Concurrent aerodynamic design of the wing and the turbines of airborne wind energy systems

Trevisi, Filippo; Cassoni, Gianni; Gaunaa, Mac; Fagiano, Lorenzo Mario

doi:https://doi.org/10.5194/wes-2025-134

Preprints

https://doi.org/10.5194/wes-2025-134

Preprints

29 Jul 2025

| 29 Jul 2025

Status: a revised version of this preprint is currently under review for the journal WES.

Concurrent aerodynamic design of the wing and the turbines of airborne wind energy systems

Filippo Trevisi, Gianni Cassoni, Mac Gaunaa, and Lorenzo Mario Fagiano

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.

Received: 21 Jul 2025 – Discussion started: 29 Jul 2025

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Filippo Trevisi, Gianni Cassoni, Mac Gaunaa, and Lorenzo Mario Fagiano

Status: final response (author comments only)

RC1:
'Comment on wes-2025-134', Anonymous Referee #1, 30 Jul 2025
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:
I think a more explicit highlighting of what your paper adds would greatly improve the impact. I see several times throughout that your results “confirm the results of…” such and such author, but it’s not quite explicit how your work adds to the current literature. I would recommend making this clearer in the introduction as well as the conclusion, then include some more high impact statements in the discussions of your studies throughout to make clear what the new results are and why they are important.

I would like to see more discussion in conjunction with

Figures 10-13

Analysis out of the design point section

Abstract:
At this point, I’m looking forward to seeing more explanation about how reducing induced drag of the wing increases power production of the turbines. This doesn’t seem like a direct consequence, and could maybe use some minor elaboration at this point.

After one read through, I don’t think this was satisfactorily answered, or perhaps not pointed out explicitly.

“Especially when they are placed near at the wing tips” — Does the wake swirl reduce induced drag when the turbines are not placed at the wing-tips? It seems like you’d need some destructive interaction with the wing tip vortices, so you’d have to at least be close.

“Moreover, conventional efficient airfoils are found to be optimal for windplanes.” — such as? And compared to what? Are NACA4421 airfoils these conventional efficient airfoils? If not, why use them instead of the optimal ones for your studies?

What do you mean by an optimal trapezoidal wing with constant twist? Optimal in what way? I’m not seeing how you could get an elliptic lift distribution with that planform? Also, optimal wing only, or optimal with the interactional aerodynamics of the turbines?

I’d like to see a quick summary of the major results from the DUST studies you did. What did those studies lead to? What are the major takeaways?

Introduction
“at very high lift coefficients” — how high is very high? 2? 5?

How do you know that KiteKraft designs their turbines and wings separately? Do you have a source for that?

Same comment about conventional airfoils as in the abstract.

Three turbine positions are considered: in front, at the wing tips and above or below the wing” — a figure would be immensely helpful here, it seems like all these are in front. Is that a position? Or are wing tips and above and below the three positions? Why can’t the turbines be in front, at the wing tips and also above and below simultaneously? I suppose I’d like to see some clarification on what is meant by “in front.”

I see you have figure 6 that explains this well. I think some re-wording here could be sufficient instead of another figure.

Windplane steady-state model
I’m unsure what is meant by: “defined to inform about the aerodynamic force applied to the wind”

Onboard turbines model
“The importance of this effect increases as the tip speed ratio is decreased.” — Please expound.

Windplane aerodynamic design problem
For the pylon mounted turbines, how far above the wing did you place the rotors to justify turning off the interactional aerodynamics?

I would like to see more discussion on figures 10-12 if you’re going to include them.

Same with figure 13 (you also have just a single sentence paragraph).

You may want to quantify in some way why a fixed 1 meter radius is reasonable (line 365).

I am not following how your study makes conclusions about conventional efficient airfoils. It seemed that your airfoils were somewhat notional and not directly tied to some sort of convention.

Please provide some quantification (based on your study) of how much power can increase with turbines placed at wing tips. (How much is “considerable”?)

Optimal aerodynamic design
Figure 19 — what causes the blade twist to rise near the tip?

Isolated turbine
It sounds like you ran 8 revolutions based on Niro’s work, is that long enough to achieve steady state?

Line 415 — please quantify “really close”

Analysis out of the design point
I’m not sure I’d say “exclusively influenced,” it seems like you’re just trying to say that you perform sweeps of wing angle of attack and rotor tip speed ratio. Unless you’ve decoupled the interactional aerodynamics, then the effects are not exclusive.

I take it back, but you do say this applies to the whole study and then immediately show figures with and without interactional aerodynamics, so something still needs to change to make this clearer.

“To reduce power production,” — why would you want to reduce power production? It seems like the sentence is backwards. I see why you’d need to reduce loads and the result would be reduced power, but it sounds here like reducing power is your goal, and reduced loads is a result.

This sentence in general (line 477-478) is confusing. I’d probably make it a couple sentences or more and be a bit more clear what you’re trying to get across.

Carefully examining figures 32 and 33, I think I’m following, but it should be clearer in the text that you’re trying to say that reducing angle of attack is a more effective way to reduce loads without losing too much power since the power coefficient is much more sensitive to tip speed ratio that angle of attack.

I’d like to see a bit more discussion of the results in this section. You have some good takeaways already, but it still feels a bit light relative to how much information should be able to be communicated with this amount of figures.

Appendix A
The comment here on at least 6 revolutions should probably be included in the main text where you also cite Niro 2024.

SUGGESTED TECHNICAL CORRECTIONS

Overview:
Miscellaneous Grammar:

I would prefer the Oxford comma to be used in lists throughout. It is present in some cases, but only a few.

If not including it, remove it everywhere for consistency.

There are several end of sentence parentheticals, especially in the abstract/intro that reduce the flow of the text. Some minor sentence restructuring would be in order for easier readability.

There are quite a few pluralization and possessive errors throughout (missing apostrophes for possessives, plurals where they shouldn’t be, etc.). I’ve tried to highlight the ones I noticed, but another read through would be good to fix those.

Figures

I find the tikz-type figure coloring to be somewhat haphazard. I feel like there are quite a few opportunities to standardize colors to mentally link between figures as well as make things more readable.

Although not necessary, I generally recommend line plots (figure 7 to the end), not have grids, upper and right spines (except for multi-axis plots), and have no border around legends.

These items are generally not required to understand the messages being communicated by the plots and removing them reduces extraneous information making it easier for readers to digest the important contents.

Similarly, rotating the y-axis labels 90 degrees makes it just a bit easier to read and there is typically sufficient space to allow for a wider y-axis label.

Abstract:
Is “windplane” plural? AWE systems is plural, and then you say “their power production” (also plural). I’d expect it to be windplanes.

This first sentence is a bit long with a parenthetical and a second clause. At the very least, put a semi-colon instead of a comma before “but,” however I would recommend splitting it into multiple sentences and be more clear on what the largely unexplored problem is specifically (what does “it” refer to? The aerodynamic design, the determination of power production?) Alternatively, rearranging the sentence could make it shorter and clearer as well.

I’m a fan of using the oxford comma rather than leaving it out in sentence 2 (between wing and “and their interactional”). You use it later in a similar sentence, so either way, just be consistent.

More comma inconsistency in line 11 starting with “the results from the vortex models…” In this case I’d definitely recommend a comma after “vortex lattice method”.

You may consider reordering this sentence as well to not have “finding very good agreement” tacked on the end but rather closer to the beginning of the sentence.

Introduction
“WESs can be classified in crosswind” — classified as crosswind…

“crosswind, tether aligned and rotational” — aligned, or rotational… (unless they can be classified as more than one, then and/or, but either way, add that comma in)

“roughly perpendicular to the wind direction and generate” — I would add either before “generate” here. I almost commented that you forgot pumping AWES since the beginning of the sentence didn’t indicate that there was a comparison to be made.

Comma after Windlift (2025)

Line 30: “multi-elements airfoils” —> muli-element airfoils.

“onboard turbines” —> onboard turbine

I’m seeing a lot of “after thought” type phrases at the end of sentences that make it harder to follow than it needs to be. Instead of tacking on parentheticals at the end of sentences, it may be better to generally restructure things to be more direct in the first place rather than requiring constant mental backtracking to put all the pieces together.

Either need to say The Windlift design, or Windlifts design.

Comma needed after disclosed

Windplane steady-state model
Because the subscript is small, the tau and r subscripts for the coordinate system are somewhat difficult to differentiate. It might be nice to use a different symbol for the tangential direction, perhaps theta, for increased clarity.

Figure 1 — you have v_w and Phi in the figure but don’t mention them in the caption (and I don’t see v_w defined nearby). If they aren’t important enough to mention, then maybe they don’t need to be in the figure in the first place? If they are vital, then they should be mentioned.

R_0 is given in the nomenclature, but not in conjunction with equation 1 like the other variables are. It would be nice to have it with everything else and perhaps included in figure 1 or 2 somehow.

Figure 2 — Is there any significance to the various colors used? I notice v_w matches colors between figure 1 and 2, but Phi does not. I almost thought there was color coordinates for the expressions in equation 1, but it doesn’t appear to be so. Also, the red, magenta, brown, and orange are difficult to differentiate without careful (and very zoomed in) consideration. I would recommend being a bit more judicious with color usage, and if so many colors are needed, I would recommend using more contrasting colors for terms in near proximity (for example, the v_w, u, v_a triangle is nicely contrasted, but does it require so many colors?)

The xi_tb/2 term could afford to be a bit closer to the arrow it’s associated with (you could also move the arrow direction since it’s just radius)

There's extra space behind “wake” in the wing wake box, maybe center “wing wake” in the box?

May want to include m with u^2/R_0 in that box just for consistency so there’s no confusion that those are the same term

It is exceptionally inconvenient to refer to figure 5 seven pages before you show it. I would either remove this reference on page 5, or if it’s vital for understanding at this point, move it up.

The in-line equations starting on page 6 (starting at equation 11, but used throughout the paper) are somewhat difficult to read. If it’s not a required style, I would break those out into multi-line expressions to increase readability and the reader’s ability to follow the math.

Onboard turbines model
“In order to evaluate the onboard turbines performance…” — should put an apostrophe after the s in turbines (turbines’) to indicate possession for multiple turbines.

“effect of their wake” —> effect of their wakes

I’d recommend not using the BEM acronym without the full term, especially since this is the only place you use it, so you don’t need the acronym anyway.

Wing model
Seems like you’d want figure 3 at the top of page 9, right when you reference it.

Figure 3 — you could use far fewer vortex elements so that your labels aren’t so crowded.

Back in figure 2, you used dotted lines at the end of the tether wake to indicate they extended back further. You specifically mention that the trailing vortices extend to the end of the fluid domain, so it would be a nice touch to add similar dots to those trailing vortex lines.

Also, if you lighten the shading on the wing, it would make things every so slightly easier to read.

Figure 4 — it would be nice if the arrow heads were a bit bigger, especially since several of them overlap with other lines or X’s.

I like that you have an X at the 3c/4 point that ties figure 3 and 4 together, but you may want to match a symbol between figure 3 and 4 for the 1c/4 point to further improve clarity (maybe a blue circle?)

Windplane aerodynamic design problem
Instead of saying “following figures” when talking about dashed lines, why not just indicate the range of figure numbers?

I also don’t think you need to include m-dashes here. Everyone knows what a dashed line is.

Same comments on dotted lines.

Figure 6 — the figure makes it look like the rotors are placed at different streamwise positions between each case (6a makes it look like the rotors are nearly touching the leading edge, 6b shows them out front, and 6c is in between), is that intentional?

Line 334-335 — “reducing the induced drag in the wing aerodynamics” —> either “in” should either be of or on depending on what you’re trying to say.

“Designs with lower tip speed ratios are typically preferable to reduce the noise emission and the erosion.” — citation?

Optimal aerodynamic design
Line 394: “increase” —> increases

“This low value of λt is also good to limit the blade erosion and the acoustic emission.” — again, citation?

“Modeling the wing with the present formulation, which is accurate even for low aspect ratio, the spanwise efficiency of the wing, accounting for the onboard turbine’s influence, can take values above one.” — multiple parentheticals make this sentence difficult to parse.

Isolated turbine
Line 411-412 : “turbines blades” —> turbines’ blades

Comma after Appendix A on line 412

Isolated wing
Figures 26 and 27, I don’t think you need a dash to indicate that Cl and Cd are unitless. You haven’t used that for any plots up to this point for other non-dimensional numbers.

Interactional aerodynamics
You could probably make figures 28 and 29 a single figure with 2 sub-figures for more easy viewing.

I don’t think figure 30 is necessary to include. It doesn’t appear to add anything to the discussion.

If you do keep it, I’d suggest moving it up to where you describe the discretization used in DUST.

You can also make some adjustments in Paraview (such as adding some opacity and maybe gaussian blur to the particles) to make it a bit more aesthetic and de-emphasize the particles if you want to highlight the discretization.

Analysis out of the design point
Perhaps analysis away from (or off of) the design point? Typically I’ve seen this called “off design cases”

“Aerodynamics is exclusively” —> aerodynamics are exclusively (shows up multiple times

Figures 31and 32 — without those tiny numbers, I’d not be able to tell the difference between these figures. I feel like a line plot at slices of lambda and alpha through the maximum Cp operating points would be clearer to compare the power with and without interactional effects.

Conclusions
A few spelling errors and missing apostrophes.

Nomenclature
You may consider using lower-case “c” for the section drag coefficients. You already use lower-case subscripts, but it could potentially be easier to differentiate if the C’s were also lower-case.
Citation: https://doi.org/10.5194/wes-2025-134-RC1
- 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
  
  Citation: https://doi.org/10.5194/wes-2025-134-AC1
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 comments
25

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
  
  Citation: https://doi.org/10.5194/wes-2025-134-AC1
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

Citation: https://doi.org/10.5194/wes-2025-134-AC1

Filippo Trevisi, Gianni Cassoni, Mac Gaunaa, and Lorenzo Mario Fagiano

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Short summary

This paper investigates the optimal aerodynamic design of the wing and of the onboard turbines of the aircraft of fly-gen Airborne Wind Energy Systems, named windplane here, with a novel comprehensive engineering aerodynamic model and with the vortex particle method implemented in DUST. Placing the turbines at the wing tips, rotating them inboard down with low tip speed ratio and using conventional efficient airfoils for the wing is found to be optimal for windplanes.


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