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That’s it. I am starting a web page called space elevators and pipelines. Granted the standard climber is more practical but I don’t think the pipeline is as impractical as you think. 70, 1 bar pumps spaced along the tube at suitable distances will be enough to pump hydrogen into space. Similarly 1000 pumps for air and 513 pumps for methane.
If you apply 80 bars of pressure at the base you will get 29 bars of air to over 560 km 10 bars of air to over 1200 km, 4 bars of air to 1760 km and 1.5 bars of air to 2320 km and 0.5 bars of air to 2880 km. That is a good chunk of the way with only one pump. Remember at 6000 km the gravity drops by 1/4 and these calculations were done assuming constant gravity. Moreover the column of air would be self supporting. I conjecture that 160 bars of pressure would be more then enough pressure to pump air into space. Bellow I will show the math for several pumps delivering one bar of pressure each.
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Calculation of the amount of pumps needed
As previously mentioned the additional amount of pumps needed per length is proportion to the force of gravity. We can neglect centripetal acceleration because it is to small to make much difference. I claim this can be written mathematically as:
dN/dh=(1/k)*/(P*g/rho)/ (P_o*g_o/rho_o)^2
Where:
rho is the density of the gas on the high pressure side of the pump
P is the pressure of the gas on the high pressure side of the pump
g is the force of gravity at the pump
G is the universal gravitational constant
M_E is the mass of the earth
R is the radius of the earth
r is the distance from the center of the earth
h is altitude
N is the number of pumps.
k is the number of attenuation constants between pumps. The fraction of gas remaining is given by e^(-k)
k=1 gives 0.3679, k=5 gives 0.0067, k=10 gives 4.5400e-005
k=1 seems the most practical.
From: http://www.elmhurst.edu/~chm/vchembook/ … tygas.html
http://www.ec.gc.ca/pdb/ghg/lfg_protocol_e.cfm]Methane Data
Here are some densities:
Densities of Common Elements and Compounds
(Substance Density kg/m^3)
Hydrogen gas 0.000089e3
Helium gas 0.00018e3
Air 0.00128e3
Carbon Dioxide 0.001977e3
Water 1.00e3
Methane 0.0006557e3
The calculations will be done for air. Notice that methane is lighter then air.
To find the number of pumps needed we integrate the above expression from the radius of the earth to GEO.
N=(1/k)int(P*g/rho),/(P_o*g_o/rho_o)^2, h=0…36e9)
Not that (P_o*g_o/rho_o) is the distance over which the pressure drops by 1/e.
=1000 Pa * 9.8 m/s^2/0.00128e3 kg/m^2=7.6563e+003 m for air.
In the calculation below we will use 6.92105e3 instead of 7.6563e+003 so are integral agrees exatly at the first pump wich will be at 7.6563e+003.
Which is about 7.7 km. If the pressure at the high pressure side of each side is the same the expression for N becomes
N=(1/(k*6.92105e+003))int(g/g_o, h=0…36e6)= (1/k)int(G M_E/(h+R)^2/g_o, h=0…36e6) /0.3013
= (1/k*6.92105e+003)*int(6.67e-11 * 5.98e24/h^2/9.9, h=6e6…42e6)
=(1/k)* (-6.67e-11 * 5.98e24)/(9.9*6.92105e+003)*((1/42e6)-(1/6.38e6))=1000/k
Now to get it for others we can do this trick
For hydrogen:
1000*(density of hydrogen/density of air)
= 1000*0.000089e3/0.00128e3=69.5313
For methane:
773.8850*0.0006557e3/0.00128e3=512.66
So that is 70 pumps for hydrogen, 513 pumps for methane and 1000 pumps for air. The pumps start out being spaced 7 km apart and get further apart as the altitude increases. Also note that when the pumps get further apart the tubes must get wider to keep the viscous forces the same.
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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.
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A Stat Mech. Review
http://www.teorfys.uu.se/people/minahan … xamination Statistical Mechanics
And
http://www.teorfys.uu.se/people/minahan … ]Solutions to Examination on Statistical Mechanics
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 in the midterm but in my equations it varies exponentialy
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See ,I knew it could be done. dN/dh=(1/k)*/(P*g/rho)/ (P_o*g_o/rho_o)^2 = Brilliant. You could use more or less pumps if you wanted, also. If you space them 2 bars apart then you would have 1/2 as many pumps.And to think such a line only needs to be an average of 1/4 inch in diameter. Brillaint.Pour me another beer.
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The only draw back I can see is that the walls of the tube would needs to be thicker where the atmosphere is thinner in order to keep it from collapsing and secondarily the tremendous amount of weight for the whole tube baring down on the lower end of it would be another issue due to length of it.
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Actually it is just hanging there like a pendulum.
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In which case it will have to be much thicker at the top to support the weight of the bottom of the pipe.
I still don't think that the estimate of 70 pumps for Hydrogen is accurate because the model ignores several properties of gasses that require a correction term (like the cohesive forces of gasses), which will cause the gas to not rise as high as calculated. However, it is probobly within an order of magnetude or so.
In any event, no practical pipe or collection of pumps and associated power & plumbing gear will possibly be able to compete against a multi-rail space elevator because of the sheer mass needed to move tonnes-per-day quantities of gas to be competitive, without reaching pressures that will destroy the pipe material that is.
[i]"The power of accurate observation is often called cynicism by those that do not have it." - George Bernard Shaw[/i]
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A little something to test space knowledge with.
Fact vs. Fiction: 10 Questions to Test Your Space IQ
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Well this would put a hold on the elevator, Scientists Discover Air Is Heavier Than We Thought
The new determination of argon content was motivated by numerous mass measurements which stubbornly failed to agree with the accepted formula for air density. The new results should lead to improved coherence among high precision mass measurements
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Yes, the thing you need to make a pipe to orbit work is multiple pumps. There's no way it would work with just one pump. But the big question is "Why?" Calculate how much mass of fluid is held inside the pipe, then compare that to propellant for a conventional rocket. How much throughput do you need to make this worth while? Will there ever be a market for that much gas in orbit? You certainly don't want to ship it to another planet, such as Mars, for terraforming. The shipping cost from Earth orbit to Mars for enough material to terraform would be prohibitive. It will always be much more economical to build a chemical factory on the planet you wish to terraform.
We had a discussion about terraforming on the old message board. Martyn Fogg joined us and said our discussion was interesting. He dropped out when guys started discussing a pipe to Earth orbit.
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How much throughput do you need to make this worth while?
That entirely depends on how much the system weighs. You would have to compare if for a given throughput if the system is cheaper then rockets. You would consider your interest payments on your fixed costs and your operating costs. I won’t speculate because I haven’t done the math yet. As far as the use of the gas, if you pump H2 use it as rocket fuel, if you pump methane (CH4) use the carbon to make more space elevators or space pipes and the hydrogen for rocket fuel, if you pump ammonia (NH4) use the nitrogen for fertilizer and the hydrogen for rocket fuel.
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You aren't competing against rockets, you are competing against the winch & car space elevator, which I am certain will win out with ease.
The sheer mass of the gas pipe, the pumps, the power transmission gear is so big - on top of the weight of the gas itself pressing down on each individual pumphead - makes the whole idea simply impractical.
It is a much, much better idea to build a two-rail spae elevator and send multiple climbers up and down simultainiously with bottled liquified gasses.
[i]"The power of accurate observation is often called cynicism by those that do not have it." - George Bernard Shaw[/i]
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Anyway if we are going to start calculating flows we will need to know:
http://md.chem.rug.nl/~mark/Courses/Kin … 3.html]The Viscosity of an Ideal Gas
http://ej.iop.org/links/q25/duZ70t1fthv … p685.pdf]A Paper on The Viscousity of an Ideal Gas
http://matsci.uah.edu/CourseWare/mts723 … C.pdf]More Stuff on The Viscousity of an Ideal Gas
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Except we aren't using an ideal gas, and the tube is HUGE so as to multiply error.
[i]"The power of accurate observation is often called cynicism by those that do not have it." - George Bernard Shaw[/i]
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Except we aren't using an ideal gas, and the tube is HUGE so as to multiply error.
You can use the ideal gas numbers to get some estimates and then look up the actual viscosity later in a table or a graph. I think the numbers will be close enough.
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That would be a safe assumption if we were only talking on the scale of thousands of meters, but this is 36,000,000 meters, and even small errors will yeild huge differenecs. There is no basis to assume that the figures calculated will be anywhere near accurate due to the massive scale involved.
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You aren't competing against rockets, you are competing against the winch & car space elevator, which I am certain will win out with ease.
You would of course have to compare the number against both options. I recall the lunar climber being rather slow taking weeks to reach the top. I suppose you could have multiple climbers but each climber you add is going to increase the weight. Also a laser will have to be built to target and power each climber along with all the power conversion gear. Clearly you would build the climber type elevator first because it can move more then liquids but if you want a large throughput I am not sure the climber comes out ahead. Perhaps it is possible to build a pipe that is capable of supporting both climbers and pumps. Install pumps for liquids, leave off pumps for climbers. Maybe the pumps can be even made light weight. BTW if a laser can target a climber it can also target a pump. How practical this will be will depend on how many climbers/pumps you have. If you have a lot then a wave guide may be better.
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That would be a safe assumption if we were only talking on the scale of thousands of meters, but this is 36,000,000 meters, and even small errors will yeild huge differenecs. There is no basis to assume that the figures calculated will be anywhere near accurate due to the massive scale involved.
You can do an error analysis to see much difference an error in a number makes.
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Except we aren't using an ideal gas, and the tube is HUGE so as to multiply error.
So what I am interested in the percent error not the fixed error.
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Anyway before I attempt any more calculations lets look at where the math will break down. You can model a gas as a fluid provided you are dealing with distances much greater then the mean free path. Anyone know the mean free path of air, hydrogen, methane, ammonia, H2 at standard temperature and pressure. As far as the smallest reasonable pipe I would say a diameter of 100 times the mean free path. Over those distances the flow equations will be more reasonable. The roughness of the pipe probably should be over distances of a few % the diameter of the pipe or less. Does anyone know how smooth you can make a carbon nanotube pipe?
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Error analysis doesn't do you any good without hard data to compare it to, all it will tell you is that your numbers could be way way off. The fact of the matter is, you don't know. It is reasonable enough to simply assume that the difference will be negligible over a small scale, but the gargantuan surface area and height change of a space pipeline will make otherwise inconsequential errors huge. Thats a little like saying "10kg, plus or minus 5,000,000kg."
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No, I'm pretty sure that the winch system will still slap the pipeline stupid. The mass due to the large diameter of the pipe and the mass of the pumps needed to compete with multiple simultainious tanker cars carrying liquified gasses will easily weigh much more, hands down.
Pumps cannot be made that much lighter, nor can the pipe if you want it to be made of somthing that resists hydrogen attack. Power will obviously NOT come from a laser, which is only suited to one or two climbers, but other transmission methods like SC wire or the waveguide.
Also, the efficency for the whole pump idea is going to be pretty lousy, since you trying to "throw" up the gas molecules in steps, and since not all will make it then alot of the energy will be lost to thermal effects. A payload in a tank however, the energy conversion will be much better.
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Error analysis doesn't do you any good without hard data to compare it to, all it will tell you is that your numbers could be way way off. The fact of the matter is, you don't know. It is reasonable enough to simply assume that the difference will be negligible over a small scale, but the gargantuan surface area and height change of a space pipeline will make otherwise inconsequential errors huge. Thats a little like saying "10kg, plus or minus 5,000,000kg."
What numbers do you think will lead to this kind of error? Pressure? Density? Temperature? Viscosity? Errors in this model will mean there will be some uncertainty in these numbers. It will not lead to 1 000 000 000% error. The biggest potential for air is if the flow is non Newtonian. For instance turbulence will lead to much more friction. But we haven’t even begun to figure out flow rates yet.
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Why wouldn't it result in orders of magnetude error? This scale is after all orders of magnetude bigger then anything we humans have dabbled with to date. The fact remains, you do. not. know.
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