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High-altitude kites can be flown in higher elevations than wind-mills, where wind speeds, energy density and capacity factors are over 10x higher. This write-up attempts to present the fundamentals, development status and quantify the technical and economic benefits. Single kites are saving 10-35% fuel on 4 commercial freighters, each providing the equivalent of 1 MW of propulsion benefits; power plants of 13 and over 100 MW are being considered. From available data, this author estimates that electricity costs of 0.04 $/kWh with 10 MW plants appear possible. This cost is lower than present tariffs, even without subsidies.
Kite Advantages – Wind speeds are highest near an altitude of 10,000 m (~33,000 feet)[1]. The force exerted on a windmill or kite increases as the square of wind velocity, while the available power increases by another factor of velocity (because power = force x velocity), so that mechanical power is proportional to the 3rd power of velocity[2]. Commercially available kites now fly at altitudes between 100 and 300 m. At 150 m they exert an average of 60% more force and produce 95% more power[3] than small sails or windmills of equal blade surface at 10 m above the ground.. Overall, relative to ground-level wind-mill-based generators:
1. Single kites can capture and generate more power (up to 25 to 100 MW?) at a steadier output because of flying at higher altitudes
2. Kites can add additional pull and power by flying in circular or figure-8 trajectories and thereby further increase “lift” in the wind direction and pull on the tether[3]
3. Require less of the weighty tower and blade hardware[4]
4. Generate less noise, and be less of a bird hazard
The steadier output is due to the significantly higher wind capacity factors (60-90%) than the 30-55% achieved from 80-120-m towers supporting wind generators today[5].
Kite Disadvantages – Although the idea of capturing the energy of high altitude winds was already being considered by John Etzler since 1833[2], thousands more windmill generators are presently in operation than power-generating kites or sky sails, especially if kite gliders, kite-surfers and ultra-light airplanes are not counted. We might list present-day the disadvantages, relative to windmills as:
1. Less experience and far fewer reliability data,
2. The area under and air space around the moving kite tether, which may need to be made of limited access to ground and aircraft activity, for both normal operation and in case of kite malfunction, is larger than the restricted area or air space near a wind turbine.
3. Power generation presently may require the kite to forcefully cyclically release tether cable against the generator load, which implies a interrupted power output as with a piston engine, and the need to overcome such intermittency, e.g. by pumping into a high-pressure reservoir or by using two (or more)[4,7] kites operating 180 degrees out of phase – unless the generator is airborne with the kite[9].
Technology Readiness -- Kites with a design pull force or load of 16 tons, made by SkySails GmbH are in operation on 4 commercial freighters[6], not for power generation but for pulling the ships and reducing the ship’s fuel bill. Such kites generate a design pull-power equivalent to ~ 1.6 MW. Present product offerings by SkySail range up to 64 tons design load (equivalent to about 6.4 MW), while increases to 130 tons (13 MW) are being considered. A US patent for kites attached to ships or to hydraulic generators was issued .to SkySails in 2009[7].
The sky sails or kites are tethered to the ground or ship via one polymer-fiber (such as Spectra) rope, braided around a core power cable, which powers the kite control gondola near the kite[7].
KiteGen reported successful stationary power generation of ~40 kW at Astia, Italy. Their estimated electricity cost of a future 100 MW system is € 0.03 or $ 0.04 per kWh, while considering the possibility of plants of up to 1000 MW. This author’s preliminary analyses place the upper limit of kite power plants closer to 25 MW, as determined by the size and weight of the tether.
A third company, Makani Power, based in Alameda, CA, also uses single tethers on their kites (shaped like aircraft wings), but generates the electricity on-board[9], which should enable continuous power generation, rather than intermittently. Saul Griffith’s video talks about flying at heights of up to 610 m (2000 feet), and projects generating power in the range between 230 kW (with a Cesna-sized wingspan of 10.3 m), 1.3 MW (Gulfstream wingspan of 28 m), 6 MW (Boeing 747, 64.4 m), and 15 MW (Spruce Goose, 97.4 m). For comparison, present 16-ton or 1-MW SkySails’ sails measure up to 600 m2 (maybe 37 x 16 m).
Much of the winch and rope design technology is available from the shipping and crane industries. One can estimate the minimum diameter of a tether to hold the kite of a 100-MW plant, by assuming a reasonable tether release velocity (~ 5 m/s) to obtain the tether force* and from there the diameter of the tether, which would correspond to the tensile stress limit of the chosen material. The force (incl. a 2x safety factor) would be 40 million newtons (4077 tons) at the tensile stress limit. For Spectra fiber, with its limit of 3.5 GPa (510,000 psi)[8], the diameter would need to be at least 12.7 cm (5.0 in.). If this diameter is perceived as too extreme, 6.4-cm (2.5-inch) diameter tethers, which are common in the shipping industry, would be enough to hold kites of 25 MW plants.
* Force = power / velocity.
Economic Aspects – To determine/estimate a kite-based electricity cost, lets bracket it between the (assumed correct claim of 10-35%) savings with SkySail ship propulsion vs. oil-based propulsion and the projected electricity cost of 0.04 $/kWh by KiteGen[4].
1. Fuel-oil-based electricity generation at 33% efficiency would cost 0.173 $/kWh worth of fuel at 80 $/barrel + ~0.022 $/kWh to maintain and amortize the generation equipment, adding up to about 0.20 $/kWh, or 0.30 $/kWh if we consider a ship’s oil-based propulsion at 20% efficiency. Adding the properly-sized kite so that it takes on half the load[3] means that the 1-MW kite propulsion cost is 0.168 $/kWh for an average ship-fuel saving of 22%.
2. KiteGen’s extrapolated electricity cost estimate for a 100 MW plant is 4 $/kWh. Applying the standard chemical engineering process size vs. cost scaling law of 0.6-power to a 10 and 1 MW kite power plant, we would get electricity costs of 0.159 and 0.634 $/kWh. This would contradict the claim by SkySails that “wind is cheaper than oil” for their 1 MW kites. It would hold if KiteGen’s cost estimate had been 0.01 $/kWh.
Therefore, given the uncertainties of converting SkySails’ system to a stationary power plant vs. the larger uncertainties by KiteGen’s extrapolations to larger size plants than the 40 kW unit tested to date, we might use an interim value of 0.04 $/kWh for a “middle” sized kite plant of 10 MW design output.
By way of comparison, 6-MW off-shore wind mill operators in Germany were to receive about 0.09 $/kWh for their electricity, but last year the rates were raised to 0.15 $/kWh for the first 12 years. This is about three times the current market price and significantly more than on-shore wind turbine operators receive.
Siting of Future Kite Demonstrations -- NELHA has an “ocean research corridor”, which might be used for kite tests and demonstrations. However, the air space above this corridor may not be included, and, as MIT researchers found out in 2001, NELHA’s ocean research corridor confers no permitting advantages[10]. Any project would still need to go through a process to obtain federal, state, and local permits. The number of permits required and agencies that need to be involved in a decision is inversely proportional to how close the project is to shore. By moving farther away from shore, the regulations governing the project would be federal; the need for local and state permits would be eliminated.[10]
Conclusions -- High-altitude kites can be flown in higher elevations than wind-mills, where wind speeds, energy density and capacity factors are over 10x higher, thus providing a heretofore unexploited source of energy, which by itself could meet all the world’s needs for energy. Supporting evidence:
1. Mapping of wind speeds and energy density vs. location and altitude, showing peak energy densities around 10,000 m;
2. Single kites are saving 10-35% fuel on 4 commercial freighters, each providing a design pull of 16 tons or the equivalent of 1 MW of propulsion benefits and commensurate with the ship’s traditional power plant [3];
3. Power plants of 13 and over 100 MW are being considered. From available data, this author estimates that electricity costs of 0.04 $/kWh with 10 MW plants appear possible. KiteGen’s estimate is 0.04 $/kWh for a 100 MW kite-based plant [4].
References
[1] Cristina L. Archer and Ken Caldeira (CA State U. & Dept. Global Ecology, Stanford,CA), "Global Assessment of High-Altitude Wind Power," Energies, 2, 307-319 (2009)
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; http://www.mdpi.com/1996-1073/2/2/307/pdf
[2] Wind power passing through an area is: Power = 1/2 x (air density) x (velocity3) x (area), see Wikipedia
[4] M. Canale, L. Fagiano, M. Milanese, M. Ippolito (Kite Gen Research S.r.l. and Sequoia Automation, Chieri, Italy), “KiteGen project: control as key technology for a quantum leap in wind energy generators,+ Proc. of American Control Conference, New York 2007 www.kitegen.com and pdf
[5] Frank Dohmen, “Germany's First Offshore Wind Farm Goes Online,” Spiegel Online International, 28 Apr. 2010 website
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[6] MS Beluga Skysails is the world's first commercial container cargo ship which is partially powered by a 160-square-metre (1,700 sq ft), computer-controlled kite. Fuel savings up to 20%. Made by SkySails GmbH & Co. KG, Hamburg, Germany
[7] Stephan Wrage and Stephan Brabeck (Skysails GmbH, Hamburg, Germany), “Wind energy plant with a steerable kite,” US Patent 7504741 issued 17 Mar 2009, filed March 30, 2007.
[8] Structural Materials, at website of islandone.org
[9] Saul Griffith (Inventor) and Corwin Hardham (PhD & CEO), Makani Power, Inc., Alameda, CA, contacts: http://makanipower.com/,
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510.629.4316 and video
[10] Mark Anthony de Figueiredo (ME Dept., MIT), ”The Hawaii Carbon Dioxide Ocean Sequestration Field Experiment: A Case Study in Public Perceptions and Institutional Effectiveness,} MS Thesis, Massachusetts Institute of Technology, June 2003, http://sequestration.mit.edu/pdf/defig_thesis.pdf |
