Review Reports

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

This paper presents a pioneering experimental investigation into the pitch-rate stability derivatives of a flapping-wing micro air vehicle (FWMAV). The use of a robotic-arm–based experimental platform successfully overcomes the limitations of conventional free-flight testing, and the study offers high academic and technical value. In particular, the ability to identify stability derivatives even in unstable flight regimes provides a significant contribution to future modeling and control research in bio-inspired flight dynamics.

However, several aspects should be further addressed to strengthen the scientific rigor of the work. The statistical validity of the experimental repetition (five trials) is not sufficiently justified, and quantitative evidence such as variance or uncertainty analysis would enhance the credibility of the reported results. In addition, the absence of explicit uncertainty quantification and error-bar representation limits the reader’s ability to assess measurement reliability. Providing a systematic uncertainty analysis based on sensor sensitivity and measurement resolution would greatly improve the clarity and reliability of the findings.

Moreover, while the fan-array setup provides a practical approximation of forward-flight conditions, the flow environment remains idealized. A quantitative characterization of the turbulence intensity, flow uniformity, and potential deviations from realistic aerodynamic conditions would help clarify how such factors may affect the extracted stability derivatives. A more thorough discussion of these limitations and their potential influence on the results would substantially enhance the technical completeness and logical consistency of the paper.

Author Response

We sincerely thank the reviewer for the constructive and insightful comments. We have carefully revised the manuscript to address all concerns. Below we provide a point-by-point response.

1. Statistical validity and repeatability of the measurements

Reviewer comment:
“The statistical validity of the experimental repetition (five trials) is not sufficiently justified, and quantitative evidence such as variance or uncertainty analysis would enhance the credibility of the reported results. In addition, the absence of explicit uncertainty quantification and error-bar representation limits the reader’s ability to assess measurement reliability.”

Response:
We appreciate the reviewer’s emphasis on repeatability. In the revised manuscript, we have included a comprehensive repeatability analysis for both the quasi-static and dynamic cases. Specifically:

• The shaded regions in Figures 12–15 now show the standard deviation across five repeated runs.
• Tables 1–4 summarize the average standard deviation, maximum standard deviation, and the repeatability ratio defined by Equation (13).
• For channels whose physical magnitudes remain near zero (e.g., and ), we explain why repeatability ratios appear large despite small absolute scatter.
• For dynamic cases, we discuss why ​​ shows larger ratios at high pitch rates and why this does not compromise the derivative extraction.

These additions quantitatively demonstrate that the primary longitudinal channels relevant to stability-derivative identification exhibit good repeatability, while the observed variability at high pitch rates is explained and accounted for.

 

2. Lack of explicit uncertainty quantification and sensor-based systematic analysis

Reviewer comment:
“Providing a systematic uncertainty analysis based on sensor sensitivity and measurement resolution would greatly improve the clarity and reliability of the findings.”

Response:
We have expanded the discussion of measurement uncertainty at the end of Section 5.1 to clarify why sensor and measurement related uncertainties are unlikely to affect the extracted stability derivatives.

Specifically, we now:

• Convert the ATI Nano17-Ti effective resolutions (0.15 gf for forces; 0.070–0.084 gf·cm for moments) into the units used in this study and compare them directly with the measured loads.
• Highlight that the Nano17-Ti has been widely used in flapping-wing MAV studies to measure aerodynamic loads of similar magnitude [Refs. 26–31], reinforcing its suitability and reliability in the present context.
• Emphasize that the stability derivatives are computed from differences between quasi-static and dynamic cases recorded under identical calibration conditions, meaning any small systematic bias is common to both and cancels out in the derivative estimation.
• Clarify that uncertainties in motion-capture angular measurements are small (<0.1°) compared with the AoA range tested.

These additions do not constitute a full formal uncertainty analysis, but they make clear that the potential sources of sensor and measurement uncertainty are significantly smaller than the observed variability across repeated runs, and therefore have only a minor effect on the extracted pitch-rate stability derivatives.

 

3. Flow non-uniformity and turbulence characteristics of the fan-array setup

Reviewer comment:
“… while the fan-array setup provides a practical approximation of forward-flight conditions, the flow environment remains idealized.”

Response:
We thank the reviewer for this important observation. The revised manuscript now includes a detailed discussion of the limitations of the fan-array inflow:

• We explicitly acknowledge that the fan-array does not produce the spatial uniformity or turbulence control of a low-turbulence wind tunnel.
• We cite prior work on similar fan-array systems to provide context regarding expected turbulence behavior (Refs. [24–25]).
• We clarify that although the inflow is not fully uniform, both quasi-static and dynamic measurements experience the exact same inflow condition, so any steady or slowly varying non-uniformity acts in a common-mode manner and does not bias the extracted pitch-rate derivatives.
• We note future improvements such as flow-field characterization or addition of flow-straightening elements.

This revision clarifies how inflow non-uniformity affects the experiment and why the derivative extraction remains valid.

Reviewer 2 Report

Comments and Suggestions for Authors

This work is an extension of earlier publications.

In order to understand the description of the MAV model studied in this work, it is necessary to familiarize oneself with certain items in the literature.

The additional material attached to the publication, including a video representing the experimental part, is an important element of the work, facilitating its understanding.

A fairly precise description of the measurement setup.

Based on literature data on the velocity distribution generated by the fan array, which turned out to be not very uniform [23], ], I would suggest using, in the stream generated by the set of small fans, a flow straightener in the form of a honeycomb aluminum-foil plate to dissipate the large vortex structures produced by the operation of the group of fans generating local swirl components.

Fig. 10 is unclear. I did not understand the purpose of its presentation.

The operating scheme of the oscillating wings in the adopted configuration relies mainly on the clap-and-fling effect, and this applies to both the dorsal and the lateral regions.

Attention should be drawn to the interesting conclusions from the traces shown in Fig. 12.
They concern longitudinal stability at small angles of attack.

In general, the use of the robot arm to study the unsteady stages of insect flight, where the movement of the object is linked to the tip of the arm through a system measuring of six component forces and moments, is an interesting idea and seems to be effective.

The authors have pointed out the limitations of the research method used.

It seems that writing a tracking/feedback control code for the motion of the robot arm, coupled with the object and augmented with additional degrees of freedom, and controlling it online with an objective function that drives the forces and moments measured by the sensor to zero, would make it possible to obtain information that is currently available only from the analysis of stereoscopic videos of the MAV model’s flight.

The results are presented in a clear form. Correct conclusions from their analysis.

The work is suitable for publication after adding minor explanations (Fig. 10).

Author Response

We sincerely thank the reviewer for the careful and insightful reading of our manuscript. We greatly appreciate the reviewer’s accurate summary of the essence of our work and their positive evaluation of the methodology, measurement setup, and conclusions. We are encouraged by the reviewer’s remark that the paper is suitable for publication, and we thank them for the constructive suggestions. Our responses to the two main concerns raised by the reviewer are provided below.

 

Comment 1: Suggestion to use a flow straightener in the fan-array inflow.

Response:
We thank the reviewer for this thoughtful suggestion. We agree that incorporating a honeycomb flow straightener would improve the inflow uniformity of the fan array. In the present study, however, the mildly turbulent inflow is acceptable because the flapping wings themselves generate highly unsteady wake structures, and our analysis focuses on the quasi-steady aerodynamic response rather than instantaneous flow features. To address the reviewer’s comment, we have added a paragraph in Section 3.1 acknowledging the inflow non-uniformity and noting that future refinements may include the use of a flow straightener.

Revision in manuscript:
A paragraph was added in Section 3.1 to acknowledge the flow non-uniformity of the fan-array system and to note that future refinements may incorporate a flow straightener to improve inflow uniformity and repeatability.

 

Comment 2: Fig. 10 is unclear. I did not understand the purpose of its presentation.

Response:
We thank the reviewer for pointing this out. Figure 10 is intended to illustrate the geometric differences between CKopter-1 and the DelFly II, specifically their flapping amplitudes and mean dihedral angles which directly relate to the expected differences in pitch-rate stability derivatives. To clarify this purpose, we have expanded the explanation of Figure 10 in Section 5 and provided the relevant geometric reasoning before presenting the derivative comparison.

Revision in manuscript:
Paragraph 2 of Section 5 has been expanded to explain Figure 10.

 

Summary

We again thank the reviewer for their detailed and constructive comments, as well as their positive assessment of the manuscript. All required revisions have been implemented, and the clarifications requested for Figure 10 have been incorporated into Section 5 and the figure caption.

Reviewer 3 Report

Comments and Suggestions for Authors

This paper demonstrated a laboratory methodology to identify pitch-rate stability derivatives of a FWMAV using a fan-array robotic-arm setup with synchronized motion capture and six-axis force/moment measurements. The paper is written with some analytical and experimental results, but I have some minor concerns on the current version. Firstly,  the data-based modeling method is employed to get the pitch-rate stability derivatives, but I wonder if the the first principle-based modeling method is useful for this research. Some remarks could be given on this topic to some extent. Secondly, I wonder if the fan-array robotic-arm setup is enough to mimic the practical flying motion of the FWMAV, some critical evaluation index could be given in simulations. Lastly, the traditional mathematical theory on the pitch-rate motion description is not enough for understanding the aerodynamics of the systems.

Author Response

We sincerely thank the reviewer for the constructive comments. We have carefully addressed all points, and corresponding revisions have been incorporated into the manuscript. Our detailed responses are provided below.

 

Comment 1

“The data-based modeling method is employed to get the pitch-rate stability derivatives, but I wonder if the first principle-based modeling method is useful for this research. Some remarks could be given on this topic to some extent.”

Response:

We appreciate the reviewer’s insightful suggestion. A new paragraph has been added at the end of Section 5 discussing the role and relevance of first-principle aerodynamic modeling. In the revised text, we clarify that analytical frameworks such as unsteady blade-element theory, added-mass formulations, and Theodorsen-type unsteady aerodynamic models can, in principle, predict damping-related aerodynamic terms. However, these models face limitations when applied to FWMAVs operating in high-AoA, low-Reynolds-number regimes where vortex dynamics, clap-and-fling, and wing deformation dominate. We explain that the experimentally identified derivatives obtained in this study serve as valuable empirical benchmarks to support and validate future first-principle or semi-empirical aerodynamic models.

Location in revised manuscript:
Section 5, paragraph beginning “Beyond these comparative results, it is also instructive to consider the role of first-principles aerodynamic modeling…”

 

Comment 2

“I wonder if the fan-array robotic-arm setup is enough to mimic the practical flying motion of the FWMAV, some critical evaluation index could be given in simulations.”

Response:

We agree with the reviewer that the fan-array inflow does not fully reproduce the instantaneous velocity fluctuations and wake interactions of free flight. We now explicitly acknowledge this limitation in the revised manuscript. Importantly, we also explain that the significance of this omission depends on the frequency separation between the flapping frequency and the natural frequency of the body motion. For FWMAVs similar to the size and flapping frequency of CKopter-1, these two frequencies are well separated, the body dynamics evolve much more slowly than the wingbeat cycle, making the rigid-body assumption appropriate and ensuring that the quasi-steady aerodynamic response remains the dominant contribution. This justification is consistent with prior findings for the DelFly II [15], where a linear rigid-body model was shown to accurately capture longitudinal dynamics despite the presence of unsteady flapping aerodynamics. We therefore emphasize that, although the inflow lacks instantaneous wake reproduction, it is sufficient for extracting effective aerodynamic damping and stability derivatives.

Location in revised manuscript:
Section 6, paragraph beginning “A further limitation arises from the fact that the fan-array inflow does not reproduce the periodic velocity and positional fluctuations…”

 

Comment 3

“Lastly, the traditional mathematical theory on the pitch-rate motion description is not enough for understanding the aerodynamics of the systems.”

Response:

We thank the reviewer for this important observation. In response, we added a paragraph clarifying that the classical rigid-body pitch-rate formulation used here does not fully represent the complex unsteady aerodynamics of flapping-wing vehicles. Phenomena such as vortex shedding, wake capture, wing flexibility, and clap-and-fling effects contribute to the aerodynamic moment in ways that extend beyond the linearized rigid-body description. We explain that, in this work, the traditional derivative framework is employed primarily as an organizing structure to interpret the measured aerodynamic response. We also highlight that a more complete theoretical description would require incorporating unsteady aerodynamic models or reduced-order flow representations, which forms an important direction for future research.

Location in revised manuscript:
Section 6, paragraph beginning “Finally, we note that the traditional rigid-body formulation…”

 

Summary

All comments have been addressed with additional discussion and clarification in the Results and Discussions and the Conclusions sections. These revisions improve the manuscript by explicitly acknowledging model limitations, clarifying the applicability of the experimental setup, and outlining the relationship between empirical results and first-principle aerodynamic theory.

We thank the reviewer once again for the constructive feedback.