by ARTHUR C. CLARKE
Chancellor, University of Moratuwa, Sri Lanka
-- Fellow of King's College, London.
THE PROBLEM OF MATERIALS
As we go upwards, gravity falls off according to Newton's inverse square law. But the effective weight ofthe cable diminishes even more rapidly, owing to the centrifugal force on the rotating system. At geostationary altitude the two balance and the net weight is zero; beyond that, weight appears to increase again -- but away from the Earth.
So our cable has no need to be strong enough to hang 36000 km under sea-level gravity; allowing for the effects just mentioned, the figure turns out to be only one-seventh of this. In other words, if we could manufacture a cable with sufficient strength to support 5000 km (actually, 4960) of its own length at one gee, it would be strong enough to span the gap from geostationary orbit to Equator. Mathematically -- though not physically -- Jacob's ladder need be only 5OOOkm long to reach Heaven.... This figure of 5000km I would like to call 'escape length', for reasons which will soon be obvious.
How close are we to achieving this with known materials? Not very. The best steel wire could manage only a miserable 5O km or so of vertical suspension before it snapped under its own weight. The trouble with metals is that, though they are strong, they are also heavy; we want something that is both strong and light. This suggests that we should look at the modern synthetic and composite materials. Kevlar (Tm) 29, for example  could sustain a vertical length of 200 km before snapping -- impressive, but still totally inadequate compared with the 5000 needed.
This 'breaking length', also known as 'rupture length' or 'characteristic length', is the quantity which enables one to judge whether any particular material is adequate for the job. However, it may come as a surprise to learn that a cable can hang vertically for a distance many times greater than its breaking length!
This can be appreciated by a simple 'thought experiment'. Consider a cable which is just strong enough to hang vertically for a hundred kilometres. One more centimetre, and it will snap....
Now cut it in two. Obviously, the upper 50 km can support a length of 50 km -- the identical lower half. So if we put the two sections side by side, they can support a total length of 100 km. Therefore, we can now span a vertical distance of 150 km, using material with only 100 km breaking length.
Clearly, we can repeat the process indefinitely, bundling more and more cables together as we go upwards. I'm sure that by now you've recognised an old friend -- the 'step' principle, but in reverse. Step rocketsget smaller as we go higher; step cables get bigger.
I apologise if, for many of you, I'm labouring theobvious, but the point is of fundamental importance and the rocket analogy so intriguing that I'd like to take it a little further.
We fossils from the pre-space age -- the Early Paleoastronautic Era -- must all remember the depressing calculations we used to make, comparing rocket exhaust velocities with the 11.2 km 5' of Earth escape velocity. The best propellants we knew then --and they are still the best today! -- could provide exhaust velocities only a quarter of escape velocity. From this,some foolish critics argued that leaving the Earth by chemicalrocket was impossible even in theory.
The answer, of course, was the step or multi-stagerocket -- buteven this didn't convince some sceptics. Willy Ley  recordsa debate between Oberth and a leading German engineer, who simplywouldn't believe that rockets could be built with a mass-ratio oftwenty. For Saturn V, incidentally, the figure is about fivehundred
We escaped from earth using propellants whose exhaust velocitywas only a fraction of escape velocity, by paying the heavy pricedemanded by multi stage rockets. An enormous initial mass wasrequired for a small final payload.
In the same way, we can achieve the 5000 km 'escape length', evenwith materials whose breaking length is a fraction of this, bysteadily thickening the cable as we go upwards. Ideally, thisshould be done not in discrete steps, but by a continuous taper.The cable should flare outwards with increasing altitude, itscross-section at any level being just adequate to support theweight hanging below.
With a stepped, or tapered, cable it would be theoreticallypossible to construct the space elevator from any material,however weak. You could build it of chewing gum, though the totalmass required would probably be larger than that of the entireuniverse. For the scheme to be practical we need materials with abreaking length a very substantial fraction of escape length.Even Kevlar 29's 200 km is a mere 25th of the 5000 km goal; touse that would be like fuelling the Apollo mission with dampgunpowder, and would require the same sort of astronomicalratio.
So, just as we were once always seeking exotic propellents, wemust now search for super-strength materials. And, oddly enough,we will find them in the same place on the periodic table.
Carbon crystals have now been produced in the laboratory withbreaking lengths of up to 3000km -- that is, more than halfof escape length. How happy the rocket engineers would be, ifthey had a propellant whose exhaust products emerged with 60% ofescape velocity!
Whether this material can ever be produced in the megatonquantities needed is a question that only future technologies cananswer; Pearson  has made the interesting suggestion that thezero gravity and vacuum conditions of an orbiting factory mayassist their manufacture, while Sheffield  and I  havepointed out that essentially unlimited quantities of carbon areavailable on many of the asteroids. Thus when space mining is infull swing, it will not be necessary to use super-shuttles tolift vast quantities of building material up to geostationaryorbit -- a mission which, surprisingly, is somewhat moredifficult than escaping from Earth.
It is theoretically possible that materials stronger -- indeed,vastly stronger -- than graphite crystals can exist. Sheffield[153 has made the point that only the outer electrons of theatoms contribute, through their chemical bonds, to the strengthof a solid. The nucleus provides almost all the mass, but nothingelse; and in this case, mass is just what we don't need.
So if we want high-strength materials, we should look at elementswith low atomic weights -- which is why carbon (A.W.12) is goodand iron (A.W.56) isn't. It follows, therefore, that the bestmaterial for building space elevators is -- solid hydrogen! Infact, Sheffield calculates that the breaking length of a solidhydrogen crystal is 9118 km -- almost twice 'escape length'.
By a curious coincidence, I have just received a press releasefrom the National Science Foundation headed 'New form of hydrogencreated as Scientists edge closer to creating metallichydrogen'. It reports that, at a pressure of half a millionatmospheres, hydrogen has been converted into a densecrystalline solid at room temperature. The scientistsconcerned go on to speculate that, with further research -- and Iquote -- "hydrogen solids can be maintained for long periodswithout containment".
This is heady stuff, but I wonder what they mean by 'longperiods'. The report adds casually that 'solid hydrogen is 25 to35 times more explosive than TNT'. So even if we couldmake structures from solid hydrogen, they might add a newdimension to the phrase 'catastrophic failure'.
However, if you think that crystallitic hydrogen is a trickybuilding material, consider the next item on Dr. Sheffield'sshopping list. The ultimate in theoretical strength could beobtained by getting rid of the useless dead mass of the nucleus,and keeping only the bonding electrons. Such a material hasindeed been created in the laboratory; it's 'positronium' -- theatom, for want of a better word, consisting of electron-positronpairs. Sheffield calculates that the breaking length of apositronium cable would be a fantastic 16,700,000km! Even in theenormous gravity field of Jupiter, a space elevator need have noappreciable taper.
Positronium occurs in two varieties, both unfortunately ratherunstable. Para-positronium decaysinto radiation in one-tenth of ananosecond -- but orthopositronium lasts a thousand times longer,a whole tenth of a microsecond. So when you go shopping forpositronium, make sure that you buy the brand marked 'Ortho'.
Sheffield wonders wistfully if we could stabilise positronium,and some even more exotic speculations are made by Moravec .He suggests the possible existence of 'monopole' matter, andhybrid 'electric/magnetic' matter, which would give not onlyenormous strength but superconductivity and other usefulproperties.
Coming back to earth -- or at least to this century -- it seemsfair to conclude that a small cable could certainly beestablished from geostationary orbit down to sea level, usingmaterials that may be available in the near future. But that, ofcourse would be only the first part of the problem -- a meredemonstration of principle. To get from a simple cable to aworking elevator system might be even more difficult. I would nowlike to glance at some of the obstacles, and suggest a fewsolutions; perhaps the following remarks may stimulate othersbetter qualified to tackle them.