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Harnessing High Altitude Wind Power
jakosc writes "The Economist has an interesting article about increasing the efficiency of wind-powered generators by turning them into flying wind farms. These tethered generators would harness high speed jet stream winds above 15,000 ft and in theory could give outputs of 40MW per generator (PDF). The developer's website has more details of some of the safety, technological, and economic issues."
The wind is a side effect of the atmosphere mixing. If you calculate the total amount of energy from the sun, the current human consumption of ~12 terawatts is considerably less than 1%. It's probably big enough to pay attention to, but as long as you bring the farms online a few at a time, you aren't going to do any sort of long term damage.
(sunlight reaches the earth at a rate of about 1300 W/m^2; model the earth as a big disk with a radius of ~6,000,000 meters; 1300*3.14*6000000^2 = 1.45*10^17 watts; 1 terawatt= 1*10^12 watts; 1.45*10^17 watts=145000 terawatts; 12 is 0.008% of 145000.)
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I would be far more concerned with the sky falling.
... imagine terrorists blowing up the control stations, that could be pretty bad too.
Cables can snap, structures and components can fail, flying wind turbines get in the way of air traffic, etc. To be reasonably safe, flying power farms would need to be at least 50km from inhabited areas (maybe more, depending on how slowly they and their components crash given any particular failure mode) and 100km away from all commercial air corridors to avoid interference with emergency landings since planes can certainly plow through a wind farm faster than the farm's operators can land its flying turbines.
It seems simply too dangerous for deployment anywhere remotely close to populated areas.
I'm more concerned about this development further endangering general aviation, on top of the states trying to tax private pilots to death.
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Aluminum: 26.50 nm and 2.70 gcm3 Graphite: 9.8 - 41 m and 2.09-2.23 g/cm So at similar densities, graphite's an order of magnitude more resistant. A cable without metal conductor is not practical here. The aluminum component is a must.
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The resistivity of graphite fibers varies quite a bit. For example the venerable Toray T300 fibers are listed around 2000 microohms-cm, while Union Carbide P100's are around 250. You have to be careful because bulk carbon is different. Aluminum is about 2.7 in those units. Graphite can be specially made to have lower resistivity but I'll use the 250 value for ROM calcs. Use a 16km cable length.
So if we assume a 1 in^2 cable section (6 cm^2) and they can manage to get 15kV, the current for 40MW is 2667A. The total resistance of a 16km cable would be 250e-6/6*16000*100=67 ohms. The power loss would be 2667^2*67 = 491MW. So this ROM calc shows it obviously wouldn't work because you would need a ridiculously fat cable.
The paper they wrote talks about an Vectran/aluminum conductor. Let's look at that quickly. To get 10% cable losses the cable resistance would have to be 4e6/2667^2 = .5 ohms. Using resistivity=2.7e-6 ohm-cm the cable section would have to be 2.7e-6*16000*100/.5=4.3 cm^2. The volume would be 16000*.00043=6.9m^3 and the mass 2700*6.9=18630kg (19 tonnes). So there you have 40 tonnes at least for the conductors, 60 if they use 3-phase transmission.
Vectran, Spectra, and Aramid fibers are all similar crystalline organic fibers. Ultimate tensile strength is usually around 3GPa, but you would probably use at most half that for a real world application. So to hold a 19000kb cable where F=19000*10=190000N, A=190000/1.5e9=1.27e-4m^2. Density is around 1500kg/m^3 so the Vectran mass/cable would be 1.27e-4*16000*1500=3048kg or 3 tonnes. So 6 or 9 tonnes total. Just to hold the cable weight.
The aerodynamic loads are hard to figure. Let's do something really rough. In their paper they quote energy density at altitude of 20kW/m^2. Air density is at 10km is .4kg/m^3. Wind velocity would be (20000/.4)^.5=223m/s. Assume they do really well and get 50% of the energy out, the rotor projected area has to be 40000000/10000=4000m^2 or a square 63m on a side. Energy density goes with the square of V, so the delta V would be 223*(1-.707) = 65m/s. Using the momentum equation, the force per m^2 is F=rho*V*delta V=.4*223*65=5798N. The total force would be 5798*4000=23,192,000N. Thats 5 million pounds.
This is the sort of time you wish you had someone to check your calcs, because that seems high. But if it is right, that would need a Vectran cable 1.27e-4*23000000/190000=.015m^2 area or about 7cm in diameter. Well, that looks maybe doable after all.
But the thing is a monster.
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