# Bruger:Elentirmo/projekt/rumelevatoren del 1

Spring til navigation Spring til søgning

Projekt Rumelevator del 1

Fil:Principskitse for rumelevator.png
En Rumelevator ville bestå af et kabel fastgjort til jordens overfalde og strækkende sig ud i rummet. Ved at fastgøre en modvægt i den yderste ende(eller ved at gøre kablet endnu længere for samme effekt) sikrer centrifugalkraften at kablet forbliver udstrakt. Ved lave kablet sådan at centrifulgalkraften er større end tyngdekraften kan det holdes i geostationært kredsløb. Højere oppe end det geostationære kredsløb ville løfterobotter på kablet blive accelereret opad af planetens rotation hvilket betyder at en rumelevator kunne "slynge" last væk fra jorden og dermed spare raketbrændstof. Diagrammet er ikke skalatro

A space elevator is a proposed structure designed to transport material from a planet's surface into space. 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 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 the centripetal force of gravity and keeps the cable taut. Vehicles can then climb the tether and escape the planet's gravity without the use of rocket propulsion. Such a structure could theoretically permit delivery of cargo and people to orbit with transportation costs of a fraction of the traditional methods of launching a payload into orbit.

## Non-tether space elevator concepts

At this time orbital tethers are the only space elevator concept that is the subject of active research and commercial interest in space. However, there are two related concepts worth mentioning: a space fountain and a very tall compressive structure (i.e. a structure that stands on its own).

A space fountain would use pellets fired up from the ground by a mass driver, the pellets traveling through the center of a tower. These pellets would impart their kinetic energy to the tower structure via electromagnetic drag as they traveled 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.

Compressive structures would be similar to those used for aerial masts. While these 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, additional rockets or other means of propulsion would be necessary to achieve orbital speed. Arthur C. Clarke proposed a compressive space tower made of diamond in his novel 2061: Odyssey Three, a second sequel to his famous 2001: A Space Odyssey.

## 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, some believe that the necessary technology might be developed as early as 2008[1] and the first space elevator could be operational by 2018.[2][3]

## 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, though airborne stations have been proposed as well. Stationary platforms are generally 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 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 an extremely high 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.

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 can reach upwards of 20 GPa; the tensile strength of diamond filaments would theoretically be minimally higher.

Carbon nanotubes (a material that was first fabricated in the 1990s) appear to have a theoretical tensile strength and density that is well above the desired minimum for space elevator structures. The technology to manufacture bulk quantities[4] of this material and fabricate them into a cable is in early stages of development. While theoretically carbon nanotubes can have tensile strengths beyond 120 GPa, in practice the highest tensile strength ever observed in a single-walled tube is 52 GPa, and such tubes averaged breaking between 30 and 50 GPa.[5] 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.

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

Most designs call for single-walled carbon nanotubes. While multi-walled nanotubes may attain higher tensile strengths, they have disproportionately higher mass and are consequently poor choices for building the cable. One potential material possibility is to take advantage of the high pressure interlinking properties of carbon nanotubes of a single variety.[6] 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.

The technology to spin regular VdW-bonded yarn from carbon nanotubes is just in its infancy: the first success to spin 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 suitable carbon nanotube cable is anyone's guess at this time.

A possible complication not mentioned in most of the literature is the potential 'pretzel-effect' of a carbon nanotube ribbon which would, without wind mitigation, ultimately twist into a pretzel shape in the areas of the ribbon exposed to the atmosphere. The added tensile stress from these forces could break the ribbon and it admits of no simple solution. If the constant minimum load tension in the ribbon is sufficient (some have suggested 20 tons) such twisting may be mitigated by this tension alone. A cylindrical, cable shape eliminates this concern entirely as the twisting need only be mitigated at the end points.

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, computer processor interconnects, and so on. This is good for space elevators 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[7] that the cross-sectional area of the cable as a function of height is given by:

${\displaystyle A(r)=A_{0}\ \exp \left[{\frac {\rho }{s}}\left[{\begin{matrix}{\frac {1}{2}}\end{matrix}}\omega ^{2}(r_{0}^{2}-r^{2})+g_{0}r_{0}(1-{\frac {r_{0}}{r}})\right]\right]}$

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

The constants in the equation are:

• ${\displaystyle A_{0}}$ is the cross-sectional area of the cable on the earth's surface.
• ${\displaystyle \rho }$ is the density of the material the cable is made out of.
• ${\displaystyle s}$ is the tensile strength of the material.
• ${\displaystyle \omega }$ is the rotational frequency of the earth about its axis, 7.292 × 10-5 rad·s-1.
• ${\displaystyle r_{0}}$ is the distance between the earth's center and the base of the cable. It is approximately the earth's equatorial radius, 6378 km.
• ${\displaystyle g_{0}}$ 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.

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

${\displaystyle {\frac {A(r_{\mathrm {GEO} })}{A_{0}}}=\exp \left[{\frac {\rho }{s}}\times 4.832\times 10^{7}\,\mathrm {{m^{2}}\!\!\cdot \!{s^{-2}}} \right]}$

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. The exponential relationship means a small increase in base height results in a large decrease in thickness at geostationary level. Towers of up to 100 km high have been proposed. Not only would a tower of such height reduce the cable mass, it would also avoid exposure of the cable to atmospheric processes.
• 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 designs employing smaller, segmented moving cables along the length of the main cable 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, some have proposed to use pairs of rollers to hold the cable with friction. Other climber designs involve moving arms containing pads of hooks, rollers with retracting hooks, magnetic levitation (unlikely due to the bulky track required on the cable), and numerous other possibilities.

Power is a significant obstacle for climbers. Energy and power storage densities, barring significant advances in compact nuclear power, do not yet provide the desired rate of climb performance. While the technology is current, no batteries of an adequate size have yet been constructed. Current Direct Energy Conversion radioisotopic batteries can deliver approximately 35 watts per kilogram continuous (based on Sr-90 fuel), allowing for a cargo to battery mass ratio of approximately 1 and an upward travel rate, making generous efficiency assumptions, of approximately 35 miles per hour. These devices do not require recharging. Some other potential solutions have involved laser or microwave power beaming, and solar power.

The primary power methods (laser and microwave power beaming) have significant problems with both efficiency and heat dissipation on both sides, although with optimistic numbers for future technologies, they are feasible.

Climbers must be paced at optimal timings so as to minimize cable stress and oscillations and to maximize throughput. The weakest point of the cable is near its planetary connection; new climbers can typically be launched so long as there are not multiple climbers in this area at once. An only-up elevator can handle a higher throughput, but has the disadvantage of not allowing energy recapture through regenerative down-climbers. Additionally, an up-only elevator would require some other method to return people to Earth. Finally, only-up climbers that don't return to earth must be disposable; if used, they should be modular so that their components can be used for other purposes in space. In any case, smaller climbers have the advantage over larger climbers of giving better options for how to pace trips up the cable, but may impose technological limitations.

### Counterweight

There have been two dominant 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.

### Angular momentum, speed and cable lean

Som robotten kravler opad vil elevatoren tilde med 1 grad på grund af at toppen af elevotoren bevæger sig hurtigere end bunden rundt om jorden(corioliseffekten). Dette diagram er ikke skalatro

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 (if the relative mass of the elevator and cable have certain values) 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[8] 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

We can determine the velocities that might be attained at the end of Pearson's 144,000 km cable. 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.

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.

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. 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 and physical technology. NASA has identified "Five Key Technologies for Future Space Elevator Development":

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 industry and economy

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

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. This would be very expensive.

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 0.2 kilogram per kilometer. Conventional copper telephone wires running to consumer homes weigh about 4 kg/km.

### Other designs

These are far less well developed, and will be mentioned here only in passing.

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.[9]

Other structures such as mechanically-linked multiple looped designs hanging off of a central exponential tether might also be practical, and would seem to avoid the laser power beaming; this design has higher capacity than a single loop, but still requires perhaps twice as much tether material.

## Referencer

1. ^ "Space Elevator Concept". LiftPort Group. Hentet 2006-03-05.
2. ^ David, Leonard (2002). "The Space Elevator Comes Closer to Reality". Ukendt parameter |accessdtate= ignoreret (hjælp)
3. ^ "The Space Elevator". Institute for Scientific Research, Inc. Hentet 2006-03-05.
4. ^ Cascio, Jamais (2005). "Ribbons, Sheets and the Nanofuture". Hentet 2006-03-05.
5. ^ Min-Feng Yu, Bradley S. Files, Sivaram Arepalli, and Rodney S. Ruoff (2000). "Tensile Loading of Ropes of Single Wall Carbon Nanotubes and their Mechanical Properties". Phys. Rev. Lett. 84: 5552-5555.
6. ^ T. Yildirim, O. Gülseren, Ç. Kılıç, S. Ciraci (2000). "Pressure-induced interlinking of carbon nanotubes". Phys. Rev. B. 62: 12648-12651.
7. ^ J. Pearson (1975). "The orbital tower: a spacecraft launcher using the Earth's rotational energy". Acta Astronautica. 2: 785-799. Ekstern henvisning i |title= (hjælp)
8. ^ [1]
9. ^ Gassend, Blaise. "Exponential Tethers for Accelerated Space Elevator Deployment?" (PDF). Hentet 2006-03-05.