Betz limit and power available in the wind

AWE lift power systems are also named as yo-yo or reel-out/reel-in or pumping mode systems.

Now what would become of the value of 4/27 if, instead of crosswind kites, tether-aligned devices like High drag coefficient parachutes (without their own lift) or Parasail-based Airborne Wind Energy Systems (with their own lift) are used to harvest the power available in the wind which is delimited by their projected area, knowing that very high coefficients (Cd) of 2.2 and more were reported?

For example if a tether-aligned (non-crosswind) parachute has a Cd of 3 (assuming it has no lift to simplify, or even a thrust coefficient (Tc) including a Cd of 3 and a lift coefficient (Cl) of about 1) “the power available in the wind” (in pumping mode, so with the quoted limit of 4/27) would be 3 times, so 12/27, is not it?

This is where the paradox becomes blinding: we will place in the “AWE lift power systems” category a tether-aligned parachute which only generates drag or, at most, a minimal part of lift compared to that of drag within the generated power.

The explanation comes from the fact that the AWES mostly envisaged are crosswind AWES, generating lift to fly at several times the wind speed while sweeping a large area and producing great power relative to their respective kite area. This does not prevent the fact that for yo-yo mode, whatever the type of flight, the swept surface “retreats” and causes a loss of power compared to the Betz limit (16/27). But this loss or limit is measured on the swept area.

So, in yo-yo mode, a crosswind kite with a very high L/D ratio, will have a power potential equal to or less than that of a tether-aligned drag parachute whose area (filled with fabric) corresponds to the optimized swept area of said crosswind kite, and even very lower if our parachute has a very high Cd.

This raises a question: why persist in wanting to use a very efficient (high L/D ratio) glider in relation to its kite area, to ultimately sweep less area than a parachute with equal masses, and that with a lower efficiency per swept area unity?

It is believed that a small kite going faster will take up less space: this is without taking into account the length of the tether, and the take of fast crosswind figures requiring more spacing between unities, and diminishing the Power to space use ratio.