concepts, a space tether reaches from a large mass (the counterweight) beyond geostationary orbit to the ground. This structure is held in tension between A space elevator, also referred to as a space bridge, star ladder, and orbital lift, is a proposed type of planet-to-space transportation system, often depicted in science fiction. The main component would be a cable (also called a tether) anchored to the surface and extending into space. An Earth-based space elevator would consist of a cable with one end attached to the surface near the equator a A… The construction of a space elevator would need reduction of some technical risk. Some advances in engineering, manufacturing and physical technology are required. Once a first space elevator is built, the second one and all others would have the use of the previous ones to assist in construction, making their costs considerably lower. Such follow-on space elevators would also benefit from the great reduction in technical risk achieved by the construction of the first space elevator. Prior to the work of Edwards in 2000, most concepts for constructing a space elevator had the cable manufactured in space. That was thought to be necessary for such a large and long object and for such a large counterweight. Manufacturing the cable in space would be done in principle by using an asteroid or Near-Earth object for source material. These earlier concepts for construction require a large preexisting space-faring infrastructure to maneuver an asteroid into its needed orbit around Earth. They also required the development of technologies for manufacture in space of large quantities of exacting materials. Since 2001, most work has focused on simpler methods of construction requiring much smaller space infrastructures. They conceive the launch of a long cable on a large spool, followed by deployment of it in space. The spool would be initially parked in a geostationary orbit above the planned anchor point. A long cable would b A space elevator, also referred to as a space bridge, star ladder, and orbital lift, is a proposed type of planet-to-space transportation system, often depicted in science fiction. The main component would be a cable (also called a tether) anchored to the surface and extending into space. An Earth-based space elevator would consist of a cable with one end attached to the surface near the equator and the other end attached to a counterweight in space beyond geostationary orbit (35,786 km altitude). Decades later, in 1960, Yuri Artsutanov independently developed the concept of a "Cosmic Railway", a space elevator tethered from an orbiting satellite to an anchor on the equator, aiming to provide a safer and more efficient alternative to rockets. In 1966, engineer and oceanographer John D. Isaacs and his colleagues developed the concept of the "Sky-Hook", proposing a satellite in geostationary orbit with a cable extending to Earth. === Innovations and designs === The space elevator concept was reinvented and advanced further in 1975, when Jerome Pearson began studying the idea, inspired by Arthur C. Clarke's 1969 speech before Congress. After working as an engineer for NASA and the Air Force Research Laboratory, he developed a design for an "Orbital Tower", intended to harness Earth's rotational energy to transport supplies into low Earth orbit. In his publication in Acta Astronautica, the cable would be thickest at geostationary orbital altitude, where tension is greatest, and narrowest at the tips to minimize weight. He proposed extending a counterweight to 144,000 kilometers (89,000 miles), as without a large counterweight, the upper cable would need to be longer due to the way gravitational and centrifugal forces change with distance from Earth. Since 1959, most ideas for space elevators have focused on purely tensile structures, with the weight of the system held up from above by centrifugal forces. In the tensile concepts, a space tether reaches from a large mass (the counterweight) beyond geostationary orbit to the ground. This structure is held in tension between Earth and the counterweight like an upside-down plumb bob. The cable thickness is tapered based on tension; it has its maximum at a geostationary orbit and the minimum on the ground. The concept is applicable to other planets and celestial bodies. A payload released at this point would go into a highly eccentric elliptical orbit, staying just barely clear from atmospheric reentry, with the periapsis at the same altitude as low earth orbit (LEO) and the apoapsis at the release height. With increasing release height the orbit would become less eccentric as both periapsis and apoapsis increase, becoming circular at geostationary level. When the payload has reached GEO, the horizontal speed is exactly the speed of a circular orbit at that level, so that if released, it would remain adjacent to that point on the cable. The payload can also continue climbing further up the cable beyond GEO, allowing it to obtain higher speed at jettison. The overall effect of the centrifugal force acting on the cable would cause it to constantly try to return to the energetically favorable vertical orientation, so after an object has been lifted on the cable, the counterweight would swing back toward the vertical, a Since 2001, most work has focused on simpler methods of construction requiring much smaller space infrastructures. They conceive the launch of a long cable on a large spool, followed by deployment of it in space. The spool would be initially parked in a geostationary orbit above the planned anchor point. A long cable would be dropped "downward" (toward Earth) and would be balanced by a mass being dropped "upward" (away from Earth) for the whole system to remain on the geosynchronous orbit. Earlier designs imagined the balancing mass to be another cable (with counterweight) extending upward, with the main spool remaining at the original geosynchronous orbit level.

One of the biggest perceived challenges in building megastructures, such as the space elevator, is the unavailability of materials with sufficient tensile strength. The presumed necessity of very strong materials stems from a design paradigm which requires structures to operate at a small fraction of their maximum tensile strength (usually, 50% or less). This criterion limits the probability of failure by giving structures sufficient leeway in handling stochastic components, such as variability in material strength and/or external forces. While reasonable for typical engineering structures, low working stress ratios-defined as operating stress as a fraction of ultimate tensile strength-in the case of megastructures are both too stringent and unable to adequately control the failure probability. We draw inspiration from natural biological structures, such as bones, tendons and ligaments, which are made up of smaller substructures and exhibit self-repair, and suggest a design that requires structures to operate at significantly higher stress ratios, while maintaining reliability through a continuous repair mechanism. We outline a mathematical framework for analysing the reliability of structures with components exhibiting probabilistic rupture and repair that depend on their time-in-use (age). Further, we predict time-to-failure distributions for the overall structure. We then apply this framework to the space elevator and find that a high degree of reliability is achievable using currently existing materials, provided it operates at sufficiently high working stress ratios, sustained through an autonomous repair mechanism, implemented via, e.g. robots. tendons composed of collagen fibres, bones made of osteons, etc.). So how does biological design create such stable structures? The answer is not only to maximize the strength of the materials used, but also to cheaply repair by recycling material, while operating at very high loads. Although it is a good rule of thumb in reliability Note that, (and ) at geostationary height, (and ) below and the reverse is true for an element above this height. Figure 1. Space elevator diagram. ( a ) The space elevator tether is anchored at the Equator, extends past geostationary orbit and is balanced by a counterweight. The tether is made up of independent horizontal segments stacked vertically. Each segment is made up of filaments. The number of filaments for each segment varies exponentially with height. ( b ) A tether segment experiences four forces: its weight , the outward centrifugal force , and upward/downward forces and , owing to the part of the cable above/below the element. At equilibrium, , leading to tension in the bundle. ( c ) Segment filaments are active if they carry load. Otherwise, they are inactive. Active segments can become inactive through rupture and inactive cables can become active through repair. Pearson suggested that a desirable design is to maintain a constant stress σ throughout the tether [ 10 ]. Then, for an element below geostationary orbit, we have , where A is the cross-sectional area of the cable. This results in an exponential tapering of A shown schematically in figure 1 a : A increases from a small value at the base to a large one at geostationary height and back to a small one thereafter. The taper ratio—defined as area at geostationary height divided by area at the Earth’s surface—is given by T = exp( K / L c ). Here, K is a constant that depends on Earth’s radius and geostationary height and L c = σ/ w is the characteristic length of the material, i.e. the ratio between the constant stress in the tower σ and the specific weight w . It can be seen that, to avoid prohibitively large cross-sectional areas, one should use light (small w ) materials able to sustain high stresses (large σ ). We see that with higher repair rates, not only do we eliminate trajectories ending in failure, but we also speed up the time to reach the stable regime. Figure 4. Effects of repair on filament dynamics and on bundle stability. A sample of 100 paths (grey) are shown for the number of filaments n ( t ) (right) and corresponding working stress ratio ω ( t ) : = σ( t )/σ max (left). The blue and red dashed lines show the initial working stress ratio and the maximum stress ratio at which failure occurs. Results show that with sufficient repair, the space elevator is stable when operating at near 100% of the material tensile strength. From data shown in table 1 , a space elevator made of M5 is potentially feasible. The model in this manuscript focuses primarily on the dynamics of the non-interacting sub-components (in this case, filaments) and describes how fluctuations in their number, owing to rupture and repair, translate into the reliability probability of the larger structure. Estimating the repair rates for carbon nanotubes remains an open question, contingent on the availability of data regarding their creep-rupture lifetime distribution, which has not yet been thoroughly studied to our knowledge. More research in this direction is necessary to quantify the exact requirements, but it is very encouraging to see that Kevlar, a material weaker by an order of magnitude compared with the theoretically predicted strength of carbon nanotubes, can operate reliably without much material turnover. Incidentally, the inferences drawn from our model have biological applications: while healing, tendons remain under tension owing to cells exerting active forces to stretch the collagen, similar to how repairing robots would stretch the filaments in the space elevator. This allows for a better understanding of the dynamics of biological repair, with possible applications to many different structures (e.g. bones, tendons and muscle). Furthermore, our analysis provides the necessary framework to consider more complex models in which filaments can interact, material strengths are stochastic and external noise on the cable is present.