Another Space Elevator Concept

[CraigD]

All this space elevator stuff got me to figuring, the result of which was this simple ([M]UMPS) program

S D=1440,S=2.76e9 ;density (in kg/m^3) and tensile strength (in N/m^2) of kevlar
S R=.05 ;initial radius (in m) of cable
S (M,W)=0,H0=6378,H1=42200,WF=0
F H=H0:1 S CA=R*R*$zpi,A=398600000/H/H-(H/189089),MI=CA*1000*D,F=A*MI,W=W+F,M=M+MI S:W/CA>S H=H-1,W=W-F,M=M-MI,CA=0,R=R*1.01 I CA W $J(H-H0,8),$J(H1-H,8),$J(R,16,2),$J(M,32,0)," (",$L(M\1),")",! Q:H'<H1(M>6e24)

What this does is simulate raising a cable from the ground (H=6378 km) to geostationary orbit (42200 km), increasing its radius (R) from an given initial value as needed to avoid exceeding its tensile strength (S). If the mass of the cable exceeds the mass of the earth (M>6e24 kg), it gives up.

In the real world, of course, you couldn’t build a space elevator like this – the usual approach proposes dropping equal weights of cable up, above geostat, and down, toward the ground. The end result is the same, though, so this program gives a decent approximation of half the mass of cable needed.

I think this provides some answers to some of the last couple of day’s questions. My calculations are badly in need of an independent (not me) check and corroboration, however, so anyone so inclined, please jump in!

Here’s output for a space elevator made out of high-strength steel, Kevlar, semi-theoretical giant carbon molecule tubes (“carbon nanotubes”, or “buckytubes”), and 2 fictional materials needed to get a constant-thickness cable to work: “2*Buckytube”, the same density but twice as strong as a buckytube, an “light buckytube”, the same strength as buckytube but half the density. All start with a cable capable of supporting 25 tons. I’ve just included output for interesting heights – ground level (0 km), GEO (35822), and half way (17911)

  Height            Cable Radius                            Mass
D: 7840  S: 1500000000  Steel
       0   35822          0.0016                              65 (2)
    1132   34690   96609376.8335       6154320793811586380000000 (25)
                                    W=43550661170960867800000000 (72%)
D: 1440  S: 2760000000  Kevlar
       0   35822          0.0012                               7 (1)
   17911   17911         94.5240                 106627525649432 (15)
   35822       0        258.2265                3530743734692777 (16)
                                               W=572688616807228 (2%)
D: 1440  S: 2760000000  Kevlar
       0   35822          0.0012                               7 (1)
   17911   17911         94.5240                 106627525649432 (15)
   35822       0        258.2265                3530743734692777 (16)
                                               W=572688616807228 (2%)
D: 2600  S: 65000000000  Buckytube
       0   35822        0.000247                               1 (1)
   17911   17911        0.000368                           13895 (5)
   35822       0        0.000399                           36209 (5)
                                                         W=32244 (9%)
D: 2600  S: 162500000000  2.5*buckytube
       0   35822        0.000156                               0 (1)
   17911   17911        0.000156                            3582 (4)
   35822       0        0.000156                            7165 (4)
                                                          W=9690 (14%)
D: 1300  S: 65000000000  Light buckytube
       0   35822    0.0002474135                               0 (1)
   17911   17911    0.0002474135                            4478 (4)
   35822       0    0.0002474135                            8956 (4)
                                                         W=12113 (14%)

I didn’t expect steel to be feasible, and it isn’t, requiring more than the mass of the Earth before it reached 1200 km. Ordinary Kevlar worked, but requires a mass greater than 35 million aircraft carriers!

Buckytubes seem to be the first really feasible material. A single-strand to GEO, with a counterbalancing strand above GEO, masses just a bit more than 2 Apollo spacecraft, within current launch capabilities.

Note, though, that the Buckytube-based system requires a variable cable thickness, making a “pulley” type space elevator like kayra proposes unworkable. My numeric fiddlings show 2 ways to achieve a material strong enough to have a constant cable thickness:
1) increase the strength of a buckytube by about a factor of 2.5 (a “2.5*buckytube”)
2) decrease the density of a buckytube by about a factor of 2 (a “light buckytube”).

Note also that all of these potentially feasible space-elevators have much thinner cables than we’re accustom to seeing in ordinary engineering: around .0005 meters, or about half the thickness of a typical human hair. Due to their unusual, molecular structure, buckytubes are likely to be much “poofier” than ordinary engineering material, but even if they’re 99% empty space, they’d still be less than .01 meter thick, less than the thickness of ordinary cotton clothesline!

All this leads me back to the conclusion that space elevators are a daunting engineering challenge, requiring that the strongest material currently being researched – buckytube – can be made several times stronger than expected. Actual experiments, such as 1992 and 1996’s joint US-Italian shuttle experiments show that there can be unexpected and catastrophic problems with space tethers, while
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.

If these challenges can be overcome, though, Earth’s gravity well could be made hardly a barrier:

• The energy cost of lifting payloads into space with such a system is fantastically low – ignoring friction, about 50 MJ/kg (based on a variation of the program above). At US residential electric power costs, this comes to about $0.30/Kg, for a one-person ticket to geostationary orbit cost of about $60. Of course, the investment capitol and maintenance cost of such a system would likely be many times its energy cost, but still, it’s likely to remain fantastically inexpensive.
• The total mass of a space elevator cable is likely to be fairly small – around 10,000 kg, so operations are likely to involvre using multiple cables and dropping them on-demand to the surface.
• Maintaining the system in orbit would, I expect, be a trivial challenge. Due to the small cable weight, a modest counter-weight system could be used to offset any lifted or dropped payloads while no more than doubling the energy cost of the lift.

[CraigD]

Originally Posted by Jay-qu

I stick with what I said earlier: hanging anything from a satellite is going to just pull the satellite out of orbit.. I just cant get my head around having all the weight suspended from a satellite and it not having any effect on its motion..

The usual solution to the “pulling out of orbit” problem is to “hang” a mass above (in a higher orbit) the satellite at the same time you hang a mass below it.

The net force on a satellite is
F = Fcentripetal –Fgravity
For a satellite in GEO (orbital radius about 42200 km), with a mass Ma hanging Da above and a mass Mb hangin Db below is
(1/189089646)Ma(42200+Da) –(398600)Mb(42200-Db)

One can see that, for any Ma and Da, and Mb, the equation can be solved for Db.

Since the mass of the cable connecting Ma and Mb to the satellite are not negligible, this calculation is actually harder than this, but still solvable.

[alxian]

lets just all read friday by heinlein and say that a tri axial fountain could lift a payload of several humans at a time.

where "elevator" is taken quite literally. maybe it could be good for launching micro satelite too.. it'll need all the business it can get to remain operational.

but not something like a space ship or large amount of freight.

i like this idea but its only practical for something like a lunar transfer station, where people working shift on the moon would constantly be going to and from earth, also tourism would keep it running.

what i don't get is why they don't feed it power from solar powered satelites. it couldn't be that power hungry that a few satelites attached by tethers couldn't porvide enough power, possibly in surplus enough for the fountain to supply that power to the local power grid.

just for the purposes of pushing matter into low earth orbit this would be a collosal waste of time.

[Kayra]

Originally Posted by CraigD

Note, though, that the Buckytube-based system requires a variable cable thickness, making a “pulley” type space elevator like kayra proposes unworkable. My numeric fiddlings show 2 ways to achieve a material strong enough to have a constant cable thickness:
1) increase the strength of a buckytube by about a factor of 2.5 (a “2.5*buckytube”)
2) decrease the density of a buckytube by about a factor of 2 (a “light buckytube”).

I had suspected that might be the case.
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?

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.

Main issues with this concept:
1) More complex (greater opportunity for failure)
2) Difficulty transfering cargo from one tether segment to another (an engineering issue)
3) Not able to monitor entire tether from ground
4) Not able to repair entire tether from ground.
5) Construction MUCH more daunting

CraigD, would a staged system still exceed current estimates of Buckytube tensile strength?

[CraigD]

Originally Posted by Kayra

… 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]

Originally Posted by Jay-qu

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]

Originally Posted by TheBigDog

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

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

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.