# Optimization of a soft wing with turbines aloft

It is an updated and completed report with some corrections and comprising a first study of a 350 kW range flexible flygen kite. With an elevation angle of 30 degrees the power is 245 kW due to cosine loss. After other losses it can be about 150 kW.

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It would be good to see the derivations and workings explained, referenced and explored in a bit more depth

It is an old report that is updated and corrected. All the paper is about the appropriate swept area rA by the turbines aloft in regard to the kite area kA as the turbines aloft should add 50% drag of the kite alone. 221.47466 m² (kite area) x 0.3 (drag coefficient) = 66.442398, so two times 33.2212 (turbines area x drag or thrust coefficient = 1).

All is in the table about parameters.

In the utility-scale model 33 m² rA (swept area by the turbines, r = rotor, estimated drag coefficient being 1) go with a 221 m² soft wing.
33 m² = 8 turbines of 2.3 m diameter that are used for the 600 kW Makani M600.

All this is precised in the paper. But, as the conclusion indicates, a deeper analysis is required.

Hypothesis for a calculation of M600: 2/27 x 1.2 x 1.2 x 50 [supposed area] x 1000 x (10.6)² = roughly 600 kW before cosine loss.
L/D ratio wing alone = 10.6; optimized L/D ratio with turbines = 7.0666666; wing area estimated at 50 m². With a lift coefficient CL of 1.2, wing area x CL = 60; so wing area x CD should be 5.66, leading to a drag coefficient of 0.1132. The thrust (drag) of the turbines should add 50% of 5.66, so 2.83. The thrust coefficient of the turbines is 2.83/33 = 0.0857575.
Verification: 33 x 1.2/2 x 70.666666 x70.666666 x 70.666666 x 0.0857575 = roughly 600 kW.
It looks that the turbines are large due to E-VTOL requirement, then the thrust coefficient is lower during operation.

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Some precision: in the utility-scale example the kite area kA is 221.47466 m², and the drag coefficient of the kite alone kDC is 0.3, as specified in the document. 221.47466 m² x 0.3 = 66.4424, so two times the value of rD [rA (area swept by the turbine(s), in m²) x estimated drag coefficient of 1] for the turbines, so 33.2212 as specified, adding 50% drag to the kite alone.

Some precisions and corrections:
The drag coefficient rD of the turbines aloft is also called the thrust coefficient which is used for wind turbines or propellers for planes. The thrust coefficient depends of the propeller design https://web.mit.edu/16.unified/www/FALL/thermodynamics/notes/node86.html. On the report it is 1, that is a rather high value.