MaxwellBuchanan, Mar 30 2008

//Theoretically, you could suspend a very large number of keystones around an entire planet//
If the planet is very small, like an asteroid. But you said that.
//if they were positioned in a ring at the right height//
What does height have to do with it? As long as this thing doesn't rotate, you could try a section of it in your back yard with bricks. And it shouldn't take very long to discover that it doesn't work.
//The angle on the keystones would probably be very small.//It can be whatever you want, depending on the size of the stones. To make this work geometrically, the stones would have to be hundreds of miles on a side. But no material that massive could even support itself. Not around the Earth.
 — ldischler, Mar 30 2008

Sure it would! According to [Maxwell], you just need to find a strong material or decrease the force on a given keystone by either making the arch smaller or choosing a celestial body of lesser mass. Unless your back yard encircles a planet and you have enough bricks of absolutely perfect construction and properties, which I don't consider unnecessary, you can't try it in your backyard.

Why not? It's just an arch (though an almost perfectly flat one), so you need only support the ends of the segment. And when it falls down, you'll see the problem--ie, it only works when you have a single enormous stone crossing your entire backyard.
 — ldischler, Mar 30 2008

 ldischler - Yes, you only need support the ends of a segment if the arch is small enough that the direction of gravity is effectively constant. But this is not the case in a globe-circling arch (or ring). The proposal would work, given an adequate material (which may not exist).

 [pain au salsa] making it smaller (narrower) won't help: the loading per unit area will be the same.

I'm not sure what the best available ratio of compressive strength to weight is. Compressive strength is highly dependent on the geometry, and the best solution will be some kind of composite or geodesic frame, but I don't think even this will save you.
 — MaxwellBuchanan, Mar 30 2008

 If you make the stones of the arch narrow, it's going to bend and collapse. You'd want to make the sections tubular, ideally. But, as [MaxB] so well points out, the compression strength of any known material simply isn't up to the job.

 To parrot Larry Niven's description of the Ringworld, this idea is simply an arch bridge with no endpoints. Design hints could be taken from modern arch structures. And, since we've given up on arch bridges for modern construction, you might take the hint that it won't work.

 In theory, this could be built, given the right materials and design and planet. But that's already known, and kind of obvious--so this idea isn't really new. The spherical arch, which is a bubble, has figured in a few SF stories.

 If there was something new to this idea, I'd give it a bun, maybe. But this idea leaves out one very important factor.

 A hoop arching around a gravity well is fundamentally unstable--it cannot be balanced--you can take that for granite. When it drifts off center, by even the quiver of an atom, it will fall further and further off balance, and crumple and crash. And crumple and crash some more. And more. Then get you sued.

 Stabilizing such a structure can be attempted, but the methods for doing so are nowhere in the idea. And would get even further away from the original idea.

 An unsupported stone arch around the Earth is impossible. It's not hard to think one up, but it's also easy to see why it won't work, and easy to think of what would be needed to make it less impossible.

I'd wander off without fishboning, but this impossibility has a lot of buns, and that chaps me. [-]
 — baconbrain, Mar 30 2008

If it was round an asteroid like Toutatis, which doesn't spin on one axis, what would happen?
 — eleventeenthly, Mar 30 2008

 If it wasn't touching the asteroid, it wouldn't matter how the asteroid spun. Until the arch went off center, which it would, balance it how you will, and it touched the asteroid, then it would throw rocks off in random directions.

See, that's what gets me about ideas like this. Folks who don't know anything about the mechanics of it, seem to like it. It's a pretty concept, yes. But not new and not possible.
 — baconbrain, Mar 30 2008

 What if you picked a small asteroid and used a bunch of keystones to make a sphere, which you could supported gently from beneath with an inflated, compartmentalized, clear balloon. If the balloon were a habitable area, then you would have a really good shield against flying space debris without having to have any columns to support it.

 As a backup measure, each keystone could have a small aerosol attitude thruster to maintain the integrity of the whole arch. The firing of the aerosols could be orchestrated by a central computer that would use radio frequency triangulation to verify the spatial coordinates of the sphere's components. The aerosols could be periodically replaced.

That would work, wouldn't it? Or is it really impossible?

 I dunno. The balloon idea is also unstable, though you could put cables up to keep any part from going upwards, which would give stability AND, unfortunately, greater compressive forces on the structure (we've discussed a balloon over a planet here before). The dynamic stability mechanisms are possible. A hollow spherical stone dome is possible up to a certain size, though I don't know what that is.

I'm also not sure how the Roche Limit would relate to a non-orbiting arch. That is, "The smallest distance that a fluid satellite can orbit from the center of a planet without being torn apart by tidal forces." (See link.)
 — baconbrain, Mar 30 2008

 One of those impossibility buns up there is mine.I would love to see a man-made ring around the moon. Each "age" needs its mysteries for the next age to ponder.This'n do just fine.

...and unless you can tell me just how them there pirymids was built, it's stayin.
 — 2 fries shy of a happy meal, Mar 30 2008

A ring around the moon would require a material with only 40 times the compressive strength (per unit weight) of granite. That may be feasible, if anyone had the money to fease it.
 — MaxwellBuchanan, Mar 30 2008

 The pyramids were built by people. I will soon reveal to you the reason they were built.

 We could easily enough make a ring around the moon of loose particles. We could arrange those particles into a nice triangular girder and truss structure while it all orbits. We might even be able to stop its orbit so it stands like an arch. But we cannot make it stay centered on the moon, and we cannot make it only a meter wide.

 Orbiting structures are easy. The HB has self-supporting ring structure idea or two.

This one is just impossible. Sorry.
 — baconbrain, Mar 30 2008

If the arch is well-centred initially, the forces to keep it that way would be quite modest. This, after all, is why the atmosphere stays where it is, instead of all flopping over to one side. It's all to do with the Coriolis effect, as described by Bernoulli.
 — MaxwellBuchanan, Mar 30 2008

 [nineteenthly] - either you've forgotten to log in, or else [eleventeenthly] knows too much.

[everyone else] - surely if the ring was rotated at sufficient speed the angular acceleration (inertial centrifugal force..? I get confused...) would counteract the gravitational compression and you could achieve this with granite or almost any material?
 — wagster, Mar 30 2008

//if the ring was rotated at sufficient speed// Indeed, but then it's basically a series of satellites that happen to be touching eachother, and it'll have to be very high and very fast.
 — MaxwellBuchanan, Mar 30 2008

 [wagster], that was him. He knows about Toutatis because of the "lots of planets have a North" comment on Doctor Who, which led to a conversation about how it could be that a planet didn't have a north, to which the answer is that if it hasn't got a magnetic field or axis of rotation, it wouldn't have a north.

I think he was probably expecting it would fall apart more quickly.
 — nineteenthly, Mar 30 2008

 //surely if the ring was rotated at sufficient speed the angular acceleration (inertial centrifugal force..? I get confused...) would counteract the gravitational compression and you could achieve this with granite or almost any material?//

 Hmmmm.. Very interesting. [MB] is right, if you balance the centrifugal force and the gravitational, this becomes somewhat of a different beast. I propose to go a little further. Basically, any beam under compressive forces is unstable. The buckling paradox really means that for "narrow" members {generally, L > 10W } you can get tension-to-weight far higher than compression-to-weight for unsupported members. Try it with just about anything - the extreme being say a thin piece of fencing wire a foot long. Good for 100's of kilo's in tension, maybe as much as 1 kilo in compression before failure. IIRC compressile capacity is inversely proportional to lenght to the FOURTH power, whereas tensile capacity is, for all extents and purposes, unrelated to length. [MB]'s analysis does not take buckling of thin members into account - I'd say you'd end up with an arch with a cross section of many kilometers just to withstand buckling. His comments regarding compressive modulus still stand.

 What I'm saying is try spining your arch so as to overcome gravity and apply tension to it. Keep tension within reason, say 1/2 the tensile capacity - and you'll have a fairly stable structure. It'll probably need to be spun fairly fast.

I'm sure that's not a new idea, either.
 — Custardguts, Mar 30 2008

 The buckling problem is why I keep saying that this would have to be a tube or a truss or something. If you want to push hard on the two ends of a long stick and not bend it, you had better be damn sure it's perfectly straight, and as wide as possible, and that your pushes are perfectly directed. Once again, the VERY least little error in this design, and it all goes smush. Another way that a stone arch around the Earth is impossible.

 Yes, at orbital velocity all these problems go away. But at orbital velocity you don't need an arch. At even slightly less than orbital velocity, I say, all the problems I've been snarling about will kick in awfully fast.

 If you were to spin things at over orbital velocity, you could tie them together make a road that would stay up and support non-orbiting objects, provided they had really fast wheels underneath. That's a Vernon idea that's around here somewhere.

That and this impossible arch can both be stabilized with cables running down to the Earth, so could the atmosphere bubble mentioned elsewhere. The forces would be light, yes.
 — baconbrain, Mar 30 2008

Please keep working on this. I'm hoping for a planetary hula hoop.
 — bneal27, Mar 31 2008

What exactly would be the purpose of building such a thing? Other than to see if we could build it, that is.
 — qt75rx1, Mar 31 2008

 "To parrot Larry Niven's description of the Ringworld, this idea is simply an arch bridge with no endpoints."

[baconbrain], please be more complete when you reference something and modify it. While you are correct that this Idea is an arch bridge without endpoints, you should have mentioned that the Ringworld is a suspension bridge without endpoints.
 — Vernon, Mar 31 2008

//What exactly would be the purpose of building such a thing? Other than to see if we could build it, that is. //
You're new around here, aren't you [qt75rx1]?
 — coprocephalous, Mar 31 2008

The mass of the ring will increase linearly with diameter (assuming constant cross-section). Gravitational acceleration decreases with the square of distance. Hence weight will decrease linearly with diameter, and thus reducing the stresses to a manageable level should just be a matter of picking a big enough diameter.
 — david_scothern, Mar 31 2008

[MaxwellB] - I think the 2/3 in your calculation should be 1/2 (i.e the integral of sin(x) between 0 and 180 degrees) - but your objection still stands. It would be more practical to build a "ring around the Earth" supported by tensile forces: E.g. a 40,000km bit of string (thanks, [coprocephalous]) with helium ballons attached to it every couple of metres.
 — hippo, Mar 31 2008

 Yet another idea inspired by my user name.

I like the idea if you make it elastic and include a giant string you can pull to squeeze it real tight... oh, and include a ratchet, of course.
 — globaltourniquet, Mar 31 2008

//...or choosing a celestial body of lesser mass//
Keep going to zero, and that's the solution. Eliminate the planet entirely and build the ring in open space, letting self-gravity hold it together.
 — ldischler, Mar 31 2008

 Arches are sufficiently advanced technology that some folks perceive them as magic. So let's make some comparisons, eh? ([Vernon], you are right. I should have been clearer on my Ringworld comparison. Thanks. ("The Ringworld is unstable!"))

 Nobody is saying the concept is of a stone space arch is impossible. Hell, it's even obvious. Practically baked. it's just unworkable for a stone arch around the Earth. (And pretty damn pointless at any scale, but this is the HB.)

 It's possible to build several variations of this idea, provided you keep the scale small enough. You could make two of a Borobudur-style stupa, the pierced stone dome, or any other sort of dome, as a space sphere. You could even just start with a big asteroid and hollow out the center.

 A ring arch of some sort would work, too, but a torus made of hoops or pipes would be better, a sphere would be more stable, while a thick-skinned sphere would work best of all. It's all do-able, within certain limits, just like any other sort of construction. It's just stacking blocks, provided you do it right.

 But you couldn't expect to make a stack of stone blocks 24,000 miles high. Which is what a ring around the Earth would be like. A single-stone-wide structure would have to be absolutely fricking perfect to avoid falling over/apart, and still the bottom stones would explode. And in a ring, every stone is the bottom stone.

 A wall would be more stable in one way, but not if it's 24,000 miles tall and long, and only a stone block thick. That is what the situation for a shell would be. (But you could pull out a few blocks and make it lace-like.)

 Nor could you expect to balance a tower perfectly upon a single point. Which is what putting a hoop or a shell around a planet would be like doing. You might be able to guy it with dental floss, if you built perfectly, but you'd need SOMEthing. (Without a planet in the middle, that's not an issue.)

 So, yes, you can enclose your giant space Buddha in a self-sufficient stone sphere, but you'll need some string between the two. Same for an Appian way above and around an asteroid.

 You could make a big mortarless block sphere out past Jupiter, to protect you from meteoroids, but you couldn't make one with Jupiter in the middle of it. You can make a stone jogging track somewhere past Saturn's rings, but you'd best be careful that your footsteps don't start it ringing and falling in on you, 'cause it won't be stable.

 This idea is one of those things that's so obvious that it isn't discussed much. It's exactly like suggesting that we build a tower to the stars. We can build towers, and we'll build them on Mars, someday. We just aren't ever going to build a tower all the way to Mars.

Somebody, someday, is going to shape some asteroids into polygons, clump them together with a hollow center and bake this idea. Or at least some of the variations on it discussed in the annotations. But they'll never make a freestanding, freestone arch around the Earth, no matter how pretty it would be.
 — baconbrain, Mar 31 2008

 Just throwing this out there:

Acceleration due to gravity is inversely proportional to the distance squared from the center of mass (earth) therefore, however unfeasable it would be to construct, a ring around the earth could exist. I'm willing to bet [Maxwell] that you could find a certain earths radius' altitude in which your granite would survive.
 — MikeD, Mar 31 2008

I'll see [Maxwell], and raise you [ldischler] that it wouldn't ever work. The bigger the radius, the more mass in the ring. But I can't do the math.
 — baconbrain, Mar 31 2008

For the math, I imagine you could use the same math that you'd use on a pipe. Instead of internal pressure trying to blow it up, you have weight trying to crush it. Divide the ring in two. Now, the compressive pressure on the ends (and anywhere) is equal to the (weight/unit length) times the projected length (the diameter) divided by the twice the cross-sectional area.

There are equations for buckling too, but I don't think it will get that far, as for a ring just outside the atmosphere, the compressive pressure would exceed the strength of granite by a factor of more than 2000. Doesn't matter how thick or wide it is, though those dimensions would factor into its stability against buckling.
 — ldischler, Mar 31 2008

I seem to recall a physics puzzle that might apply to a big ring, specifically an infinitely big ring. If blocks were stacked one atop the other, in a straight line through space for ever, even though any one distant block would not exert much pull on any example block, the number of distant blocks is is infinite AND the pressure transfers from block to block. That, to me, implies that making things bigger isn't going to reduce forces.
 — baconbrain, Mar 31 2008

 [baconbrain], I challenge that your infinite stack of blocks example, while illustrative, is moot, given that as you approach the edge of space, the blocks would begin to grow individually taller as you stack them, until eventually you would find that the block on top of your stack was infinitely tall, thus terminating all further stacking activities.

 Unless you built it in null space...

...mmm, bacon...
 — Alterother, Apr 01 2008

This is brilliant, similar to my old idea of a vacuum sphere made entirely of interlocking keystones (although not stone, obviously)
 — simonj, Jul 08 2008

Didn't the gravity measuring statellites find that gravity is more like a warpped curtain than a const straight vector ? If this is so then the ring would be buffetted by gravity rather than being structurally supporting .
 — wjt, Jul 08 2008

They are tring to prove that now with LIGO: Laser Interferometer Gravity-wave Observatory.