Nomenclature
The following symbols are used to define aerodynamic quantities in this chapter:
- Symbol :
-
Meaning
- AR:
-
Wing aspect ratio (= b 2∕S)
- b :
-
Wing span
- \(C_{D_{t} }^{e} \) :
-
Effect of tether drag experienced at the aircraft
- CL :
-
Aircraft lift coefficient
- \(C_{L_{\alpha _{vt} }}\) :
-
Vertical tail lift-curve slope
- CN :
-
Normal drag coefficient of the tether
- d :
-
Diameter of the tether
- e :
-
Oswald’s spanwise efficiency factor
- F centrifugal :
-
Magnitude of the centrifugal force
- \(F_{\mbox{drag}}^{r}\) :
-
Tether drag force projected along the tether direction
- \(F_{g}^{r}\) :
-
Gravity force on the aircraft projected along the tether direction
- \(F_{t}^{r}\) :
-
Effective gravity force on the tether projected along the tether direction
- Ge :
-
Effective glide ratio of the aircraft modified to take into account the contribution of tether drag experienced by the aircraft (\(=C_{L} /\left ( {C_{D} +C_{D_{t} }^{e} } \right ))\)
- h :
-
Altitude of aircraft
- h 0 :
-
Reference height used by wind power law model
...
Notes
- 1.
- 2.
The derivation of this result relies on an approximation of the tether drag and should only be regarded as indicative.
- 3.
Note that the cut-in wind speed shown in the diagram is shown at the threshold of positive power. However, in a practical system, this would likely be set at a higher wind speed.
- 4.
- 5.
- 6.
A plain flap uses the tailing edge part of the airfoil on a separate hinge.
- 7.
Experimental data was taken from Vandenberg and Oskam (1979) with measurements at three angles of attack: 6, 10.1, and 13.1 deg. The OpenFOAM flow conditions were treated as incompressible single phase with constant density and viscosity. The turbulence model is SST k-omega without wall function (low Reynolds formulation). Results were computed as AoA =  6 deg, Cd =  0.0257 CFD, 0.0228 experiment, Cl =  2.392 CFD, 2.415 experiment; AoA =  10.1 deg, Cd =  0.0367 CFD, 0.0322 experiment, Cl =  2.862 CFD, 2.882 experiment; AoA =  13.1 deg, Cd =  0.0507 CFD, 0.0443 experiment, Cl =  3.123 CFD, 3.142 experiment. These are differences of less than 1% for Cl and up to about 14.4% for Cd at AoA =  13.1 deg. Note that CFD is overpredicting the drag. The accuracy can be improved by refining the mesh further and incorporating more accurate turbulence models that better account for the laminar to turbulent transition. However, for the full-sized aircraft, the majority of the drag comes from induced drag, which depends on C\(_{\mathrm {L}}^{\mathrm {2}}\), so the accuracy of the lift prediction is more important.
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Acknowledgements
The information in this chapter was partly generated as a result of funding provided by Horizon 2020 SME Instrument (grant no. 666793 – AMPYXAP3).
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Williams, P., Pechenik, E. (2021). Kites for Wind Energy. In: Stoevesandt, B., Schepers, G., Fuglsang, P., Yuping, S. (eds) Handbook of Wind Energy Aerodynamics. Springer, Cham. https://doi.org/10.1007/978-3-030-05455-7_63-1
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