Wind Fisher

[Windy_Skies]

@PierreB

The principle is in this excerpt of these sentences: “we might call the loss that is due to the fact that the total aerodynamic force is not perfectly in line with the wind direction the cosine loss.”

See also the equation (45) page 7, which includes the cosine cubed (cos³), below:

I didn’t see the cosine cubed term in the Diehl chapter. The Magnus paper doesn’t give the derivation of the cosine cubed loss equation and doesn’t explain why it also should apply to rotating cylinders.

A refutation of my point should probably include a reference to either of these papers, just before equation (45), page 7:

In the frame of equilibrium motion theory, the power that can be generated with a tethered airfoil in crosswind conditions has been set by Loyd (1980) and refined in Argatov et al. (2009) to take into consideration the β losses

Ctrl+F for “cos” in the Loyd paper didn’t give a to me obvious cosine cubed equation. In the Argotov paper equation (69) seems to. I wasn’t able to follow along where the cosine cubed came from.

Earlier in the paper:

2. The dual line kite mathematical model
   2.1. Newton’s law of motion in spherical coordinates

In the simplest model of a tethered kite system [7], the tether is treated as inelastic and straight, the actual kite dynamics is not considered, and the forces on the kite are modelled purely as lift and drag, whose magnitudes are functions of the kite angle of attack [4]

Which according to the earlier quote is not the case for Magnus effect-based systems, unless I am reading the above and or below quote wrong.

@Windy_Skies

Page 3-4:

In addition, as opposed to the AWE systems using airfoil kites or wings whose lift and drag vector magnitudes depend on the angle of attack measured between airfoil chord and apparent wind velocity, Magnus effect-based systems only change lift and drag vector direction, and not magnitude, when there is a change in apparent wind direction