Design and Deployment of a Space Elevator
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Acta Astronautica Vol. 47, No. 10, pp. 735–744, 2000 ? 2000 Elsevier Science Ltd. All rights reserved Printed in Great Britain www.elsevier.com/locate/actaastro PII: S0094-5765(00)00111-9 0094-5765/00/$ - see front matter DESIGN AND DEPLOYMENT OF A SPACE ELEVATOR BRADLEY C. EDWARDS Los Alamos National Laboratory, Mail Stop D436, Los Alamos, NM 87544, USA (Received 23 November 1999; revised version received 2 March 2000) Abstract—The space elevator was ÿrst proposed in the 1960s as a method of getting into space. The initial studies of a space elevator outlined the basic concept of a cable strung between Earth and space but concluded that no material available at the time had the required properties to feasibly construct such a cable. With the discovery of carbon nanotubes in 1991 it is now possible to realistically discuss the construction of a space elevator. Although currently produced only in small quantities, carbon nanotubes appear to have the strength-to-mass ratio required for this endeavor. However, fabrication of the cable required is only one of the challenges in construction of a space elevator. Powering the climbers, surviving micrometeor impacts, lightning strikes and low-Earth–orbit debris collisions are some of the problems that are now as important to consider as the production of the carbon nanotube cable. We consider various aspects of a space elevator and ÿnd each of the problems that this endeavor will encounter can be solved with current or near-future technology. ? 2000 Elsevier Science Ltd. All rights reserved 1. INTRODUCTION 2. CABLE FABRICATION In the exploration and use of space there is cur- In 1991 the ÿrst carbon nanotubes were made rently only one system that can deliver payloads [6]. These structures have promise of being the to their destinations, rockets. However, during strongest material yet discovered (Table 1). This the ÿrst decades of the space age, 1960s and strength combined with the low density of the 1970s, an alternative means of getting to space material makes it critically important when con- was proposed, a space elevator [1–5]. The basic sidering the design of a space elevator. concept is to string a cable from the Earth’s sur- The tensile strength of carbon nanotubes has face to an altitude beyond geosynchronous orbit been theorized and simulated to be 130 GPa (35; 800 km altitude). The competing forces of (see Table 1) compared to steel at ¡ 5 GPa and gravity at the lower end and outward centrifugal Kevlar at 3:6 GPa. The density of the carbon nan- acceleration at the farther end keep the cable un- otubes (1300 kg=m3) is also lower than either steel der tension and stationary over a single position (7900 kg=m3) or Kevlar (1440 kg=m3). The critical on Earth (Fig. 1). Theoretically, the cable could importance of these properties is seen in that the be constructed 144; 000 km long and would be taper ratio of the cable is extremely dependent on balanced in equilibrium [5]. However, placing a the strength-to-weight ratio of the material used. counterweight at the far end of a shorter cable, (In our discussions the taper ratio refers to the once the Earth end is anchored, would simplify cross-sectional area of the cable at geosynchronous construction and give the same stability. The compared to the cross-sectional area of the cable cable would be tapered such that it is thickest at Earth. A taper in the cable is required to pro- at the point of highest tension (geosynchronous vide the necessary support strength.) For example, orbit) and thinnest where the tension is the lowest based on Pearson’s [5] work and operating at the (at the ends) [5]. This cable, once deployed, can breaking point, the taper ratio required for steel be ascended by mechanical means to Earth or- would be 1:7 × 1033; for Kevlar the ratio would be bit. If a climber proceeds to the far end of the approximately 2:6 × 108; and for carbon nanotubes cable it would have sucient energy to escape the ratio is 1.5. Since the mass of the cable, to from Earth’s gravity well simply by separating ÿrst order, is proportional to the taper ratio, carbon from the cable. The space elevator thus has the nanotubes dramatically improve the feasibility of capability in theory to provide easy access to producing the cable for a space elevator. In our Earth orbit and most of the planets in our solar discussions below we will implement a safety fac- system [5]. tor of two. This means that at all points the cable 735 736 B. C. Edwards Fig. 1. Basic space elevator design: the basic space elevator concept and the e ective acceleration as a function of position for an object stationary above a point on Earth. Positive accelerations are directed toward Earth while negative accelerations are directed away from Earth. The plot is based on Eqn. (2) from reference [3]. Table 1. Properties of carbon nanotubes Theory Measured Density 1300 kg=m3 — Tensile strength 130 GPa† — Melting temp. 7800◦C‡ — Resistivity — 1 × 10−4 cm§ Young’s modulus 630 GPa† 1800 Gpak †Reference [7]. Fig. 2. Illustration (not to scale) of a ribbon cable with ‡Reference [8]. micrometeor damage and an additional ribbon epoxied §Reference [9]. to right edge. kReference [10]. This design would also imply that the minimum will have twice the strength needed to support nanotube length that would allow construction of the cable below it and the suspended mass of the the cable is about 4 mm. One processing tech- climber. nique has produced several square centimeters of Due to meteor impact considerations (see straight, parallel, tightly packed, nanotubes 50 m Section 4.1) we believe that a ribbon-type, long at rates of 120 m=h [12]. A second produc- epoxy=nanotube-composite design for the cable is tion process has produced a tangled web of nan- optimal (Fig. 2). A ribbon for our discussions is a otubes 10 mm × 50 mm in less than 30 min [13]. cable that is much smaller in one cross-sectional dimension than the other. The ÿlling factors of 3. SPACE ELEVATOR DEPLOYMENT standard composite materials are 60% ÿbers to In considering the deployment of a space eleva- 40% epoxy [11]. To further reduce the mass of tor we can break the problem into three largely the epoxy component in the cable it can be con- independent stages: (1) deploy a minimal cable, (2) structed with alternating sections of composite increase this minimal cable to a useful capability, and bare nanotubes. To insure that the nanotubes and (3) utilize the cable for accessing space. are secure in the epoxy the composite sections must be much longer than the individual nanotube 3.1. Initial cable deployment ÿbers and thick. This would imply a design that has composite segments of 100 m or greater in Based on previous and on-going work, there are length separated by sections of bare nanotubes three ÿxed design components that we will adopt millimeters to centimeters in length. This would for our discussions. First, our space elevator de- allow the construction of a composite cable with sign will be based on carbon nanotube technol- less than 2% of its mass being epoxy. ogy as stated above. Second, our cable design will Space Elevator 737 Table 2. FortÃe mass breakdown Mass (kg) Mass (kg) for initial cable SC Structures 56 300 Payload 74 5000 Power 36 50 Att. control 14 50 Command 6 15 Comm. 3 10 Thermal 15 20 Total 204 5445 Total w=o payload 130 445 Fig. 3. Deployment of a space elevator: (a) unspooling of an initial cable from a spacecraft in geosynchronous orbit. Ends of a spooled cable are deployed upward and downward. (b) Once the initial cable is deployed and anchored the spacecraft moves upward. (c) After the spacecraft reaches the far end of the cable it acts as a counterweight. Climbers can now be attached to the cable and ascend. (d) A useful cable is realized after successive climbers reach the far end of the cable and increase the cable’s overall lift capability. Fig. 4. Taper proÿle and mass distribution. The diameter be tapered as presented by Isaacs et al. [2] and taper proÿle and relative masses are shown for a cable Pearson [5]. Third, deployment of the initial cable extending up to the given radius from Earth center. will be from geosynchronous orbit [2]. Deployment of the initial cable will entail plac- ing a spacecraft carrying a spooled cable in geosyn- quired to deploy the cable in a controlled method, chronous orbit. The cable will be on two spindles and join cable segments on orbit. For a baseline, a such that each end can be deployed separately, one spacecraft such as FortÃe can be used [14]. FortÃeisa end downward toward Earth (pulled by gravity) small mission with roughly the size and capabilities and the second upward (pulled by outward cen- that are required here for the spacecraft bus. The trifugal acceleration, Fig. 3). Once both ends are primary di erence is the payload mass. Aspects of fully extended, the end at Earth is retrieved and an- the FortÃe mission that match with our discussion chored. After the cable is anchored the spacecraft include the carbon composite space frame, solar bus that has been at geosynchronous orbit moves power, basic attitude control, communications and outward along the cable to become the counter- command systems. The mass breakdown for FortÃe weight at the far end of the cable. This will com- can be seen in Table 2.