How long would it take to travel up an orbital elevator?

[psychotick]

Hi,

I still can't see a solid, i.e. building like elevator as a possibility. Sure the stresses involved in creating such a structure and keeping it stable would go far beyond the capabilities of any existing material to withstand them. Ignore the counter weights tohold things up, just think about the weight / mass of the elevator itself. Say its built like a skyscraper of some sort. A mass of a hundred tons per meter of building height - Purely a guess. 36,000 kms of elevator at this ratio means it would mass 3.6 billion tons. And its width asuming it was made of solid water, would be a square ten meters along its side. Steel I assume would allow the structure to have an internal space for an elevator at the same weight per width since its denser and rigid.

Now what material forming a ten meter wide square could support 3.6 billion tons? Some of it being pulled down by the Earth's gravity, some of it being pulled away by the counterweight?

After that you have to throw in the effects of minor fluctuations in gravity due to the moons orbit, torsional effects perhaps from the atmosphere and the movement of the elevator within the shaft, heating / cooling effects from sunlight etc. This is the same problem as the one cm wide diamond rod lifting up to the height of the Eiffel Tower that was discussed before. Except its much worse.

I mean one cm width over 200 meters height or so was a ration of 1 to 20,000. Ten meters width to 36,000,000 meters is a ration of 1 to 3,600,000.

Even if my calculations were off previously as I missed the height needed for a stationary orbit by roughly 36,000 kms (or all of it more or less!), I still think the only viable option is some sort of microfilament lifting small amounts of mass a long distance in a non rigid structure.

Even ignoring the fact that you can ignore many of those forces I just mentioned thanks to the microfilament's flexibility, there's a huge strength to weight advantage in microfilaments versus larger diameter fibres / structures. I mean torsional strength, lifting strength in a structure / fibre is largely proportional to its cross sectional area (speaking as a biologist) while weight / mass is proportion to its volume. There is a reason that insects can jump so high and lift so much in comparison to their body size.

Now I've just got to come up with a fibre that could achieve even this next to impossible task.

Cheers, Greg.

 

[Vertigo]

I can't really comment on the other calculations but you misunderstand the basic structure. The ground does not support any weight at all. The whole thing is constructed so that the centre of gravitity is always exactly in geostationary orbit. Most approaches have the elevator 'growing' out of both sides of the main station satellite, and they keep growing at the same rate so the centre of gravity is always at the centre of the station in geostationary orbit. Eventually, when the Earth-side end 'touches down' they both stop growing and all you have to do is anchor the Earth-side end in place. Not that that isn't going to be a difficult task on its own.

 

[Sapheron]

After all this I can't help but repeat my orginal view on the matter:

Easier to strap rockets to stuff.

 

[psychotick]

Hi Vertigo,

It doesn't actually matter where the centre of gravity is as far as I can see. So assume you can build this structure with a centre of gravity 36,000 kms above Earth. The stuff further away from the Earth doesn't impact too greatly, save that as far as I can tell, given it's orbit it would have a centrifugal force on it pulling it away from the Earth. The stuff below is being pulled toward it by gravity. And the piece in the middle is being pulled apart by two equal and opposite forces.

Or lets look at it another way. Ignore the centre of gravity part, and assume you build down from your asteroid, but not all the way to the ground. You stop one meter off it. Now there's no Earth supporting anything, it's all aboutthe asteroid holding it up. In short your asteroid is trying to hold up 3.6 billion tons. So what sort of material in a ten by ten meter square could hold up that sort of weight without being torn apart?

Cheers, Greg.

 

[Sapheron]

Now I'm not one of the physics folks (I prefer stones and minerals and oil and such, and not even the placing of them in orbit), but as I understand it, psychotick, there is no weight to support because the whole thing is in freefall. If you're being suspended in free fall in a powerful wind tunnel and you have a ton weight strapped to your back it doesn't matter that it could crush you because you're weightless. If you put your hand against the wall or floor, as the elevator would touch the ground, you're still weightless, the arm doesn't take any actual weight.

At least, that's how I understand it. Someone will doubtless correct me if I've misunderstood. And, of course, the moment the wind tunnel was turned off you'd be flat...

 

[Vertigo]

Yes that's exactly right Psychotick, I'm sorry it was the way you worded your original comment made me think you were talking about the ground. The material of the elevator (both halves) would all be under tension rather than compression so nothing is actually being supported, rather it is being anchored. However the critical bit is the middle as, you are quite right, that would be under huge tension and certainly we have nothing today that could handle it but maybe in the future.

The only way to avoid the anchoring problem would be to have just one single cable that would be 72,000km long (twice 36,000km) with it's centre point exactly at the geostaionary orbit. and the main station built around that. This way no actual anchoring is involved but the material that the cable is made out of needs to be immensely strong; the tension will peak at the midpoint and gradually diminish the further you go out to the ends of the cable. And, of course, that remains the biggest stopper on the production of such an elevator. On the plus side everything is under tension not compression and most materials are stronger that way around.

Folk talk about growing the main 'cable' as a single crystal, however I have always thought the problem is that you can't grow a crystal from the middle outwards, or if you can I haven't heard of it. The only way I could see would be to grow the crystal at the ends which would mean having the manufacturing 'machine' gradually climbing down the cable as it grows, which would present some interesting supply problems.

 

[Venusian Broon]

Hi Vertigo,

Or lets look at it another way. Ignore the centre of gravity part, and assume you build down from your asteroid, but not all the way to the ground. You stop one meter off it. Now there's no Earth supporting anything, it's all aboutthe asteroid holding it up. In short your asteroid is trying to hold up 3.6 billion tons. So what sort of material in a ten by ten meter square could hold up that sort of weight without being torn apart?

Cheers, Greg.

I think you've got the wrong image in you head what people are suggesting. It's not a massive block of material 10 by 10 metres all the way down from the counterweight. But, if my understanding is correct, instead a cable that tapers at ground level to a diameter of ~1cm, from a 'fat' bulge anywhere between 2-10 times the tapered point, (I think, thus 2-10cm - Am I correct??) at the point of maximum stress, at geosynchronus orbit.

This cable has to be light and strong (clearly ) and you are perfectly right to state, that even shedding huge quantities of mass to make this slender cable compared to your skyscraper, there is currently no known materials that can accomplish this on the scale that such an engineering project requires.

But, there are candidates coming through in material science that do suggest they might have the right properties for such a cable, so you never know.

 

[psychotick]

Hi Sapheron,

No, the object is in freefall, but that is not the same as weightless. In the middle the force of gravity pulling it down is balanced by the centrifugal force pushing it outwards. The parts of it lower to the ground are being pulled down more strongly by gravity, so at ground level they weigh / feel the force of gravity in exactly the same way that they would if they weren't attached to the asteroid. But this weight is precisely countered by the centrifugal force lifting the entire object up from the parts of the elevator higher up than the asteroid. So the entire object is more or less weightless, but not all the parts of it. The result is that the elevator is being pulled apart by two immense forces, gravity at the bottom, centrifugal force at the top.

Vertigo, no you're right, I was originally thinking of an elevator being erected upwards from the ground and thus seeing the object suffering immense crush pressures as it rose higher. But if instead its built downwards, the crush pressure simply becomes a pulling apart pressure, But either way I simply can't conceive of a material capable of either lifting or supporting such an incredible mass.

Venusian Broom, I'll have to reread all the posts to find the model you describe, but yes it does make more sense then a tower with a lift. In fact it sounds much closer to my microfilament cable car idea.

Cheers, Greg.

 

[Venusian Broon]

Venusian Broom, I'll have to reread all the posts to find the model you describe, but yes it does make more sense then a tower with a lift. In fact it sounds much closer to my microfilament cable car idea.

I believe it's all about trying to combat exactly the idea that your talking about, namely really restricting the mass of the cable from the earth to the counterweight and the point of maximum stress, so that the material that you use (whatever that is) can handle it.

I think I have been guilty in this thread of using the word tower, in a loose metaphorical way, when I really meant cable as described above.

There will of course probably be a lovely small tower at the Earth terminus, like a sheath over the cable.

 

[RJM Corbet]

... It doesn't actually matter where the centre of gravity is as far as I can see. So assume you can build this structure with a centre of gravity 36,000 kms above Earth ...

Uh uh. The earth is the center of gravity, if that's the right term, and the asteroid counterweight is like a weight on the end of a string, swinging in orbit around the earth in a circle.

The centrifugal pull of the asteroid's orbit keeps the 'string' taut. The problem is going to be balancing the asteroid's orbit against the earth's rotation, so the 'string' stays straight, etc.

As Vertigo & VB say, the structure on earth only has to be strong enough to withstand the centrifugal pull upon it. It doesn't support any weight. It's like a hook to which one end of the cable is attached. Nano carbon technology is the most likely direction for the material of the cable.

EDIT: and so the faster that asteroid is moving, and the heavier it is, the more tension upon the graphene cable. Crispen says 35 000km is the minimum functional distance from earth to asteroid. I don't understand why, but take his word for it ...

 

[Sapheron]

Hi Sapheron,

No

Dammit, and I thought I had it this time.

 

[Venusian Broon]

EDIT: and so the faster that asteroid is moving, and the heavier it is, the more tension upon the graphene cable. Crispen says 35 000km is the minimum functional distance from earth to asteroid. I don't understand why, but take his word for it ...

Ah the joys of orbital mechanics

Off the top of my head, its the only point where you can put a satellite in a stable geosynchronus orbit.

Essentially a stable orbit is created when the force of gravity on the satellite is balanced by the centripital force of the motion of the satellite. It means that there is a one-to-one relationship between the velocity of the satellite and the orbit radius and therefore a one-to-one relationship between the angular velocity and the orbit radius.

The only orbit for a satellite that has an identical angular velocity to the Earth is the one where the orbital radius is approximately 42,000 km, or about 35,000km above an observer on the surface of Earth (EDIT - going around the Equator, I should add, just to be covered!). Hence said satellite stays stationary in the sky relative to the Earth observer.

It means that stable orbits closer to the Earth must go faster (to generate more force to counterbalance the stronger pull of the Earth) and hence have much higher angular velocity, going around the earth in 80mins in Low Earth Orbit.

 

[psychotick]

Hi RJM,

Correct, I should have used the term centre of mass for the asteroid. And I do understand that using the build down model from the asteroid approach there is no supporting / pushing upwards from the Earth surface force.

But gravity still plays a vital role in determining the force being pulled down upon the centre of mass. At every point along that tower hanging below the centre of mass, gravity is exerting a force pulling downwards that is less than the counterbalancing force of centrifugal force. A force that the structural strength of the tower has to resist. At every point above the centre of mass if our elevator goes both ways, centrifugal force is exerting a force pulling away from the Earth that is greater than the force of gravity pulling down. A force that once again must be resisted by the structural strength of the elevator. And stuck smack bang in the middle of it all is our asteroid, being pulled apart in both directions like a Christmas cracker.

My point is that I can't imagine a substance light enough and strong enough to be built into a physical structure like an elevator tower, that could resist those astronimical forces. A microfilament might, simply because it has a far better tensile strength to weight ratio, but even that I have doubts about.

Cheers, Greg.

 

[RJM Corbet]

... My point is that I can't imagine a substance light enough and strong enough to be built into a physical structure like an elevator tower, that could resist those astronimical forces. A microfilament might, simply because it has a far better tensile strength to weight ratio, but even that I have doubts about...

http://en.wikipedia.org/wiki/Carbon_nanotubes

 

[chrispenycate]

It could actually be built using present day materials. This would not be reasonable in any way, it's a pure thought experiment, but consider a steel cable hanging straight down; I don't know, it could probably support a couple of kilometres of its own weight before breaking. So beyond that we need something that can handle more weight = a thicker steel cable. If we keep making the cable thicker as we approach the free-fall point, fast enough that the strength is going up more than the weight, we can get a stable situation, a sort of upside-down elongated pyramid. Certainly the cable is many kilometres in diameter at the top for a finger width reaching the surface, but saying the operation is impossible is much like the 'proofs' that a chemical powered rocket could never achieve orbit (because the energy in the fuel was not enough to accelerate its mass, the fallacy being that you had to accelerate all the fuel).

Not that I am suggesting for a moment that this equivalent of a multi-stage rocket is a reasonable way to go, just possible.

Oh, and please don't reduce the cable where it touches down to finger width; I need to attach two railway tracks and my accelerator coils to it, plus bring in power cables. I see about twenty metres a face about minimum. And as the taper rate is independent of the absolute size, that makes quite a thick cable when it reaches the point of greatest stress at the counterweight.

In the optimum solution (which is a mathematical model, not a practical engineering work) you could have the end of the cable detached, with a six-inch step to walk from the ground to the elevator, and it would show no tendency to rise or fall, or drift off in any direction (unless the wind blew). The force flinging the counterweight out would exactly balance the gravitational attraction of it, the tower (inwards and outwards) and the trains. To keep everything rigid we build out a fraction, but only a tiny percentage.

So you see the mass of the counterweight has very little to do with the tension anywhere; it is the mass of the tower/elevator/beanstalk that is important.

 

[Ursa major]

Would any benefit be gained by building an actual tower** beneath the elevator, thus reducing the length of the elevator slightly, but also reducing its exposure to the atmosphere (in particular the densest part that's closest to the surface of the planet)?






** - Built on the highest land on the equator (in, probably, Ecuador or Kenya).

 

[Venusian Broon]

Would any benefit be gained by building an actual tower** beneath the elevator, thus reducing the length of the elevator slightly, but also reducing its exposure to the atmosphere (in particular the densest part that's closest to the surface of the planet)?

There would definitely be a benefit of some magnitude (I think). But whether or not that makes any difference to the overall engineering problem re: earth orbit. My first guess is not.

 

[Vertigo]

Ursa the main benefit of putting it on higher ground would be to minimise the effects of weather. However to do that effectively it would probably need to be above the height of the jet stream (approximately the same height as Everest).

For the same reason the end of the cable would need to be anchored, otherwise the effect of weather (wind) would be to move the end of such a long pendulum by, I suspect, quite large distances (probably in the order of kilometres). So the higher you can place the cable end the more weather you are avoiding. I'm just not sure you could place it high enough to really make a big difference.

That is also another consideration in terms of the strength of the material used. The cable will certainly be subject to weather up to the top of the Stratoshpere (50km) but I suspect it will still be subject to significant weather through the Mesosphere (up to 85km). 85km worth of side pressure from wind, that will be acting in different directions at different heights, is going to add all sorts of additional stresses to a cable that is anchored which, as stated above, this would have to be.

An interesting thought: would there be a risk of the extra tension caused by those side stresses actually pulling the main station/asteroid out of its geostationary orbit? Would you potentially need thrusters on the station that would be used when say a big storm is passing across the cable, or maybe if the movement of the jet stream means that it is caught in that?

 

[RJM Corbet]

I wonder if we can extend this thread to 35 000km.

Getting there is half the fun

 

[Ursa major]

Sounds like it could be a long weight....