Another Space Elevator Concept

[CraigD]

… Since it is unlikely that the density of new materials will decrease while maintaining the tensile strength, that leaves 2 alternatives for my concept.

1) That a stronger material be found. (still a possibility)

2) That a method for using different thickness materials at different altitudes be found.

 

Would a system like this fit the bill for #2?

Yes, it appears.

Instead of a constantly increasing cable thickness, have the thickness increase in stages. At each cable thickness change junction, have 2 sets of pullies connected to each other. One connected to the lower tether, and one connected to the higher tether. This would allow for a series of connected loops to be used.

Plugging that design into my program, it appears to work. Replacing the rate at which it increases the cables radius from 1.01 to 1.05 or 1.25, and showing the height where each increase occurs, gives the following

     Height            Cable radius                    Mass
D: 2600  S: 65000000000  Buckytube
  1       0   35822      0.00024741                       1 (1)
  2    4306   31516      0.00025978                    2154 (4)
  3    5030   30792      0.00027277                    2553 (4)
  4    5862   29960      0.00028641                    3058 (4)
  5    6832   28990      0.00030073                    3708 (4)
  6    7977   27845      0.00031577                    4554 (4)
  7    9356   26466      0.00033156                    5678 (4)
  8   11059   24763      0.00034814                    7207 (4)
  9   13236   22586      0.00036554                    9362 (4)
 10   16180   19642      0.00038382                   12575 (5)
 11   20621   15201      0.00040301                   17919 (5)
 12   30904    4918      0.00042316                   31561 (5)
 13   35822       0      0.00042316                   38755 (5)
                                                        W=33476 (9%)

D: 2600  S: 65000000000  Buckytube
  1       0   35822      0.00024741                       1 (1)
  2    4306   31516      0.00030927                    2154 (4)
  3    7819   28003      0.00038658                    4899 (4)
  4   15327   20495      0.00048323                   14064 (5)
  5   35822       0      0.00048323                   53156 (5)
                                                        W=40923 (8%)

This design requires 12 or 4 stages. Notice that this causes a increase in the cable’s total mass – from 36209 to 38755 kg or 53156, not including the additional mass for the extra pulleys, etc, which should, however, be fairly negligible.

[TheBigDog]

Having a series of stations would also allow a higher throughput on the elevator as you could have more items in the lift process at a time. Imagine at each transition point there is a warehouse level. This would allow the lift process to be a series of lifts and let each independant elevator work at an independant if dependant rate.

 

Bill

[Pyrotex]

That wont work, the reason things end up in orbit is because they are spinning around the planet - there is no outward force, only an inwards.. Trying to haul something up would result in pulling it back down to earth IMO

 

The trick is, the cargo itself (and supporting structure) amounts to about one billionth the mass of the the elevator. The elevator wouldn't feel a thing.

 

I once rode the cable car near Albuquerque, NM, to the top of Sandia (sp?) mountain. The longest unsupported span was a mile!!!! the cable car could carry 50 people!!!! I wondered at this, and mentally began computing the mass of just the steel cables. I think there were six of them. Turns out, even fully loaded, the cable car was like a ladybug crawling along a huge tree branch.

[Pyrotex]

You lost me here Pyro. The cable is being stretched, not compressed. So the tension should be equal over the whole length....

Sorry, Bill,

but I stand by my statement. The cable is under tension, or being stretched as you say. But the tension is NOT the same over the whole length. That isn't the way tension works.

 

Pick up a piece of cooked spagetti, allowing six inches to hang under its own weight. Easy--no probelm. Now try this again allowing three feet of pasta to hang under its own weight. It breaks immediately. Why? If the tension in the lowest 6 inches is the same throughout the noodle, then why does it break at all?

[Jay-qu]

thanks craig that helps a lot :steering:

 

and pyro I see what you mean but craig said the cable itself may have a mass of 10,000kg that sounds like a lot but im sure it couldnt lift a shuttle...

[Kayra]

OK Craig, nice solution. I have another parameter to plug into your program :steering:

 

Since each segment loop is effectively one cable in regards to the total amount it can support (at least from the perspective of the loops above and below it). Could this meant a reduction in the size of the cable for each loop segment?

 

I think that the only time the up or down side cable strength matters is in regards to lifting/lowering a cargo pod on that segment. Otherwise they should be considered a single, combined cable.

 

Hmm.. this might not apply, as the part of the cable going around the pulley (a single strand) would have to bear the entire weight (on a single strand) Or?

 

Has anyone thought of a decent method to transfer cargo pods from segment to segment? That part still eludes me. Only in Geosync orbit can the cargo pod actually let go of the cable.

[CraigD]

Since each segment loop is effectively one cable in regards to the total amount it can support (at least from the perspective of the loops above and below it). Could this meant a reduction in the size of the cable for each loop segment?

Yes.

 

The strength of the cable at a particular height depends on the area of its cross-section. For simplicity, I’ve been giving that with a single radius ® variable, but the cable could actually have any shape, or be multiple cables, as long as the sum of the area of all the cross sections at a particular height is the same as a single strand with the given R.

 

Since mass per unit height also depends on cross section area, changes in the size, shape, and number of the cables doesn’t change its total mass, so, for rough calculations, these factors aren’t too important.

 

To get an accurate intuitive picture of this thing, it’s important to consider just how thin the cables are even for a single-strand design. For buckytubes, I calculated a diameter of .0005 to .0008 meters – about the thickness of spider silk. By comparison, a typical human hair is .001 meters thick. So, unlike some artists conceptions of massive, building-sized cables, the buckytube-based systems I’ve been calculating would be practically as invisible as spiderwebs.

 

Since it can be expected that such cables will be severed by micrometeorites every few days, a workable design might need to have many (hundreds) of cables to assure that the system could continuously repair itself without it’s net strength becoming too small.

I think that the only time the up or down side cable strength matters is in regards to lifting/lowering a cargo pod on that segment. Otherwise they should be considered a single, combined cable.

I agree. This will be true provided the cable(s) is not accelerated (eg: stopped, then restarted) by an amount approaching the local net acceleration (centrifugal – gravity). As net acceleration approaches zero as height approaches GEO (about 35800 km), this is a significant issue, so the strength and “spin-up” acceleration of the upper cable(s) will need to be carefully calculated, resulting in a minor increase in the total mass of the system.

Has anyone thought of a decent method to transfer cargo pods from segment to segment? That part still eludes me. Only in Geosync orbit can the cargo pod actually let go of the cable.

I’ve not given it much detailed thought. Compared to the structural and high-stress engineering of the thing, this problem seems minor. If the number of stages is kept small – a dozen or so – bringing the cargo to a stop at each stage and transferring it to the next stage cable using a conventional system (rollers and robot arms, etc.) seems practical, though some sort of more exotic “toss and catch” system might work, particularly in the microgravity above the first few stages.

 

Here’s a table showing the net force at various heights, as percentage of hight to GEO and the force of gravity at the surface:

Height %  Acceleration %
      0          100.00
      5           60.65
     10           40.52
     15           28.85
     20           21.46
     25           16.47
     30           12.94
     35           10.34
     40            8.36
     45            6.81
     50            5.57
     55            4.56
     60            3.72
     65            3.01
     70            2.40
     75            1.87
     80            1.41
     85            1.00
     90            0.63
     95            0.29
    100            0.00

[Kayra]

To get an accurate intuitive picture of this thing, it’s important to consider just how thin the cables are even for a single-strand design. For buckytubes, I calculated a diameter of .0005 to .0008 meters – about the thickness of spider silk. By comparison, a typical human hair is .001 meters thick. So, unlike some artists conceptions of massive, building-sized cables, the buckytube-based systems I’ve been calculating would be practically as invisible as spiderwebs.

 

Hmm. Since once we prove that the cable can lift itself, as well as a reasonable cargo amount, the cable can effectively be any thickness beyond the minimum you have calculated, Right?

 

Since it can be expected that such cables will be severed by micrometeorites every few days, a workable design might need to have many (hundreds) of cables to assure that the system could continuously repair itself without it’s net strength becoming too small. I agree.

 

From your earlier post

 

1992’s Small Expendable-Tether Deployer System (SEDS) experiment showed that a thin (.008 meter) tether can be expected to last about 4 days until destroyed by a micro-meteorite collision.

 

On the site, I found this reference

 

One way to solve this problem was demonstrated by the Tethered Physics and Survivability experiment, which was conducted by the Naval Research Laboratory. That experiment used the SEDS system to deploy a tether constructed as a hollow braid that had ordinary knitting yarn stuffed in the middle to puff it out. Launched on June 20, 1996, the 4-kilometer-long (2.5 miles), 2.5-millimeter-diameter (0.098 inches) tether has been orbiting in space uncut for more than five years.

 

Since we can make the cable any shape we need, then a ribbon or hollow structure might just do the trick.

More research would have to be done to determine optimal shape to avoid such issues. Ultimately, it could have just been cosmic back luck that the first tether only lasted 4 days :steering:

Time will tell

 

 

This will be true provided the cable(s) is not accelerated (e.g.: stopped, then restarted) by an amount approaching the local net acceleration (centrifugal – gravity). As net acceleration approaches zero as height approaches GEO (about 35800 km), this is a significant issue, so the strength and “spin-up” acceleration of the upper cable(s) will need to be carefully calculated, resulting in a minor increase in the total mass of the system. I’ve not given it much detailed thought. Compared to the structural and high-stress engineering of the thing, this problem seems minor. If the number of stages is kept small – a dozen or so – bringing the cargo to a stop at each stage and transferring it to the next stage cable using a conventional system (rollers and robot arms, etc.) seems practical, though some sort of more exotic “toss and catch” system might work, particularly in the microgravity above the first few stages.

 

What if we kept that speed of the cable constant all the time.

If the Cargo pod was clamped onto the tether using a series of wheels, it could actually control it's acceleration along the cable simply by applying or releasing the brakes on those wheels (At least on the way up). If carefully balanced, they could even bring themselves to a complete stop at each junction while the cable remained at full speed.

 

Craig, I think your right about the transfer method. That is a solvable engineering problem not limited by physics, but ingenuity.

[Kayra]

Here we go.

 

http://www.tethers.com/Hoytether.html

 

Space is getting closer all the time.

[TheBigDog]

The more I think about it the better I like the idea of having a series of platforms that take you into space. The platforms would be every few kilometers, with increasingly thick supercables connecting them. The lifting systems between platforms would be a swithcing stations from one cable to another. The lifting cables would all be the very thin type as they would only need to be the few kilometers high, and independant of each other. With a single lift you would need it to complete the top to bottom journy of several thousand miles between payloads. With this method you could have a payload begin the lift process every few hours instead of every few days. You could also do repairs to the lift without having to replace strands thousands of miles long or create splices. I am going to noodle on this some more.

 

Bill

[TheFaithfulStone]

Interesting thread.

 

Let me get straight what we're talking about here - there is a space station orbiting at GEO - on it are several tens of thousands of kilometers of buckyball cable about the width of a strand of hair. It only weighs about 10,000kg, so that's not outside the realm of possibility. As "elevator services" are required, the station lowers spider silk to the ground, and then a climber jumps on it and goes up to GEO. Alternatively, several sections are lowered, with pulleys in between each section to facilitate driving the climber from the station.

 

Just to play devils advocate for a minute - I'm following the orbital mechanics conversations pretty well (I think) - but I have a chemistry question... Is there a lower limit to the cost of buckytube production?

 

We've talked about having this orbiting "elevator station" that basically lowers new cable all the time, since anything less than a millimeter thick is bound to get chopped in half by something. An errant bird perhaps? How much exactly do buckytubes cost to make? If it requires an expenditure of 1000 kJ for each kilometer of buckytube fiber, your space elevator quickly becomes uneconomical, since you have to make this stuff all the time. The buckytube fiber becomes kind of like the "fuel" in the equation - the consumable mass that gets X amount of junk into orbit.

 

TFS

[CraigD]

Let me get straight what we're talking about here - there is a space station orbiting at GEO - on it are several tens of thousands of kilometers of buckyball cable about the width of a strand of hair. It only weighs about 10,000kg, …

That’s what I think we’re talking about. The mass of buckytube cable below GEO actually masses about 40,000 kg, still a reasonable mass for conventional space launching. That doesn’t include the satellite itself, or the cables and “counterweight” mass(es) above GEO that the system needs. The counterweight mass needs to be on the order of 100 times the max lift payload mass to avoid requiring an unfeasible length of cable (I ran a simple simulation of this, but haven’t posted it)

Just to play devils advocate for a minute - I'm following the orbital mechanics conversations pretty well (I think) - but I have a chemistry question... Is there a lower limit to the cost of buckytube production?

In principle, a kg of buckytube costs the same as a kg of elemental carbon, plus the energy to create the right conditions for it to assemble itself, plus the cost of maintenance and eventual replacement of the machine that makes this assembly possible. Carbon and energy are pretty cheap, but the machine we’re talking about is currently the stuff of science fiction, giving it a cost of … you can’t buy one with all the money in the world.

 

As TFS notes, it’s expected that many of the small cables will be getting severed (by micrometeorites, though, not birds – it’d have to be a fast, hard bird to sever a spider silk-thickness cable with several tons of tensile strength!) and replaced continuously. A possible solution is for the system to recycle the severed cables, regrowing buckytube from the point where the cable is severed. This allows the amount of new carbon, energy, and machine time to be minimal.

 

One challenge we haven’t discussed yet is the mechanics of handling a nearly microscopic strand of buckytube massing hundreds of kg. Such stuff would, I expect, cut through ordinary materials such as steel like a hot wire through butter. This challenge is especially troubling when you consider that we’ve been talking about having all, or a substantial fraction of, these strands moving at high speeds through pulleys! Whatever could we make the pulleys out of? Would even diamond be hard enough, and not too brittle? :confused:

[Kayra]

Interesting thread.

 

Let me get straight what we're talking about here - there is a space station orbiting at GEO - on it are several tens of thousands of kilometers of buckyball cable about the width of a strand of hair. It only weighs about 10,000kg, so that's not outside the realm of possibility. As "elevator services" are required, the station lowers spider silk to the ground, and then a climber jumps on it and goes up to GEO. Alternatively, several sections are lowered, with pulleys in between each section to facilitate driving the climber from the station.

 

Just to play devils advocate for a minute - I'm following the orbital mechanics conversations pretty well (I think) - but I have a chemistry question... Is there a lower limit to the cost of buckytube production?

 

We've talked about having this orbiting "elevator station" that basically lowers new cable all the time, since anything less than a millimeter thick is bound to get chopped in half by something. An errant bird perhaps? How much exactly do buckytubes cost to make? If it requires an expenditure of 1000 kJ for each kilometer of buckytube fiber, your space elevator quickly becomes uneconomical, since you have to make this stuff all the time. The buckytube fiber becomes kind of like the "fuel" in the equation - the consumable mass that gets X amount of junk into orbit.

 

TFS

Let's see.

 

The thickness quoted here is for a starting line, the smallest required that would allow for the tether to support itself, and some small amount of cargo. I would expect that a tether more like this: http://www.tethers.com/Hoytether.html

 

This tether design is far less likely to get consumed regularly.

 

One challenge we haven’t discussed yet is the mechanics of handling a nearly microscopic strand of buckytube massing hundreds of kg. Such stuff would, I expect, cut through ordinary materials such as steel like a hot wire through butter. This challenge is especially troubling when you consider that we’ve been talking about having all, or a substantial fraction of, these strands moving at high speeds through pulleys! Whatever could we make the pulleys out of? Would even diamond be hard enough, and not too brittle? :confused:

 

Ouch. I had not considered that.

Tons of force applied on a very small area = something that could cut faster then a laser.

 

It would seem a possible sollution to several problems (breakage, support structure, handling issues) could be resolved by making the tether a ribbon, no? Spreading the stresses across a larger cross section. If it can support a single strand of itself, supporting multiple strands should not be a big trick? Hmm.. I wonder what the increased mass would demand from the pully system though. CraigD is right, it would have to be some pretty tough stuff.

 

I think I may have a solution to another problem. That of the bottom and top of the loop (right at the tips of the pullies) acting as a single strand, instead of sharing the load across both strands. If the ribbon were looped twice (or more) around the pully, that should divide the weight across several sections of the cable, instead of a single point.

[TheFaithfulStone]

it’d have to be a fast, hard bird

 

:confused: Like the Thunderbirds!!

 

Actually, I don't really know much about buckytubes. The tensile strength is obviously really high, but what about shear strength?

 

(I point you 20lb test fishing line. That stuff'll clog up the propeller on a boat motor or catch a 20lb fish, but you can cut it with a knife, or even your teeth.)

 

Could a bird bite the stuff in half? Could a terrorist slice down the space stalk with a DR brush mower?

 

Otherwise, if a Bird flew into the wire at full speed, would it be split in half, or otherwise... cut.

 

TFS

[Kayra]

Thunderbirds.. I like that one :naughty:

 

OK, lets see just how far off the wall I can get on this. ( in regards to the pulley problem pointed out by CraigD)

 

One challenge we haven’t discussed yet is the mechanics of handling a nearly microscopic strand of buckytube massing hundreds of kg. Such stuff would, I expect, cut through ordinary materials such as steel like a hot wire through butter. This challenge is especially troubling when you consider that we’ve been talking about having all, or a substantial fraction of, these strands moving at high speeds through pulleys! Whatever could we make the pulleys out of? Would even diamond be hard enough, and not too brittle?

 

As I see the problem, the part of the tether going through the pulley would be applying a compressive force on it. While we have materials that can handle massive tensile forces, there is nothing that i can think of that could withstand that large a compressive force on such a small area. The pounds per square inch would be staggering.

 

Could a solution like this work?

What if we used the speed of this system to our advantage, and turned as much of that compressive force as possible into tensile force (I am not even certain Tensile is a word :umno: ).

 

How to do this? This might be one solution. If the pulley was not a solid structure, but rather a light, strong design that would simply help the pulley hold it's shape. The outside surface of the pulley that the tether rides on would be a 1 meter (Just an example. Engineering would determine its parameters) wide loop of the same material that the tether is made of. As the pulley is spun up to speed, the centrifugal force could be used to counter the weight of the tether.

 

This would mean that each progressively higher tether loop segment would require a progressively larger pulley to create the required centrifugal force used to counter all of the weight below it. While such a pulley would need to be large, I do not think it would need to be particularly massive.

 

I think that in order for a system like this to work we would probably need to:

1) Increase the tether width, using a wider tether at higher loop segments

2) Possibly require a system to help control precession

3) never ever ever stop the tether (ever)

 

I wonder if, at higher segments, we would need the pulley to be something like 1 KM in diameter (not that it would be particularly problematic)

 

Just how far off the wall is this idea?

[Kayra]

:naughty:

 

Would the Pulley need to get larger, or smaller? I am having trouble visualizing this aspect of it.

 

Alternately, we might be able to just add more mass to the outside edge.

[CraigD]

Could a solution like this work?

…

As the pulley is spun up to speed, the centrifugal force could be used to counter the weight of the tether.

I don’t think this can be made to work

 

Regardless of how you configure the pulleys, or how fast the cable travels, it must exert a net downward force equal to it’s mass times the local acceleration of gravity. Any upward centrifugal acceleration at the upper pulley will be exactly opposed by a downward acceleration of the lower one. Decreasing the radius of the pulley increases the centrifugal force on a particular length of cable (F=v^2/r), however, the length of cable subject to the force is reduced (L=2*Pi*r), such that radius ® is irrelevant. In short, the faster the cable moves, the greater the additional tensile stress on it. However, for the speeds that could practically be used for moving payloads, this should be negligible.

 

Fortunately, I don’t think exotic schemes like this are necessary.

One challenge we haven’t discussed yet is the mechanics of handling a nearly microscopic strand of buckytube massing hundreds of kg. Such stuff would, I expect, cut through ordinary materials such as steel like a hot wire through butter.

This statement assumes a dense, many-walled buckytube with a density over twice that of water. Buckytubes are, however, just rolled-up sheets of single atom-thick graphite. In the extreme, a buckytube can be single walled, so that, compressed laterally as by a pulley, would be effectively 2 single atom-thick sheets of graphite. Doing the math, a 40000 kg, 35922 km single-walled buckytube, flattened out, averages about 700 meters wide! The pressure on a 700-meter wide pulley would be very slight – less than ordinary car tire pressure!

 

So, I think that pulley pressures can be managed by carefully choosing the number of buckytube walls.