SPACE ELEVATORS Robert L. Forward Hans P. Moravec March 22, 1980 Copyright 1980 Dr. Robert L. Forward and Hans P. Moravec Mankind has always yearned to reach the star-embedded sphere of space that seems to lie so tantalizingly close overhead. In the days of legends, a few ambitious humans reached for the heavens with towers. Towers of brick, with a stairway on which they hoped to climb into the skies. They failed--the towers crumbling under their own weight. By the time of Newton, humanity's bag of tricks had grown, and included guns to shoot things toward the heavens. The cannon of the nineteenth century were at one time thought to be the best method for entering space, and during the First World War, projectiles from long range guns grazed the top of the atmosphere. Airplanes came next, but they were unsuitable for travel to the planets and stars, for there is no air in space. Rockets--simple metal tubes stuffed with gunpowder, had been used for entertainment and war for centuries, but did not become a serious weapon until World War II. Rockets were always felt to be too ancient and too crude for an ascent to the sky. Calculations by early space enthusiasts, however, predicted that a rocket could propel objects out into space more gently than a cannon. Today, we all know that the once-scorned rocket became the way to achieve space travel. In fact, rockets have been so successful that other methods to reach the heavens have been nearly forgotten. Taking a cannon to the stars is still too dangerous to consider, but how about the other techniques? Can we build a stairway to the stars? And if not a stairway, how about an elevator? Out at the very special distance of 36,000 kilometers from the surface of the earth, there now exist dozens of satellites in synchronous orbit. Here the rotation of the satellite in its orbit is 24 hours, exactly equal to the rotation of the earth below. Thus, as you stand on the earth and look up in the sky, the synchronous satellites stay fixed in one position above you while the stars slowly rotate from east to west. A simple ground antenna pointed at such a satellite can transmit and receive communication signals 24 hours a day, with no tracking required. Suppose someone in the satellite were to let down a long cable--36,000 kilometers long. If it were strong enough to hold its own weight, then the cable would reach down to the earth's surface--a skyhook. Given adequate supplies, a light-weight spacesuit, and enough time, you would be able to climb into space on the skyhook stairway (resting along the way occasionally to enjoy the scenery) instead of having to use a rocket. One way to construct such a skyhook would be to start with a cable making machine at a central station in synchronous orbit. For balance, the machine would extrude two cables, one upward and one downward. The cables would be thin at first, then, as the length of cable hanging down becomes longer, the thickness of the cable would be increased to provide enough strength to support the increasing weight below. The thickness of the upward-growing cable would also increase as the cable became longer, but for a different reason. Instead of gravity pulling on the cable, the pull is due to the centrifugal force from the once per day rotation of the satellite and cable about the earth. If the extrusion rates of the two cables were carefully controlled, then the net pull on the central station would be zero and the cable laying machine would remain at synchronous orbit. Eventually, the lower end would reach the ground (or the top of some convenient mountain) 36,000 kilometers below. At that time the outgoing cable would be 110,000 kilometers long (the outgoing cable has to be longer than the earth-reaching cable because of the way the gravity forces and centrifugal forces vary with distance). If everything were done properly, there would be no horizontal motion of the cables. In fact, the gravity and the centrifugal force would combine to produce a force that helps to maintain the cable exactly vertical. The bottom end of the long cable could now be anchored to the ground so it doesn't blow about in the winds, and a large counterweight (a small asteroid) attached to the outer tip. The counterweight, like a stone in a giant sling, would keep the cable under moderate tension to help keep it straight. An unusual material would be needed for the skyhook. A material that is both strong and light. Even the best steel is too heavy for an earth skyhook. Crystalline graphite is presently the best candidate material for a skyhook. Theoretically it is twenty times as strong as conventional steel and four times less dense, making it potentially 80 times better than steel for skyhook cables. Actual measurements of graphite whiskers show a tensile strength of 2.1 million newtons per square centimeter. With that strength, a one square centimeter cable of crystalline graphite could lift 210 tons in the gravity field of the earth. Partially crystalline graphite fibers imbedded in epoxy binders are presently the wonder materials of aerospace and sports equipment manufacturers. It is because of its high strength-to-weight ratio that you find graphite fibers used in tennis racquets, fishing rods, golf clubs, and other sports equipment. The main engines of the Space Shuttle are extremely light in weight for the amount of power they generate because they are built using graphite fibers. Weaving large cables of graphite fibers with strengths near that of the present tiny whiskers is the major technical hurdle that must be overcome if terrestrial skyhooks are to become a reality. Although the present graphite fibers are strong, they are at best still ten times weaker than the theory predicts. In the coming years we can expect the strength of the fibers to improve until they are adequate for terrestrial skyhooks. Interestingly enough, they are already more than strong enough for constructing skyhooks on the moon and Mars. A one centimeter cross-section crystalline graphite cable would weigh about 220 kilograms per kilometer of length. With a 210 ton lifting capability, the cable could support almost a 1000 kilometer length of itself in the earth's gravity field. If the cable were built with a taper to it, so it is thicker at the supporting end where it needs more strength, then even longer cables could be considered. Fortunately, the pull of the earth's gravity also decreases with altitude, so that less taper is needed on very long cables. With a taper of ten to one, a graphite cable could be built to go all the way out to synchronous orbit, 36,000 kilometers above the earth's surface--and beyond. Once the cable is in place, then it could be climbed like the proverbial beanstalk. For smaller diameter cables, special electrically powered cars would be built to climb up the outside. If the skyhook design used a number of cables arranged in a hollow square, then electrified tracks could be built inside the structure. As each car climbs the beanstalk from the earth's surface into synchronous orbit, it would consume an appreciable amount of electrical energy. The cost of the electricity, a few dollars per kilogram, would be much less, however, than the cost of using rockets. When the cable cars climb up the cable, although they always stay above their anchor point on the rotating earth below, they would be moving horizontally through the surrounding space at higher and higher velocities because of the once per day rotation of the earth and cable. An object dropped from the cable car during the first few kilometers would fall nearly straight down to the surface of the earth. As the car climbs higher, the point of impact would move toward the east, since the object would leave the cable car at a higher horizontal velocity than the surface of the earth below. Above 25,000 kilometers, an object dropped from the car would have so much horizontal velocity that it would shoot past the earth's horizon and go into orbit. The turnover point for the cable cars would be at the central station, 36,000 kilometers up, where the gravity and centrifugal forces balance. Here the cable would be traveling horizontally at synchronous orbit velocity, and communication satellite payloads brought up on the cars would be simply floated out to become synchronous satellites. Cars continuing beyond the central station would be pulled along the cable by the ever-increasing centrifugal force, like a skater at the end of a "crack-the-whip". The cars would have to brake to keep from flying out too fast. If the braking were by an electric motor, the braking energy could be turned into electricity instead of heat and used to raise the next cable car on its way up. On reaching the ballast stone, the cable car would be 150,000 kilometers from the center of the earth and moving with a horizontal velocity of 11 kilometers per second. If it were to let go of the cable, the car (now turned spacecraft) would be able to coast to Saturn on a minimum energy orbit and travel rapidly to all the other planets nearer than Saturn. An earth skyhook would be an engineering marvel. The job of building the 36,000 kilometer section down to the earth would be equivalent to building a suspension bridge around the equator. In order to lift appreciable loads, say 100 tons at a time, the skyhook would have to weigh 600 thousand tons. Fortunately, the carbon needed for the graphite fibers can be found in special kinds of asteroids called carbonaceous chondrites. After the carbon was extracted from the asteroid, the remaining slag could be used as the counterweight. The construction job would be staggering in its scope. To build the 36,000 kilometer earthgoing section of the skyhook in 5 years would require an average construction rate of cable and track of 20 kilometers a day. After the skyhook was built, the cable cars would have to travel at more than 6,000 kilometers per hour in order to make the trip time to the central station less than 6 hours. Some kind of magnetic levitation design for the track would be needed, for no rubbing or rolling contact can be tolerated at those speeds. A skyhook for Mars is easier than one for the earth. Since the rotation rate for Mars is nearly the same as that of earth (24.5 hours) while its gravity field is lower (0.38 gravities), a Mars skyhook using graphite would only mass 42 times what it could lift. Mars is the best planet in the solar system for a synchronous cable, having both a shallow gravity well and a high rotation rate. It also has a 21 kilometer high mountain, Mons Pavonis, on the equator and a small moon, Deimos, that is available at almost just the right orbit to act as the counterweight. There is a new version of the skyhook, called the space elevator, that uses a cable that is much shorter than the synchronous orbit skyhook. The space elevator rotates as it orbits about the earth, the ends of the cable touching down near the earth's surface. One design for a space elevator uses a cable that is 8500 kilometers long, two-thirds the diameter of the earth. The central portion of the cable would be put into an orbit 4250 kilometers high with a period of 183 minutes. The cable would also set to spinning at one revolution every 122 minutes. The long cable would rotate in space like two spokes on a bicycle wheel, the imaginary rim of the wheel rolling along the surface of the earth below as the spacecraft orbits the earth. Three times each orbit, once every 61 minutes, one of the ends of the cable would touch down into the upper portion of the earth's atmosphere. These entry points would be the three ports of embarkation for the space elevator transportation system. Because of the large dimensions of the bodies involved, the ends of the cable would seem to come down into the upper atmosphere nearly vertically, with no horizontal motion. There is more to the cable dynamics than pure rotation. The cable, although made of one of the stiffest materials known, still has some stretch to it. A piece of graphite cable will stretch about 1/52 of its original length when a maximum load is applied to it. Thus, a cable with a nominal length of 4250 kilometers could stretch 80 kilometers without exceeding its design. This means that a coupling vehicle at the end of the cable could use jets and aerodynamic forces to fly the end of the cable to a rendezvous point ahead of its nominal touchdown time and delay the return to orbit. This would allow almost a full minute to effect dropping off and picking up cargo and passengers. The three-touchdown space elevator would have a taper of about twelve to one. A cable with a mass of only 7500 tons could lift a 100 ton cargo into space. At touchdown the end of the cable would approach and leave the earth with an acceleration of 0.4 gravities. Counting the 1 gravity of the earth, there will be a total acceleration at liftoff of 1.4 gravities. It will not be a comfortable ride, but much milder than a ride on the Shuttle. A futuristic scenario for the Space Elevator Transportation System would probably work like this: You check in at any one of the major hypersonic airports around the world, clear customs, and board a small capsule 8 meters in diameter and 20 meters long. It will look like a section cut out of a modern widebodied jet aircraft. There are seats for about 30 passengers, with cargo space below, and a diminutive cockpit/control center at one end, containing an alert capsule crew. The crew checks on the sealing of the capsule as it is carried away on the bed of a truck to a corner of the field, where a crane lifts it onto the flatbed spine of a hyperlift cargo plane. Fairings are attached to merge the body of the capsule into the empty section of the plane. Now aerodynamically restored, the aircraft taxis down the field and takes off. It reaches altitude over the nearby ocean and accelerates to Mach 3. The capsule crew has little to do except monitor the radar displays while the crew of the hyperlift plane takes it higher in altitude and speed, heading southward for a rendezvous in space and time with the Space Elevator. The rate of climb of the aircraft slows as the atmosphere becomes thinner. The plane passes though the 50 kilometer altitude that used to mark the difference between an airplane pilot and an astronaut, but there is no pause as it climbs higher on its powerful oxygen-augmented jets. There is crackling conversation between the aircraft crew, the capsule crew, and the space beings still hundreds of kilometers overhead, diving downward in the rapidly dropping grapple-craft at the end of the space elevator cable. Everything looks good, so the aircraft unlatches the capsule and slowly drops away, leaving the wingless egg to soar on though the nearly empty upper atmosphere in a long arching trajectory that will end in a parachute recovery if something goes wrong. The capsule sails upwards toward the rendezvous point with the capsule crew busy. Looking out the sides of the heavily tinted windows, you can see attitude control jets flash as the crew keeps the capsule in proper position and orientation for the pickup. You look out the upper port to see a similar flaring of jets from the grapple-craft streaking vertically downward, trailing a long thin thread. The grapple-craft comes to a hovering stop, then slowly drifts in. Carefully, taking its time, the crew attaches the three grapple hooks to the lifting lugs at the top of the capsule. The capsule crew confirms attachment, then the grapple-craft adds its jets to those of the capsule to match speeds with the cable. The free fall of the dropping capsule is slowly replaced with an upward acceleration. In 10 seconds, the acceleration reaches 1.4 gravities, and you are glad that you are strapped in the comfortable seat beneath you. Having started at 80 kilometers altitude, in 5 minutes the capsule has reached 260 kilometers altitude and a velocity of 1.2 kilometers per second. The acceleration slowly drops as you continue your ride into outer space, traveling on the whip end of a fine thread. After a half-hour the capsule is at the high point in its giant swing through space, and you look down on the blue-white globe 8500 kilometers below. There is a warning klaxon and an announcement from the capsule pilot. You strap in securely, there is a multiple click as the grapples release, then you and the capsule are in free fall, heading for the moon with a velocity of 9 kilometers per second. You settle down with a good book. It will be 12 hours before you get there. After two books, two meals, and a nap (disturbed by the unfamiliarity of free fall) the capsule arrives in the vicinity of the moon, where it is again met by a grapple-craft crew on a space elevator orbiting the moon and is lowered almost to the lunar surface. There the capsule is handed over to a jet-tug that takes you to Copernicus Base. You are home again in familiar surroundings and glad to get away from the oppressive gravity, air, and crowds of earth. A space elevator on the moon has an enormous advantage over rockets for providing resupply and crew rotation needed for space industrialization. A lunar space elevator could be made with presently available materials, like the super-plastic Kevlar made by DuPont. With a density of 1.44 grams per cubic centimeter and a tensile strength of 280 thousand Newtons per square centimeter, it has about 5 times the strength-to-weight of steel. Kevlar is presently being used in large quantities for bullet-proof clothing, radial tires, and parachutes. A 3700 ton Kevlar space elevator about the moon would be able to lift and deposit 100 tons every 20 minutes, and would subject payloads to a maximum of 0.66 gravities. Rotating space elevators could also be used on any of the moons in the solar system. Jupiter's Ganymede and Saturn's Titan are larger than the earth's moon, but a Kevlar space elevator with a taper of six to one would suffice for these bodies. Similar spinning cables in solar orbits between the planets could act as shuttle points to cut the transfer time between points in the solar system. Instead of heading off on a low velocity trajectory toward a distant planet that may be in a bad position at that time of year, the capsules would head at high speed for the nearest transfer cable. As they approach the cable, they would chose the point along the spinning thread that matches their approach velocity. Once attached, the capsule would then move along the cable, climbing up or down in the centrifugal field, until it reached the point in the cable that had the velocity needed for the next leg in the journey. There would be a short waiting period until the direction was correct, then with a command to the attachment hooks, the capsule would be freed from the cable to go flying off into space toward its distant objective. The cable would slow slightly as some of its energy is lost, taken away by the disappearing capsule, but it will gain it back when the capsule returns with its massive cargo and passengers, and its equally important, but weightless, cargo of knowledge. As long as more mass is dropped inward down the sun's gravity well than is going out, no energy source would be needed to operate this space transportation system once it were set into motion. Skyhooks and space elevators are definitely a second generation space transportation system. Yet progress will come. In San Francisco, horse drawn trollies preceded the cable cars. In the same way, in space, the slow, smelly rockets must ultimately give way to the cable cars of space.