Space Elevators

Space elevator

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A space elevator would consist of a cable anchored to the Earth's surface, reaching into space. By attaching a counterweight at the end (or by further extending the cable for the same purpose), Inertia ensures that the cable remains stretched taut, countering the gravitational pull on the lower sections, thus allowing the elevator to remain in geostationary orbit. Once beyond the gravitational midpoint, carriage would be accelerated further by the planet's rotation. Diagram not to scale.

A space elevator is a proposed megastructure designed to transport material from a celestial body's surface into space, first conceived by Konstantin Tsiolkovsky.^[1] Many different types of space elevators have been suggested. They all share the goal of replacing rocket propulsion with the traversal of a fixed structure via a mechanism not unlike an elevator in order to move material into or beyond orbit. Space elevators have also sometimes been referred to as beanstalks, space bridges, space lifts, space ladders, skyhooks or orbital towers.

The most common proposal is a tether, usually in the form of a cable or ribbon, spanning from the surface to a point beyond geosynchronous orbit. As the planet rotates, the inertia at the end of the tether counteracts gravity, and also keeps the cable taut. Vehicles can then climb the tether and get in orbit without the use of rocket propulsion. Such a structure could theoretically permit delivery of cargo and people to orbit at a fraction of the cost of launching a payload into orbit, and without the substantial environmental harm caused by some rocket fuels.^[2]

Recent proposals for a space elevator are notable in their plans to incorporate carbon nanotubes into the tether design, thus providing a link between space exploration and nanotechnology.

Contents 1 Non-tether space elevator concepts 2 Orbital tethers 3 Physics and structure 3.1 Base station 3.2 Cable 3.2.1 Cable taper 3.3 Climbers 3.4 Powering climbers 3.5 Counterweight 3.6 Angular momentum, speed and cable lean 3.7 Launching into outer space 3.8 Extraterrestrial elevators 4 Construction 4.1 Traditional way 4.2 Brad Edwards' proposal 4.3 Loop elevator design 5 Failure modes, safety issues and construction difficulties 5.1 Satellites 5.2 Meteoroids and micrometeorites 5.3 Failure cascade 5.4 Corrosion 5.5 Radiation 5.6 Material defects 5.7 Weather 5.8 Sabotage 5.9 Vibrational harmonics 5.10 In the event of failure 5.10.1 Cut near the anchor point 5.10.2 Cut up to about 25,000 km 5.10.3 Elevator climbers 5.11 Van Allen Belts 6 Economics 7 Political issues 8 History 8.1 Early concepts 8.2 Twentieth century 8.3 21st century 9 See also 10 References 10.1 Specific 10.2 General 11 External links 11.1 Organizations 11.2 Animations 11.3 Miscellaneous links 11.4 Articles/ Interviews

Non-tether space elevator concepts

As of 2004 orbital tethers are the only space elevator concept that is the subject of active research and commercial interest in space.^[3]

Nevertheless, two related non-tether concepts are: a space fountain and a very tall compressive structure - a structure that stands on its own.

The space fountain concept fires pellets, with a mass driver, up from the ground through the center of a tower. These pellets then impart their kinetic energy to the tower structure via electromagnetic drag as they travel up and again as their direction was reversed by a magnetic field at the top. Thus the structure would not be supported by the compressive strength of its materials, and could be hundreds of kilometers high. Unlike tethered space elevators (which have to be placed near the equator), a space fountain could be located at any latitude. Space fountains would require a continuous supply of power to remain aloft.

The compressive structure concept is similar to an aerial mast. While such structures might reach the agreed altitude for space (100 km), they are unlikely to reach geostationary orbit (35,786 km). Due to the difference between sub-orbital and orbital spaceflights, a means of propulsion (such as a rocket) would be necessary to achieve orbital speed. Arthur C. Clarke proposed a compressive space tower made of diamond in his novel 2061: Odyssey Three.

Orbital tethers

This concept, also called an orbital space elevator, geosynchronous orbital tether, or a beanstalk, is a subset of the skyhook concept. Construction would be a vast project: a tether would have to be built of a material that could endure tremendous stress while also being light-weight, cost-effective, and manufacturable in great quantities. Today's materials technology does not quite meet these requirements, although carbon nanotube technology shows promise. A considerable number of other novel engineering problems would also have to be solved to make a space elevator practical. Not all problems regarding feasibility have yet been addressed. Nevertheless, the LiftPort Group believes that the necessary technology might be developed as early as 2008^{[citation needed][4]} and that by developing the technology, the first space elevator could be operational by 2014.^[5][6]

Physics and structure

One concept for the space elevator has it tethered to a mobile seagoing platform.

There are a variety of tether designs. Almost every design includes a base station, a cable, climbers, and a counterweight.

Base station

The base station designs typically fall into two categories—mobile and stationary. Mobile stations are typically large oceangoing vessels,^[7] though airborne stations have been proposed as well.^{[citation needed]} Stationary platforms would generally be located in high-altitude locations, such as on top of high towers.

Mobile platforms have the advantage of being able to maneuver to avoid high winds, storms, and space debris. While stationary platforms don't have these advantages, they typically would have access to cheaper and more reliable power sources, and require a shorter cable. While the decrease in cable length may seem minimal (typically no more than a few kilometers), that can significantly reduce the minimal width of the cable at the center, and reduce the minimal length of cable reaching beyond geostationary orbit significantly.

Cable

The cable must be made of a material with a huge tensile strength/density ratio (the stress a material can be subjected to without breaking, divided by its density). A space elevator can be made relatively economically feasible if a cable with a density similar to graphite and a tensile strength of ~65–120 GPa can be mass-produced at a reasonable price.

Carbon Nanotubes would be a highly useful material for creating a space elevator

By comparison, most steel has a tensile strength of under 2 GPa, and the strongest steel resists no more than 5.5 GPa, but steel is dense. The much lighter material Kevlar has a tensile strength of 2.6–4.1 GPa, while quartz fiber^{[citation needed]} and carbon whiskers^[8] can reach upwards of 20 GPa; the tensile strength of diamond filaments would theoretically be minimally higher.

Carbon nanotubes' theoretical tensile strength has been estimated between 140 and 177 GPa (depending on plane shape),^[8] and its observed tensile strength has been variously measured from 63 to 150 GPa, close to the requirements for space elevator structures.^[8][9] Even the strongest fiber made of nanotubes is likely to have notably less strength than its components. Improving tensile strength depends on further research on purity and different types of nanotubes.

Designs call for single-walled carbon nanotubes. While multi-walled nanotubes are easier to produce and have similar tensile strengths, there is a concern that the interior tubes would not be sufficiently coupled to the outer tubes to help hold the tension. However, if the nanotubes are long enough, even weak Van der Waals forces will be sufficient to keep them from slipping, and the full strength of individual nanotubes (single or multiwalled) could be realized macroscopically by spinning them into a yarn. It has also been proposed to chemically interlink the nanotubes in some way, but it is likely that this would greatly compromise their strength. One such proposal is to take advantage of the high pressure interlinking properties of carbon nanotubes of a single variety.^[10] While this would cause the tubes to lose some tensile strength by the trading of sp² bond (graphite, nanotubes) for sp³ (diamond), it will enable them to be held together in a single fiber by more than the usual, weak Van der Waals force (VdW), and allow manufacturing of a fiber of any length.

A seagoing anchor station would incidentally act as a deep-water seaport.

The technology to spin regular VdW-bonded yarn from carbon nanotubes is just in its infancy: the first success in spinning a long yarn, as opposed to pieces of only a few centimeters, has been reported only very recently (March 2004); but the strength/weight ratio was not as good as Kevlar due to the inconsistent quality and short length of the tubes being held together by VdW.

Note that as of 2006, carbon nanotubes have an approximate price of $25/gram, and 20,000 kg - twenty million times that much - would be necessary to form even a seed elevator. This price is decreasing rapidly, and large-scale production would reduce it further, but the price of an economically viable carbon nanotube cable has not been estimated at this time.

Carbon nanotube fiber is an area of energetic worldwide research because the applications go much further than space elevators. Other suggested application areas include suspension bridges, new composite materials, lighter aircraft and rockets, armor technologies, and computer processor interconnects. This is good news for space elevator proponents because it is likely to push down the price of the cable material further.

Cable taper

Due to its enormous length a space elevator cable must be carefully designed to carry its own weight as well as the smaller weight of climbers. The required strength of the cable will vary along its length, since at various points it has to carry the weight of the cable below, or provide a centripetal force to retain the cable and counterweight above. In an ideal cable, the actual strength of the cable at any given point would be no greater than the required strength at that point (plus a safety margin). This implies a tapered design.

Using a model that takes into account the Earth's gravitational and "centrifugal" forces (and neglecting the smaller solar and lunar effects), it is possible to show^[11] that the optimal cross-sectional area of the cable as a function of height is given by:

Cable Taper Plot

Where A(r) is the cross-sectional area as a function of distance r from the Earth's center.

The constants in the equation are:

• A₀ is the cross-sectional area of the cable on the earth's surface.
• ρ is the density of the material the cable is made out of.
• s is the tensile strength of the material.
• ω is the rotational frequency of the Earth about its axis, 7.292 × 10^-5 rad·s^-1.
• r₀ is the distance between the Earth's center and the base of the cable. It is approximately the Earth's equatorial radius, 6378 km.
• g₀ is the acceleration due to gravity at the cable's base, 9.780 m·s^-2.

This equation gives a shape where the cable thickness initially increases rapidly in an exponential fashion, but slows at an altitude a few times the Earth's radius, and then gradually becomes parallel when it finally reaches maximum thickness at geostationary orbit. The cable thickness then decreases again out from geosynchronous orbit. The relative thickness at all points is determined by the strength density ratio. This is shown in the figure to the right.

Thus the taper of the cable from base to GEO (r = 42,164 km),

Using the density and tensile strength of steel, and assuming a diameter of 1 cm at ground level, yields a diameter of several hundred kilometers at geostationary orbit height, showing that steel, and indeed most materials used in present day engineering, are unsuitable for building a space elevator.

The equation shows us that there are four ways of achieving a more reasonable thickness at geostationary orbit:

• Using a lower density material. Not much scope for improvement as the range of densities of most solids that come into question is rather narrow, somewhere between 1000 kg·m^-3 and 5000 kg·m^-3.
• Using a higher strength material. This is the area where most of the research is focused. Carbon nanotubes are tens of times stronger than the strongest types of steel, hugely reducing the cable's cross-sectional area at geostationary orbit.
• Increasing the height of a tip of the base station, where the base of cable is attached. If the cable is properly tapered, however (see next point) this will not make much difference unless a tower of the order of 1000 km is built.
• Making the cable as thin as possible at its base. It still has to be thick enough to carry a payload however, so the minimum thickness at base level also depends on tensile strength. A cable made of carbon nanotubes (a type of fullerene), would typically be just a millimeter wide at the base.

Climbers

Most space elevator designs call for a climber to move autonomously along a stationary cable.

A space elevator cannot be an elevator in the typical sense (with moving cables) due to the need for the cable to be significantly wider at the center than the tips. While various designs employing moving cables have been proposed, most cable designs call for the "elevator" to climb up a stationary cable.

Climbers cover a wide range of designs. On elevator designs whose cables are planar ribbons, most propose to use pairs of rollers to hold the cable with friction. Usually, elevators are designed for climbers to move only upwards, because that is where most of the payload goes. For returning payloads, atmospheric reentry on a heat shield is a very competitive option, which also avoids the problem of docking to the elevator in space.

Climbers must be paced at optimal timings so as to minimize cable stress and oscillations and to maximize throughput. Lighter climbers can be sent up more often, with several going up at the same time. This increases throughput somewhat, but lowers the mass of each individual payload.

Powering climbers

Both power and energy are significant issues for climbers- the climbers need to gain a large amount of potential energy as quickly as possible to clear the cable for the next payload.

Chemical energy storage (batteries, fuel cells or internal combustion engines) will not work- hydrogen/Oxygen is the chemical fuel with the best energy/mass ratio, but will not lift its own weight all the way to GEO.

Nuclear energy and solar power have been proposed, but generating enough energy to reach the top of the elevator in any reasonable time without weighing too much is not feasible.^[12]

The current method of favour is laser power beaming, using megawatt powered free electron or solid state lasers in combination with adaptive mirrors approximately 10 m wide and a photovoltaic array on the climber tuned to the laser frequency for efficiency.^[7] A major obstacle for any climber design is the dissipation of the substantial amount of waste heat generated due to the less than perfect efficiency of any of the power methods.

It is often proposed that climbers be powered through the ribbon itself. Unless the cable material itself can be made superconducting at high temperature, the distances involved and low mass requirements make electrical transmission impractical. Fuel Pipelines are similarly not practical because of the enormous pressure that would build, as well as the low mass requirement. The most practical method for cable power transmission seems to be mechanical movement of the cable itself. The cable could be continuously let out from the bottom, or formed into a continuously revolving loop(s). Both methods would prohibit taper, and require stronger material than the fixed design. A pair of tapered cables could be made to oscillate up and down, with the climber switching from one to the other periodically. All of these mechanical methods have the advantage of unpowered climbers, but also have their own problems and none have been developed to nearly the same extent as the stationary design.

Counterweight

There have been several methods proposed for dealing with the counterweight need: a heavy object, such as a captured asteroid or a space station, positioned past geosynchronous orbit, or extending the cable itself well past geosynchronous orbit. The latter idea has gained more support in recent years due to the relative simplicity of the task and the fact that a payload that went to the end of the counterweight-cable would acquire considerable velocity relative to the Earth, allowing it to be launched into interplanetary space.

Additionally, Brad Edwards has proposed that initially elevators would be up-only, and that the elevator cars that are used to thicken up the cable could simply be parked at the top of the cable and act as a counterweight.

Angular momentum, speed and cable lean

As the car climbs, the elevator takes on a 1 degree lean, due to the top of the elevator traveling faster than the bottom around the Earth (Coriolis effect). This diagram is not to scale.

The horizontal speed of each part of the cable increases with altitude, proportional to distance from the center of the Earth, reaching orbital velocity at geosynchronous orbit. Therefore as a payload is lifted up a space elevator, it needs to gain not only altitude but angular momentum (horizontal speed) as well.

This angular momentum is taken from the Earth's own rotation. As the climber ascends it is initially moving slightly more slowly than the cable that it moves onto (Coriolis effect) and thus the climber "drags" on the cable, carrying the cable with it very slightly to the west (and necessarily pulling the counterweight slightly to the west, shown as an offset of the counterweight in the diagram to right, slightly changing the motion of the counterweight). At a 200 km/h climb speed this generates a 1 degree lean on the lower portion of the cable. The horizontal component of the tension in the non-vertical cable applies a sideways pull on the payload, accelerating it eastward (see diagram) and this is the source of the speed that the climber needs. Conversely, the cable pulls westward on Earth's surface, insignificantly slowing the Earth, from Newton's 3rd law.

Meanwhile, the overall effect of the centrifugal force acting on the cable causes it to constantly try to return to the energetically favourable vertical orientation, so after an object has been lifted on the cable the counterweight will swing back towards the vertical like an inverted pendulum. Provided that the Space Elevator is designed so that the center of mass always stays above geosynchronous orbit^[13] for the maximum climb speed of the climbers, the elevator cannot fall over. Lift and descent operations must be carefully planned so as to keep the pendulum-like motion of the counterweight around the tether point under control.

By the time the payload has reached GEO the angular momentum (horizontal speed) is enough that the payload is in orbit.

The opposite process would occur for payloads descending the elevator, tilting the cable eastwards and insignificantly increasing Earth's rotation speed.

Launching into outer space

The velocities that might be attained at the end of Pearson's 144,000 km cable can be determined. The tangential velocity is 10.93 kilometers per second which is more than enough to escape Earth's gravitational field and send probes as far out as Saturn. If an object were allowed to slide freely along the upper part of the tower, a velocity high enough to escape the solar system entirely would be attained. This is accomplished by trading off overall angular momentum of the tower for velocity of the launched object, in much the same way one snaps a towel or throws a lacrosse ball. After such an operation a cable would be left with less angular momentum than required to keep its geostationary position. The rotation of the Earth would then pull on the cable increasing its angular velocity, leaving the cable swinging backwards and forwards about its starting point.

For higher velocities, the cargo can be electromagnetically accelerated, or the cable could be extended, although that would require additional strength in the cable.

Extraterrestrial elevators

A space elevator could also be constructed on some of the other planets, asteroids and moons.

A Martian tether could be much shorter than one on Earth. Mars' surface gravity is 38% of Earth's, while it rotates around its axis in about the same time as Earth. Because of this, Martian areostationary orbit is much closer to the surface, and hence the elevator would be much shorter. Exotic materials might not be required to construct such an elevator. However, building a Martian elevator would be a unique challenge because the Martian moon Phobos is in a low orbit, and intersects the equator regularly (twice every orbital period of 11 h 6 min). A collision between the elevator and the 22.2 km diameter moon would have to be avoided through active steering of the elevator, or perhaps by moving the moon itself out of the area. One simpler way to resolve the problem of Phobos (1.1 degree orbital inclination) or Deimos (1.8 degree orbital inclination) interaction is to position the tether anchor perhaps five (5) degrees off the Martian equator. There would be a small payload penalty, but the tether would pass outside the orbital inclination of the two moons. Also, the tether would depart the Martian anchor at 5–10 degrees from vertical.

Conversely, a Venusian space elevator would need to be much longer. Although a tether placed at the stationary orbit of the slowly rotating Venus would intersect the Sun, one could be constructed that rotated with the fast-moving cloud decks of the planet which take only four Earth days to make a complete cycle. The cable would need to exceed 100,000 kilometers long but, counter-intuitively, would experience less stress due to the slightly smaller gravity exerted on the cable. Such an elevator could service aerostats or floating cities in the benign regions of the atmosphere.

Another Venusian design would require the anchor to be a mobile ground level platform that would circle Venus at the same rate that it rotates, 6.52 km/h. The counterweight on the other end would be hung toward the sun at all times, past the point where the Sun's and Venus's gravity cancel each other out, thereby keeping the tether balanced by the Sun's pull of gravity. This point is called a Lagrangian point, specifically L1. This is 1,000,000 km from Venus.

A lunar space elevator would need to be very long (more than twice the length of an Earth elevator) but due to the low gravity of the Moon, can be made of existing engineering materials. Alternatively, due to the lack of atmosphere on the Moon, a rotating tether could be used with its center of mass in orbit around the Moon with a counterweight (e.g. a space station) at the short end and a payload at the long end. The path of the payload would be an epicycloid around the Moon, touching down at some integer number of times per orbit. Thus, payloads are lifted off the surface of the Moon, and flung away at the high point of the orbit.

Rapidly spinning asteroids or moons could use cables to eject materials in order to move the materials to convenient points, such as Earth orbits; or conversely, to eject materials in order to send the bulk of the mass of the asteroid or moon to Earth orbit or a Lagrangian point. This was suggested by Russell Johnston in the 1980s. Freeman Dyson, a physicist and mathematician, has suggested using such smaller systems as power generators at points distant from the Sun where solar power is uneconomical. For the purpose of mass ejection, it is not necessary to rely on the asteroid or moon to be rapidly spinning. Instead of attaching the tether to the equator of a rotating body, it can be attached to a rotating hub on the surface. This was suggested in 1980 as a "Rotary Rocket" by Pearson^[14] and described very succinctly on the Island One website as a "Tapered Sling"^[15]

It may also be possible to construct space elevators at the three smaller gas giants, Saturn, Uranus and Neptune. These would all involve tapering several times greater than those of the inner solar system, and would need to be approximately 50–60 thousand kilometers long, yet are still within the limits of advanced nano-tubes.^{[citation needed]} These outer space elevators could facilitate the exchange of supplies and helium-3 between floating mining colonies in the atmospheres and local moon settlements. However, difficulties such as the equatorially orbiting lower rings and moons of these giant planets would first need to be overcome.

Construction

The construction of a space elevator would be a vast project, requiring advances in engineering, manufacture and physical technology. David Smitherman of NASA has published a paper that identifies "Five Key Technologies for Future Space Elevator Development":^[16]

1. Material for cable (e.g. carbon nanotube and nanotechnology) and tower
2. Tether deployment and control
3. Tall tower construction
4. Electromagnetic propulsion (e.g. magnetic levitation)
5. Space infrastructure and the development of space-based industry and economy

Two different ways to deploy a space elevator have been proposed.

Traditional way

One early plan involved lifting the entire mass of the elevator into geosynchronous orbit, and simultaneously lowering one cable downwards towards the Earth's surface while another cable is deployed upwards directly away from the Earth's surface.

Tidal forces (gravity and centrifugal force) would naturally pull the cables directly towards and directly away from the Earth and keep the elevator balanced around geosynchronous orbit. As the cable is deployed, coriolis forces would pull the upper portion of the cable somewhat to the West and the lower portion of the cable somewhat to the East; this effect can be controlled by varying the deployment speed.

However, this approach requires lifting hundreds or even thousands of tons on conventional rockets, an expensive proposition. Hypothetically, such a plan could make extensive use of materials available in space to reduce costs, but this would require considerable space mining and space-based processing of materials, neither of which is currently practical using existing technology.

Brad Edwards' proposal

Bradley C. Edwards, former Director of Research for the Institute for Scientific Research (ISR), based in Fairmont, West Virginia has presented a plausible scheme showing how a space elevator could be built in little more than a decade, rather than the far future.

He proposes that a single hair-like 18 metric ton (20 short ton) 'seed' cable be deployed in the traditional way, giving a very lightweight elevator with very little lifting capacity.

Then, progressively heavier cables would be pulled up from the ground along it, repeatedly strengthening it until the elevator reaches the required mass and strength. This is much the same technique used to build suspension bridges.

Although 18 tonnes for a seed cable may sound like a lot, it would actually be very lightweight — the proposed average mass is about 200 gram per kilometer. In comparison, conventional copper telephone wires running to consumer homes weigh about 4 kg/km.

Loop elevator design

This is a less well developed design, but offers some other possibilities.

If the cable provides a useful tensile strength of about 62.5 GPa or above, then it turns out that a constant width cable can reach beyond geosynchronous orbit without breaking under its own weight. The far end can then be turned around and passed back down to the Earth forming a constant width loop. The two sides of the loop are naturally kept apart by coriolis forces due to the rotation of the Earth and the cable. By exponentially increasing the thickness of the cable from the ground a very quick buildup of a new elevator may be performed (it helps that no active climbers are needed, and power is applied mechanically.) However, because the loop runs at constant speed, joining and leaving the loop may be somewhat challenging, and the strength of the loop is lower than a conventional tapered design, reducing the maximum payload that can be carried without snapping the cable.^[17]

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. However, such movements would excite transverse oscillations of the cable. While Edwards claims that these oscillations could be controlled so as to ensure that the cable avoids satellites on known paths, that claim needs careful analysis because the oscillations could well be chaotic, and thus it might not be possible to predict the effect of moving the fixing point in which case satellites could not be so avoided.

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.

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 a standard .223 caliber (5.56 mm) round fired from 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 on the nanoscale (by replacing individual fibers) or in segments.

Radiation

The effectiveness of the magnetosphere to deflect radiation emanating from the sun decreases dramatically after rising several earth radii above the surface. This ionizing radiation may cause damage to materials within both the tether and climbers.

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,^[18][19] 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 24 GPa down to only 1.7 GPa 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.

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 an unstable orbit.

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 up to 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. Simulations have shown that as the descending portion of the space elevator "wraps around" Earth the stress on the remaining length of cable increases, resulting in its upper sections breaking off and being flung away. The details of how these pieces break and the trajectories they take are highly sensitive to initial conditions.^[20]

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

Van Allen radiation 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.^[21][22] Some speculate that passengers would continue to travel by high-speed rocket, while space elevators haul 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

Main article: Space elevator economics

With a space elevator, materials might be sent into orbit at a fraction of the current cost. Conventional rocket designs give prices 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. Even optimistic rocket proposals (such as the DH-1) only claim to bring prices down to $200 per kilo. 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.^{[citation needed]}

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.^{[citation needed]}

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.

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 West Field's efforts to build the first transatlantic telegraph cable, "the Apollo Project of its age".^[23]

History

Early concepts

Konstantin Tsiolkovsky.

The concept of the space elevator appeared in 1895 when 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.^[24]

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^[11] 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.-December 1977)

Arthur C. Clarke introduced the concept of a space elevator to a broader audience in his 1979 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 was loosely based on Sri Lanka, albeit moved south to the equator.

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

In 1982 Paul Birch wrote a paper for the British Interplanetary Society discussing the possibility of building an Orbital Ring System. This system could be build with materials such as Aluminum and Kevlar.

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 an elevator. His publication, "Space Elevators: An Advanced Earth-Space Infrastructure for the New Millennium",^[25] 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 and material development, and begin construction of the first elevator. Funding to date has been through a grant from the 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.^[26] Multi-walled carbon nanotubes have been measured with tensile strengths up to 63 GPa.^[27]

In order to speed development of space elevators proponents are planning several competitions, similar to the Ansari X Prize, for relevant technologies.^[28][29] Among them are Elevator:2010 which will organize annual competitions for climbers, ribbons and power-beaming systems. The Robolympics Space Elevator Ribbon Climbing competition^[30]. As well as NASA's Centennial Challenges program which, in March 2005, announced a partnership with the Spaceward Foundation (the operator of Elevator:2010), raising the total value of prizes to US$400,000.^[31][32]

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."^[33] 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.^[34] 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' (sic) 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.^[35]

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

In 2007, Elevator:2010 will be holding the 2007 Space Elevator games which will feature US$500,000 awards for each of the two competitions, (US$1,000,000 total) as well as an additional US$4,000,000 to be awarded over the next five years for space elevator related technologies.^[36]