Comparison of the traction force of a static parachute kite and a crosswind kite, both with the same projected surface

[PierreB]

@PierreB

An underestimated problem may be the significant kinetic energy as the kite descends, preventing it from ascending.

@PierreB

These last losses are due to the kinetic energy increase when the kite goes faster within the trajectory, and having to be dissipated when the kite slows down, at the cost of enormous energy consumption.

It’s as if, in a car, you were constantly accelerating and braking instead of maintaining the same pace, for an identical average speed.

To my knowledge, this point has not been taken into account in the various equations derived from Loyd’s model.

Perhaps some Makani’s videos could provide some clues.

20190430 CW-07 - First Night Flight of Makani M600 [Full Flight, Data Overlay]

At 14:34: wind speed (in the left) aloft: 12.7 m/s. M600’s speed: 40 to 60 m/s. Tension on the tether: 45 to 125 kN. Power: -250 kW (negative power) to 750 kW (positive power).

I don’t remember exactly M600’ surface area, but with its span of 28 m, an area of 35 m² seems to be plausible. Its lift coefficient (Cl) seems to be only about 0.65. Average M600’ speed: 50 m/s.

Average tether tension force: about 80 kN. Lift-to-drag ratio (glide number) is noted as: (L/D). Rough calculation:

35 x 1.2 (air density) / 2 x 12.7² x 0.75 (cosine² for an average elevation angle of 30 degrees) x (2/3)² (M600’ velocity² with turbines in relation to M600’ velocity² without turbines) = 1.129 kN: so, 80 (kN) / 1.129 (kN) would provide 0.65 (L/D)² (without turbines) = 70.86, leading to (L/D)² = 109, so (L/D) being about 10.44 (without turbines).

For a rigid wing, it is a slightly lower value than expected 12 (without turbines) by taking account of tether drag. And if the area and the Cl are higher, the (L/D) would be still lower for a same tether tension of about 80 kN. We can note that 50 m/s (M600’ average speed) / 12.7 m/s (wind speed aloft) lead to a (L/D) value of about 4, which is a far lower value, but requiring correction due to the circular trajectory in relation to a supposed straight trajectory.

We can therefore think (without yet having formal proof because of unknows) that in connection with the losses due to the variable cosine according to the position in the flight window, we have the losses by speed variations that result from the consequences of variations in the cosine, exacerbated by the mass aggravating the force of gravity, so kinetic energy issues towards the ground.