Windpower at 35,000 feet

nexium · Sep 2, 2005

I just discovered www.skywindpower.com I was skeptical, but it now appears workable. It has been tested to 15,000 feet, uses 2 heliocopter blades, each 15 feet in diameter. The tether (I'm guessing) is two electrical conductors insulated for 50,000 volts. I presume 4 wire for three phase insulated for 1/2 million volts is needed for the 40 megawatt unit thought possible. Electric power is sent up the tether to fly the assembly part way to altitude, after which wind will pull the tether taut in a kite/autogyro fashion. The motors then become generators which convert 30% of the wind energy to electricity. Perhaps half the power heats the tether (I squared R losses) which hopefully prevents ice forming on the tether. 50,000 volt alternators may be available, but airborne transformers will be essential to produce 1/2 million volts. I'm guessing the tether is 1/3 longer than the altitude. Wind is typically several times stronger at high altitudes from 30 degrees latitude to 50 degrees latitude. An altenative is to use part of the power for a satellite type transponder which could provide long distance telephone and data links, up to about 100 miles in all directions. Please refute, embellish, comment and/or do detailed analysis. Neil

vogon13 · Sep 2, 2005

This is a refinement of my VLEC concept. Interesting take on the original idea. <div class="Discussion_UserSignature"> TPTB went to Dallas and all I got was Plucked !!So many people, so few recipes !!Let's clean up this stinkhole !! </div>

nexium · Sep 2, 2005

VLEC = very long extension cord. In the future we may have electric powered heavy lift vehicals and super conductor extension cords to power them to about 40 kilometers altitude which is about maximum to avoid air friction heat damage as the VLEC falls back to Earth for re-use. Neil

vogon13 · Sep 2, 2005

Sorry, couldn't resist a jokey this morning, news is so grim today. IIRC, I saw an artists concept of a tethered balloon with photo-voltaics all over it. This concept might have better economics as the wind would usually blow 24/7. Photo cells don't work at night. <div class="Discussion_UserSignature"> TPTB went to Dallas and all I got was Plucked !!So many people, so few recipes !!Let's clean up this stinkhole !! </div>

siarad · Sep 2, 2005

I think transformers would be too heavy unless a much higher frequency was used, as do aircraft with 400Hz, as the size is proportional to frequency squared. Of course losses increase with frequency <img src="/images/icons/frown.gif" />

nexium · Sep 2, 2005

400 hertz might be an improvement, which would also make the alternators (they are thinking 4 or 8 alternators and rotors for 40 megawatts) lighter, but the web site clamed only a small percent of the average wind energy was needed to keep the assembly at altitude, so perhaps a few tons of transformers is no big deal. Neil

henryhallam · Sep 2, 2005

Why do you need to increase the voltage to a full 500kV? 50kV ought to be more than sufficient to carry several megawatts. If we have a steel conductor (for strength), 1.5 inch in diameter, this gives a cross-sectional area of 11.4cm^2. At 11km length (a little more than 35000ft) its resistance will be around 4.4 ohms. The cable will weigh 100 tonnes. At 40MW and 50kV the current is 800A. Through a resistance of 4.4 ohms you lose 2.8MW. The surface area of the cable is 1320m^2. We can find an upper bound for the equilibrium temperature by Stefan's law for black-body radiation: P=(sigma)AT^4 2800000=(5.7 * 10^-8) * 1320 * T^4 T^4 = 3.7 * 10^10 T=440K or about 170 degrees Celsius or 330 Fahrenheit. In reality the temperature would be a bit lower due to the airflow past the cable. My hunch is that although the steel will be weakened somewhat by being this warm, a 1.5 inch cable is going to be pretty strong in the first place... I don't know what force it needs to exert to keep the platform in one place. Actually I just realised the cable will have to be longer than 11km because it must be at a certain angle to provide a horizontal force. So that will increase the total loss in the cable but I don't think it should affect the temperature. Increasing the voltage does allow you to use a lighter cable but I think you will need a fairly thick one anyway in order to be strong enough to keep the platform in one place. Also you have issues with losses due to corona at voltages much over 50kV which might require insulation, adding more weight. The weight of the transformers at the top has already been mentioned. Question: What do you do about lightning?

spacester · Sep 2, 2005

An 11 km tether made of 40 mm diameter (1.575 inch) steel at 4.53 kg / m^3 will mass pi * (0.02 m)^2 * 11000 m * 4.53 kg / m^3 = 62.6 tonne Less than I expected. The top of the tether will need to support that weight. The cross-sectional area is pi*0.02*0.02 = 0.001256 m^2 If under pure tension, the stress will be 62600 kg / 0.0001256 m^2 = 498 MPa 498 MPa = 72.2 ksi ( ksi = psi * 1000 = 1000 lb per sq. inch) That is a large number compared to the yield strength of mild steel at 51.2 ksi, but high strength steel (massing the same) can provide higher strengths. If we consider transverse stress due to the actual catenary curve of the VLEC, Mohr's Circle tells us that the maximum Von Mises' stress would be no more than um twice the pure tensile load case (IIRC). Oops out of time . . . <div class="Discussion_UserSignature"> </div>

henryhallam · Sep 2, 2005

Of course I guess we need two of them for a complete circuit.. and be VERY careful not to let them touch! Maybe a couple of platforms at intermediate heights with rotary wings for lift (powered from the cables) could help support the cables and reduce the tensile loads a bit.

nexium · Sep 2, 2005

According to the web site: Variable pitch rotors and increasing wind speed typically offset the decreasing pressure up to about 35,000 feet. The rotors near the midpoint can pull the top to a slightly lower altitude. A winch (not wench) at the ground end can shorten the tether if energy harvesting conditions are better at 30,000 feet than at 35,000 feet. Likely the average angle the tether makes with Earth's surface can be adjusted by changing the rotor pitch. The tether can be tapered, perhaps halving the weight and thus the strain at the top end. If the wind stops for a few minutes, the alternators can run as motors to keep the tether taut. The jerk that results when a slack tether is pulled taut suddenly, is likely to break the tether. Neil

scottb50 · Sep 2, 2005

I would hope that wench could bring you a beer once in a while also? <div class="Discussion_UserSignature"> </div>

vogon13 · Sep 2, 2005

Fatigue life of a cable at that high of a (presumably) variable load will be short. Stress highest at top end, weight of lower portions will offset pull of turbine. Maybe taper the cable ? (tapered cable will complicate I^2 R loss calculations, btw) <div class="Discussion_UserSignature"> TPTB went to Dallas and all I got was Plucked !!So many people, so few recipes !!Let's clean up this stinkhole !! </div>

scottb50 · Sep 2, 2005

So, how much does 6 miles of cable weigh? <div class="Discussion_UserSignature"> </div>

igorsboss · Sep 2, 2005

Would microwave power transmission from sky-to-ground help? This would let you use a dialectric cable, such as stronger, lighter kevlar for the tether. I know virtually nothing about microwave power transmission, except that it has been proposed to transmit power from a satellite to Earth... Spaceter, I think you calculated only the static load on the cable, as if the cable it were hanging from a suported platform. I really like your calculation, but since this is a power station, it has a huge dynamic load as well. The dynamic forces of (a) lift and (b) the force to turn the alternators are all coming from the cable tension. That is, since only thing that keeps this kite from flying away is the kite string, all the generated power is also coming from the kite string. That is, your cable strength estimate is reasonably close only when the power station is at idle. Once you generate power, the string tension would increase dramaticly.

nexium · Sep 3, 2005

According to my wire table anealed copper 0000 gauge (0.46 inches in diameter) wire is 0.06 ohms per 1000 feet at about 80 degrees c =2.1 ohms for 35,000 feet. The 4.4 ohms is about right for steel, 1.5 inches in diameter at 100 degrees c. Some kinds of steel are higher, I think, perhaps as much as 10 ohms at 350 degrees f. I think the tether needs to be a composite of aluminum or another metal that is both stronger and a better electrical conductor by weight than steel. Has anyone details on electrically conducting tethers for high current and lots of flexing/fatigue? Neil

spacester · Sep 3, 2005

hmmm . . . igorsboss, certainly the stress calculation is incomplete, I was just getting warmed up and ran out of time. lol Yeah, the first calc was for a vertically hanging tether, a long ways from the VLEC's loading. The dynamic load will determine the fatigue life for a given material. An aluminum alloy would be called for if the tether transmits power, maximizing the combination of conductivity and ductility. I like the kevlar if we can beam the power down. Microwave energy beaming is a very viable technology. The problem with Solar Power Satellites is that they operate way up in GEO and so the rectenna (receiving antenna) is huge. Here, the beam density could be kept high, birds would fry but only in a narrow beam :-( and the rectenna size would be practical. The loads on a curving cable are interesting to ponder. (I'm gonna work without a net (no google) and see if I get this right.) Being a flexible cable, presumably braided wire, this is not like standard beam equations. The cable will assume the shape of a catenary curve. Deviation from vertical will force the cable to support its own mass at some angle to the centerline of the cable, this is called shear stress. Shear stress is pretty much always the structural failure mode when things fail, it's a bad thing. The dynamic loads, hmmm... the kite string is under tension, but cannot be the source of power. Power is energy over time and energy is work and work is force times distance, and the kite string isn't moving , it's just sitting there under tension. A theoretical steady state condition would have no movement in the tether at all; it cannot be generating power. The kite string may be vibrating, but the energy associated with that movement will be a function of the mass of the string itself, not the source of the tension. The tension on the tether is in opposition to the drag force on the turbines. um IIRC: F = rho *Cd * velocit <div class="Discussion_UserSignature"> </div>

igorsboss · Sep 3, 2005

The dynamic loads, hmmm... the kite string is under tension, but cannot be the source of power. Power is energy over time and energy is work and work is force times distance, and the kite string isn't moving , it's just sitting there under tension. A theoretical steady state condition would have no movement in the tether at all; it cannot be generating power. The kite and the string are indeed moving: relative to the wind! Your steady state condition is called "dead calm". I think the lesson here is to look for places in the world where a steady wind blows closer to the ground, rather than 35,000 feet. Keep the tether short. Here are two: 1) Fly the kite in trade winds. (ie. Aruba's southwestern shore) Steady winds. (One Happy Island: I've was there for the Eclipse... fond memories!) If you fly in the trade winds off shore, you'll need to transport the energy back to shore somehow. In that case, you might consider harvesting ocean current energy as well. 2) Mountain tops. Everest sometimes intersects the jet stream. The jet stream is a tiny target, and it meanders hundreds of miles a day. The wind isn't always available at 35,000 feet, at least not in the same place every day.

igorsboss · Sep 3, 2005

If the turbine is blocked from turning, its coefficient of drag will actually be higher than if it is turning, all else equal. A loaded alternator loads the turbine, which increases the coefficient of drag. Feather the props when they aren't loaded. Don't just apply the brakes, or the whole thing will snap in two.

nexium · Sep 3, 2005

Bad news if a rotor or alternator bearing seizes up? Neil

nexium · Sep 3, 2005

Dielectric cable = kevlar or other insulating tether might help the lightning and hurt the icing problem. A ten meter parabolic dish would likely produce a sufficiently tight beam at microwave frequencies. As the assembly got jostled by wind gusts and transients traveling up and down the tether, the dish would need to reposition quickly to a void cooking people and pets close to rectenna. Microwave power trasmission, perhaps, if the the icing, lightning and weight of the tether threaten the project. A film of water on a kevlar tether may increase the possibility of a lightning hit as compared to wire. 62 tons of tether may be enough if the tether is tapered and several power making assemblies (at intervals along the length) can switch quickly to motor mode when the tether is approaching double average stress. Multiple power making assemblies means a broken tether can land gently like an autogyro, minimising danger to people living near a tether winch. CNT = carbon nano tubes or other carbon fibers can only carry a few amps without heat damage. I think we need metal wire conductors unless laser or microwave power beaming is best. Neil

igorsboss · Sep 3, 2005

...increase the possibility of a lightning hit... I agree, lightning hits are inevitable.

spacester · Sep 3, 2005

The kite and the string are indeed moving: relative to the wind! Your steady state condition is called "dead calm". Aha, now I see the communication disconnect! We are working out of the same physics book after all. <img src="/images/icons/wink.gif" /> You're talking about the wind loading on the tether. I thought you were talking about the tensile force in the tether. I need to add a wind load vector to my free-body diagram of a finite element of a length of tether. (This would be a simple problem for FEA.) Transporting energy ashore: ship it as hydrogen. Mountaintops make sense. The whole trick here is establishing two frames of reference, one stationary relative to the wind and one stationary relative to the surface of the planet. The FAA will not be amused by this idea. Sorry, had to mention that. <div class="Discussion_UserSignature"> </div>

rogers_buck · Sep 3, 2005

Think of the bonanza they'd get when a thunderhead shows up at the straw. The whole cloud would make nice the path to ground and all of its friends would show up to discharge. I wonder if you could take an abandoned salt mine and turn it into a giant condensor. Let the thunderheads do there worst and charge up your underground cap. Don't know what kind of dielectric you'd need for such and extreme component...

j05h · Sep 3, 2005

general comments. Very interesting idea. Split the tether from power cables - use a Kevlar/kapton tethers to hold each fan-set down, then a different cable for power transmission (or beamed micros/laser). 35,000 feet isn't much of a problem at sea. You'd need full air traffic control for power site, though. FAA only has authority in territorial waters, but something like this can be incorporated into flight rules anywhere. I like the idea of powering concrete/seacrete/pykrite floating cities with high-altitude fans. You could follow the trades as suggested, carrying enormous loads of cargo containers among the other possible projects. Steering should be interesting (I'm picturing a "spinnaker" mesh of fans) but it would be designed to dock easily into the next sea-city. This could be done by individual segments or cities. Another source of power is damping on the line. This could be done in the fan assembly, it would both stabilize and add power. There is a Scottish sea-power pilot plant that does this with floating buoys. Smart materials that are self-illuminating would be useful along the cables/tethers. Is the autogyro feature enough to keep it aloft at altitude? Is a kite/glider needed as well? Josh <div class="Discussion_UserSignature"> <div align="center">We need a first generation of pioneers. </div> </div>

igorsboss · Sep 3, 2005

You're talking about the wind loading on the tether. I thought you were talking about the tensile force in the tether. For all I know, we might be on the same page, but I'm not quite sure yet. I'm not precicely sure what you mean by "wind loading on the tether". I'm not talking about the friction of the wind on the tether. I am concerned with the tensile force in tether. Perhaps if I explain my thoughts with a bit more precision and less handwaving... First, the set-up: Please consider the lift/weight/drag/thrust force vectors on the kite (on average, relative to the ground). I'm sure you will agree that since the kite is stationary, these force vectors must sum to zero. Also, consider the kite's power generation, relative to the moving fluid around it. This fluid's motion lets the turbine generate power, 'cause work is force over a distance. The kite's wings and rotors can only generate lift and drag when the fluid is moving. Since the kite carries a wind turbine, the kite's drag force varies; the more power the kite generates, the higher the kite's drag force. This kite is tethered by a downward sloping tether, which pulls with a tensile force. The forward component of this force acts as thrust, and the downward component of this force acts as weight. This tether is the kite's only source of thrust. Now, when somone turns on a light bulb, the bulb puts an electrical load on the alternator. The alternator puts a torque load on the turbine. The turbine puts a drag load on the fluid. Since the fluid is moving, the turbine turns, the alternator spins, electrical power is generated, and the bulb lights up. Now for my point: When power is generated, the drag force on the kite increases. To keep the kite anchored, thrust must increase, to balance drag. Since the only source of thrust is the tether's tension, the tether's tension increases.

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