Flywheel Power to Orbit?
Background Regarding this Topic
In the latter 1970's, the well-known science fiction writers, Arthur C. Clarke and Charles Sheffield, in their respective novels, "The Fountains of Paradise" and "The Web Between the Worlds", introduced the concept of a "skyhook"... a cable that would run from a 22,350-mile-high geosynchronous orbit, where a satellite rotates with a 24-hour period of rotation and appears to a terrestrial observer below to remain fixed in the sky over a fixed point on the equator. Such an "elevator cable" could then be used to hoist cargo from the surface of the Earth up to a geosynchronous satellite, whish would house a solar-array-powered electric motor and cable reel.
Beaming power over distances of tens of thousands of kilometers wouldn't be easy or efficient.
At the time, there was no material that could even begin to bear its own weight from 22,350 miles up. (The weight isn't quite as great as it might seem because gravity falls off as 1/r2, where r is the altitude, expressed in Earth radii. The actual hanging eight of the cable would be equivalent to a cable about 3,100 miles long.) Piano wire could break under its own weight if it were more than about 18 miles long. In 1979, the graphite composite material with the highest strength-to-weight ratio available would have been "Spectra", and it might have supported its own weight up to an altitude of, perhaps, 150 miles. In their 1980 paper entitled "Space Elevators", Dr. Robert L. Forward and Hans P. Moravec show how the cross-sectional area of a cable could be increased with increasing altitude in such a way that Spectra might have been used to construct such a cable. However, it would have been marginal, and it wasn't tried.
Arthur Clarke uses diamond fibers as a literary device to justify his super-strong cable material in "Fountains of Paradise", while Charles Sheffield recruits hypothetical "silicon fibers". But this was all "pie-in-the-sky" (in more ways than one) science fiction at the time.
In the early 1990's, carbon nanotubes entered the picture--material that possesses the hitherto-mythical strength-to-weight ratios (at least 600 times that of the strongest steel) sufficient to enable "skyhooks". Carbon-nanotubes held together by a plastic matrix are just now entering pilot production. These will be very popular materials for many types of applications. The Chinese have allegedly found a way to fuse carbon nanotubes to make an ultra-strong material with no dilution of its strength by plastic binders.
The current instantiation of this idea would use a wide, thin ribbon running from the equator to a geosynchronous satellite. Cargo would be raised and lowered by "lifters" that would grip the cable with rollers powered by an electric motor on each "lifter". Power would be beamed from the ground up to the "lifter" using lasers on the ground and 80%-efficient gallium-arsenide solar cells on board the "lifter".
No electric wires could be run up and down the cable for several reasons having to do with the weight and the electrical resistance of the copper.
There is some evidence that carbon nanotubes can become superconductors at sufficiently low temperatures. The problem is that maintaining superconducting temperatures at the Earth's distance from the Sun would be a very challenging problem when you can't add any weight to a ribbon that's thinner than paper.
Propelling the Lifters with Flywheel-Stored Energy
One interesting alternative for the energy storage to power a lifter that would eliminate the need for a laser/solar-cell power supply might be a nanotube-based flywheel. As estimated in the article, Carbon_Nanotube_Flywheel_Energy_Storage, a carbon nanotube flywheel, if its rim could rotate at 10 kilometers/second, should be able to store 5,000,000 joules per kilogram of rim weight. Five megajoules would lift a kilogram 5,000,000 meters or 5,000 kilometers in a one-gee field... just enough to boost a kilogram all the way to synchronous orbit (remembering that the integrated effect of the Earth's gravitational field from the ground to a geosynchronous orbit is equivalent to about 5,000 kilometers in a one-gee field).
Five megajoules would be equivalent to a little more than 1,200 kilocalories per kilogram (recognizing that what we call a "calorie" in our diets is really a kilocalorie).
Quadrupling the Energy Storage of the Flywheel
Of course, boosting a kilogram of the flywheel rim to geosynchronous orbit wouldn't be enough to lift the rest of the flywheel to geosynchronous orbit, let alone the rest of the lifter. However, the flywheel could be made quite large and could spin in the plane perpendicular to the cable. This would reduce the centrifugal acceleration at the rim and might permit the flywheel rim to move at 20 kilometers/ second, quadrupling the energy storage capacity of the flywheel. In this scenario, it could store enough energy to elevator the lifter and its payload all the way to geosynchronous orbit (with the flywheel rim weighing ¼ the total weight of the lifter and its payload).
This would obviate the need for power beamed up by laser.
Fuel cells might be another energy storage gambit. (It might be necessary to recharge the fuel cells at a solar-array-powered recharging station along the way) The problem with fuel cells is that, like chemical rocket fuel, an oxidizer would have to hauled up along with their fuel, and this would lower their effectiveness compared to ground-based fuel cells.
The True Sky-Hook
I'm still concerned about wear-and-tear on the tether.
An alternative could be a hook and line that would haul small payloads to orbit along the tether. A solar-array-powered electric motor would be located at geosynchronous orbit to hoist the line and its payload. The problem with this approach is that the cable would weigh so much that a lot of the lifting energy would be spent just lifting the cable.
One way around this problem would be to allow the cable to fall, or even to lower a weight to the ground, thereby offsetting the weight of the cable that was being reeled in.
In the limit, this could become the space elevator, in which cargo from space (e. g., asteroid metals) were continuously lowered on the down side of the cable, while cargo from the ground were continually hauled up.
Of course, rotovator concepts might also be attractive.