Geese achieve stationary takeoff via synergistic wing kinematics and enhanced aerodynamics

TL;DR

This modular control strategy orchestrates a stereotyped wing kinematics featuring an accelerated translational downstroke and a rapid tip-reversal upstroke, and quantified the aerodynamic forces and found that entirely positive lift and thrust are generated throughout the motion cycle.

Abstract

Stationary take-off, without a running start or elevated descent, requires substantial aerodynamic forces to overcome weight, particularly for large birds such as geese exceeding 2 kg. However, the complex wing motion and high-Reynolds-number (Re $\approx$$10^5$) flow dynamics challenge conventional expectations of avian flight aerodynamics, rendering this mechanism elusive. Analyzing 578 stationary take-offs from seven geese (\textit{Anser cygnoides}) and applying Principal Component Analysis (PCA), we reveal that the complex wing kinematics collapse onto a low-dimensional manifold dominated by two synergies: a Stroke Synergy responsible for fundamental rhythmic stroke, and a Morphing Synergy governing spanwise geometry. This modular control strategy orchestrates a stereotyped wing kinematics featuring an accelerated translational downstroke and a rapid tip-reversal upstroke. By integrating wing kinematic analysis with the mass distribution of the geese, we quantified the aerodynamic forces and found that entirely positive lift and thrust are generated throughout the motion cycle. The enhanced aerodynamic performance of geese takeoff results from three principal mechanisms. During the downstroke, significant lift generated from wing acceleration is predicted by the quasi-steady framework. Flow visualization reveals that wake capture further enhances the lift generation in downstroke by orienting the position of wake vortices. During the upstroke, the distal wing performs a rapid pitching motion and generates a substantial thrust, the vertical component of which contributes significantly to weight support.

Figures (4)

• Figure 1: Aerodynamic regimes and the high-lift paradox of goose stationary takeoff. An overview of maximum lift coefficients ($C_{L,\max}$) and lift coefficients ($C_{L}$) under typical flight conditions reported in the literature across a range of Reynolds numbers ($Re$). Here, the suffix 'static' (across birds, bats, and insects) denotes data obtained under static flow conditions. For insects, 'revolving wings' refers to propeller-like experiments. Across all species, 'forward flight' and 'hovering' represent motion data derived from in vivo observations or motion capture systems. Notably, the data points of geese stationary takeoff are derived from typical morphological ranges ($m=2.1\text{--}3.5 \text{ kg}$, $S=0.296\text{--}0.36 \text{ m}^2$) and a characteristic wing velocity of $U \approx 7 \text{ m/s}$. The estimates yield a Reynolds number of $Re \approx 9.6 \times 10^4$ and a required lift coefficient range of $C_L \approx 1.9\text{--}3.9$. Detailed calculation methods and data sources are provided in the Supplementary Information.
• Figure 2: Motion capture and anatomical reconstruction of goose take-off. (A) Experimental setup for synchronized force and motion capture. Geese were trained to initiate take-off from a force platform within a calibrated motion capture system. (B) Wing kinematics were driven by the humerus, radius/ulna, and manus, reconstructed from 10 anatomical key points on both torso and wings (8 of which were marked; circular dots). The goose was modeled as a composite geometric system, allowing real-time calculation of the CoM (denoted by cross) based on key point positions and anatomical measurements. (C) Spatial distribution of CoM trajectories across all $n=578$ take-off trials ($n=7$ geese). Bin counts represent the number of CoM samples falling within a 2 cm × 2 cm space in the lateral view. (D) Horizontal (green cycle) and vertical (blue square) displacements of the CoM plotted against initial lift-off velocity and mean aerodynamic force within three wingbeat cycles. Solid lines show linear regressions in the vertical (pink) and horizontal (purple) directions, respectively.
• Figure 3: Stereotyped take-off wing kinematics. (A) Schematic diagram of the degrees of freedom of the goose wing. Wing motion was described relative to the shoulder (P5) in global reference frame. The humerus exhibited three DoFs: elevation/depression (HUed), pronation/supination (HUps), and protraction/retraction (HUpr). Elbow flexion/extension (ELfe) was enabled by the radius/ulna, while wrist flexion/extension (WRfe) and pronation/supination (WRps) were facilitated by the manus. (B) Time history of wing skeletal motion. (C) Superimposed phase space trajectories of the Stroke Synergy versus the Morphing Synergy across all experimental trials. (D) Correlation matrix between the PCA modes derived from wing marker coordinates and the six anatomical DoFs. (E) Lateral and top views of a complete wingbeat. A typical wingbeat cycle from downstroke to upstroke consists of four key phases—flap, sweep, raise, and reverse—are marked in (B, C and E), with the orange line marks the boundaries of the each phases. The gray area marks the downstroke.
• Figure 4: Aerodynamic force generation and wing kinematics.A, B, Time-resolved aerodynamic forces ($F_{\text{aero}}$), wing inertial forces ($F_{\text{iner}}$), and torso inertial forces ($F_{\text{torso}}$) in the horizontal (A) and vertical (B) directions. Specific aerodynamic forces (red lines) were resolved by analytically decoupling wing inertial contributions (blue lines) from the total translational kinetics (black lines). C, Mean aerodynamic forces in horizontal (light blue) and vertical (dark blue) directions across four phases (flap, sweep, raise, reverse) and the full wingbeat cycle. D--F, Horizontal kinematics and kinetics of wing segments relative to the torso: relative velocity (D), relative acceleration (E), and derived inertial forces based on segmental mass (F). Data are presented for three representative segments: humerus (proximal, P), radius-ulna (middle, M), and manus (distal, D); inertial contributions from other wing elements were negligible. G, Decomposition of instantaneous aerodynamic forces based on wing velocity at the radius of gyration. Solid lines represent measured lift (purple) and drag (pink); The thin purple line indicate theoretical predictions from quasi-steady models. H, I, Angle of attack (AoA) (H) and velocity (I) of the proximal, middle, and distal wing sections. J Schematic of flow structures observed from flow visualization, showing the generation of a starting vortex (STV, blue loop) and a leading-edge vortex (LEV, orange loop) during the wingbeat. Solid loops represent vortices from the current wingbeat cycle, while dashed loops indicate those from the previous cycle. The schematic is based on experimental flow visualization results (see Flow Pattern Visualization). Gray shading indicates the downstroke; orange vertical lines delimit the four wingbeat phases.