Pith. sign in

REVIEW 3 major objections 5 minor 76 references

Passive aerodynamic robustness reduces disturbance amplification in flight

T0 review · 3 major / 5 minor · reviewed 2026-08-06 · deepseek-v4-flash

Pith's one-line read Avian wings passively reduce disturbance amplification, expanding stable flight without active control.

desk verdict The wing-level comparison is a solid new empirical result; the system-level stability-envelope claim is plausible but outruns the linear model the authors themselves flag as non-physical in the high-alpha regime where the avian advantage is largest. read the letter →

arxiv 2507.14550 v2 pith:XPCCBADR submitted 2025-07-19 physics.flu-dyn

classification physics.flu-dyn
keywords passiveaerodynamicrobustnessdisturbanceamplificationavianflightlift-responsegainstabilityturbulentinflowefficiency-robustnesstrade-offwindtunnelexperiment
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

By comparing a real swan-goose wing with a geometrically matched S1223 airfoil wing in a wind tunnel across three turbulence intensities, this paper argues that avian wings passively attenuate incoming disturbances before any active control acts. The avian wing shows a smaller lift-response gain $dC_L/d\alpha$, a smoother stall, lower lift fluctuations, and a wider operative angle-of-attack range; in a linear longitudinal model of a rigid flyer with identical inertial properties, those wing-level properties shift the passive stability boundary outward. The paper traces the mechanism in the flow: delayed large-scale separation, a turbulent kinetic energy peak closer to the wall, and a more three-dimensional separated shear layer that is less effective at concentrating unsteady energy. The cost is aerodynamic efficiency, so the paper frames flight in turbulence as an efficiency-robustness trade-off rather than an efficiency-only problem. The reason to care is that disturbance sensitivity and control demand, not peak lift-to-drag ratio, become the design metrics for resilient flight.

What carries the argument

The load-bearing objects are the lift-response gain $dC_L/d\alpha$ and the linear small-perturbation longitudinal model $\dot{x}=Ax$ of a rigid flyer. The quasi-steady identity $\Delta C_L \approx (dC_L/d\alpha)(w_{\mathrm{gust}}/u_\infty)$ turns the slope of the measured lift curve into a disturbance-amplification factor, so the paper's key comparison is between two wings' $dC_L/d\alpha$ and lift-fluctuation level $C'_L$ under controlled turbulence. The stability model then converts these measured aerodynamic derivatives into eigenvalues of $A$; passive stability is declared when the largest real part $\mathrm{Re}_{\max}$ is negative. The flow-side mechanism is identified through boundary-layer shape factor, edge-pressure coefficient, and the wall-normal position of the turbulent-kinetic-energy peak, which together distinguish delayed, three-dimensional separation on the avian wing from large-scale coherent separation on the airfoil.

What would settle it

Measure the dynamic lift response to sinusoidal vertical gust perturbations at $\alpha=18^\circ$–$30^\circ$, $Tu=7.4\%$, and the same Reynolds number: if the avian wing's transfer gain from gust velocity to lift equals or exceeds the airfoil wing's, the paper's core claim is falsified.

Watch

Extended reading notes

Core claim

The central claim is that passive wing aerodynamics, not just active actuation, contribute to flight stability in turbulence. In controlled wind-tunnel tests at chord Reynolds numbers around $10^5$, the real avian wing compared with a matched S1223 rigid wing of identical planform has a systematically lower lift-response gain, a more gradual post-stall variation, smaller pitching-moment sensitivity, and lower lift fluctuations at turbulence intensities $Tu=1.5\%$, $2.5\%$, and $7.4\%$. Under the quasi-steady relation $\Delta C_L \approx (dC_L/d\alpha)(w_{\mathrm{gust}}/u_\infty)$, the smaller slope means a given vertical gust produces a smaller load perturbation. Feeding measured stability derivatives into the linear small-perturbation longitudinal model of a rigid flyer with the same mass and inertia, the authors find the avian-wing flyer keeps all eigenvalues with negative real part over a far broader angle-of-attack range than the airfoil-wing flyer, which becomes passively unstable above about $10$–$18$ degrees depending on turbulence level. The authors also show the flow-side reasons: delayed separation, a turbulent kinetic energy peak closer to the surface, stronger spanwise Reynolds-stress anisotropy, and less concentrated TKE production. The paper concludes that passive aerodynamic robustness expands the passive stability envelope and reduces the demand for active stabilization, at the price of a higher cost of transport.

Load-bearing premise

The argument rests on treating static wind-tunnel force measurements as aerodynamic stability derivatives in a linear small-perturbation dynamic model up to 30 degrees angle of attack, including post-stall conditions where the model itself produces a non-physical re-stabilization that the authors exclude.

Editorial extensions

If this is right

  • A wing designed for low $dC_L/d\alpha$ and smooth stall can passively extend the angle-of-attack range over which a rigid flyer remains stable without feedback control.
  • Flight performance in turbulence should be judged by disturbance sensitivity and control demand, not only by peak lift-to-drag ratio.
  • There is a measurable efficiency-robustness trade-off: configurations with high peak efficiency are more disturbance-sensitive and require more active stabilization.
  • Autonomous vehicles could offload part of the stabilization burden to wing morphology, reducing dependence on sensor-actuator feedback loops.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • The paper's static, quasi-steady framework likely understates the avian wing's advantage under rapid dynamic gusts; a dynamic pitch-oscillation test at the same Reynolds numbers would show whether the lower gain persists.
  • Because the two wings share planform, the robustness is attributed to surface roughness, compliance, or permeability; progressively adding those features to an airfoil would isolate which one carries the effect.
  • The same metrics ($dC_L/d\alpha$, operative range, control-power proxy) could be screened early in fixed-wing drone design for gusty urban environments.
  • The efficiency penalty of passive robustness might shrink at higher Reynolds numbers where real birds cruise, so a Reynolds-sweep study could sharpen the claimed trade-off.
Share X Bluesky LinkedIn Reddit HN

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

3 major / 5 minor

Summary. The paper compares a real swan-goose wing with a planform-matched rigid S1223 airfoil wing in a wind tunnel at three turbulence intensities (Tu = 1.5%, 2.5%, 7.4%) and Reynolds numbers near 1.2–1.65×10^5, using six-axis force measurements and stereoscopic PIV. It reports that the avian wing has lower lift-response gain dC_L/dα, a more gradual stall, lower lift fluctuations, and a broader operative angle-of-attack range. The authors then feed static measured force coefficients into a linear small-perturbation longitudinal model and argue that the avian-wing flyer has an expanded passive stability envelope. Flow diagnostics attribute the robustness to delayed separation and near-wall redistribution of turbulent kinetic energy, and a trade-off between aerodynamic efficiency and passive robustness is proposed.

Significance. The wing-level measurements are a genuine strength: the planform-matched comparison, repeated turbulence conditions, and simultaneous force and flow-field data provide direct evidence that the avian wing transmits less disturbance into force fluctuations. The lower lift slope and reduced C_L' shown in Figure 2 are visible in the data and do not depend on the stability model. The proposed efficiency–robustness trade-off, if supported, would be of interest for bio-inspired aerial vehicle design. However, the paper's headline system-level claim—that wing-level properties 'translate into an expanded passive stability envelope'—rests on a linear static-derivative model whose validity in the post-stall regime is the central weakness. I do not see circularity: the eigenvalues are computed from measured aerodynamic data and the trade-off is read off the same measurements; the problem is model validity, not circularity. The system-level prediction is falsifiable but currently unvalidated in exactly the regime where the claimed advantage is largest.

major comments (3)
  1. [Dynamic stability analysis; Figure 3 caption] The system-level claim is not supported in the regime that carries it. The stability envelope in Figure 3A,B and the time-domain tests in Figure 3E–J are computed from Eq. (1) using static wind-tunnel derivatives, and the authors themselves exclude the airfoil-wing flyer's apparent re-stabilization at alpha >= 24 degrees and Tu = 1.5% as a 'non-physical artifact of the linear small-perturbation model.' The avian-wing flyer's advantage is largest in exactly this post-stall range (alpha = 24-30 degrees), where the flow is separated, unsteady, and not represented by static dC_L/dalpha and dC_M/dalpha. The Limitations section also concedes that the quasi-steady framework 'may not fully represent the response to large, unsteady gusts.' Excluding the artifact for one configuration while trusting the same kind of model for the other in the same regime is not justified. Please either restrict the passive-stability conclusion to the pre-stall range where the linear model is plausible, or validate the high-alpha dynamics with an unsteady or nonlinear aerodynamic model, dynamic wind-tunnel tests, or flight data.
  2. [Methods, Dynamic stability analysis; Eq. (1)] The stability calculation is not reproducible as written. Eq. (1) states only the state vector and says that the system matrix A was 'constructed from aerodynamic derivatives obtained from measured force data,' but the expressions for the derivatives (e.g., C_Lalpha, C_Malpha, C_Dalpha), the trim equations, the conversion from wind-tunnel coefficients to dimensional stability derivatives, and the numerical values of all model parameters are not given. The reader cannot verify that the two flyers are identical except for the measured wing aerodynamics, nor can the reader check the effect of omitted rate derivatives such as C_Lq and C_Mq. Please provide the full A-matrix construction and a parameter table.
  3. [Results, Figure 2E and Figure S3] The operative angle-of-attack range alpha_op,w is a data-dependent construct. The Figure S3 caption states that data with normalized PSD below 10^-3 are omitted and that the resulting blank regions are used to identify the operative range; the main text calls this the range over which lift fluctuations 'remain bounded.' No justification or sensitivity analysis for this threshold is provided, yet alpha_op,w is one of the four wing-level robustness metrics and forms the horizontal axis of the trade-off map in Figure 5D. Please test the robustness of alpha_op,w and of Figure 5D to the threshold, or define alpha_op,w from an independently motivated criterion.
minor comments (5)
  1. [Throughout] Several cross-references appear as unresolved placeholders, such as 'section .' and 'section S1'; please insert the correct section numbers.
  2. [Figures 2, 3, and 5] Several axis labels are garbled in the provided text (for example, 'dCL /d/s97', '/s97o p,W', and 'min(CoT) /s97 / °D'); the final figures require clean, correctly typeset labels.
  3. [Author list] The name 'Y ong Chen' in the author list should read 'Yong Chen'.
  4. [Supplemental Information, Eq. (S17)] The expression for the control-rate variance sigma^2_dot(delta_e) includes a term K G Q_w G^T K^T but omits possible cross-correlations between the state and the white-noise process w; please clarify the stochastic convention or state that w is a unit-variance white process with no state correlation.
  5. [Control cost analysis, Figure 5B] The claim that the avian-wing flyer requires higher active control effort when stabilization is engaged appears surprising given its lower disturbance sensitivity; please clarify whether this comparison applies only to unstable trim points and how strongly the arbitrary choice Q=I, R=1 affects the result.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the stability envelope is a derived consequence of measured aerodynamic derivatives, and self-citations are limited to experimental methods.

full rationale

The paper's central claim is that avian wings passively attenuate disturbance transmission, evidenced by direct wind-tunnel measurements of lower lift-response gain dCL/dalpha, smoother stall, lower force fluctuations, and a broader operative angle-of-attack range. These are measured quantities, not predictions obtained from a fitted model. The system-level stability claim is computed from the linear longitudinal model of Methods Eq. (1), with aerodynamic stability derivatives obtained from the same measured force data and inertial properties taken from independent anatomical studies. This is a genuine derivation: the eigenvalues and stability envelope could in principle have gone the other way had the measured Cm_alpha and related derivatives differed. The 'operative angle-of-attack range' is a measurement convention (a threshold on lift fluctuations or PSD), not a parameter fitted to reproduce the stability envelope. No step in the derivation assumes the conclusion. Self-citations (e.g., Refs. 12, 34, 35, 36, 60, 68) concern experimental apparatus, wind-tunnel procedures, SPIV processing, and specimen sourcing; none is load-bearing for the aerodynamic-sensitivity or stability conclusions, and no uniqueness theorem or ansatz is imported from same-author prior work. The paper's own caveat that the apparent re-stabilization at alpha >= 24 degrees is a non-physical artifact of the linear small-perturbation model is a model-validity limitation in the post-stall regime, not a circularity; it is a correctness risk outside the scope of this pass. Overall, the derivation is self-contained and no circular step was identified.

Assumptions & free parameters 7 free parameters · 5 assumptions · 0 invented entities

The paper's central claims rest on standard flight-dynamics assumptions (quasi-steady, linear small-perturbation) plus several hand-chosen thresholds and model parameters (PSD cutoff, LQR weights, tail geometry). The most fragile entry is the validity of the linear model at post-stall angles, which the paper itself flags as producing non-physical artifacts.

free parameters (7)
  • Operative-range PSD threshold = 10^-3 (normalized PSD cutoff)
    Defines the operative angle-of-attack range in Figure S3; chosen by hand, no sensitivity analysis given.
  • LQR weighting matrices Q and R = Q = I_4x4, R = [1]
    Chosen to provide a consistent comparative benchmark; affects the absolute values of C_P,control.
  • Disturbance intensity Q_w = 1 (nondimensionalized)
    Set to unity for all configurations; arbitrary but equal, so relative comparison unaffected.
  • Equivalent tail geometry S_h, X_h = S_h = 0.0180 m^2, X_h = 0.261 m
    Used in the longitudinal stability model; taken from swan goose anatomy in Ref. 33, not fitted here, but choices affect absolute stability envelope.
  • Tail/elevator effectiveness eta_h, tau_e = eta_h = 1, tau_e = 1
    Assumed unity in the control analysis; affects C_P,control magnitudes.
  • Trim airspeed range filter = 10-30 m/s
    Solutions with trim airspeeds outside this range were excluded; could affect which alpha points enter the stability envelope.
  • Boundary-layer edge thresholds = du_c/dy_c < 0.02, u_c > 0.85 u_c,max
    Used to identify boundary-layer edge for H, C_p,e, etc.; arbitrary thresholds in flow diagnostics.
assumptions (5)
  • domain assumption Quasi-steady approximation for gust response: delta C_L ~ (dC_L/dalpha)(w/u_infinity)
    Used to interpret lift-response gain as disturbance amplification (Results, near 'Under a quasi-steady approximation').
  • domain assumption Small-perturbation linear longitudinal dynamics for a rigid flyer
    The basis of the stability analysis (Methods Eq. 1, Ref. 32); assumes linearity and small perturbations about trim.
  • domain assumption Static aerodynamic derivatives measured in the wind tunnel are representative of the dynamic response of a rigid flyer
    The A matrix is constructed from static force measurements at each alpha; unsteady and inertial effects are neglected.
  • domain assumption Equivalence of the real avian wing to a passive aerodynamic system for the purposes of comparison
    The avian wing is treated as an integrated system; differences vs. the airfoil are attributed to surface morphology and structural features rather than planform geometry.
  • ad hoc to paper Validity of the linear model up to alpha=30 degrees despite stall
    The model produces a non-physical re-stabilization for the airfoil-wing flyer at alpha>=24 degrees (Fig. 3B), which is excluded; the same model is used for the avian-wing flyer at high alpha.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Passive aerodynamic robustness reduces disturbance amplification in flight." pith.science (2026). https://pith.science/paper/XPCCBADR

@misc{pith2026250714550,
  author       = {Pith},
  title        = {Pith review of: Passive aerodynamic robustness reduces disturbance amplification in flight},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/XPCCBADR}},
  note         = {Machine review of arXiv:2507.14550}
}
read the original abstract

Flight in turbulence is constrained not only by aerodynamic efficiency, but also by how strongly flow disturbances are transmitted into unsteady loads and dynamic responses. Although disturbance rejection is typically attributed to active control, birds often sustain fixed-wing gliding in disturbed air, suggesting that the wing itself may passively attenuate aerodynamic perturbations. Here, we show that avian wings reduce aerodynamic sensitivity to incoming disturbances. Compared with a geometrically matched airfoil wing, the avian wing exhibits lower lift-response gain, smoother stall transition, reduced force fluctuations, and a broader operative angle-of-attack range across turbulence intensities. These wing-level properties translate into an expanded passive stability envelope in rigid-flyer dynamics. Flow diagnostics indicate that this robustness is associated with delayed separation and redistribution of turbulent kinetic energy, which suppress large-scale flow instability and weaken disturbance transmission. This passive robustness comes at the cost of reduced aerodynamic efficiency, revealing an efficiency-robustness trade-off in disturbed flows. Our results identify aerodynamic sensitivity and control demand as essential metrics for flight performance in turbulence, and suggest passive aerodynamic robustness as a design principle for resilient flying systems.

Figures

Figures reproduced from arXiv: 2507.14550 by the authors.

Figure 1
Figure 1. Passive aerodynamic robustness as a mechanism for disturbance-resilient flight. (A) Birds can actively respond to strong atmospheric disturbances through rapid wing or body adjustments, whereas under milder or persistent perturbations they may sustain fixed-wing gliding with limited ac￾tuation. This contrast raises the question of whether passive aerodynamic properties of the wing can attenuate disturbance transmiss… view at source ↗
Figure 2
Figure 2. Reduced aerodynamic sensitivity under turbulent disturbances. Compared with the geo￾metrically matched S1223 airfoil wing, the avian wing exhibits lower sensitivity to turbulent perturbations, characterized by a smaller lift-response gain, a more gradual stall transition, reduced pitching-moment sensitivity, lower lift fluctuations, and a broader operative angle-of-attack range across increasing tur￾bulence intensit… view at source ↗
Figure 3
Figure 3. Expanded passive stability envelope at the system level. The avian-wing flyer maintains passive stability over a broader range of conditions than the airfoil-wing flyer across varying turbulence intensities. (A,B) Maximum real part of the eigenvalues, Remax, as a function of angle of attack α, where Remax < 0 denotes stable flight. The corresponding operative stability range is denoted αop,f . (C,D) Natural frequenc… view at source ↗
Figures from the paper (2 more)
Figure 4
Figure 4. Figure 4: Flow–structure interactions associated with delayed separation and redistributed tur￾bulent activity over the avian wing. Definitions of the reported flow quantities are provided in section . (A–D) Normalized time-averaged velocity fields, u/u ¯ ∞ at z/b = 0.3 for T u …
Figure 5
Figure 5. Figure 5: Energy–stability trade-off across aerodynamic and control metrics. (A) Base aerody￾namic cost, quantified by the Cost of Transport (CoT), as a function of angle of attack α under varying turbulence intensities. (B) Dynamic control expenditure, represented by the averag…

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

76 extracted references · 76 canonical work pages

  1. [1]

    Weimerskirch, H., and Prudor, A. (2019). Cyclone avoidance behaviour by foraging seabirds. Sci- entific reports9, 5400

  2. [2]

    Lempidakis, E., Shepard, E.L., Ross, A.N., Matsumoto, S., Koyama, S., Takeuchi, I., and Y oda, K. (2022). Pelagic seabirds reduce risk by flying into the eye of the storm. Proceedings of the National Academy of Sciences119, e2212925119

  3. [3]

    Weimerskirch, H., Bishop, C., Jeanniard-du Dot, T., Prudor, A., and Sachs, G. (2016). Frigate birds track atmospheric conditions over months-long transoceanic flights. Science353, 74–78

  4. [4]

    Kempton, J.A., Wynn, J., Bond, S., Evry, J., Fayet, A.L., Gillies, N., Guilford, T., Kavelaars, M., Juarez-Martinez, I., Padget, O. et al. (2022). Optimization of dynamic soaring in a flap-gliding seabird affects its large-scale distribution at sea. Science advances8, eabo0200

  5. [5]

    Akos, Z., Nagy, M., and Vicsek, T. (2008). Comparing bird and human soaring strategies. Proceed- ings of the National Academy of Sciences105, 4139–4143

  6. [6]

    Bishop, C.M., Spivey, R.J., Hawkes, L.A., Batbayar, N., Chua, B., Frappell, P .B., Milsom, W.K., Natsagdorj, T., Newman, S.H., Scott, G.R. et al. (2015). The roller coaster flight strategy of bar- headed geese conserves energy during himalayan migrations. Science347, 250–254

  7. [7]

    Shamoun-Baranes, J., Bouten, W., Van Loon, E.E., Meijer, C., and Camphuysen, C. (2016). Flap or soar? how a flight generalist responds to its aerial environment. Philosophical Transactions of the Royal Society B: Biological Sciences371, 20150395

  8. [8]

    Richardson, P .L. (2011). How do albatrosses fly around the world without flapping their wings? Progress in Oceanography88, 46–58

Show all 76 references
  1. [9]

    Mohamed, A., Taylor, G.K., Watkins, S., and Windsor, S.P . (2022). Opportunistic soaring by birds suggests new opportunities for atmospheric energy harvesting by flying robots. Journal of the Royal Society Interface19, 20220671

  2. [10]

    Sachs, G. (2005). Minimum shear wind strength required for dynamic soaring of albatrosses. Ibis 147, 1–10

  3. [11]

    Bousquet, G.D., Triantafyllou, M.S., and Slotine, J.J.E. (2017). Optimal dynamic soaring consists of successive shallow arcs. Journal of The Royal Society Interface14, 20170496

  4. [12]

    Chen, L., Lu, J., Yin, Y ., Huang, J., Xiang, Y ., and Liu, H. (2026). Learning step-level dynamic soaring in shear flow. . URL:https://arxiv.org/abs/2604.12413.arXiv:2604.12413

  5. [13]

    Fukami, K., and Taira, K. (2023). Grasping extreme aerodynamics on a low-dimensional manifold. Nature Communications14, 6480

  6. [14]

    Reynolds, K.V., Thomas, A.L., and Taylor, G.K. (2014). Wing tucks are a response to atmospheric turbulence in the soaring flight of the steppe eagle aquila nipalensis. Journal of The Royal Society Interface11, 20140645. 16

  7. [15]

    Cheney, J.A., Stevenson, J.P ., Durston, N.E., Song, J., Usherwood, J.R., Bomphrey, R.J., and Windsor, S.P . (2020). Bird wings act as a suspension system that rejects gusts. Proceedings of the Royal Society B287, 20201748

  8. [16]

    Tucker, V.A. (1972). Metabolism during flight in the laughing gull, larus atricilla. American Journal of Physiology-Legacy Content222, 237–245

  9. [17]

    Ortega-Jimenez, V.M., Sapir, N., Wolf, M., Variano, E.A., and Dudley, R. (2014). Into turbulent air: size-dependent effects of von k ´arm´an vortex streets on hummingbird flight kinematics and energetics. Proceedings of the Royal Society B: Biological Sciences281, 20140180

  10. [18]

    Harvey, C., Baliga, V.B., Lavoie, P ., and Altshuler, D.L. (2019). Wing morphing allows gulls to mod- ulate static pitch stability during gliding. Journal of The Royal Society Interface16, 20180641

  11. [19]

    Laurent, K.M., Fogg, B., Ginsburg, T., Halverson, C., Lanzone, M.J., Miller, T.A., Winkler, D.W., and Bewley, G.P . (2021). Turbulence explains the accelerations of an eagle in natural flight. Proceedings of the National Academy of Sciences118, e2102588118

  12. [20]

    Lentink, D., M ¨uller, U.K., Stamhuis, E., De Kat, R., Van Gestel, W., Veldhuis, L., Henningsson, P ., Hedenstr¨om, A., Videler, J.J., and Van Leeuwen, J.L. (2007). How swifts control their glide performance with morphing wings. Nature446, 1082–1085

  13. [21]

    Cheney, J.A., Stevenson, J.P ., Durston, N.E., Maeda, M., Song, J., Megson-Smith, D.A., Windsor, S.P ., Usherwood, J.R., and Bomphrey, R.J. (2021). Raptor wing morphing with flight speed. Journal of The Royal Society Interface18, 20210349

  14. [22]

    Harvey, C., and Inman, D.J. (2022). Gull dynamic pitch stability is controlled by wing morphing. Proceedings of the National Academy of Sciences119, e2204847119

  15. [23]

    KleinHeerenbrink, M., France, L.A., Brighton, C.H., and Taylor, G.K. (2022). Optimization of avian perching manoeuvres. Nature607, 91–96

  16. [24]

    Watkins, S., Millbank, J., and Loxton, B. (2006). Atmosheric winds and their effects on micro air vehicles. AIAA Journal of Aircraft44

  17. [25]

    Wordley, S., and Saunders, J. (2008). On-road turbulence. SAE International Journal of Passenger Cars-Mechanical Systems1, 341–360

  18. [26]

    Lempidakis, E., Ross, A.N., Quetting, M., Garde, B., Wikelski, M., and Shepard, E.L. (2022). Es- timating fine-scale changes in turbulence using the movements of a flapping flier. Journal of the Royal Society Interface19, 20220577

  19. [27]

    Williams, H.J., Shepard, E., Holton, M.D., Alarc´on, P .A.E., Wilson, R., and Lambertucci, S.A. (2020). Physical limits of flight performance in the heaviest soaring bird. Proceedings of the National Academy of Sciences117, 17884–17890

  20. [28]

    Liechti, F ., Witvliet, W., Weber, R., and B ¨achler, E. (2013). First evidence of a 200-day non-stop flight in a bird. Nature communications4, 2554

  21. [29]

    Rattenborg, N.C., Voirin, B., Cruz, S.M., Tisdale, R., Dell’Omo, G., Lipp, H.P ., Wikelski, M., and Vyssotski, A.L. (2016). Evidence that birds sleep in mid-flight. Nature communications7, 12468

  22. [30]

    Nakata, T., Liu, H., and Bomphrey, R.J. (2015). A cfd-informed quasi-steady model of flapping-wing aerodynamics. Journal of fluid mechanics783, 323–343

  23. [31]

    Wang, Q., Goosen, J., and van Keulen, F . (2016). A predictive quasi-steady model of aerodynamic loads on flapping wings. Journal of Fluid Mechanics800, 688–719. 17

  24. [32]

    Bossert, D.E., Morris, S.L., Hallgren, W.F ., and Y echout, T.R. (2003). Introduction to aircraft flight mechanics: Performance, static stability, dynamic stability, and classical feedback control. American Institute of Aeronautics and Astronautics

  25. [33]

    Harvey, C., Baliga, V.B., Wong, J.C., Altshuler, D.L., and Inman, D.J. (2022). Birds can transition between stable and unstable states via wing morphing. Nature603, 648–653

  26. [34]

    Qiu, S., Cheng, Z., Xu, H., Xiang, Y ., and Liu, H. (2021). On the characteristics and mechanism of perturbation modes with asymptotic growth in trailing vortices. Journal of Fluid Mechanics918, A41

  27. [35]

    Qin, S., Mou, Y ., Wang, W., Xiang, Y ., and Liu, H. (2025). Flow transport enhancement of alula maintaining high lift on fixed wing. Physics of Fluids37

  28. [36]

    Wu, Y ., Xiao, Z., Xiang, Y ., Li, D., and Liu, H. (2025). The response and receptivity mechanism of wingtip vortex under the effect of external disturbance. Physics of Fluids37

  29. [37]

    Zhou, P ., Zhong, S., and Zhang, X. (2021). On the effect of velvet structures on trailing edge noise: experimental investigation and theoretical analysis. Journal of Fluid Mechanics919, A11

  30. [38]

    Matloff, L.Y ., Chang, E., Feo, T.J., Jeffries, L., Stowers, A.K., Thomson, C., and Lentink, D. (2020). How flight feathers stick together to form a continuous morphing wing. Science367, 293–297

  31. [39]

    Schlichting, H., and Gersten, K. (2017). Boundary-Layer Theory. 9 ed.. Berlin, Heidelberg: Springer. Pp. 198–199

  32. [40]

    Thompson, C., Biler, H., Symon, S., and Ganapathisubramani, B. (2023). Effects of integral length scale variations on the stall characteristics of a wing at high free-stream turbulence conditions. Journal of Fluid Mechanics974, A9

  33. [41]

    Schlichting, H., and Kestin, J. (1961). Boundary layer theory vol. 121. Springer

  34. [42]

    Pope, S.B. (2000). Turbulent Flows. Cambridge: Cambridge University Press. Sect. 5.4 (p. 124) and Sect. 11.1 (p. 359)

  35. [43]

    Lee, M., and Moser, R.D. (2015). Direct numerical simulation of turbulent channel flow up to. Journal of fluid mechanics774, 395–415

  36. [44]

    Orlandi, P . (2019). Turbulent kinetic energy production and flow structures in flows past smooth and rough walls. Journal of Fluid Mechanics866, 897–928

  37. [45]

    Balin, R., and Jansen, K.E. (2021). Direct numerical simulation of a turbulent boundary layer over a bump with strong pressure gradients. Journal of Fluid Mechanics918, A14

  38. [46]

    Pennycuick, C.J. (2008). Modelling the flying bird vol. 5. Elsevier

  39. [47]

    Withers, P .C. (1981). An aerodynamic analysis of bird wings as fixed aerofoils. Journal of Experi- mental Biology90, 143–162

  40. [48]

    Lees, J.J., Dimitriadis, G., and Nudds, R.L. (2016). The influence of flight style on the aerodynamic properties of avian wings as fixed lifting surfaces. PeerJ4, e2495. doi:10.7717/peerj.2495

  41. [49]

    Y ap, T.C., Abdullah, M.Z., Husain, Z., Ripin, Z.M., and Ahmad, R. (2001). The effect of turbulence intensity on the aerodynamic performance of airfoils. In Proceedings of the 4th International Con- ference on Mechanical Engineering (ICME 2001). Dhaka, Bangladesh pp. 31–36

  42. [50]

    Cao, N., Ting, D.S.K., and Carriveau, R. (2011). The performance of a high-lift airfoil in turbulent wind. Wind Engineering35, 179–196. doi:10.1260/0309-524X.35.2.179. 18

  43. [51]

    Tsuchiya, T., Numata, D., Suwa, T., and Asai, K. (2013). Influence of turbulence intensity on aerody- namic characteristics of an naca 0012 at low reynolds numbers. In 51st AIAA Aerospace Sciences Meeting including the New Horizons Forum and Aerospace Exposition. Grapevine, Te...

  44. [52]

    Blickhan, R., Seyfarth, A., Geyer, H., Grimmer, S., Wagner, H., and G¨unther, M. (2007). Intelligence by mechanics. Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences365, 199–220. doi:10.1098/rsta.2006.1911

  45. [53]

    M ¨uller, V.C., and Hoffmann, M. (2017). What is morphological computation? On how the body contributes to cognition and control. Artificial Life23, 1–24. doi:10.1162/ARTL_a_00219

  46. [54]

    Floreano, D., and Wood, R.J. (2015). Science, technology and the future of small autonomous drones. nature521, 460–466

  47. [55]

    KleinHeerenbrink, M., Johansson, L.C., and Hedenstr ¨om, A. (2017). Multi-cored vortices support function of slotted wing tips of birds in gliding and flapping flight. Journal of the Royal Society Interface14, 20170099

  48. [56]

    Mohamed, A., Watkins, S., Clothier, R., Abdulrahim, M., Massey, K., and Sabatini, R. (2014). Fixed- wing mav attitude stability in atmospheric turbulence—part 2: Investigating biologically-inspired sensors. Progress in Aerospace Sciences71, 1–13

  49. [57]

    Harvey, C., de Croon, G., Taylor, G.K., and Bomphrey, R.J. (2023). Lessons from natural flight for aviation: then, now and tomorrow. Journal of experimental biology226, jeb245409

  50. [58]

    Reynaga, C.M., and Azizi, E. (2026). Mechanical control: parallel pathways for modulating move- ment. Journal of Experimental Biology229, jeb251237

  51. [59]

    Broatch, A., Margot, X., Garc´ıa-T´ıscar, J., and Felgueroso, A. (2022). An automatized methodology to generate velocity distortion panels for wind tunnel testing. Journal of Wind Engineering and Industrial Aerodynamics227, 105065

  52. [60]

    Huang, J., Xiang, Y ., Chen, L., Qin, S., Lu, J., Y e, S., Chen, Y ., and Liu, H. (2025). Geese achieve stationary takeoff via synergistic wing kinematics and enhanced aerodynamics. arXiv preprint arXiv:2512.20894

  53. [61]

    Harvey, C., Baliga, V., Goates, C., Hunsaker, D., and Inman, D. (2021). Gull-inspired joint-driven wing morphing allows adaptive longitudinal flight control. Journal of the Royal Society Interface18, 20210132

  54. [62]

    Shyy, W., Berg, M., and Ljungqvist, D. (1999). Flapping and flexible wings for biological and micro air vehicles. Progress in aerospace sciences35, 455–505

  55. [63]

    Usherwood, J.R., Hedrick, T.L., and Biewener, A.A. (2003). The aerodynamics of avian take-off from direct pressure measurements in canada geese (branta canadensis). Journal of Experimental Biology206, 4051–4056

  56. [64]

    Maeng, J.S., Park, J.H., Jang, S.M., and Han, S.Y . (2013). A modeling approach to energy savings of flying canada geese using computational fluid dynamics. Journal of theoretical biology320, 76–85

  57. [65]

    doi:10.2514/6.2013-65

  58. [66]

    Rader, J.A., and Hedrick, T.L. (2023). Morphological evolution of bird wings follows a mechanical sensitivity gradient determined by the aerodynamics of flapping flight. Nature Communications14, 7494. 19

  59. [67]

    Favier, J., Dauptain, A., Basso, D., and Bottaro, A. (2009). Passive separation control using a self- adaptive hairycoating. Journal of Fluid Mechanics627, 451–483

  60. [68]

    Charonko, J.J., and Vlachos, P .P . (2013). Estimation of uncertainty bounds for individual particle image velocimetry measurements from cross-correlation peak ratio. Measurement Science and Technology24, 065301

  61. [69]

    Chen, L., Li, Z., Wu, Q., Yin, Y ., Xiang, Y ., and Liu, H. (2026). On the load-shifting phenomenon of accelerating reconfigurable circular plates. Journal of Fluid Mechanics1029, A8

  62. [70]

    Vinuesa, R., Bobke, A., ¨Orl¨u, R., and Schlatter, P . (2016). On determining characteristic length scales in pressure-gradient turbulent boundary layers. Physics of fluids28

  63. [71]

    Anderson, J.D. (2017). Fundamentals of Aerodynamics. 6 ed.. New Y ork: McGraw-Hill Education

  64. [72]

    Kalman, R.E. et al. (1960). Contributions to the theory of optimal control. Bol. soc. mat. mexicana 5, 102–119

  65. [73]

    Anderson, B.D., and Moore, J.B. (2007). Optimal control: linear quadratic methods. Courier Corpo- ration

  66. [74]

    Beard, R.W., and McLain, T.W. (2012). Small unmanned aircraft: Theory and practice. Princeton university press

  67. [75]

    Hearst, R.J., and Lavoie, P . (2014). Decay of turbulence generated by a square-fractal-element grid. Journal of Fluid Mechanics741, 567–584

  68. [76]

    Kitamura, T., Nagata, K., Sakai, Y ., Sasoh, A., Terashima, O., Saito, H., and Harasaki, T. (2014). On invariants in grid turbulence at moderate reynolds numbers. Journal of fluid mechanics738, 378–406. 20 S1 Control cost analysis To quantify how passive stability alters the n...

Pith tools

Reviewed August 6, 2026 · model on record in the stance chip above.