the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
Concurrent aerodynamic design of the wing and the turbines of airborne wind energy systems
Abstract. The aerodynamic design of the aircraft of fly-gen Airborne Wind Energy Systems, named windplane here, is one of the main aspects determining their power production, but it is still a largely unexplored problem. To this end, an engineering model for the aerodynamics of the onboard turbines, the aerodynamics of the wing and their interactional aerodynamics is developed and coupled to a steady-state windplane model and a far-wake model. This comprehensive model is then used to design the windplane aerodynamics for a given wingspan. Initially, a design space exploration study reveals that placing the turbines at the wing tips and rotating them inboard down increases the power production compared to other locations and rotation direction. This is because the turbines' wake swirl reduces the wing induced drag, especially when they are placed at the wing tips. Moreover, conventional efficient airfoils are found to be optimal for windplanes. Later, NACA4421 airfoils are used for the design of the wing and the turbines, placed at the wing tips. The optimal trapezoidal wing, modeled with constant twist, has an aspect ratio of 5.1, a taper ratio of 0.60 and the onboard turbines operate at a design low tip speed ratio of 1.9 to increase the wake swirl. The results from the vortex models of the wing, the turbines, and their interaction is extensively compared with the lifting line, the vortex lattice method and the vortex particle method implemented in the well-established code DUST, finding very good agreement. Finally, the windplane is studied with DUST at different wing angles of attack and at different turbine tip speed ratios to characterize its behavior away from the design point.
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Status: final response (author comments only)
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RC1: 'Comment on wes-2025-134', Anonymous Referee #1, 30 Jul 2025
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AC1: 'Comment on wes-2025-134', Filippo Trevisi, 22 Oct 2025
Dear Editor, dear Reviewers,
Thank you very much for your comments and for taking the time to review our work.
In the attached document we go through your comments and provide, for each one, both our responses and the actions we have taken to accommodate your feedback in the revised manuscript.
When answering your comments we refer to the figures and lines number of the manuscript with the highlighted changes.
Best regards,
The Authors
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AC1: 'Comment on wes-2025-134', Filippo Trevisi, 22 Oct 2025
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RC2: 'Comment on wes-2025-134', Anonymous Referee #2, 28 Aug 2025
General comments
Engineering models for turbine and wing aerodynamics are used to optimize a power coefficient and then validated against a higher fidelity aerodynamic analysis. The model itself is highly simplified, but presents a method that can be used to optimize the aerodynamics of an AWE system, rather than designing one aerodynamic component at a time.
Specific comments25
The article mentions the different flight modes required for a flygen system and other flygen AWE companies. The Kitekraft and the Makani M600 designs use 8 rotors and the Windlift and Makani Wing 7 designs use 4 rotors which allow for pitch, roll, and yaw control using the rotors in takeoff and landing. The model in this paper uses two rotors. It's worth mentioning how the design is intended to perform those flight modes, especially because of the emphasis on the benefits of putting rotors at the wingtips.60
The article states that the rotors are designed for the generation phase only, not considering whether they generate enough thrust in hover. It's worth looking at how stalled the rotors are in static thrust, and whether the analysis tools are reliable for that operating point.330 "Higher taper ratios are preferable if the turbines are placed at the wing tips. This is because higher taper ratio wings have more lifting area behind the turbines, enhancing their beneficial effect on the power production."
I would guess that higher taper ratios are preferable because the turbines at the wing tips are reducing airspeed and lift, so a higher taper ratio produces a distribution closer to eliptical. I'd be interested to see if this method considers the most eliptical lift distribution to be the most optimal or whether there are other factors.
320
"The trends show that it is optimal to design the wing such that it operates the airfoils at their maximum efficiency."Because most drag in an airborne wind system is induced drag and tether drag rather than wing airfoil profile drag, the highest system lift to drag ratio shouldn't usually occur at the same angle of attack as the airfoil max lift to drag ratio. I'd like to see an explanation on why figure 7 looks like it does (what are the induced drag, tether drag, rotor force, and profile drag doing around those points)?
Technical corrections
50
"they reduce the apparent wind speed felt by the involved wing aerodynamic sections, which in principle would lead to a lower lift force. On the contrary, airplanes with propellers in front of the wing achieve an increase in aerodynamic lift."Awkward language sounds like its arguing the turbines might increase lift. I'd change it to "they reduce the apparent wind speed felt by the involved wing aerodynamic sections, which reduces lift force. Conversely, airplanes with propellers in front of the wing achieve an increase in aerodynamic lift"
Citation: https://doi.org/10.5194/wes-2025-134-RC2 -
AC1: 'Comment on wes-2025-134', Filippo Trevisi, 22 Oct 2025
Dear Editor, dear Reviewers,
Thank you very much for your comments and for taking the time to review our work.
In the attached document we go through your comments and provide, for each one, both our responses and the actions we have taken to accommodate your feedback in the revised manuscript.
When answering your comments we refer to the figures and lines number of the manuscript with the highlighted changes.
Best regards,
The Authors
-
AC1: 'Comment on wes-2025-134', Filippo Trevisi, 22 Oct 2025
-
AC1: 'Comment on wes-2025-134', Filippo Trevisi, 22 Oct 2025
Dear Editor, dear Reviewers,
Thank you very much for your comments and for taking the time to review our work.
In the attached document we go through your comments and provide, for each one, both our responses and the actions we have taken to accommodate your feedback in the revised manuscript.
When answering your comments we refer to the figures and lines number of the manuscript with the highlighted changes.
Best regards,
The Authors
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GENERAL COMMENTS
I find this to be an overall well-done paper filling a gap in the current literature. While analogous studies have been performed for propulsive cases, this paper provides somewhat detailed findings for wind turbine-wing interactions currently missing from the literature. The methods and models are generally clear and the results appear to be reasonable. I also appreciate the recommendations throughout this work concerning potential future work stemming from the studies presented herein.
SPECIFIC COMMENTS/QUESTIONS
Overview:
Abstract:
Introduction
Windplane steady-state model
Onboard turbines model
Windplane aerodynamic design problem
Optimal aerodynamic design
Isolated turbine
Analysis out of the design point
Appendix A
SUGGESTED TECHNICAL CORRECTIONS
Overview:
Abstract:
Introduction
Windplane steady-state model
Onboard turbines model
Wing model
Windplane aerodynamic design problem
Optimal aerodynamic design
Isolated turbine
Isolated wing
Interactional aerodynamics
Analysis out of the design point
Conclusions
Nomenclature