Day: February 5, 2024

A recent comment on Space Sunday, from Gwyneth Llewelwyn concerning the concept of space elevators got me thinking as to whether or not I should cover this idea in a little more detail – or as much as I can in under 2,500 words! So here we go.

For those unfamiliar with the concept, a space elevator is a proposed means of payload transfer (cargo and people) between Earth and geostationary equatorial orbit (GEO – 35,786 km) by means of large scale transport units called “climbers” moving up and down a cable system generally referred to as a tether. Such a system would, it is claimed, make routine, shirt-sleeve access available to everyone, and would reduce the cost of payloads from the current average of around US $12,125 per kg to as little as US $200 per kg and without the need for all that tedious mucking about with cylindrical things using propellants with a propensity to go BANG! in unwanted ways if given the chance.

The concept actually dates back as far as 1895, when the “grandfather of modern rocketry”, Konstantin Eduardovich Tsiolkovsky (1857-1935) was inspired by Eiffel’s tower in Paris. He calculated that any object carried up a tower reaching as far as GEO would acquire sufficient horizontal velocity during its ascent so has to remain in orbit on reaching 35,786 km altitude and being released.

Tsiolkovsky’s idea was more an exercise in mathematics and orbital mechanics than an actual design proposal; even the title of his paper on the subject was Day-Dreams of Heaven and Earth. He was well aware that any tower built from the ground up would increase in mass to a point where it could no longer support itself and so collapse under its own weight long before reaching any significant altitude.

However, with the arrival of the space age, the concept was reborn, thanks to Yuri Nikolaevich Artsutanov (1929-2019). He actually never heard of Tsiolkovsky’s paper, although he was similarly aware that building up was a non-starter, so he came up with the idea of building down – starting from GEO and using a tensile structure.

He first published his idea in 1959, outlining how a large space station in GEO could be used as an “anchor point” for two cables – one going towards Earth, and the other on the opposite side of the station to counter the mass of the first cable, helping to keep the station in place and, once the Earth cable was anchored to the planet, act as a counterweight to maintain tension throughout the structure.

In writing his paper, Artsutanov also calculated that in order to maintain a constant stress throughout its length, aiding its stability and strength, the cable extending down to Earth would need to tape as it descended, becoming gently narrower and narrower. Thus, he laid the foundations for what has become the most recognised concept for building a space elevator.

Unfortunately, Artsutanov’s work didn’t reach an audience outside of the former Soviet Union until the mid-1960s. By that time, and quite independently, similar proposals for a tensile space elevator had by written by David Edward Hugh Jones (1938-2017) in the UK (1964) and by US engineers J.D. Isaacs, A. C. Vine, H. Bradner and G. E. Bachus in 1966 (although they called their idea the “sky hook”), which led to Artsutanov’s ideas passing largely uncredited until the late 1970s, when his paper finally gained the international recognition it deserved.

Only of the key points of the tensile system has is its potential flexibility of use, as identified and proposed by numerous researchers over the past 60 years. For example, if a waystation were to be built some 8,900 km above the Earth as the tether descended, it would have a gravity environment equivalent to that of the Moon, while a second waystation built some 3,900 km altitude would have a gravity environment equivalent to Mars. These could thus be used as training facilities for crews heading for the Moon and Mars, allowing them to acclimatise to the lower gravity environments.

Similarly a waystation built on the counterweight tether at a distance of 23,750 km from Earth would mean that any satellites or craft released from it would have insufficient velocity to maintain a stable orbit. Instead, they would spiral down towards Earth, gaining a small degree of angular momentum in the process, such that by the time they reached an altitude of 300-400 km, they would be moving at orbital velocity and remain there.

Further, if the counterweight tether was extended out to 100,000 km from Earth, it would provide points from which vehicles and payloads could be released with sufficient velocity to enter transfer orbits to the Moon or the L1 or L2 Earth-Sun Lagrange points; whilst those released from the end of the tether could be sent on their way to Mars and beyond.

All of these ideas helped promote the concept as both potentially viable and very desirable, and by the late 1970s, the idea of the space elevator was starting to enter public consciousness – helped, no doubt in part by science fiction authors like Arthur C. Clarke, who made the space elevator the nucleus for his 1979 novel The Fountains of Paradise (in fact Clarke became so enamoured with the idea, he wrote his own scientific paper on the subject, also published in 1979,entitled The Space Elevator: “Thought Experiment” or Key to the Universe?).

However, despite decades of research and ideas – and even s further resurgence of the idea in the last decade or so, the space elevator is still only a concept and despite predictions to the contrary, is likely to remain so for the foreseeable future.

This is because right now, we simply do not have a material with the necessary tensile strength / density ratio required for a space elevator to support both its own mass and the mass of anything built on it or travelling along it whilst also remaining somewhat flexible. This ratio has been calculated  as being 77 megapascal (MPa)/(kg/m³). By comparison, titanium, steel or aluminium alloys have a tensile strength / density ratio of just 0.2–0.3 MPa/ kg/m³ (and would result in a structure far too heavy and rigid even if they could be used), whilst Kevlar and carbon/graphite fibre are more flexible, lighter a, stronger and better suited – but still only have a ratio of 1.0–4.0 MPa/ kg/m³.

Much has been made of carbon nanotubes (CNTs) providing the solution. First invented in the early 1990s, these are tiny tubes about 100,000 times smaller than the width of a human hair with a huge amount of tensile strength for their mass (perhaps as much as 100 MPa / kg/m³. But there is a snag. Thus far, the longest researchers have been able to grow individual CNTS is just 50 cm, whilst CNT “forests” (hundreds of CNTs grown together so that they can be drawn out into a thread-like length (the idea being that the threads can then be woven together in increasing thickness to produce super-strong cables, as well as being used in other ways) haven’t exceeded 14 cm in length when drown out before they start to collapse. Thus, there is a long way to go before CNTs can be used to manufacture something as massive as a space elevator cable.

The reason the tether must be capable of flexing and moving is two-fold. Firstly, as climbers ascend and descend along the tether, they either gain or shed angular momentum. This means that an ascending climber will reach a point where its angular momentum is greater than that of the cable it is travelling along. As a result, a Coriolis force will be applied, causing the cable to bend to the west. Similarly, a descending climber will reach a point where its angular velocity is less than that of the section of tether it is travelling along, and the resultant Coriolis force with flex the tether to the east.

Whilst some of this flexing (and the oscillations it might induce in the entire structure) can be mitigated to some degree – the oscillations can be countered by placed the structure’s centre of mass somewhere above GEO, for example, whilst pairing-up climbers so that when one is ascending another of an identical mass is descending so that the forces they apply to the cables of the tether can cancel one another out to some degree – it will still be necessary for the tether to be able to bend, flex and sway (within reason!) in response to forces placed on it through the movement of climbers (as well as natural forces like winds).

The second reason for the tether being capable of movement is a matter of safety: much of the space it will be moving through is cluttered with thousands of satellites and millions of piece of space debris on 10 cm or grater in size. While collisions between such debris and space vehicles are rare, they do occur – so it is essential the tether has a means  – however limited – to avoid any debris large enough to be tracked (and thus risk significant damage on impact) and any satellites in orbit which cannot get out of its way should their orbits intersect with its passage through space.

There are other issues – location of the base station (most of the Earth’s equator is open ocean, after all), power requirements (which will be huge), and so on. However, none of these are actually insurmountable, so in the interests of brevity I’ll take them as read here.

All of which mean that, while the construction of a space elevator is not beyond the realms of possibility – technologies such as CNT production will improve, for example – it is not something we’re likely to see happen in the next few decades. Not that this has stopped some like Japan’s Obayashi Corporation from dreaming, as the video below demonstrates – just take the timeline with a pinch of salt!

But were a space elevator to be built, what would travelling it be like? Well, for a start you can forget the zooming ride depicted on the above video! Whilst being cost-effective means getting payloads to and from GEO as quickly as possible, there are actually limitations as to how fast climbers can realistically ascend / descend in order to avoid over-stressing the cables section they are travelling along.

Speed also needs to be limited to ensure passengers are not subjected to prolonged periods of excess of G-forces. As such, a speed of between 300-400 km/h has been suggested for climbers. Whilst this might sound fast, it actually means that a trip to GEO would take as long as crossing the Atlantic on an ocean liner – 4 to 5 days. Given this, climbers used for passenger operations will have to offer a range of passenger amenities – including the ability to move around relatively feely. All of which means climbers will be fairly substantial vehicles, even if only carrying a modest number of passengers – so forget the Disney-esque all sitting in a little capsule and watching Earth recede behind you and *ping* you’re there; riding a space elevator to GEO is liable to be quite the experience!

Which brings me to a final point in this rapid-fire run-down of the concept. And that’s the fact that perhaps the space elevator is best suited for use not here on Earth, but on Mars (as identified by Kim Stanley Robinson in his Mars trilogy). There are several reasons for this.

Mars’ gravity is 38% that of Earths. This means its equatorial orbit distance is just 17,032 km above the planet. These facts combine to mean that not only can a Mars space elevator be much smaller (or shorter, if you prefer) than one on Earth, it could be built out of existing materials – no need for exotic CNTs. That said, there are two slight hiccups with this idea. first, we have to actually get to Mars and reach a point in its development where a space elevator is warranted. Secondly, Mars’ inner moon, Phobos, orbits inside the planet’s equatorial orbit distance, crossing the equator every 5.8 hours. As such, it presents a significant threat to any space elevator, which must therefore have an ability to move itself aside on those occasions went it and Phobos would otherwise be occupying the same volume of space.

However, most intriguingly is an idea to use Phobos itself  – which is tidally locked with Mars, so always has the same side facing the planet) as the platform for a novel space elevator system. This would see two tethers built out from the Moon – one towards Mars and the other as the counterweight – to a distance of 6,000 km. This would place the end of the Mars-facing  tether just above the denser atmosphere of the planet, and travelling some 0.52 km/s fast that the planet is rotating. Craft could then be launched from Mars with a delta-V of just 1,872 km, much less than required to reach orbit, to dock with the tether as it skims around the planet, and / or landers could be dropped off to touch down without the need to slam into the atmosphere at Mach 25.

Meanwhile, the counterweight end of the tether would by moving at 3.2 km/s – just 1.8 km/s short of Mars escape velocity. So it could be used to start payloads on their way back to Earth with only minimal propellant needs at launch – or it could give a kick-start to crewed vehicles designed to rendezvous with a Mars cycler craft as it skips around the planet, allowing the crew to make a return to Earth aboard the cycler, again for far least propellant use than would be required with a launch from the planet’s surface.

Again, this is not intended to be an in-depth look at space elevators, so there are aspects I’ve not mentioned or glossed over to piece this piece to a reasonable length. However, if the subject is new to you, I hope this acts as a reasonable primer, and we’ll be back to the more usual format for Space Sunday next week!