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.

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.

The authors have conducted a numerical study on the three possible airborne wind flight patterns: circular, figure of eight (up), and figure of eight (down) to determine their pros and cons.

The conclusions are interesting and should be disseminated. However, the paper might need some major restructuring.

The value-added content is section 3.2, which are just over 6 pages long (not to mention that many of the figures and discussions in this section could be combined). On the other hand, almost half of the manuscript (page 1-13) was for describing the model, controller, and the optimisation algorithm. The model description and the controller provide some technical details, but they neither add much insight to the discussion nor is detailed enough to be replicated. I don’t know much about optimisation, but it feels like the authors have provided some technical facts without many justifications or links to the discussion. One of the other reviewers also seem to have concerns about the optimisation objectives.

Overall, the paper in its current form is split between control design, optimisation, and comparing figure of 8 and circular flights. I suggest reducing the paper to a brief communication, focusing on what’s reported in section 3.2. The authors should include some high-level detail about the controller (which control structure was used? What’s the objective?) and the optimisation (where it’s from? What’s the objective?), and upload the code to an open source depository. Otherwise, a much more detailed study on how the controller and optimisation were deployed are necessary.

MINOR COMMENTS

Line 21-22: missing citation.

Line 103: a dynamic system -> a dynamical system

Line 104: I don’t know much about L0 and L1 controller. Based on what’s written, L1 is the distance between the kite and the target (i.e., the error). If so, how could L1 be an adjustable parameter?

End of line 140: the -> to

Equation 3: are the phi_tau terms the roll angles (desired/actual) on the Earth axis or the tangent axis? I assume it’s the latter. Please specify.

Line 157: is lift F_L taken directly from the aerodynamic model, or is there a way to measure it in-flight in real life?

Line 193: ‘this thesis’ – please update.

Line 217: please specify whether this is the tether force on the winch or the aircraft body, or are they the same?

Line 256: I guess the word ‘using’ shouldn’t be there.

Lien 286: become -> be

Line 288: the maximum -> the maximum velocity

Line 307 and others: the authors use the term ‘most optimal’. I don’t think that’s appropriate because an optimal point is the best one, unless we are referring to local and global optima.

Line 315-316: “the winch needs to retract a bit to insert energy into the system to get it to the top of the circle.” Is this common in airborne wind? I would have thought that if one needs to add more energy to the kite via the winch, it means the target trajectory is too challenging and the kite should fly at a lower height.

Line 330-331: “Compared to the down-loop, this indicates a higher likelihood of fatigue damage over time as the kite will go through more load cycles more quickly.” This is unclear. Does the figure-of-eight frequency cover 1 orbit on 1 side or 2 orbits (1 on each side)? If it is 2 orbits (1 on each side), then the figure of eight is expected to have a lower frequency than circular flight, but each figure of eight cycle stresses the aircraft (roughly) twice as much a circle cycle because we are doing 2 circles (1 on each side).  The comments on aircraft stressing might need some further thinking.

The authors look at the merits of figure of 8 vs. circular paths for AWE. Overall the paper is well written, with a clear presentation. Additionally, it is an interesting topic for the AWES community. However, there wasn't a lot of depth to the analysis. There have already been many contributions that have showed similar conclusions as this paper. What is interesting about this paper is that they used multi-objective optimization to find optimal path and controller gains for the study. They obtained their optimal configuration through a weighted objective approach, but only looked at 1 point on the Pareto front. It wasn't clear how they chose the values for the weighting. Nor did they carry out any sensitivity analysis on the choice of gains. Hence, there is uncertainty on whether their results would change significantly if they chose a different set of weights.



line 21: Citation seems to be noted, but not given

Figure 2: The variables l and s are not defined

Line 129: given the focus of this article on paths, I think some further description on what Lissajous, Lemniscate are.

Line 150: is referenced before 4 or 5, I can see the logic in the chosen ordering of figures, in that this out-of-order reference to 6 is to better illustrate a detail. However, since this section already discussing geometry, for example equation 3 refers to different components of gravity along different axis. I would suggest that figures 5 and 6 are described early to establish the kinematic convention at the start.

Figure 4: It's assumed that the same structure is used for both longitudinal and lateral control. Could be made more specific. Labels are a bit vague, could be made more specific. Instead of angle, pitch/roll angle, instead of rate, angular of pitch/roll rotation, instead of deflection, elevator/aeleron deflection

Equation 8: PAPR not defined, cross-track error not described, P_mech is intuitive, but again, not described. Maybe it's described later, but since the multi-objective problem is given here, all these different objectives should be elaborated here.

Section 2.5, the objectives of comparison are given, it could be helpful to give the mathematical definition of these metrics that were used by authors. One could imagine alternative equations for the same metrics.

Line 303, refers to figure 9, but seems to talk about figure 10 results.

Throughout the paper, the author refers to the frequency of lift variations as an indication that fatigue. However, the magnitude of the force oscilations is also an important factor. Looking at this parameter, further supports the authors conclusion. This should be mentioned to give more weight to their arguments. They could even estimate a damage rate directly from the data to give a more solid conclusions on fatigue.