The design of the cable entails numerous considerations many of which we cover in detail in other sections. In this section we will try to cover all the relevant components of the design and the influences that shape the design. We will begin with a background on the status of carbon nanotube progress and then address the specifics or our proposed design.
In 1991 the first carbon nanotubes were made[Iijima, 1991]. These structures have promise of being the strongest material yet discovered. This strength combined with the low density of the material makes it critically important when considering the design of a space elevator.
The tensile strength of carbon nanotubes has been theorized and simulated to be 130 GPaB&D compared to steel at <5 GPa and Kevlar at 3.6 GPa. The density of the carbon nanotubes (1300 kg/m3) is also lower than either steel (7900 kg/m3) or Kevlar (1440 kg/m3). The critical importance of these properties is seen in that the taper ratio of the cable is extremely dependent on the strength to weight ratio of the material used. (In our discussions the taper ratio refers to the cross-sectional area of the cable at geosynchronous compared to the cross-sectional area of the cable at Earth. A taper in the cable is required to provide the necessary support strength [Pearson, 1975]) For example, based on Pearson's work and operating at the breaking point, the taper ratio required for steel would be 1.7x1033, for Kevlar the ratio would be approximately 2.6x108, and for carbon nanotubes the ratio is 1.5. Since the mass of the cable, to first order, is proportional to the taper ratio, carbon nanotubes dramatically improve the feasibility of producing the cable for a space elevator. In all of our discussions we have implemented a safety factor of two over the theoretical 130 GPa value. This means that at all points the cable will have twice the strength needed to support the cable below it and the suspended mass of the climber.
Carbon nanotube research is a very active area with many hundreds of papers appearing in technical journals each year. The progress in understanding the properties of carbon nanotubes and their production is encouraging. Two papers that appeared recently illustrate some of this progress.
The first paper appeared in Applied Physics Letters in April [Choi, 2000]. In this paper parallel, straight, clean nanotubes were grown on a nickel substrate. This in itself is not new, many researchers have now grown nanotubes by the same technique up to two millimeters long [Ren, 1998] and others have grown, with a different technique, roughly aligned nanotube ropes up to 3 cm long [Cheng, 1998]. However, Choi went a step further and characterized the growth. They clearly show an understanding of the process and demonstrate the capability to grow highquality, densely-packed, nanotubes. They discuss the dependence of the nanotube size (multi- or single-walled) and growth rate on the initial surface preparation.
The second paper that is of interest appeared in Science in January [Yu, 2000a] with a follow-up of additional measurements appearing in Physical Review Letters in June [Yu, 2000b]. In these papers, Yu presents some of the first measured tensile strengths of nanotubes. Yu and colleagues appear to have done a thorough and well thought out experiment and got impressive results. Tensile strengths of 11 to 63 GPa were measured for individual nanotubes compared to Yu's references of theoretical tensile strengths of 300 GPa. (We used 130 GPa, Yakobson and Smalley, 1997, in all of our calculations.) The high measured tensile strength in one of the first such experiments is encouraging.
In our pursuit of understanding all aspects of the space elevator system we have initiated a collaboration with one of the leading nanotube researchers. The collaboration is to entail growth of long, single-walled carbon nanotubes for implementation in a space elevator cable and examining scenarios to increase the production rate of carbon nanotubes. To date we have received singlewalled carbon nanotube ropes over 3 cm long (figures 2.1 and 2.2) for examination and testing. The carbon nanotube ropes we have are essentially straight, clean, 12 micron diameter single-walled carbon nanotube bundles, almost ideal for our application. These have been implemented in a carbon nanotube/PVC composite (Li, 2000) and found to have an estimated strength of 22 GPa. The composite itself had a lower strength (3.6 GPa) due to problems with adhesion between the PVC and nanotubes.
Another new development is the commercial sale of carbon nanotubes by Carbon Nanotechnologies Inc. (CNI). These nanotubes come in the form of a tangled mat of ropes that can be straightened through chemical methods. The individual nanotubes are thought to be several hundred nanometers in length.Large-scale structure of the cable
The large-scale structure of the cable depends most basically on the physics of a space elevator and the tensions that the cable must support [Pearson, 1975]. The overall shape is tapered on both ends and has its largest cross-sectional area at geosynchronous orbit. The other basic design characteristic that has been known for some time is that it is best to have one cross-sectional dimension much larger than the other to reduce the damage meteors can inflict on the cable.
The length of the cable would be 144,000 km if no counterweight were used[Pearson, 1975]. With a counterweight on the upper end of the cable any length that reaches beyond geosynchronous orbit is theoretically possible. The shorter the cable the larger the counterweight mass required with it eventually reaching infinity when the cable only reaches geosynchronous. The interdependence of the total system mass, counterweight and cable length are shown in Edwards, 2000. The length of the cable should be determined by the counterweight available, cable size required, and the solar system destinations that are to be accessible from the cable (see Chapter 7: Destinations). In our proposed system we find that a cable 91,000 km long is optimal from both a construction and destination stand point. By choosing this length our cable mass to counterweight mass has a set ratio of 0.87. This ratio will define the masses of cables, spacecraft and climbers in our system.
Variations on the basic tapered design can be implemented within limits. Some modifications to our simple, uniformly thick and standard taper will help with several problems we expect to encounter. The first modification we suggest is to reduce the ratio of the width to thickness from 10,000 (10 cm by 1 micron) down to 200 (2 cm by 5 microns) at altitudes below about 7 kilometers (figure 2.3). This keeps the cross sectional area and strength of the cable the same but reduces the wind drag for the part of the cable in the Earth's atmosphere by a factor of five (see Subsection 10.4 Wind). The second modification we would recommend is increasing the width of the initial cable by a factor of 2 at altitudes between 500 and 1700 km (2. 3). This second modification will reduce the cable's susceptibility to meteor damage by a factor of 5 (see Subsection 10.2:Meteors)and only increase the total mass deployed by 0.65%.
The small-scale design, microscopic up to centimeters, is also critically important to the overall success of the space elevator. The factors that will impact the small-scale design include: 1) material availability, 2) mass minimization, 3) meteor impacts, and 4) atomic oxygen. The design we are proposing for the initial cable has a width of 5 to 11.5 centimeters, a thickness of microns, alternating segments of bare nanotubes and epoxy/nanotube composite, and two thicker fibers running the length dividing the cable in thirds (figures 2.4 and 2.5).
Once carbon nanotubes of sufficient quantity and quality for our needs can be obtained the question becomes one of producing the cable. The cable we are proposing is a carbon nanotube/epoxy composite as shown in figure 2.4. The initial ribbon cable will be 5 cm wide at the base and taper to 11.5 cm at geosynchronous orbit. The thickness of this ribbon will be one micron on average. By this we mean the ribbon can be continuous as in a solid sheet one micron thick or it could be 1200 - 10 micron diameter fibers spaced across the 5 cm width.
The nanotubes making up the ribbon will be parallel and overlap in the composite sections. The filling factors of standard composite materials are 60% fibers to 40% epoxy [Rohweller, 1999]. To further reduce the mass of the epoxy component in the cable we have proposed a construction with alternating sections of epoxy composite and bare nanotubes. The bottom line is that a cable could be constructed with about 2% epoxy mass and require nanotubes of at least a centimeter in length. Figure 2.4 also shows how the cable distorts around damaged areas. In reality the distortions extend 100's of segments, only a few are shown in figure 2.4. Further consideration of the design and its performance requirements in terms of surviving meteor damage suggest that additional strengthening of the epoxy sections with perpendicular nanotubes may be worth considering (figure 2.5). If a ribbon composed of a finite number of thicker fibers (1200 - 10 micron diameter) is used instead of the solid-sheet, idealized ribbon then the reinforcing nanotubes are probably a requirement. In the end a ribbon cable could easily have 10% (instead of our theoretical possible 2%) of its mass in epoxy and reinforcing nanotubes.
Further design aspects are driven by the affects of meteors on the cable. One aspect as discussed in the meteor and space debris section (Subsection 10.2: Meteors) pertains to curving the ribbon (figure 2.5). A curved ribbon is much less susceptible to damage by grazing incident micrometeors. A second design modification to deal more effectively with large meteors that may damage the edge of the cable is to insert two thicker support "ribs" can run the length of the cable. These thicker bundles of nanotubes would reduce the chance of a meteor hole becoming a tear where the tension stresses would be highest (figure 2.3). In redistributing the tension in damaged segments of the cable, the epoxy used will need to be strong and yet flexible to deal with meteor damage (figure 2.4). As discussed in the section on damaged cables (Subsection 10.9: Environmental Impacts) the epoxy will also need to disintegrate at a relatively low temperature to insure the cable will break-up if it were to re-enter Earth's atmosphere. Additional studies and tests will be required before choosing the best epoxy.
Several alternative cable designs have been suggested. One is a design by Hoyt under a study for NASA's Institute for Advanced Concepts (figure 2.6). Hoyt's design of a space tether consists of both straight fibers under tension running the length of the cable and crossed diagonal fibers to take up and distribute the load in the case of meteor damage. Depending on the specific design, the Hoytether could be approximately 64% heavier (Hoyt's continuous high load tether) for the same load compared to our proposed design. In many tether applications this is not serious, in our system it would increase our system mass and launch mass by a factor of four. However, as published by Hoyt, this design may be more robust in terms of handling meteor damage and should be seriously considered at least for possible implementation in critical sections of the cable (Epstien, 2000).
A hybrid version of our proposed cable and the Hoytether is shown in figure 2.7. We have implemented the diagonal fibers as in the Hoytether but will have these under tension. If we place these diagonal fibers at a few degrees from the axial fibers it will increase our overall cable mass by only a few percent and allow for transfer of the tension in the case of meteor damage. We have kept the nanotube/epoxy composite sections to connect the short nanotubes, keep the shape of the curved ribbon and isolate the segments of the cable. The reinforcing fibers from our proposed cable above have also been kept to reduce the chance of edge damage propagating across the cable. This design may combine the best of both our design and the Hoytether without increasing the mass dramatically.
Prior to deciding on a final cable design the problem must be examined in detail and segments of cables with various designs must be made and tested. The critical parameters include the strength to mass ratio and the resistance to damage.
One of the major hurdles in the space elevator program will be production of the cables. The cables are unique in their design and have high performance requirements. Let's consider our design and starting points and then determine where the major production hurdles will be. To begin with we have:
One possible scenario for producing the cable is shown in figure 2.8. If the carbon nanotubes are grown in an aligned mass it may be possible to use a weak adhesive tape to grab an aligned set of the nanotubes. These individual sets of nanotubes can be offset and aligned with each other then fed under tension into a set of treads to hold the nanotubes in position. While being held, strips of the nanotubes can be epoxied to produce the alternating composite and bare nanotube sections we require. Once epoxied the cable section is ready for spooling. If the nanotubes are grown in many centimeter lengths, they can be aligned and fed into the holding treads to be epoxied without the first adhesive pickup stage.
The difficulties will arise in insuring a good adhesion to the extremely small (1.7 nm diameter) nanotubes, elimination of all weak spots, and producing the segments fast enough. In general epoxies are cured under vacuum to produce maximum strength and adhesion. As an example let's assume that the epoxy that we use can cure in 5 minutes inside a vacuum oven. If we want to produce the cable as one segment in one year this implies that a length of 866 meters of cable will need to be traversing through the vacuum oven at any given time. Not impossible by any means but it does need to be considered.
Either during production or after the cable is complete several tests need to be done. These tests include:
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