the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
Optimal Flight Pattern Debate for Airborne Wind Energy Systems: Circular or Figure-of-eight?
Abstract. The computational study compares the performance of circular and figure-of-eight flight patterns for fixed-wing ground-generation airborne wind energy (AWE) systems using a PID-based basic controller that effectively controls the kite during each patterns pumping cycle in a Matlab® Simulink® environment. A simple, adjustable control framework enables a steady analysis within consistent operational parameters, allowing for fair comparisons of power output, power quality, ground surface area requirements, and structural load impacts. The simulation results reveal that using the 150 m2 MegAWES reference kite at 15 ms−1 the circular flight pattern achieves the highest cycle-averaged power output, providing 1.85 MW at a power density of 2.94 MWkm−2, making it advantageous for maximizing energy within limited spatial constraints. Conversely, the figure-of-eight down-loop pattern demonstrates superior power quality with lower power peaks (a peak-to-average-power ratio of 3.85) and lower expected structural fatigue due to a reduced load frequency of 0.034 Hz, supporting greater operational stability and system longevity. The up-loop variation performed the worst on all metrics considered in this work. This study offers insights into the trade-offs between energy output, efficiency, and structural demands associated with each flight path, providing a foundation for future AWE flight path selection and control strategy optimizations.
Competing interests: At least one of the (co-)authors is a member of the editorial board of Wind Energy Science.
Publisher's note: Copernicus Publications remains neutral with regard to jurisdictional claims made in the text, published maps, institutional affiliations, or any other geographical representation in this preprint. The responsibility to include appropriate place names lies with the authors.- Preprint
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Status: open (until 13 Mar 2025)
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RC1: 'Comment on wes-2024-139', Anonymous Referee #1, 01 Feb 2025
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The paper is well written and technically correct, however its originality and impact are not high enough, in my opinion. In fact, the employed model is taken from literature, the control approaches are also not new or have minor differences, and the type of study (loop vs. figure-eight) is not new as well. The main finding is consistent with results already available in the state of the art, especially using simulations (it would be very different if an experimental comparison was provided). Overall, my impression is that the work is more suitable for a conference contribution than a high-level journal contribution.
Citation: https://doi.org/10.5194/wes-2024-139-RC1 -
RC2: 'Comment on wes-2024-139', Anonymous Referee #2, 05 Feb 2025
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GENERAL COMMENTS
This paper covers a topic of interest in airborne wind energy. The authors analyze the behavior of a large-scale kite they previously designed, simplifying the control system to enable tracking of circular and figure-eight trajectories. However, the methodology used to compare these trajectories lacks sufficient explanation and justification. In particular, the choice of the optimization algorithm and objective function is not well-motivated. Specifically, the objective function is defined as a weighted sum of five objectives, but there is no discussion on how the weights were determined. This makes the results highly dependent on the weight values, raising concerns about how this methodology could be applied to other systems. I recommend expanding on the methodology and either analyzing the impact of weight selection or considering an alternative optimization approach.
DETAILED COMMENTS
Line 21: Missing citation.
Line 31: "These flight paths have been extensively studied in the context of AWE systems." Please, include the citations of the relevant studies.
Line 48: Predictable path shapes are not necessarily superior (see, for example, Makani Report No. 1). I suggest rephrasing this sentence.
Section 1: The following reference is missing from the literature review:
G. Licitra et al., Performance assessment of a rigid wing Airborne Wind Energy pumping system (https://doi.org/10.1016/j.energy.2019.02.064).Line 167: It’s unclear whether CL and CD refer to the airfoil or the entire aircraft. If they refer to the airfoil, how are 3D effects accounted for? Including a figure showing the aircraft polars (perhaps with and without the tether) would be helpful.
Line 173: For aircraft, the lift-to-drag ratio is typically maximized well before stall. Is this also true for the tethered aircraft in this study?
Line 177: If the polar plots were given, it would be clearer whether a 4-degree angle of attack is close to stall. What CL corresponds to 4 degrees?
Line 200: What is the kite position? Its center of mass?
Line 213: Again, which reference point on the wing is used?
Line 222: What is the "equivalent wind speed"?
Line 225: Please provide a brief definition of f*.
Line 233: Why was this optimization algorithm chosen? Please justify this choice. Also, the reference for the algorithm links to a presentation rather than a peer-reviewed paper.
Line 243: I have concerns about the objective function. Why not use average power as the sole objective function and treat the other factors as constraints? If the chosen optimization algorithm does not support constraints (which I suspect), why not use a different algorithm? The choice of the objective function directly impacts the results, making this a multi-objective optimization problem where the five objectives have completely arbitrary weights. Please justify the weights selection. How could these weights be applied to other systems?
Additionally, some of these objectives may be insignificant (based on the figures, I suspect pVk = 0 and pFt = 0), while others may have large values (PAPR values in Table 3 exceed 2.5). However, these details are not explicitly provided in the results and should be included.
Section 2.5: The comparison criteria should align with the objectives. Two of the criteria are included in the objective function, but one is not—please elaborate on the reasons.
Line 276: Why was 15 m/s chosen? Does this represent below-rated condition? Which wind shear is considered for the study? I cannot find this information.
Line 285: Please provide citations for these statements. A low turning radius causes the aircraft to bank inward, reducing its projected area relative to the wind direction. As discussed in Makani’s first report, this is one reason for avoiding low turning radii. Additionally, low turning radii experience greater wind speed reduction, though this effect does not appear to be considered in this study.
Figures 8, 9, 10: These figures might be more appropriate for the appendix. Since this paper focuses on optimization results rather than the optimization process itself.
Citation: https://doi.org/10.5194/wes-2024-139-RC2
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