The history of space elevators

For this new Space Law article on Space Legal Issues, let us have a look at the history of space elevators. The goal for a satellite is to gain altitude above the Earth’s surface, a lot of altitude, and to stay there. So we basically want to go up, get out of the atmosphere, reach the heavens and have a quiet life of observation, communication and science; hay of all these complex and expensive rockets and large machines, expensive and energy-consuming, it would suffice in theory to climb on an ad hoc structure until the good altitude.

The great Newton understood this: in his drawings of 1687 presenting the principle of satellites, he was already drawing his sidereal object horizontally from a hypothetical mountain some two hundred kilometers above sea level, with sufficient speed for the point of fall to exceed the antipodes (Principia Mathematica). Unfortunately, such natural headlands do not exist on our planet, so we have to build them.

The promoters of space elevators generally do not fail to mention the first published concrete attempt, that of the Tower of Babel. Literally “The Gate of the Gods”, it was a ziggurat, a two-story temple-tower, supposed to allow the Babylonians to reach a sacred domain where they would find their supreme god, who lived in the highest heavens. The business failed for the reasons we know; the tower could not have climbed high anyway, the construction technique used then, based on molded bricks baked in the oven with bitumen as mortar, not having sufficient mechanical characteristics to exceed a few hundred meters altitude.

The idea was lost for several centuries until the visit of Constantin Tsiolkovsky (yes, the one who established the rocket propulsion equation) in Paris in 1895, where he had a real revelation when he saw the Eiffel Tower. A brilliant engineer, he understood both the revolution brought by metal construction (the Tower was in fact a demonstration of this new technology), and the distribution of mechanical loads through a trellis, the weight of an element being supported by several other elements below, following the characteristic shape of the Eiffel Tower, widening downwards along a logarithmic curve. He exhumed the idea of ​​a tower, carried towards the heavens, and published following this visit a fundamental work, Dreams of the Earth and the Sky, “experiment of thought” according to his expression, in which he introduced several of basic concepts of astronautics. He imagined a gigantic tower, placed on the equator, along which an “astronaut” would gradually climb. As you climb, the two forces acting on the explorer vary:

1. Earth’s attraction, first, decreases like the inverse of the square of the distance to the center of the Earth: by doubling this distance, this force is divided by four, by multiplying this distance by one hundred, and so on; this force of attraction is of course directed towards the center of the Earth;

2. The centrifugal force, then, due to the rotation of the Earth; this effect, well known to pilots driving at high speed in a turn for example, increases with the distance to the center of the Earth for a given angular speed: by doubling this distance, this force is doubled, by increasing this distance tenfold, it is also increased tenfold; this centrifugal effect, as the name suggests, tends to move the subject away from Earth.

During the climb, the apparent weight of the traveller, the sum of the Earth’s attraction and the opposite centrifugal force, thus tends to decrease. Then comes a place on the climb where these two forces exactly offset each other. Our subject is no longer subjected to any force and is then in weightlessness; it keeps its speed of rotation around the Earth and rotates freely, always staying at the same altitude, called “geostationary altitude”, and always vertical to the same place. Tsiolkovsky calculated the geostationary altitude for the Earth, about thirty-six thousand kilometers, as well as for the five other planets identified at that time and for the Sun. He also explained that if our traveller continues to climb along the tower, the centrifugal force will become preponderant, tending to send it into space. He finally calculated the altitude necessary to be spontaneously sent to the Moon and to Mars. He had no idea, however, of using this singularity for satellites; the credit for this invention goes to Arthur C. Clarke, who in 1945, proposed the use of the geostationary orbit, often referred to as the Clarke orbit, for communication satellites.

The combination of this theoretical vision and modern construction techniques was then proposed in 1960 by a young engineer from Leningrad, Yuri Artsutanov, in an article in the Sunday supplement of Komsomolskaya Pravda, which remained completely unknown until 1967. He imagined a gigantic tower, still on the equator, rising above the geostationary altitude, built on the same principle as the Eiffel Tower, a sort of cone very flared down to distribute the formidable weight of the tower; he adorned it with the pretty name of “Paradise Funicular”.

Artsutanov knew how to calculate well, and unfortunately very quickly understood that such a tower was mechanically impossible, even with the best steel known at the time: the difficulty indeed comes from the fact that the materials work in compression, each element resting on those below; however, the materials have only low compressive strength, about ten times less than tensile. He then proposed to build the tower upside down, the flared part at the geostationary altitude and the tip down, in order to make the materials work in traction, by extending the tower well beyond the geostationary altitude in order to keep the overall center of gravity in the right place.

The idea was almost perfect, but came up against the pitfall of the general dimensions of the structure: even with the best steel known at the time, the flaring necessary for the structural strength of the tower was simply a matter of fiction. For a simple cable with a diameter equal to that of a hair on the surface of the Earth, capable of supporting half a kilogram of sugar on Earth, it would have required a diameter in geostationary greater than that of the Earth… The idea of ​​space elevators went back in the boxes for some time.

It emerged in 1967 under the initiative of a group of American oceanographers, led by John Isaacs of the Scripps Institution of Oceanography in La Jolla, California. These researchers, who were undoubtedly trying to diversify their activities, were very familiar with operations using very long cables to probe marine pits; in their publication in the journal Science, however, they recognized that it was necessary to speak of cables three thousand times longer than those they had used to probe the Marianas pit (eleven thousand meters).

Their contribution was essential because they proposed the elevator deployment scheme still in force today: from a large satellite in geostationary orbit, an extremely thin cable, therefore light, would be deployed simultaneously over and over underneath to keep the center of gravity unchanged; moreover, as soon as this cable arrives at the surface of the Earth, it would be hooked to its anchor and would be used to assemble the first “cabin” with a second cable to reinforce the first. By going back and forth, the final cable would finally be robust enough to be used operationally to mount payloads.

The primordial question of the material to be used was approached elegantly although briefly with the proposal to use quartz, graphite or diamond: their first cable, half thinner than a hair, capable of supporting a mass of three and a half kilograms on Earth, thus weighed only half a ton. The concept sinned on two aspects however: the first, micro-cable was far too thin, and would have been cut instantly by an impact of micrometeorites, microscopic dust falling on Earth at speeds of around seventy kilometers per second; moreover, but as Arthur C. Clarke points out, the diamond price being what it is, half a ton represents a pretty investment for the first cable…

The entry into the modern era of the space elevators or orbital towers, as the concept was called then, is undoubtedly the work of Jerome Pearson, American engineer then working for the flight dynamics laboratory of the U.S. Air Force in Ohio, colleague and friend of the International Academy of Astronautics (IAA). He published in 1974, in the prestigious IAA journal Acta Astronautica, a comprehensive technical review of the subject entitled “A satellite launcher using rotational energy from Earth”. Admittedly, his idea had difficulty in being accepted and he had to fight five years before making accept his paper, but thanks to his initiative, the concept could be very widely disseminated, discussed, criticised, conspired and ultimately recognized.

In his publication, Jerome Pearson explains all the equations governing the space elevators and establishes the precise theoretical form that could be used, depending on the materials considered. It establishes that the total height of the tower must be one hundred and forty-for thousand kilometers, that is to say nearly forty percent of the Earth-Moon distance, and shows that one can then, starting from the end of the cable, reach any point of the Solar System, or even completely escape it. It calculates the cable’s first oscillatory modes, its natural vibration frequencies, a bit like a piano string, and deduces the theoretical speeds to be adopted for the cabins serving the elevator. It also discusses the behaviour of the cable subject to weather conditions in atmospheric zones and describes what would happen in the event of a cable break. Finally, he identifies the two ideal geographic zones for the construction of the cable, zones of relative stability with respect to the orbital disturbances generated by the Moon and the Sun: the two gates should be located on the equator at the right of Sri Lanka, or the Pacific, west of the Galapagos. Unfortunately for him, he still lacks the miracle material that would allow him to remain within reasonable dimensions, and Jerome Pearson concludes his article by indicating that it would still take twenty-four thousand flights of a hypothetical Space Shuttle thirty times larger than the Space Shuttle for complete the construction of space elevators.

The latest actor in the historic space elevators saga is the novelist Arthur C. Clarke. Having read Jerome Pearson’s article, he maintained correspondence with him for many years in preparation for his novel “The Fountains of Paradise” published in 1978. This fascinating book tells the story of construction of the Tower of Stars on the island of Taprobana, in fact Sri Lanka. The engineer in charge of the project, Vannevar Morgan, famous in particular for his suspension bridge over the Strait of Gibraltar, has a revolutionary material, “almost invisible thread in pseudo-mono-dimensional continuous diamond crystal”; we’re almost there… Arthur C. Clarke addresses in his novel all the problems associated with such an enterprise, like the expropriation of the monks owning the premises to the funding difficulties. It is worth noting that Arthur C. Clarke has since settled in Sri Lanka, at the point closest to what he calls “The Stargate”, until his death in 2008.

At first glance, space elevators make it possible to imagine a revolution in access to outer space, very easy and inexpensive: it suffices to take the payload, potentially inhabited, aboard the cabin and press on the destination button. In reality, the shoe pinches in many ways. First, space elevators provide access only to the geostationary orbit; indeed, any point on the lower altitude cable moves more slowly than the speed that would be required to stay in orbit. Orbital speed decreases with altitude while the speed of training due to the cable increases with altitude. As a result, any separate object below GEO has a speed too low to remain in orbit, and falls back to Earth. Furthermore, these orbits are, by definition, equatorial; it is not possible from the cable to aim for an inclined orbit, for example, flying over the poles. This greatly reduces the interest of the elevator. Fortunately, there remains the prospect of using it to reach much more distant targets, beyond GEO, like the points of Lagrange, the Moon, Mars, and beyond. For that you have to climb to the right altitude: forty-five thousand kilometers for the Moon, fifty-seven thousand kilometers for Mars, ninety-six thousand kilometers for Jupiter and the asteroids, and above all, wait for a perfect phasing between orbits to go in the right direction.

Sending humans is also a problem. Indeed, assuming that there is a market for space tourism in geostationary orbit, the speed limit to around two hundred kilometers per hour of the cabins on the climb, dictated by the disruptive force of Coriolis, makes the cruise last longer than a week, with little to do. The cabin should also be well armored to cross the Van Allen radiation belt, a zone of energetic charged particles, between two thousand and six thousand kilometers in particular, a day of strong radiation. The space elevators would therefore serve a niche market composed almost exclusively of geostationary satellites, with a few planetary exploration missions.

The second point which is a bit fishy is the financial balance sheet of the system. The promoters of the space elevators estimated the cost of development at six and a half billion American dollars, comparable to the cost of development of one of the new generation reusable launchers studied around the world. Other authors, more pessimistic or realistic, have evaluated the cost of implementing the system at forty billion American dollars… A glaring feature of the space elevators is the swarming of ideas each more innovative than the other that this concept inspires. In fact, there are so many teams today who believe in the future of space elevators that we are observing the creation of very many start-ups of all kinds. Maybe one day will we see space elevators rise to paradise. That is what can be said concerning the history of space elevators.