Why does the cable weight damn the concept of airborne generators?
With an obstinate regularity airborne generator projects hit the headlines every few years. For over a decade we have seen diagrams and photographs; and now videos of grown men playing with kites and ingenious model planes doing stunts. What we do not see is any delivery of power. There are severe design problems in the proposed devices, such as the weight of high power generators, but there is never mention of the greatest problem of all, the connecting cable. This is regularly dismissed by the enthusiasts as the "tether". Granted that some of these projects are little more than investment scams, prompted by the vast amounts of taxpayers’ money available for "renewables", there are still some promoted by genuine believers. Whatever the motivation, they all shy away from the most fundamental design conundrum.
The basic constraints on cable design are manifold, in view of the fact that they need both mechanical strength and high electrical power capability: the latter to justify the whole investment. The principal requirements are that it must:
To consider fully the design features required to satisfy these requirements is to come to the conclusion that they are incompossible, which in turn means that the airborne generator is a chimera.
The least generally understood of the constraints are the electrical ones, which are the very essence of the problem. Many disputants simply ignore them, which is merely to postpone disaster. The requirement for large diameter conductors is fairly obvious, but the role of the dielectric insulation is perhaps less so. Air is the ideal insulant, as it has the valuable property of recovery from dielectric breakdown, hence the dominance of overhead power lines. Underground cables are more aesthetic but many times more expensive and difficult to maintain. Twin wires with spacers have been suggested for aerial applications, but they would be hopelessly awkward, tangled and vulnerable to cloud discharges. Solid dielectrics are mechanically stable, but they can be destroyed by electric breakdown, so designs have to be very conservative, with high safety factors, which means fat and weighty.
In breakdown studies the electric field strength tends to be referred to as electric stress, by analogy with mechanical failure. As in the mechanical case stress concentration tends to occur in regions of low radius of curvature: so, just as we avoid sharp corners in the design of aircraft windows, so we avoid sharp corners and thin conductors (unless we are designing a so-called lightning conductor). It is a popular myth that lightning follows the path of least resistance. In fact the tendency is follow the path of greatest stress concentration: so it is with electric breakdown. These considerations rule out any geometry other than a concentric one, where there is an inner conductor, an outer conductor and between them an insulator, all of circular cross section. The point of maximum electric stress is always at the surface of the inner conductor, so this is the focus of electrical design. The system thus stands or falls by the integrity of the interface between the inner conductor and the dielectric insulant. You can make kilometres of perfect cable, but one tiny gaseous bubble or metallic splinter at the inner join will eventually damn it. Once partial discharges begin, the dielectric will deteriorate until it reaches a critical condition, then all hell breaks loose. Partial discharge detectors are important instruments for monitoring the health of high voltage equipment, such as transformers, and they epitomise the reasons why such devices have a limited life.
Fortunately, the concentric conductor geometry is the easiest to analyse for stress distribution by application of the Gauss law. The stress in the dielectric is proportional to 1/r, where r is the distance from the geometric centre. The maximum stress is determined by the assumed dielectric breakdown strength, under which condition it is easy to show that the voltage rating is optimised when the ratio of the conductor diameters is e, the base of the natural logarithm (about 2.7).
Once a breakdown starts, the whole of the available electrical energy is concentrated on the breakdown site, with potentially great destructive effect. The hot electric arc will produce an explosive vaporisation of the whole caboodle, and the cable, already under considerable mechanical tension, will break with dramatic effect.
It is not possible to separate the mechanical, electrical and aerodynamic design constraints. As the Aeolian harp demonstrates, even a constant wind can produce oscillations in a cylindrical structure, while the notorious Tacoma Narrows bridge disaster highlights the dangerous combination of aerodynamic excitation and mechanical resonance. Real cables twist and snake in high winds, with resonant frequencies in the sub-hertz region, an effect that is greatly enhanced by icing. Kinks not only decrease the local radius of curvature, they also promote detachment of the dielectric from the conductor, creating a potentially disastrous void (the elastic properties of metal and dielectric are unlikely to match).
Magic solutions to the mechanical problems are often offered with total disregard for the electrical ones. Some commentators, for example, seem to blissfully unaware that carbon fibres are electrically conductive, when they advocate them for cable strength. Some even seem to be unaware that you need two conductors to complete the electric circuit.
Anyone satisfied that they have solved the design problems of the cable may now turn their attention to the design of the cable drum. Now that will be an impressive feat of engineering. What is the diameter of the drum when it is fully loaded with cable? Note that the cable, when extended, will take the form of a modified catenary, so that it is horizontal at the base. The torque on the drum as the cable is paid out or reeled in is scarcely a minor design problem. There is also the eternal challenge of the electrical connection between a rotating device and the static base. Those who advocate mobile installations would be well advised first to devise a good set of brakes. They might then even give some consideration to that little problem of making a high power connection between a rotating component and its stationary support framework.
The above are just a few of the problems that would come to the mind of any competent engineer, even before embarking on a design study: at which point he would put it away and seek a more realistic project.
Some earlier remarks on airborne generators
2001 March Missing numbers in the air
2006 February Airheads
2006 August A sense of proportion
2007 April They're back
2007 September Something in the air
2009 November Pie in the sky
2012 September Oh No!
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