Bruger:Elentirmo/projekt/rumelevatoren del 2

Projekt Rumelevator del 2

Failure modes, safety issues and construction difficulties

As with any structure, there are a number of ways in which things could go wrong. A space elevator would present a considerable navigational hazard, both to aircraft and spacecraft. Aircraft could be dealt with by means of simple air-traffic control restrictions, but impacts by space objects (in particular, by meteoroids and micrometeorites) pose a more difficult problem.

Satellites

If nothing were done, essentially all satellites with perigees below the top of the elevator would eventually collide with the elevator cable. Twice per day, each orbital plane intersects the elevator, as the rotation of the Earth swings the cable around the equator. Usually the satellite and the cable will not line up. However, except for synchronized orbits, the elevator and satellite will eventually occupy the same place at the same time, almost certainly leading to structural failure of the space elevator and destruction of the satellite.

Most active satellites are capable of some degree of orbital maneuvering and could avoid these predictable collisions, but inactive satellites and other orbiting debris would need to be either preemptively removed from orbit by "garbage collectors" or would need to be closely watched and nudged whenever their orbit approaches the elevator. The impulses required would be small, and need be applied only very infrequently; a laser broom system may be sufficient to this task. In addition, Brad Edward's design actually allows the elevator to move out of the way, because the fixing point is at sea and mobile. Further, transverse oscillations of the cable could be controlled so as to ensure that the cable avoids satellites on known paths -- the required amplitudes are modest, relative to the cable length.

Meteoroids and micrometeorites

Meteoroids present a more difficult problem, since they would not be predictable and much less time would be available to detect and track them as they approach Earth. It is likely that a space elevator would still suffer impacts of some kind, no matter how carefully it is guarded. However, most space elevator designs call for the use of multiple parallel cables separated from each other by struts, with sufficient margin of safety that severing just one or two strands still allows the surviving strands to hold the elevator's entire weight while repairs are performed. If the strands are properly arranged, no single impact would be able to sever enough of them to overwhelm the surviving strands. Lasers from earth could be directed via fiber optic cables into meteors.

Far worse than meteoroids are micrometeorites; tiny high-speed particles found in high concentrations at certain altitudes. Avoiding micrometeorites is essentially impossible, and they will ensure that strands of the elevator are continuously being cut. Most methods designed to deal with this involve a design similar to a hoytether or to a network of strands in a cylindrical or planar arrangement with two or more helical strands. Constructing the cable as a mesh instead of a ribbon helps prevent collateral damage from each micrometeorite impact.

Failure cascade

It is not enough that other fibers be able to take over the load of a failed strand — the system must also survive the immediate, dynamical effects of fiber failure, which generates projectiles aimed at the cable itself. For example, if the cable has a working stress of 50 GPa and a Young's modulus of 1000 GPa, its strain will be 0.05 and its stored elastic energy will be 1/2 × 0.05 × 50 GPa = 1.25×10⁹ joules per cubic meter. Breaking a fiber will result in a pair of de-tensioning waves moving apart at the speed of sound in the fiber, with the fiber segments behind each wave moving at over 1,000 m/s (more than the muzzle velocity of an M16 rifle). Unless these fast-moving projectiles can be stopped safely, they will break yet other fibers, initiating a failure cascade capable of severing the cable. The challenge of preventing fiber breakage from initiating a catastrophic failure cascade seems to be unaddressed in the current (January, 2005) literature on terrestrial space elevators. Problems of this sort would be easier to solve in lower-tension applications (e.g., lunar elevators).

Corrosion

Corrosion is a major risk to any thinly built tether (which most designs call for). In the upper atmosphere, atomic oxygen steadily eats away at most materials. A tether will consequently need to either be made from a corrosion-resistant material or have a corrosion-resistant coating, adding to weight. Gold and platinum have been shown to be practically immune to atomic oxygen; several far more common materials such as aluminum are damaged very slowly and could be repaired as needed.

Another potential solution to the corrosion problem is a continuous renewal of the tether surface (which could be done from standard, though possibly slower elevators). This process would depend on the tether composition and it could be done in a nanoscale (by replacing individual fibers) or in segments.

Material defects

Any structure as large as a space elevator will have massive numbers of tiny defects in the construction material. It has been suggested,^[1]^[2] that, because large structures have more defects than small structures, that large structures are inherently weaker than small, giving an estimated carbon nanotube strength of only 24GPa down to only 1.7GPa in millimetre-scale samples, the latter equivalent to many high-strength steels, which would be vastly less than that needed to build a space elevator for a reasonable cost.

Weather

In the atmosphere, the risk factors of wind and lightning come into play. The basic mitigation is location. As long as the tether's anchor remains within two degrees of the equator, it will remain in the quiet zone between the Earth's Hadley cells, where there is relatively little violent weather. Remaining storms could be avoided by moving a floating anchor platform. The lightning risk can be minimized by using a nonconductive fiber with a water-resistant coating to help prevent a conductive buildup from forming. The wind risk can be minimized by use of a fiber with a small cross-sectional area that can rotate with the wind to reduce resistance. Ice forming on the cable also presents a potential problem. It could add significantly to the cable's weight and affect the passage of elevator cars. Also, ice falling from the cable could damage elevator cars or the cable itself. To get rid of ice special elevator cars could scrape the ice off.

One reasonably recent result is that high wind speeds can flatten the elevator cable horizontally across the surface of the Earth perhaps a hundred kilometers. Surprisingly, the stress on the cable is not significantly increased (since the elevator is tens of thousands of kilometers long the percentage increase is tiny) and no major damage is predicted.

Sabotage

Sabotage is a relatively unquantifiable problem. A space elevator might prove an attractive target for a terrorist or other politically motivated attack. Concern over sabotage may have an effect on location, adding the constraint of avoiding unstable territories to the existing requirement of an equatorial site.

Vibrational harmonics

A final risk of structural failure comes from the possibility of vibrational harmonics within the cable. Like the shorter and more familiar strings of stringed musical instruments, the cable of a space elevator has a natural resonant frequency. If the cable is excited at this frequency, for example by the travel of elevators up and down it, the vibrational energy could build up to dangerous levels and exceed the cable's tensile strength. This can be avoided by the use of suitable damping systems within the cable, and by scheduling travel up and down the cable keeping its resonant frequency in mind. It may be possible to dampen the resonant frequency against the Earth's magnetosphere.

In the event of failure

If despite all these precautions the elevator is severed anyway, the resulting scenario depends on where exactly the break occurred:

Cut near the anchor point

If the elevator is cut at its anchor point on Earth's surface, the outward force exerted by the counterweight would cause the entire elevator to rise upward into a stable orbit. This is because a space elevator must be kept in tension, with greater centrifugal force pulling outward than gravitational force pulling inward, or any additional payload added at the elevator's bottom end would pull the entire structure down.

The ultimate altitude of the severed lower end of the cable would depend on the details of the elevator's mass distribution. In theory, the loose end might be secured and fastened down again. This would be an extremely tricky operation, however, requiring careful adjustment of the cable's center of gravity to bring the cable back down to the surface again at just the right location. It may prove to be easier to build a new system in such a situation.

Cut at about 25,000 km

If the break occurred at higher altitude, up to about 25,000 km, the lower portion of the elevator would descend to Earth and drape itself along the equator east of the anchor point, while the now unbalanced upper portion would rise to a higher orbit. Some authors (such as science fiction writers David Gerrold in Jumping off the Planet, Kim Stanley Robinson in Red Mars, and Ben Bova in Mercury) have suggested that such a failure would be catastrophic, with the thousands of kilometers of falling cable creating a swath of meteoric destruction along Earth's surface. However, in most cable designs, the upper portion of any cable that fell to Earth would burn up in the atmosphere. Additionally because proposed initial cables (the only ones likely to be broken) have very low mass (roughly 1 kg per kilometer) and are flat, the bottom portion would likely settle to Earth with less force than a sheet of paper due to air resistance on the way down.

If the break occurred at the counterweight side of the elevator, the lower portion, now including the "central station" of the elevator, would entirely fall down if not prevented by an early self-destruct of the cable shortly below it. Depending on the size, however, it would burn up on re-entry anyway.

Elevator climbers

Any climbers on the falling section would also reenter Earth's atmosphere, but it is likely that the climbers will already have been designed to withstand such an event as an emergency measure. It is almost inevitable that some objects — climbers, structural members, repair crews, etc. — will accidentally fall off the elevator at some point. Their subsequent fate would depend upon their initial altitude. Except at geosynchronous altitude, an object on a space elevator is not in a stable orbit and so its trajectory will not remain parallel to it. The object will instead enter an elliptical orbit, the characteristics of which depend on where the object was on the elevator when it was released.

If the initial height of the object falling off of the elevator is less than 23,000 km, its orbit will have an apogee at the altitude where it was released from the elevator and a perigee within Earth's atmosphere — it will intersect the atmosphere within a few hours, and not complete an entire orbit. Above this critical altitude, the perigee is above the atmosphere and the object will be able to complete a full orbit to return to the altitude it started from. By then the elevator would be somewhere else, but a spacecraft could be dispatched to retrieve the object or otherwise remove it. The lower the altitude at which the object falls off, the greater the eccentricity of its orbit.

If the object falls off at the geostationary altitude itself, it will remain nearly motionless relative to the elevator just as in conventional orbital flight. At higher altitudes the object would again be in an elliptical orbit, this time with a perigee at the altitude the object was released from and an apogee somewhere higher than that. The eccentricity of the orbit would increase with the altitude from which the object is released.

Above 47,000 km, however, an object that falls off of the elevator would have a velocity greater than the local escape velocity of Earth. The object would head out into interplanetary space, and if there were any people present on board it might prove impossible to rescue them.

Van Allen Belts

The space elevator would run through the Van Allen belts. This is not a problem for most freight, but the amount of time a climber spends in this region would cause radiation poisoning to any unshielded human or other living things.^[3]^[4]

Some people speculate that passengers and other living things will continue to travel by high-speed rocket, while the space elevator hauls bulk cargo. Research into lightweight shielding and techniques for clearing out the belts is underway.

More conventional and faster atmospheric reentry techniques such as aerobraking might be employed on the way down to minimize radiation exposure. De-orbit burns use relatively little fuel and are cheap.

An obvious option would be for the elevator to carry shielding to protect passengers, though this would reduce its overall capacity, of course. Alternatively, the shielding itself could in some cases consist of useful payload, for example food, water, fuel or construction/maintenance materials, and no additional shielding costs are then incurred on the way up.

To shield passengers from the radiation in the Van Allen belt, perhaps counter-intuitively, material composed of light elements should be used, as opposed to lead shielding. In fact, high energy electrons in the Van Allen belts produce dangerous X-rays when they strike atoms of heavy elements. This is known as bremsstrahlung, or braking radiation. Materials containing great amounts of hydrogen, such as water or (lightweight) plastics such as polyethylene and lighter metals such as aluminium are better than heavier ones such as lead for preventing this secondary radiation. Such light-element shielding, if it were strong enough to protect against the Van Allen particle radiation, would also provide adequate protection against X-ray radiation coming from the sun during solar flares and coronal mass ejection events.

Economics

Hovedartikel: Space elevator economics.

With a space elevator, materials might be sent into orbit at a fraction of the current cost. Modern rocketry gives prices that are on the order of thousands of U.S. dollars per kilogram for transfer to low earth orbit, and roughly twenty thousand dollars per kilogram for transfer to geosynchronous orbit. For a space elevator, the price could be on the order of a few hundred dollars per kilogram, or possibly much less.

Space elevators have high capital cost but low operating expenses, so they make the most economic sense in a situation where it would be used over a long period of time to handle very large amounts of payload. The current launch market may not be large enough to make a compelling case for a space elevator, but a dramatic drop in the price of launching material to orbit would likely result in new types of space activities becoming economically feasible. In this regard they share similarities with other transportation infrastructure projects such as highways or railroads.

Development costs might be roughly equivalent, in modern dollars, to the cost of developing the shuttle system. A question subject to speculation is whether a space elevator would return the investment, or if it would be more beneficial to instead spend the money on developing rocketry further. If the elevator did indeed cost roughly the same as the shuttle program, recovering the development costs would take less than about a hundred thousand tons launched to low earth orbit or five thousand tons launched to geosynchronous orbit.

Political issues

One potential problem with a space elevator would be the issue of ownership and control. Such an elevator would require significant investment (estimates start at about US$5 billion for a very primitive tether), and it could take at least a decade to recoup such expenses. At present, few entities are able to spend in the space industry at that magnitude.

Assuming a multi-national governmental effort was able to produce a working space elevator, many political issues would remain to be solved. Which countries would use the elevator and how often? Who would be responsible for its defense from terrorists or enemy states? A space elevator could potentially cause rifts between states over the military applications of the elevator. Furthermore, establishment of a space elevator would require knowledge of the positions and paths of all existing satellites in Earth orbit and their removal if they cannot adequately avoid the elevator (unless the base station itself can move in order to make the elevator avoid satellites, as proposed by Edwards).

An initial elevator could be used in relatively short order to lift the materials to build more such elevators, but the owners of the first elevator might refuse to carry such materials in order to maintain their monopoly.

As space elevators (regardless of the design) are inherently fragile but militarily valuable structures, they would likely be targeted immediately in any major conflict with a state that controls one. Consequently, most militaries would elect to continue development of conventional rockets (or other similar launch technologies) to provide effective backup methods to access space.

The cost of the space elevator is not excessive compared to other projects and it is conceivable that several countries or an international consortium could pursue the space elevator. Indeed, there are companies and agencies in a number of countries that have expressed interest in the concept. Generally, projects on the scale of a space elevator need to be either joint public-private partnership ventures or government ventures, and they involve multiple partners. It is also possible that a private entity (risks notwithstanding) could provide the financing — several large investment firms have stated interest in construction of the space elevator as a private endeavor.

The political motivation for a collaborative effort comes from the potential destabilizing nature of the space elevator. The space elevator clearly has military applications, but more critically it would give a strong economic advantage for the controlling entity. Information flowing through satellites, future energy from space, planets full of real estate and associated minerals, and basic military advantage could all potentially be controlled by the entity that controls access to space through the space elevator. An international collaboration could result in multiple elevators at various locations around the globe, since subsequent elevators would be significantly cheaper, thus allowing general access to space and consequently eliminating the instabilities a single system might cause.

Arthur C. Clarke compared the space elevator project to Cyrus Field's efforts to build the first transatlantic telegraph cable, "the Apollo Project of its age".^[5]

History

Early concepts

The concept of the space elevator first appeared in 1895 when a Russian scientist Konstantin Tsiolkovsky was inspired by the Eiffel Tower in Paris to consider a tower that reached all the way into space. He imagined placing a "celestial castle" at the end of a spindle-shaped cable, with the "castle" orbiting Earth in a geosynchronous orbit (i.e. the castle would remain over the same spot on Earth's surface). The tower would be built from the ground up to an altitude of 35,790 kilometers above mean sea level (geostationary orbit). Comments from Nikola Tesla suggest that he may have also conceived such a tower. Tsiolkovsky's notes were sent behind the Iron Curtain after his death.

Tsiolkovsky's tower would be able to launch objects into orbit without a rocket. Since the elevator would attain orbital velocity as it rode up the cable, an object released at the tower's top would also have the orbital velocity necessary to remain in geosynchronous orbit.

Twentieth century

Building from the ground up, however, proved an impossible task; there was no material in existence with enough compressive strength to support its own weight under such conditions. It took until 1957 for another Russian scientist, Yuri N. Artsutanov, to conceive of a more feasible scheme for building a space tower. Artsutanov suggested using a geosynchronous satellite as the base from which to construct the tower. By using a counterweight, a cable would be lowered from geosynchronous orbit to the surface of Earth while the counterweight was extended from the satellite away from Earth, keeping the center of gravity of the cable motionless relative to Earth. Artsutanov published his idea in the Sunday supplement of Komsomolskaya Pravda in 1960. He also proposed tapering the cable thickness so that the tension in the cable was constant—this gives a thin cable at ground level, thickening up towards GEO.^[6]

Making a cable over 35,000 kilometers long is a difficult task. In 1966, four American engineers decided to determine what type of material would be required to build a space elevator, assuming it would be a straight cable with no variations in its cross section. They found that the strength required would be twice that of any existing material including graphite, quartz, and diamond.

In 1975 an American scientist, Jerome Pearson, designed^[7] a tapered cross section that would be better suited to building the elevator. The completed cable would be thickest at the geosynchronous orbit, where the tension was greatest, and would be narrowest at the tips to reduce the amount of weight per unit area of cross section that any point on the cable would have to bear. He suggested using a counterweight that would be slowly extended out to 144,000 kilometers (almost half the distance to the Moon) as the lower section of the elevator was built. Without a large counterweight, the upper portion of the cable would have to be longer than the lower due to the way gravitational and centrifugal forces change with distance from Earth. His analysis included disturbances such as the gravitation of the Moon, wind and moving payloads up and down the cable. The weight of the material needed to build the elevator would have required thousands of Space Shuttle trips, although part of the material could be transported up the elevator when a minimum strength strand reached the ground or be manufactured in space from asteroidal or lunar ore.

In 1977, Hans Moravec published an article called "A Non-Synchronous Orbital Skyhook", in which he proposed a modification of the space elevator idea into a more feasible tether propulsion system. (Journal of the Astronautical Sciences, Vol. 25, Oct.-Dec. 1977)

Arthur C. Clarke introduced the concept of a space elevator to a broader audience in his 1978 novel, The Fountains of Paradise, in which engineers construct a space elevator on top of a mountain peak in the fictional island country of Taprobane (which is actually an early name for Sri Lanka).

In Robert A. Heinlein's 1982 novel Friday the principal character makes use of the "Nairobi Beanstalk" in the course of her travels.

In 1999, Larry Niven authored the book Rainbow Mars which contained a "Hanging Tree" - an organic 'Skyhook' which was capable of interstellar travel. The book skillfully discussed several merits/demerits of such an approach to the Beanstalk - the primary demerit being that the water necessary to sustain such an enormous 'tree' would require the drying up of all of its host planet's water bodies - which is used as a plot device to explain the drying up of Mars.

21st Century

David Smitherman of NASA/Marshall's Advanced Projects Office has compiled plans for such an elevator that could turn science fiction into reality. His publication, "Space Elevators: An Advanced Earth-Space Infrastructure for the New Millennium",^[8] is based on findings from a space infrastructure conference held at the Marshall Space Flight Center in 1999.

Another American scientist, Bradley C. Edwards, suggests creating a 100,000 km long paper-thin ribbon, which would stand a greater chance of surviving impacts by meteors. The work of Edwards has expanded to cover: the deployment scenario, climber design, power delivery system, orbital debris avoidance, anchor system, surviving atomic oxygen, avoiding lightning and hurricanes by locating the anchor in the western equatorial pacific, construction costs, construction schedule, and environmental hazards. Plans are currently being made to complete engineering developments, material development and begin construction of the first elevator. Funding to date has been through a grant from NASA Institute for Advanced Concepts. Future funding is sought through NASA, the United States Department of Defense, private, and public sources. The largest holdup to Edwards' proposed design is the technological limits of the tether material. His calculations call for a fiber composed of epoxy-bonded carbon nanotubes with a minimal tensile strength of 130 GPa (including a safety factor of 2); however, tests in 2000 of individual single-walled carbon nanotubes (SWCNTs), which should be notably stronger than an epoxy-bonded rope, indicated the strongest measured as 52 GPa.^[9] Multi-walled carbon nanotubes have been measured with tensile strengths up to 63 GPa.^[10]

Space elevator proponents are planning competitions for space elevator technologies,^[11]^[12] similar to the Ansari X Prize. Elevator:2010 will organize annual competitions for climbers, ribbons and power-beaming systems. The Robolympics Space Elevator Ribbon Climbing^[13] organizes climber-robot building competitions. In March of 2005 NASA's Centennial Challenges program announced a partnership with the Spaceward Foundation (the operator of Elevator:2010), raising the total value of prizes to US$400,000.^[14]^[15]

On April 27, 2005 "the LiftPort Group of space elevator companies has announced that it will be building a carbon nanotube manufacturing plant in Millville, New Jersey, to supply various glass, plastic and metal companies with these strong materials. Although LiftPort hopes to eventually use carbon nanotubes in the construction of a 100,000 km (62,000 mile) space elevator, this move will allow it to make money in the short term and conduct research and development into new production methods."^[16] On September 9 the group announced that they had obtained permission from the Federal Aviation Administration to use airspace to conduct preliminary tests of its high altitude robotic lifters.^[17] The experiment was successful.

On February 13, 2006 the LiftPort Group announced that, earlier the same month, they had tested a mile of space elevator tether made of carbon-fibre composite strings and fibreglass tape measuring 5 centimetres wide and 1 mm (approx. 6 sheets of paper) thick, lifted with balloons.^[18]

The x-Tech Projects company has also been founded to pursue the prospect of a commercial Space Elevator.

References

Specific

^ http://xxx.lanl.gov/ftp/cond-mat/papers/0601/0601668.pdf
^ Bulk Nanocrystalline Steel
^ Kelly Young (2006-11-13). "Space elevators: "First floor, deadly radiation!"". New Scientist. {{cite news}}: Tjek datoværdier i: |date= (hjælp)
^ A.M. Jorgensena, S.E. Patamiab, and B. Gassendc (februar 2007). "Passive radiation shielding considerations for the proposed space elevator". Acta Astronautica. Elsevier Ltd. 60 (3): 189-209. doi:10.1016/j.actaastro.2006.07.014. {{cite journal}}: Cite har en ukendt tom parameter: |1= (hjælp)CS1-vedligeholdelse: Dato automatisk oversat (link) CS1-vedligeholdelse: Flere navne: authors list (link)
^ Clarke, Arthur C. (2003). "The Space Elevator: 'Thought Experiment', or Key to the Universe? (Part 2)". Hentet 2006-03-05.
^ Artsutanov, Yu (1960). "To the Cosmos by Electric Train" (PDF). Young Person's Pravda. Hentet 2006-03-05.
^ Fodnotefejl: Ugyldigt <ref>-tag; ingen tekst er angivet for referencer med navnet pearson
^ http://flightprojects.msfc.nasa.gov/fd02_elev.html - 404 error as of 2006-03-05
^ Fodnotefejl: Ugyldigt <ref>-tag; ingen tekst er angivet for referencer med navnet Yu 2000 PRL
^ Min-Feng Yu, Oleg Lourie, Mark J. Dyer, Katerina Moloni, Thomas F. Kelly, Rodney S. Ruoff (2000). "Strength and Breaking Mechanism of Multiwalled Carbon Nanotubes Under Tensile Load". Science. 287. no., pp. (5453): 637-640.{{cite journal}}: CS1-vedligeholdelse: Flere navne: authors list (link)
^ Boyle, Alan. "Space elevator contest proposed". MSNBC. Hentet 2006-03-05.
^ "The Space Elevator - Elevator:2010". Hentet 2006-03-05.
^ "Space Elevator Ribbon Climbing Robot Competition Rules". Hentet 2006-03-05.
^ "NASA Announces First Centennial Challenges' Prizes". 2005. Hentet 2006-03-05.
^ Britt, Robert Roy. "NASA Details Cash Prizes for Space Privatization". Space.com. Hentet 2006-03-05.
^ "Space Elevator Group to Manufacture Nanotubes". Universe Today. 2005. Hentet 2006-03-05.
^ "Space Elevator Gets FAA Lift". Space.com. Hentet September 19. {{cite web}}: Tjek datoværdier i: |accessdate= (hjælp); Ukendt parameter |accessyear= ignoreret (|access-date= foreslået) (hjælp)
^ Groshong, Kimm (2006-02-15). "Space-elevator tether climbs a mile high". NewScientist.com. New Scientist. Hentet 2006-03-05. {{cite news}}: Tjek datoværdier i: |date= (hjælp)

General

Edwards BC, Westling EA. The Space Elevator: A Revolutionary Earth-to-Space Transportation System. San Francisco, USA: Spageo Inc.; 2002. ISBN 0-9726045-0-2.
Space Elevators - An Advanced Earth-Space Infrastructure for the New Millennium [PDF]. A conference publication based on findings from the Advanced Space Infrastructure Workshop on Geostationary Orbiting Tether "Space Elevator" Concepts, held in 1999 at the NASA Marshall Space Flight Center, Huntsville, Alabama. Compiled by D.V. Smitherman, Jr., published August 2000.
"The Political Economy of Very Large Space Projects" HTML PDF, John Hickman, Ph. D. Journal of Evolution and Technology Vol. 4 - November 1999.
The Space Elevator NIAC report by Dr. Bradley C. Edwards
A Hoist to the Heavens By Bradley Carl Edwards
Ziemelis K. "Going up". In New Scientist 2001-05-05, no.2289, p.24-27. Republished in SpaceRef. Title page: "The great space elevator: the dream machine that will turn us all into astronauts."
The Space Elevator Comes Closer to Reality. An overview by Leonard David of space.com, published 27 March 2002.
Krishnaswamy, Sridhar. Stress Analysis — The Orbital Tower (PDF)

External links