I initially intended to write about solar power in outer space. It makes sense to put an array of solar cells between the earth and the sun where they can receive direct sunlight unattenuated by the earth’s atmosphere, clouds, smog, dust, etc. But there are two major problems to be solved: How do we get the solar cells up into a stable orbit and how do we get the resulting power back down to the earth? If we can’t get the solar cells up there, the other problems don’t matter. If we do get the solar cells up there, but can’t get the energy back to earth, we might as well forget it.
Photo courtesy of Esthr
There is an additional potential benefit that may make putting arrays of solar cells in outer space worth the cost. An array of solar cells, appropriately positioned between the earth and the sun, can absorb some of the incoming solar energy reducing the earth’s temperature and possibly contributing to relief from the greenhouse effect. However, if we bring the energy down to the ground and use it there, we would help counter the greenhouse effect indirectly, since we would use less fossil and petroleum fuels and thus generate less carbon dioxide.
How can we get the solar cell arrays into outer space economically? Rockets work, but they are anything but economical. Unfortunately, to the best of my knowledge, anti-gravity and inertial drives do not work at all and magnetic drives are too weak. Many years ago I built an inertial drive to turn rotating unbalanced weights into a pulsating unidirectional force, but it didn’t work. The equations describing the inertial drive were based on LaGrange’s equations of motion which are based on the conservation of energy. Later a physicist friend explained to me that momentum is conserved, not energy. When I read the article about Michael Laine’s speech about “Nano bridges may precede space elevator”, I initially categorized the Space Elevator to go in the same file as the inertial drive.
On a trip to Dallas last weekend to do Christmas with part of my family, I kept thinking about the space elevator. It fascinated me. Earlier I had read the news release about Liftport’s planned space elevator and how they plan to shoot a rocket into outer space while spooling out a high strength carbon filament. They intend to build the elevator by shooting up multiple rockets like the Romans shot arrows across a river to build a bridge. They plan a “tethered satellite” with a tether or cable down to the ground keeping it from escaping into outer space. The cable will provide the space elevator function. To keep the tether from breaking the satellite must be in a geo-stationary orbit where its angular velocity exactly matches that of the point on the earth directly beneath it. On the way home I jotted down my ideas about the space elevator and when we got back searched the internet to see what I could find. I was surprised by the huge amount of information available on the space elevator, so I think it worth while to summarize it and to describe one possible approach to building a space elevator and to discuss some of the problems involved in building it.
Apologies to you mathophobes, but I need an equation to explain why I am excited about this. Let’s describe the centrifugal force, fC, on a tethered satellite as:
fC = m ω2 (ï²r + rB)
where m is the mass, ω is the constant angular velocity, ï²r is the difference between the actual radius and rB, and rB is the distance from the center of the earth to the radius where the centrifugal force on the mass of the rocket and cable just balances the force of gravity pulling towards the earth’s center. This is analogous to the parking radius, but takes into account the mass of the cable tether, so rB will be slightly larger than the radius for a geo-stationary orbit. The net lifting capability of the tethered satellite is:
fL = m ω2 ï²r
The angular velocity, ω, has to be constant, so we can’t do anything with it. We can use expensive rockets to send a large mass up into orbit to increase “m” in order to get a larger lifting force for the elevator. But, there is another variable available, ï²r, the distance between the balance point and m. As the tether grows longer ï²r increases and the lifting capability increases. Instead of spending a lot to increase m, you can get the same effect by just spooling out more cable.
Why this is important? Once you get the tether out past the balance point, the larger ï²r, the more the lifting force. Given a cable light enough and strong enough to handle this environment extended up past the balance point; all you have to do to strengthen the cable is to crank more stronger cable up into space.2
As you extend the cable, centrifugal force will act to move the tethered mass back to the original angle. As the cable to which the tethered satellite is attached is gradually let out the cable will move back, away from the direction of rotation, but will gradually tend to speed back up stabilizing at the new maximum distance from the surface of the earth.3
Once a stronger cable is in place, you can crank up a still stronger one and so on. However, as the cable extends and the mass moves further and further outwards the centrifugal force will increase more and more. Eventually, if you keep cranking out cable, centrifugal force will create so much tension in the cable that it will break. But, with an appropriate cable design we should be able to go for a long ways while staying within safe limits for the cable tension.
Some analysts have suggested that the optimum cable design is a gradually tapered one with the largest part at the geo-stationary orbit point where the tension is maximum.4 However, it will probably be much more economical to produce a cable with the same dimensions. In fabricating semiconductors, each parameter you have to tweak costs money to control and takes time to optimize. If we are going to be able to get a stable process operating to generate long segments of high strength carbon filament cable, we need to make the process as simple as possible. Varying the dimensions will complicate the cable fabrication process which is already very difficult. So it makes sense to just make one size of cable. If this cable is light enough and has enough surplus strength to support a reasonably sized mass extended several hundred kilometers beyond the balance point, it could be used to build a space elevator.
Once we get a good functioning space elevator, the resulting space station needs to have enough reserve propulsion capability to correct it’s orbit if the cable is cut. A series of links to other cable stations would be logical. However, if all of their cables were cut, they would need a way to keep from sailing off into outer space. Probably the best thing to do would be to keep the stations near the geo-synchronous orbit and if the cable is cut, cut the upper cable to their ballast masses. That way if the tether cable is cut they will not go sailing off into outer space.
Of course this is a simplistic analysis to illustrate the concept, in real life we should include the effect of the decrease in earth’s gravity as the radius increases and other second order effects such as the moon’s gravity, the oblateness of the earth, etc. My goal for this article is to explain the concept, leaving the details for future articles.
That is what amazed me, the math says it will work! Not only will the Space Elevator work, but depending on the cost, availability, and reliability of light weight high strength cable, it makes good economic sense!
The ideal location for the base of the space elevator would be a high mountain on the earth’s equator in order to start as far as possible from the earth’s center. The higher you start, the less energy you have to spend to climb out of the earth’s gravity well and the less cable you need.
The highest point on the Equator is 4,690 m, at 77° 59′ 31″ W on the south slopes of Volcan Cayambe (summit 5,790 m) in Ecuador. This is a short distance above the snow line, and is the only point on the Equator where snow lies on the ground. 5 Other possible locations include Adam’s Peak in Sri Lanka which Arthur C. Clarke used as a base for a space elevator in his 1978 novel, “The Fountains of Paradise”.6
On the other hand, Michael Laine’s company, Liftport, seems to favor a sea level launching pad according to the news release, this could solve a lot of the political problems of trying to build a the base for the space elevator within some foreign country.
According to Bradley Carl Edwards “some of these challenges would be met merely by locating the elevator’s Earth anchor in the eastern equatorial Pacific, west of the Galapagos Islands, where the weather is unusually calm and the threats from hurricanes, tornadoes, lightning, jet streams, and wind are greatly reduced. This location is also about 650 km from any current air routes or sea lanes, significantly reducing the chance of an accidental collision and making the site easier to secure against terrorists. An anchor in the Pacific obviously implies a floating platform, but such structures are already commercially available, thanks to the offshore oil industry.” 7
Next, assume that we can get the needed ultra light high strength cable, what are the risks involved in the Space Elevator? As my old supervisor used to say, “It’s the questions you don’t ask, that get you”. One potential show-stopper may be Van Allen Belt and other radiation in outer space changing the molecular properties of the cable causing possible fracture. Also, the motion of the cable may cause a phenomenon called strain hardening which can leads to stress fractures. This may be exacerbated by some of the cable crawlers they are postulating which would flex the cable a lot.
Brad Edwards ribbon cable idea with a cable composed of many parallel fibers may reduce flexing by using cable climbers with roller clamps which cause minimum damage to the cable.7 A way is needed to check for developing fractures in the cable before they become catastrophic.
Other risks include: corrosion; airplanes; other satellites; space debris; meteors; mechanical resonances such as they had in the Tacoma Narrows bridge 8; Terrorists/Sabotage; if the cable or part of it is conductive the effect of electromagnetic waves from the sun or from a nearby nuclear event must be taken into account; and finally the political Implications of deploying solar cells between the earth and the sun. This could absorb some of the incoming solar energy reducing the earth’s temperature and relieving the greenhouse effect. But, will some countries be upset or sue if we deliberately change their temperature?
So to conclude, when ultra-light, ultra-strong cable fiber becomes available in large quantity, at a low enough price, we should seriously consider building a space elevator. Before building it, we need to evaluate and minimize the various risks, and to build a robust, redundant system which will not easily fail catastrophically, or have significant vulnerabilities. Given an operational space elevator with a solar array generating plenty of power, we will leave the transmission of the power back to earth for future study.
References 1) Nano bridges may precede space elevator Michael Kanellos CNET News.com http://news.cnet.co.uk/gadgets/0,39029672,39193526,00.htm 2) http://encyclopedia.thefreedictionary.com/space%20elevator "Brad Edwards' proposal" 3) http://encyclopedia.thefreedictionary.com/space%20elevator "Launching into outer space" 4) http://encyclopedia.thefreedictionary.com/space%20elevator "Cable Taper" 5) http://en.wikipedia.org/wiki/Equator 6) http://encyclopedia.thefreedictionary.com/space%20elevator "History" 7) http://www.spectrum.ieee.org/aug05/1690 "A Hoist to the Heavens" By: Bradley Carl Edwardshttp://www.vibrationdata.com/Tacoma.htm by Tom Irvine
As a result of its design, the Tacoma Narrows Bridge experienced rolling undulations which were driven by the wind. Strong winds caused the bridge to collapse on November 7, 1940. Initially, 35 mile per hour winds excited the bridge’s transverse vibration mode, with an amplitude of 1.5 feet. At that time engineers did not fully understand the forces acting upon bridges and how they would react with the natural frequency of the bridge structure.
I’m not a physicist, but won’t the tethered satellite apply to earth an equal and opposite force to the centrifugal force? What if the satellite changes the earth’s orbit or rotation?
Tricia
Tricia,
Good comment. For the sort of space elevator I am thinking of, the mass of the space elevator and ballast will be much less than that of a flea compared with the mass of a bowling ball (the earth), i.e. the effect will be minimal.
If we ever do get a really big space elevator up like the one on the cover of Arthur C. Clarkes old novel, we would probably have to put one on the other side of the world to balance it or build a ring all the way around. However, for now, that’s a bit much.
Thanks for you comment, I didn’t think of that. That’s the value of a discussion board. Sometimes people see what you miss.
I love the things you find out on this site! keep up the good work!
Since the sun is far enough away that we can treat its rays as parallel won’t you have to have humongous solar panels to have a measurable effect on the amount of radiation reaching the earth? Something like the size of a small country?
The solar array would be large, I haven’t calculated the exact size. A number of issues will arise. Solar panels wear out. How do you replace them? But with an operational space elevator such things change from the silly to the practical. The two little robots sent to wander around Mar’s surface are still going. I expect we could come up with some sort of repair robots.
Even if the shading of the earth by the solar power array is minimal, the big benefit of lots of available solar power would be the reduction of our current need to burn fossil and petroleum fuels to get the energy we need. This would reduce the greenhouse effect and hopefully lower the earth’s temperature.
Another issue of interest is that the space elevator will be located in a fixed overhead area at a point over the earth, so the solar cells will have to have a rotational capability to keep them pointing at the sun. Or alternatively we may want to deploy them at a fixed point between the earth and the sun using the space elevator to get them to the needed altitude and rockets to propel them into the desired orbit. If we do this how do we get the energy back to the space elevator to transmit it to the ground?
And we want to be sure that the resulting orbit doesn’t impact the SE cable at some point.
Lots of details to work out, but what a fun set of things to work on.
This proposal was addressed by the late Professor Gerard O’Neill in the late 1970′s. In his book “The High Frontier” he proposed a set of solar collecting satellites that had microwave transmitters that would “beam” the converted photon flux to microwave receiving farms on the surface of the Earth. His construction efforts hinged on mining of the Moon and Mars with mass loaders shooting raw aluminum and other elements to Space Colonies for satellite assembly and deployment at L4 and L5 points.
Overlooked by this plan is the massive amount of energy required to initiate colonization of space and lunar and martian mining operations. Are we to waste our precious one-time bonanza of petroleum on such a gamble? Or would we be better off using it to build a more sustainable “public infrastructure” of communities using lower amounts of non-renewable energy? Remember that solar cells are built using machinery and mining operations powered by, you guessed it, dwindling and ever-more costly petroleum fuels. Perhaps if we had started these projects back in the 1970′s we’d be on track for a planet of 6.5 billion happy and healthy people. But we’ve blown that opportunity and “all but destroyed this once salubrious planet as a life-support system in fewer than two hundred years, mainly by making thermodynamic whoopee with fossil fuels (Kurt Vonnegut, “A Man without a Country,” p. 43)”.
At some point we have to start thinking about redesigning our lives, communities, and world (including the delusional neo-classical economic system of perpetual growth in a closed system of finite resources and waste mitigation) by initiating some demand-side solutions. Unfortunately, the longer we wait, the more vocal “Nature” will be in constraining our options in how we adapt to her reality.
Believing that science and technology will wake us from our nightmare to a rosy new day is simply denial of our situation. Understanding the predicament and going great guns after the remaining non-renewable resources of the world (as the neoCons seem to be hell-bent on doing) is a game of the last man standing where a ravaged few survive at the expense of the meek, weak, and impoverished. Only a powering-down effort at relocalization of economies, coupled with lifeboat building to save assets that transcend the post-petroleum interval (eg, seed banks, folk medicine, organic/biodynamic farming) will allow for greater prosperity (of a different sort than defined by consumerism) for subsequent generations.
I agree, however I think we have two problems, the greenhouse effect causing a gradual increase in the temperature of the earth and the pending depletion of the world’s supply of petroleum. But I don’t think we need to panic. The thing to do when you have a problem is to realistically evaluate the problem and look at the possible solutions and the cost/risk of each one. Doing nothing is one option, but in the long run the cost/risk for doing nothing about these two problems is not acceptable. We need to do something.
When evaluating solutions we need to realistically look at all of them. To attack science or technology is counter productive, we all sink or swim with our technology these days. I am alive because Alexancer Fleming discovered penicillin, etc. Some solutions sound like science fiction, but having spent more than 40 years designing electronics circuits and systems, we need to be careful what we throw out as ridiculous. I have designed equipement used on the moon and on Mars, not science fiction, reality, but considered ridiculous when I was in school until the Russians launched Sputnik.
Becaue of our American love affair with the automobile, I don’t think we will easily give them up. The average American is in love with his car (or truck if you’re a redneck). It’s a status symbol and a coming of age symbol. If gasoline becomes unavailable, we will convert to battery power or hydrogen power. See my article on new ways to generate and to use hydrogen http://www.sprol.com/?p=318 and on Alternative Energy for Nebraska, http://www.sprol.com/?p=319. Hopefully, the electricity or hydrogen to drive the cars will be provided from clean power sources, but if we don’t get enough clean sources working in time, we will build more nuclear power plants. Yes, they scare me too, I used to work on ICBM’s and even with lots of safeguardsnuclear power makes me nervous. But given the choice of no cars or electric or hydrogen powered cars with the power coming from more nuclear power plants, it’s a safe bet as to what the majority will choose.
We need to get busy developing alternative energy, before it’s too late. I think the solution as to what to do when the petroleum based power runs out is to gradually power down by providing bicycle only roads where it makes sense, building more windmills, pushing the development of hydrogen power vehicles and generators, looking more at ocean power generators, and keeping on looking for new and developing other alternative power sources, there are several. The DOE has an interesting web page where they describe what is currently going on, http://www.eia.doe.gov/fuelrenewable.html
If we do have to build more nuclear power plants, the Space Elevator could come in handy to dump the nuclear wastes into outer space. I remember one old TV show, Space 1999, where they used the far side of the moon as a dump to store nuclear waste.
Thank you for your comments.
“Overlooked by this plan is the massive amount of energy required to initiate colonization of space and lunar and martian mining operations. Are we to waste our precious one-time bonanza of petroleum on such a gamble?”
Considering that even our primitive Space Shuttle is fueled by hydrogen, I don’t see this as being an issue…the boosters are something else, but not petroleum-based. It takes seven Shuttle flights to boostrap the Elevator, after which all further lifting is done by the Elevator cars which are powered by a laser from the ground….which of course, could derive its power from solar, wind, waves, nuclear, whatever. Total energy usage by the Elevator is far less than with the rocket, since it doesn’t have to lift its own fuel.
Look at this
The Earth spins at or around 25,000 miles per hour on its axis. Your elevator would be burned off at the reentry line.
fL = m ω2 ï²r= your an idiot
And the atmosphere spins with it.