Betz limit and power available in the wind

[PierreB]

@blimpyway

I get an efficiency of 0.24 for dragging a parachute at 1/3 wind speed and a drag coefficient of 1.62

I agree. In my previous comment I preferred to simplify with a drag coefficient of 1, mainly to be able to reuse a previous example. That said, when the Reynolds number increases—that is, when the dimensions and speed of the parachute increase—the drag coefficient tends to decrease and approach 1.

I also noted that when the drag coefficient Cd is above 1, the power available in the wind in yo-yo (“lift”) mode would be above 4/27.

@blimpyway

I doubt that the same formulae are directly transferable to a lifting kite because, as in propeller-lift turbines, it has to account for swept area. e.g. doubling the wing’s aspect ratio also doubles the swept area, increases L/D ratio, etc..

In this case, we use the complete formula, as indicated in the quote 4, including CL(CL/CD)². Unlike what happens with a parachute, the swept area is not the same as the surface area of the kite, being far larger. But the principle is the same, as the power available in the wind within the swept area in yo-yo mode (for crosswind or parachute kites) remains 4/27 (excepted if the drag coefficient Cd is above 1 for a parachute where surface area is the swept area in yo-yo (“lift”) mode, the swept area going downwind?).