Carbon Nanotube Cable, or Elevator shaft ? - Eifel Tower to Geosynchronous

ERRORIST · 2004-11-22 12:44:32

I was wondering if it would float like a H2 balloon or He balloon. If it did then maybe you could get by with a carbon fiber material.Of course if you pump enough pressure to a gas it will become a liquid.

GCNRevenger · 2004-11-22 12:55:28

Actually no, if you double the pressure, it does NOT double how high it will go linearly, it will just double the amount of gas molecules that only make it part way. All you will accomplish is raising the pressure near the bottom, it won't push the gas up any further.

No signifigant number of molecules of Hydrogen travel above 3.0km/sec at 300K. Statistically speaking, some fraction of molecules can reach high enough speeds to hit GEO, and so if you double the pressure you will get twice this number, but the number that actually reach these velocities is vanishingly small. I doubt 80ATM of pressure would do the job.

The kinds of pressure you are talking about will run into another problem, that the Hydrogen will simply slip between the atoms of most materials (especially metals) and cause them to shatter from within (see Hydrogen embrittlement). Plus, the higher the pressure you go, the more readily Hydrogen will react with the carbon of the CNT material, and it will just disolve.

The reason that Venus has so much higher pressure as Earth is infact a good example why pumping more gas into the tube won't do much good. Venus's atmosphere has high pressure but not high altitudes because gasses ARE compressable and if one molecule can't escape its gravity at that temperature, then neither will two. Or three. Or uncounted quadrillions...

ERRORIST · 2004-11-22 13:06:16

All you will accomplish is raising the pressure near the bottom, it won't push the gas up any further.

If you change the pressure near the bottom then also change the pressure near the top.

GCNRevenger · 2004-11-22 13:13:30

Yes it will Errorist, but doubling or trippling or times-eighty-ing of vanishingly small is still vanishingly small. The amount of pressure at the top of the pipe is going to be far, far, far far FAR less then at the bottom.

If the pressure at ground level is 1ATM and 0.0000000001ATM at the top, and you increase the pressure to 100ATM, that really doesn't do you any good.

John Creighton · 2004-11-22 14:02:59

The reason that Venus has so much higher pressure as Earth is infact a good example why pumping more gas into the tube won't do much good. Venus's atmosphere has high pressure but not high altitudes because gasses ARE compressable and if one molecule can't escape its gravity at that temperature, then neither will two. Or three. Or uncounted quadrillions...

On earth the pressure drops 1/e bellow 7km. It would be 7km if the temperature was constant. Compare the height at which the atmosphere of venues drops by 1/e to the height at which earths does. Anyone have any data? Anyway one might not be exactly 90 times the other because I think C-O2 weighs more then N2

GCNRevenger · 2004-11-22 14:05:20

The altitudes of our atmospheres are comperable is all I'm saying, that even though the atmosphere is 100 times as thick, it isn't 100 times as high.

We aren't totally sure what the atmosphere is made of near the Venutian surface, it may be a truely horrible substance called Carbonyl Sulfide and not a brew of CO2 and H2SO4 vapor.

John Creighton · 2004-11-22 14:09:33

Yes it will Errorist, but doubling or trippling or times-eighty-ing of vanishingly small is still vanishingly small. The amount of pressure at the top of the pipe is going to be far, far, far far FAR less then at the bottom.
If the pressure at ground level is 1ATM and 0.0000000001ATM at the top, and you increase the pressure to 100ATM, that really doesn't do you any good.

It doesn’t work linearly like that. For instance say you had air filled tube at constant temperature with one atmosphere at the base. At 7km the pressure would be 1atmoshere/e at 14 km the pressure would be (1 atmoshere/e^2). Now if you double the pressure at the base the pressure at 14 km would equal (1 atmosphere/e) not (2 atmosheres/e^2)
1/e= 0.3679
2/e^2= 0.2707
The difference would be more drastic for greater distances and greater preasure changes. For instance at 90*7 km with a 90 bar change at the base.
1/e>>>>>90/e^90

John Creighton · 2004-11-22 14:20:43

The altitudes of our atmospheres are comperable is all I'm saying, that even though the atmosphere is 100 times as thick, it isn't 100 times as high.

If you keep the temperature of the base the same and increase the pressure by 100 times at the base then the height at which the pressure decreases by the same fraction say 1/e will be at a point 100 times higher. For the derivation of the math see:

http://physicsx.pr.erau.edu/Courses/Cou … f]Pressure Variation With Altitude

P=P_oe^(-h/a) where a=P_o/(g*rho_o)=8.55 Km for air.

If this were an RC circuit, 'a' would be called the time constant. We will call it the decay constant. 'a' is such that when h is equal to 'a', the pressure drops by one over e. You can see that if double the pressure at the base P_o you double a and hence the height the pressure drops by one over e. If you refuse to believe the math well there is not much I can do about it.

GCNRevenger · 2004-11-22 14:27:38

I think that your mathematical model is a little over-simplified, as it doesn't take into account molecular weight/kenetic velocity at all. I see no reason whatsoever that my kenetic reasoning is incorrect, that there will NOT be a signifigant height change with pressure over the huge distance, as the kenetics is what is actually happening, not the idealized contiguous blob.

Your math may be correct, it just that the math is only an aproximation of reality, one where the errors and assumptions increase as the scale does.

For instance, there is indeed real gas fractionation at an altitude, and at very high altitudes the atmosphere is increasingly made of lighter and lighter and lighter gasses. The Earth infact has a "halo" of extremely diffuse and low pressure light weight gasses... Your model does not take these kinds of things into account, because it was never intended to be used on this scale.

Edit: Even say that your math is pretty close, even if it isn't perfect, the column you are putting the gas in is thirty six thousand kilometers tall, and will still be vanishingly small even at elevated pressures, wouldn't it? There is no air at this altitude on Venus, so why should there be in GEO around Earth at that pressure?

ERRORIST · 2004-11-22 14:40:08

That is beacuse we are pumping the gas from our lower atmosphere through the pipe and actually bypassing the gasses in the upper atmosphere you mention.Remember where the openings are near sea level.

Yes it will Errorist, but doubling or trippling or times-eighty-ing of vanishingly small is still vanishingly small. The amount of pressure at the top of the pipe is going to be far, far, far far FAR less then at the bottom.

If the pressure at ground level is 1ATM and 0.0000000001ATM at the top, and you increase the pressure to 100ATM, that really doesn't do you any good.

It sounds more like a ratio John. If by pumping more in the bottom causes more to flow over the top then a flow is occuring.

GCNRevenger · 2004-11-22 14:44:03

It doesn't make a bit of difference Errorist, the gasses outside the tube don't blow away because of Earth's gravity. The gasses inside the tube won't rise to the top because of Earth's gravity. Earth's gravity is a constant, and it will affect the gasses in the tube just as readily as those outside.

There will, in theory, be a flow. A small flow. A VERY small flow. So small, that it is useless. Don't you dare and blow off the concept of "vanishingly small" Errorist, you MUST address the quantity of flow, and not dance and sing praises for your pipe if a few grams a year reach the top.

Edit: John, lets say that your math is pretty close, even if it isn't perfect, the column you are putting the gas in is thirty six thousand kilometers tall, and will still be vanishingly small even at elevated pressures, wouldn't it? There is no air at this altitude on Venus, so why should there be in GEO around Earth at that pressure?

John Creighton · 2004-11-22 14:57:07

I think that your mathematical model is a little over-simplified, as it doesn't take into account molecular weight/kenetic velocity at all. I see no reason whatsoever that my kenetic reasoning is incorrect, that there will NOT be a signifigant height change with pressure over the huge distance, as the kenetics is what is actually happening, not the idealized contiguous blob.

The best I can find on the web is:
http://www.teorfys.uu.se/people/minahan … xamination Statistical Mechanics
And
http://www.teorfys.uu.se/people/minahan … ]Solutions to Examination on Statistical Mechanics
Anyway what you are missing in your model is heat flow. The flow of heat from the bottom of the tube to the top of the tube gives the particles at the top of the tube more energy. So increasing the pressure does make a difference. It just so happens that there is not much atmosphere past 7 km and we need to go 6000 km before gravity drops by ¼ and 36 000 km to reach GSO. So we need a lot of pressure. As far as other gasses go there is no reason we can’t keep the tube with only one gas in it and at a uniform temperature.

P.S. you can derive the same equations using statistical mechanics. The reason the midterm gives a different answer is the volume is constrained. Thus preasure varies linearly and not exponentialy

GCNRevenger · 2004-11-22 15:08:38

Most statistical mechanics also use some "simplifying" aproximations. To calculate how high a gas would actually go, you are getting out of the "plumbing math" and into paticle physics. Of course you can derive the same equations from the statistics, if you use the same assumptions... The thing is, reality just doesn't behave according to the simplified back-of-envelope equations.

I am not missing the heat flow, because the heat flow doesn't affect the molecules' kenetic velocity any more then simply heating it up on the ground does. You cannot heat the gas to a high enough temperature before it will simply obliterate the pipeline.

I stand by my assertion that you cannot raise the pressure high enough to get the gas to the top in bulk without reaching conditions that will make the pipeline impossible.

ERRORIST · 2004-11-22 15:09:24

Thus preasure varies linearly and not exponentialy

Same thing with photon collisions within such a tube?

GCNRevenger · 2004-11-22 15:13:55

No it doesn't Errorist. If you double the pressure, you do not double the height at that pressure.

Don't even get started about some laser pump thing.

John Creighton · 2004-11-22 15:24:18

I am not missing the heat flow, because the heat flow doesn't affect the molecules' kenetic velocity any more then simply heating it up on the ground does. You cannot heat the gas to a high enough temperature before it will simply obliterate the pipeline.
I stand by my assertion that you cannot raise the pressure high enough to get the gas to the top in bulk without reaching conditions that will make the pipeline impossible.

Your assertion may be right but the math is not wrong. The only simplify assumption made is the gas is monotonic. Meaning that all energy is distributed over translational states and not vibration modes. All the rest a good mathematical approximations (e.g. starlings approximation). I don’t think these approximations would make a significant difference to the exponential law. The gas at the base does not have enough energy to reach escape velocity. However if by chance this molecule travels up the tube it can run into other molecules where by collisions increase the energy of this molecule traveling up and decrease the energy of the others. The reason the molecules at the top have a higher energy is due to heat flow. So say the column of gas that extended into space was compressed to say 7km and allowed to cool to room temperature. When the piston is initially removed the temperature will drop and the molecules will not have enough energy to reach space. However as heat flows in the tube some of the molecules will eventually get enough energy to reach space.

P.S. Why do you assume your intuition is better then formulas derived by statistical mechanics?

John Creighton · 2004-11-22 15:25:46

No it doesn't Errorist. If you double the pressure, you do not double the height at that pressure.
Don't even get started about some laser pump thing.

Oh of course the continous laser pump all the way up the tube.

GCNRevenger · 2004-11-22 15:31:40

If the mathematical model does not take into account the higher kenetic velocities of gasses of different molecular mass, and doesn't take into account the attractive forces between gas molecules, then it is not accurate.

Now, it might be pretty good, and I think it is probobly not too far from the truth over limited distances, but the height difference is so large that I worry that the things the model doesn't account for will ruin its usefulness in any quantitative sense.

I am not disputing that some molecules will reach the top, through sheer random chance some molecules will reach escape velocity by multiple impacts roughly along the same direction... BUT, take into account probabilities of this happening, even with the lightest gasses, and you will see that essentially none of the gas molecules ever will reach these speeds in the needed direction and the flow will be negligible.

John Creighton · 2004-11-22 15:41:41

I am not disputing that some molecules will reach the top, through sheer random chance some molecules will reach escape velocity by multiple impacts roughly along the same direction... BUT, take into account probabilities of this happening, even with the lightest gasses, and you will see that essentially none of the gas molecules ever will reach these speeds in the needed direction and the flow will be negligible.

This is where your thinking is wrong. You are right at the base a very few percentage of the molecules have the energy to reach escape velocity. However the higher up you go the greater the percentage of molecules have the energy to reach escape velocity provide the temperature is the same. If the temperature is not the same there will be a heat flow until the temperature is the same. Now the molecules at the base may not have the kinetic energy to reach escape velocity but say they have the kinetic energy to reach half way at which point a good percentage of the molecules may have the kinetic energy to reach escape velocity. Upon colliding with these molecules there is a much greater chance this particle which started at the base will have the kinetic energy to reach escape velocity. If there are extra attractive or compressive forces between molecules you can account for this using a generalized compressibility model. Numerically you could show the results are the same as you get with statistical mechanics. However a derivation could be rather difficult if not impossible.

GCNRevenger · 2004-11-22 15:47:54

No it is not John, I am assuming that the system is not energy limited at all, and that you can impart as much thermal energy to the gas at any altitude as you want. The limitation is temperature, that if you get the gas too hot... boom. The fact of the matter is, that the probability of these extremely fortunate collsions occuring is so small as to be ignored for safe conditions.

ERRORIST · 2004-11-22 15:52:21

So use an after cooler before admitting the gas to the tube like modern day air compressors use.This will keep the gas cold.

GCNRevenger · 2004-11-22 16:23:21

If you cool the gas, then it will slow down, and it will not reach the top.

ERRORIST · 2004-11-22 17:28:37

So pump more of it to make up the difference.

GCNRevenger · 2004-11-22 18:26:41

Again, you ignore the compressability of gasses. If you pump more gas up, then all you get is high pressure, not proportionally taller height.

ERRORIST · 2004-11-22 18:30:49

Yes you do.

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#26 2004-11-22 12:44:32

Re: Carbon Nanotube Cable, or Elevator shaft ? - Eifel Tower to Geosynchronous

#27 2004-11-22 12:55:28

Re: Carbon Nanotube Cable, or Elevator shaft ? - Eifel Tower to Geosynchronous

#28 2004-11-22 13:06:16

Re: Carbon Nanotube Cable, or Elevator shaft ? - Eifel Tower to Geosynchronous

#29 2004-11-22 13:13:30

Re: Carbon Nanotube Cable, or Elevator shaft ? - Eifel Tower to Geosynchronous

#30 2004-11-22 14:02:59

Re: Carbon Nanotube Cable, or Elevator shaft ? - Eifel Tower to Geosynchronous

#31 2004-11-22 14:05:20

Re: Carbon Nanotube Cable, or Elevator shaft ? - Eifel Tower to Geosynchronous

#32 2004-11-22 14:09:33

Re: Carbon Nanotube Cable, or Elevator shaft ? - Eifel Tower to Geosynchronous

#33 2004-11-22 14:20:43

Re: Carbon Nanotube Cable, or Elevator shaft ? - Eifel Tower to Geosynchronous

#34 2004-11-22 14:27:38

Re: Carbon Nanotube Cable, or Elevator shaft ? - Eifel Tower to Geosynchronous

#35 2004-11-22 14:40:08

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#36 2004-11-22 14:44:03

Re: Carbon Nanotube Cable, or Elevator shaft ? - Eifel Tower to Geosynchronous

#37 2004-11-22 14:57:07

Re: Carbon Nanotube Cable, or Elevator shaft ? - Eifel Tower to Geosynchronous

#38 2004-11-22 15:08:38

Re: Carbon Nanotube Cable, or Elevator shaft ? - Eifel Tower to Geosynchronous

#39 2004-11-22 15:09:24

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#40 2004-11-22 15:13:55

Re: Carbon Nanotube Cable, or Elevator shaft ? - Eifel Tower to Geosynchronous

#41 2004-11-22 15:24:18

Re: Carbon Nanotube Cable, or Elevator shaft ? - Eifel Tower to Geosynchronous

#42 2004-11-22 15:25:46

Re: Carbon Nanotube Cable, or Elevator shaft ? - Eifel Tower to Geosynchronous

#43 2004-11-22 15:31:40

Re: Carbon Nanotube Cable, or Elevator shaft ? - Eifel Tower to Geosynchronous

#44 2004-11-22 15:41:41

Re: Carbon Nanotube Cable, or Elevator shaft ? - Eifel Tower to Geosynchronous

#45 2004-11-22 15:47:54

Re: Carbon Nanotube Cable, or Elevator shaft ? - Eifel Tower to Geosynchronous

#46 2004-11-22 15:52:21

Re: Carbon Nanotube Cable, or Elevator shaft ? - Eifel Tower to Geosynchronous

#47 2004-11-22 16:23:21

Re: Carbon Nanotube Cable, or Elevator shaft ? - Eifel Tower to Geosynchronous

#48 2004-11-22 17:28:37

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#49 2004-11-22 18:26:41

Re: Carbon Nanotube Cable, or Elevator shaft ? - Eifel Tower to Geosynchronous

#50 2004-11-22 18:30:49

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