Aerodynamic significance of mass distribution on diverse samara descent behaviors

Abstract

Samaras, or wing seeds, feature fibrous appendages that act as wings to enable wind-driven dispersal. Diversity in morphologies and structures subtly contributes to the flight patterns of various seeds, thereby serving as a key factor in the reproductive strategies of plants. To explore the mechanisms underlying various samara flight behaviors, we proposed an effective framework by manipulating the mass distribution on a plate to mimic various three-dimensional descent behaviors of samaras. Through this approach, we experimentally identified and characterized four distinct flight modes. The three-dimensional vortical structures were then numerically analyzed to gain insights into the samara-inspired flight behaviors. Our study innovatively demonstrates how strategic mass distribution in samaras leads to diverse flight behaviors that leverage vortices to enhance seed dispersal, offering a fresh perspective for the design of biomimetic fliers.

The diverse flight patterns of samaras are key to their dispersal. Here, the authors show that strategically altering mass distribution on a plate induces four distinct samara-like flight modes, offering a new inspiration for biomimetic flier design.

Introduction

Seed dispersal is a fundamental ecological process that enhances plant reproduction and drives evolutionary developments across diverse species^1,2. Samaras, such as those from maple, ash, elm, and mahogany trees, consist of seeds with wing-like structures. This unique configuration enables them to descend slowly to exploit wind currents, facilitating seed dispersal over distances ranging from several meters to kilometers^3–5. In pursuit of this, a variety of morphologies and structural adaptations have evolved (see Fig. 1a), resulting in distinct flight patterns that leverage aerodynamics in different ways.

Fig. 1. Framework inspired by samaras.

a Photographs of various samaras from the following species, in order: Acer pictum (maple), Acer negundo (maple), Fraxinus (ash), Pterolobium punctatum, Swietenia mahagoni (mahogany), Ventilago leiocarpa, Pterocarpus santalinus (red sandalwood), and Eucommia ulmoides. b Schematic of falling trajectories and mass distribution of maple and ash samaras. The normalized thickness distributions and center of mass (COM) locations are presented, based on data obtained from actual samaras. Maple samaras demonstrate autorotative flights due to mass concentration at the terminal end, whereas ash samaras, with more centrally distributed mass, spiral downward, rotating along their longitudinal axis. $h/h_m$ represents the normalized thickness. c Schematic of the samara-inspired framework. A rectangular thin plate with an aspect ratio of 3.0 mimics the typical light flattened wing structure of samaras. Heavier and lighter weights are attached to the plate to emulate the mass concentrations at the nut and leading edge, respectively. Adjusting their distance from the plate’s centerlines allows for precise control of the mass distribution.

The flight capabilities of samaras have long intrigued researchers across various fields. Studies have documented a wide range of flight behaviors among different samara species, suggesting a correlation between these behaviors and the samaras’ mass distribution^6–8. For example, samaras from maple and mahogany trees, with mass concentrated at the terminal end and leading edge, exhibit autorotative flight^9–11 (Fig. 1b). Research on maple samaras shows that this specific mass distribution facilitates the formation of the leading-edge vortex (LEV) to generate lift^6,12–14, a mechanism also observed in animal locomotion to enhance propulsion^15–17. Although the maple-like flight mode has been relatively well studied^11,18–20, the descent behaviors of other samaras remain largely unexplored. For instance, samaras from ash and elm trees, which have more centrally distributed mass, tend to tumble downward along curved trajectories^10,21–23 (Fig. 1b). Despite sharing a common wing–seed structure, these samaras exhibit subtle differences in mass distribution that may critically influence their diverse flight modes—an aspect that remains largely underexplored.

Freely falling bodies are a common occurrence in nature²⁴. Previous studies have primarily focused on the two-dimensional (2D) descent of plates, showing that variations in rotational inertia and Reynolds number ($\mathrm{Re}$) can lead to transitions between tumbling, fluttering, and chaotic trajectories^25–27. However, the vortical structures and dynamics associated with three-dimensional (3D) falling trajectories differ remarkably^28,29. For instance, a circular disk undergoes helical spiral descents, with flow structures noticeably different from those observed in 2D motions^30–32. Given the diverse structural configurations and flight patterns of samaras, exploring their behaviors in 3D scenarios is essential.

Since samaras facilitate flight solely through structural configuration without the neuromuscular control present in animals¹⁴, they have provided inspiration for the field of robotics. Electronic samara-inspired microfliers have been designed for environmental monitoring and other applications^33–36. A thorough understanding of the fundamental mechanisms governing the flight patterns of samaras is vital for designing these bioinspired devices. Existing designs typically adopt a single configuration to achieve specific flight behaviors, suggesting that investigating more diverse and flexible control strategies could be beneficial.

In this study, we introduced a framework to explore a broad range of samara-inspired flight behaviors. By manipulating the mass distribution on a plate to mimic the descending behaviors of various samaras, we experimentally identified four distinct flight modes and analyzed their flight patterns. Using computational fluid dynamics (CFD), we focused on the characteristic vortices underlying 3D flight patterns. Our research highlights the critical role of mass distribution in the 3D descent of samaras and its influence on the formation of vortices and wake interactions that produce lift and sustain flight patterns. These findings offer potential strategies for designing future flying devices.

Results

Samara-inspired flight modes

Focusing on the influence of mass distribution on aerodynamic behaviors of samaras, we developed a framework (see Methods) that enables manipulation of mass distribution to emulate various falling patterns inspired by wing-seed structures (Fig. 1c). We employed a rectangular thin plate^27,37–41 to represent the typical wing structure of samaras. To mimic the seed and the unevenly distributed mass on the wing of real samaras, two weights were attached to the plate.

By adjusting the weight positions on the plate, we identified four distinct flight modes: Autorotation (AR), Spiral Tumbling (ST), Chaotic (CH), and Falling (FA). These modes are systematically mapped in Fig. 2a across the parameter space defined by the center of mass (COM) location, with their corresponding flight patterns illustrated in Fig. 2b–f. Additionally, our measurements of natural samaras’ mass distribution align well with the results from the samara-inspired framework (see Supplementary Note 1).

Fig. 2. Parameter space and trajectories of distinct flight modes.

a Distribution of flight modes within the parameter space defined by the COM location. $x_c$ and $y_c$ represent the COM locations along the plate’s longer and shorter centerlines, while $a$ and $b$ denote the half-lengths of the plate’s length and width, respectively ($a=L/2$, $b=W/2$). Yellow diamond scatters indicate mass configurations for the Autorotation (AR) mode, red triangles and circles for the continuous and segmented Spiral Tumbling (ST) modes respectively, blue triangles for the Chaotic (CH) mode, and purple squares for the Falling (FA) mode. Hollow circle scatters represent mass configurations of real samaras exhibiting these modes (see Supplementary Note 1). b AR mode, characterized by stable descent with rotation around a vertical axis. c Continuous ST mode, featuring continuous rapid tumbling and spiral downward along a vertical axis. d Segmented ST mode, exhibiting rapid tumbling with distinct turning points along its trajectory. e, CH mode, marked by irregular tumbling and oscillations with abrupt changes in direction. f FA mode, involving a rapid, predominantly vertical descent.

The AR mode exhibits pronounced periodicity, triggered when both weights are placed towards the plate’s edges. This mode represents samaras with autorotative flight patterns, such as those of maple and mahogany trees. These samaras from different groups of plants have convergently evolved into a configuration where seed is positioned near the terminal end and a lighter wing with ridged leading edge^42,43. This configuration facilitates stable descent while rotating around a vertical axis (Fig. 2b), enabling efficient and stable dispersal^9–11.

The ST mode primarily features the plate rapidly tumbling during spiral descent. Within this mode, two divergent spatial trajectories emerge – continuous and segmented ST motions (see Fig. 2c and d, respectively). The continuous ST flight follows a steady helical path around a vertical axis. This continuous descent motion represents the dispersal strategies of several natural samaras, such as those from elm and ash trees, which utilize a similar flight pattern for seed propagation^10,21–23. This continuous flight pattern is achieved when both weights are centrally placed, mimicking the structure of samaras with seeds are placed near the wing’s center. In contrast, the segmented ST flight presents a distinct trajectory with multiple turning points between each spiral phase. This variation arises when the lighter weight is positioned further from the plate’s centerline, resulting in a unique spatial trajectory.

The CH mode is characterized by irregular rotational and translational flight patterns during descent^27,32,44,45. As a transitional regime between the ST and AR modes on the parameter map (Fig. 2e), its motion varies with weight distribution. When mass is positioned closer to the ST side, the motion is predominantly tumbling; however, unlike the ST mode, it cannot sustain a stable, periodic tumbling motion. Similarly, with the COM closer to the terminal end, the motion is primarily translational, resembling the AR flight posture, but it is frequently interrupted by sudden tumbling events. This mode exhibits chaotic behavior similar to that of falling disks and plates, with random transitions between tumbling and fluttering motions^27,32,46. Lacking consistent motion patterns, the CH mode experiences substantial fluctuation in both velocity and orientation, making its flight appear unpredictable to the observer.

The FA mode occurs when the heavier weight is near the terminal end and the lighter weight is positioned close to the plate’s centerline, resembling the mass distribution found in Ventilago leiocarpa samaras. This configuration intuitively leads to a rapid descent, with the plate tilting towards the side with the concentrated mass, thereby remarkably increasing the falling speed (Fig. 2f).

The previous studies have shown that transitions between two-dimensional motions of plates or disks are primarily governed by the $\mathrm{Re}$ and the moment of inertia^25–27. Within our framework, we demonstrate that variations of COM alone can drive transitions in samara-inspired three-dimensional flight modes. When both $x_c$ and $y_c$ are relatively large (yellow region in Fig. 2a), the COM shifts toward the terminal end of the plate, generating a torque with the aerodynamic lift that sustains uniform autorotation along the vertical axis during descent. In contrast, when both $x_c$ and $y_c$ are small (red region in Fig. 2a), the COM moves closer to the plate’s central region, producing a different torque that guides the plate along a helical trajectory during continuous tumbling descent (see Supplementary Note 2). The chaotic (CH) mode emerges in the intermediate region, where the aerodynamic torque is insufficient to maintain any single periodic mode. As a result, the CH mode exhibits irregular combinations of rotational and translational motions throughout descent.

Kinematics of typical flight patterns

To quantitatively examine and compare the kinematic characteristics of different flight patterns, we measured six-degree-of-freedom kinematic data of the plate during descent. Using this data, we reconstructed the 3D descent trajectories corresponding to various flight modes and analyzed their aerodynamic performance. The previous studies have confirmed generally consistent kinematic behavior within specific flight modes^11,23. Therefore, we selected a representative case for each flight mode to capture typical behaviors without compromising generalizability.

In the AR mode ($x_c/a=0.39$, $y_c/b=0.17$), the trajectory mainly exhibits a vertical descent with slight horizontal displacement. The 3D reconstruction reveals that the plate rotates around the vertical axis while maintaining a small cone angle ($\theta =-11.4{\pm 4.2}^{\circ }$) and virtually no tilt ($\psi \approx 0^{\circ }$) (Fig. 3a).

Fig. 3. Reconstruction of descent trajectories using experimental kinematic data.

Trajectories of various flight modes are visualized, with dimensions normalized by the plate’s length ($L$) and reconstructions overlaid at $5ms$ intervals (see also movie S1). a AR mode. b Continuous ST mode. c Segmented ST mode. The 3D trajectories of the plate are shown along with its projections. 3D reconstructions in the upper right use the self-rotation angle ($\psi$) around the plate’s longer axis, coloring the plate from green to orange. 3D reconstructions in the lower right use the revolution angle ($\phi$) around the vertical axis, coloring the plate from blue to red. d Top view projection of the continuous ST motion. The variation of $\psi$ in a counterclockwise (CCW) revolution cycle is presented. e Top view projection of the segmented ST motion with a zoomed-in view around the turning point. The motion initially resembles the CCW ST, which is shifted to clockwise (CW) ST after the turn. The variation of $\psi$ near the turning point is displayed. f Comparison of the mean angular velocities ($<\mid \phi \prime \mid >$ and $<\mid \psi \prime \mid >$) among the continuous ST (CST), segmented ST (SST), and AR modes, with ticks indicating the magnitude of fluctuation around the mean values.

The ST mode primarily involves tumbling motion, with variations in mass distribution leading to distinct spatial trajectories. In the continuous ST flight ($x_c/a=0.06$, $y_c/b=0.04$), the plate follows a steady helical path, maintaining a nearly constant cone angle ($\theta =-38.2{\pm 2.3}^{\circ }$) between its longer axis and the horizontal plane (Fig. 3b). In contrast, the segmented ST flight ($x_c/a=0.10$, $y_c/b=0.10$) exhibits dynamics similar to the continuous ST motion but with more pronounced fluctuations in the cone angle ($\theta =-38.3{\pm 13.0}^{\circ }$). This trajectory features abrupt transitions at turning points, where both translational and rotational movements change drastically (Fig. 3c). The divergence between the continuous and segmented ST trajectories is likely due to mass distribution asymmetry. In 2D scenarios, plates with symmetric mass distributions tend to exhibit tumbling motion toward a single direction^25–27. However, asymmetric front-weighting results in tumbling motion that involves flips along its trajectory⁴⁷. This may also explain why, in 3D situations, a shift in mass distribution away from symmetry drives the transition from continuous to segmented spiral tumbling motion.

To compare the continuous and segmented ST trajectories, we plotted their top-view projections in Fig. 3d and e, respectively. In the continuous ST motion ($x_c/a=0.06$, $y_c/b=0.04$) (Fig. 3d), the plate performs a counter clockwise circular motion in the horizontal plane with a radius of approximately $1.25L$. During its descent, the plate completes roughly seven tumbling rotations per spiral revolution, as its tumbling angular velocity notably exceeds that of its spiral motion. Conversely, the segmented ST motion ($x_c/a=0.10$, $y_c/b=0.10$) displays a trajectory featuring a critical turning point (Fig. 3e, left). Initially, the motion resembles counter clockwise ST, which is then shifted to clockwise ST after the turn. The horizontal projection of both segments is close to circular segments with a radius of about $1.89L$. As the plate approaches the turning point, its cone angle increases, followed by a reversal in the tumbling direction. A zoomed-in view of the trajectory around the turning point (Fig. 3e, right) reveals a peak self-rotation angle ($\psi \approx 0.4\pi$), accompanied by an angular reversal. Compared to the continuous ST motion, the sudden transition introduces noticeably higher fluctuations in angular velocities (Fig. 3f ), highlighting the unique dynamic transitions in the segmented ST motion.

In the CH mode ($x_c/a=0.18$, $y_c/b=0.08$) (Fig. S1), we observed transitions between two primary forms of motion. The plate may display periods of translational motion, where lateral drift and stable descent are prominent, or it may enter phases dominated by tumbling motion, with rotational motion and reduced horizontal drift. Similar with the chaotic mode of falling plates^27,32,44,45, this mode exhibits unpredictable behavior, with irregular shifts between phases dominated by translational and rotational motions.

The FA mode ($x_c/a=0.35$, $y_c/b=0.08$) is characterized by a rapid descent with limited horizontal displacement (Fig. S2). Throughout most of the motion, the plate maintains a relatively large tilting angle, with the heavier side consistently facing downward. This results in a relatively small windward area, thus increasing the falling speed.

Statistical characteristics of the descent process

To explore the dispersal capabilities of various flight modes in quiescent air, we focused on the falling velocity and horizontal propagation distance of static releases. We selected typical configurations for each mode and conducted multiple releases from a fixed height and location. The landing point and time of each release were recorded, allowing us to calculate the average falling velocity ($V_d$) and dimensionless horizontal propagation range ($R/H$), as depicted in Fig. 4.

Fig. 4.

Distribution of average descent velocities ($V_d$) and horizontal propagation ranges ($R/H$) in quiescent air. The graph displays $V_d$, the averaged vertical velocity, and $R/H$, the ratio of propagation distance to release height. Yellow diamonds indicate mass configurations for the AR mode, red triangles and circles represent the continuous and segmented ST modes, respectively, blue triangles correspond to the CH mode, and purple squares denote the FA mode. The mass distributions for each mode are consistent with those in the kinematic measurements, and each configuration was tested 12 times. Covariance ellipses with a 0.6 confidence level illustrate the statistical distribution of the different flight modes.

Although the AR mode shows a limited horizontal propagation range in quiescent air, it benefits from the lowest falling velocity, resulting in an extended duration aloft. This mode’s efficient lift generation is particularly advantageous in the presence of crosswinds, enabling broader seed dispersal.

Conversely, the ST mode, despite its faster falling velocity compared to the AR mode, achieves a wider horizontal spread in quiescent air. This characteristic may explain why various samaras employ a spiral tumbling mode to enhance seed dispersal. Specifically, while the horizontal propagation ranges of the continuous and segmented ST motions are comparable, the segmented ST motion demonstrates a slightly higher average falling velocity. The greater cone angle around turning points likely reduces the windward area, leading to faster descent.

Arising from its unpredictable flight dynamics, the CH mode showcases notable variability in both falling velocity and horizontal dispersion. Finally, the FA mode achieves the highest falling velocity and a relatively moderate horizontal propagation range, emphasizing its rapid vertical and slightly inclined descent.

The periodic flight modes such as AR and ST showed relatively stable descent behaviors, which may contribute to their widespread occurrence in natural samaras. In these modes, the samara reaches a terminal velocity shortly after release^11,23,48. A lower terminal velocity extends the time aloft, increasing the opportunity for wind-assisted dispersal over a longer distance. The AR and ST modes have independently evolved multiple times across numerous orders of plant taxa, spanning both monocotyledons and dicotyledons^49,50. This phenomenon represents a case of convergent evolution, which refers to the independent evolution of similar traits or functional adaptations in distantly related lineages^51,52. Comparing the statistical characteristics of different modes, the instructive traits of the AR and ST modes elucidate the evolutionary convergence in samaras dispersion. The convergent evolution driven by fluid dynamic performance, also occurs in other contexts, e.g., hummingbird and hawkmoth^29,53, and the ununiform swimming mode in marine animals^54,55.

To understand how the terminal velocity depends on key system parameters, we conducted measurements across samara-inspired models with different parameters (Table S2). These results were compared with data from real samaras. Our statistical analysis reveals that for both the AR and ST modes, the terminal velocity follows a linear relationship with the mean square root of the system’s average surface density (Fig. 5). This finding aligns with the scaling relationship derived from our dimension analysis (see Methods), highlighting average surface density as a key determinant of the terminal velocity. Moreover, for the same average surface density, the AR mode generally achieves a lower terminal velocity than ST mode. This is likely due to the AR mode’s stable flight posture, which allows for more efficient lift generation. Additional statistical results on the terminal angular velocity are presented in Fig. S3.

Fig. 5. Scaling relationship of terminal velocity with average surface density.

Scaling relationship between the terminal velocity ($V_d$) and the average surface density ($\sigma$) for a the AR mode and b the ST mode. Here, $\rho$ denotes the air density and $g$ denotes the gravitational acceleration. Red points represent measurements from samara-inspired models, where size, mass, and aspect ratio were varied while preserving the intended flight modes. Blue points correspond to measurements from natural samaras. Dashed lines show the linear fitting for each dataset. Each point represents the average of six repeated measurements from the same sample.

Aerodynamics and vortical structures

Through CFD simulations of the AR and ST modes, we explored the 3D vortical structures associated with samara-inspired falling trajectories. Our results reveal that leading-edge vortices (LEVs), trailing-edge vortices (TEVs), and tip vortices (TVs) are essential elements, shaping the aerodynamic behaviors of the samaras’ falling trajectories in distinct ways.

Specifically, in the AR mode ($x_c/a=0.35$, $y_c/b=0.18$), the instantaneous 3D vortical structures at two different instants ($t_{A1}$ and $t_{A2}$) are visualized by the iso-surfaces of Q-criterion⁵⁶, as shown in Fig. 6a. At $t_{A1}$, a prominent LEV forms as the rotating plate encounters the flow, inducing a strong negative pressure zone near the leading edge. By $t_{A2}$, the pressure distribution remains largely unchanged, indicating that the LEV stays stably attached to the plate and continues to contribute to lift. This force-enhancing mechanism, widely utilized in animal propulsion, also plays a vital role in samaras’ flight^6,12–14. Additionally, a TEV is observed along the plate’s trailing edge, similarly generating lift by creating a low-pressure region. The TEV mechanism, which is observed in both insect flight^57,58 and fish swimming^55,59, illustrates shared aerodynamic strategies across different forms of life. Unlike the continuous tip vortex shedding observed in previous studies, several discrete rib-like TVs (RLVs) form at the plate’s tip and are shed into the wake. They induce a downwash momentum that contributes to lift production^60–63.

Fig. 6. Vortical structures and aerodynamic properties in periodic flight modes.

Iso-surface of $Q$-criterion ($Q=60$) illustrates the vortical structures around the plate, colored by vertical vorticity (${\omega }_z$). Pressure distributions on upper and lower surfaces are also depicted at several instants in a the AR mode and b the ST mode, respectively. For each instant, the pressure distribution on the upper side of the plate is shown above, while the lower side is shown below. Orientation markers, represented by hollow and solid dots along the plate’s shorter edge, indicate the plate’s orientation. The vortical structures of the AR and ST modes are also shown in movie S2. c Evaluation of aerodynamic forces and torques during a motion cycle in the AR and ST modes. The forces and torques are non-dimensionalized by ${\rho }_f{u}_0^2{L}^2$ and ${\rho }_f{u}_0^2{L}^3$, respectively, with the characteristic velocity $u_0=\sqrt{gL}$. All force and torque components are projected as follows: the $x$-axis is defined by the projection of the plate’s longer axis onto the horizontal plane, the $y$-axis is perpendicular to the $x$-axis within that plane, and the $z$-axis is aligned with the vertical direction.

Instantaneous vortices in the ST mode ($x_c/a=0.06$, $y_c/b=0.00$) at various instants are demonstrated in Fig. 6b. Due to the plate’s tumbling motion around the plate’s longer axis, the flow separates along the longer edge, forming a pronounced LEV that creates a low-pressure zone at $t_{S1}$. By $t_{S2}$ (valley of the lift force), the LEV sheds into the wake and no longer contributes to lift. During this tumbling motion, tip vortices (TVa, TVb) shed from two shorter edges and gradually stretch as the plate descends ($t_{S2}$). By $t_{S3}$ (peak of lift force), TVa and TVb are further elongated and eventually merge into a Ω-shaped vortex tube (ΩVa). The TEV, initially aligned with the trailing edge shortly after shedding ($t_{S1}$), gradually deforms under the induction of the stretching TVs and also forms an Ω-shaped vortex tube (ΩVb) by $t_{S3}$. These Ω-shaped vortex tubes generate a downwash momentum aligned with the tumbling direction, helping to sustain the plate’s continuous rotation.

The projected forces and torques during a rotation cycle in the AR and ST modes are evaluated in Fig. 6c. In the AR mode, all force and torque components exhibit only slight fluctuations. The vertical aerodynamic force (lift) is notably larger than the horizontal force components, while the horizontal aerodynamic torque ($M_y$) dominates during descent, sustaining the revolving motion. In contrast, the aerodynamic properties in the ST mode display pronounced periodic fluctuations. The vertical force ($F_z$) has the same average magnitude to that in the AR mode but undergoes substantial periodic variations. These variations result from the periodic changes in the windward area due to the tumbling rotation, leading to a higher descent velocity. This unsteady aerodynamic behavior also gives rise to large fluctuations in torque. In particular, the torque along the tumbling axis ($M_x$) shows the greatest amplitude among all the torque components. Our theoretical analysis (see Supplementary Note 2) suggests that these differences in aerodynamic characteristics arise from the displacement between the center of lift and the COM, driven by the variation of mass distribution.

Discussion

In this study, we proposed a framework that manipulates mass distribution on a plate to present the diverse aerodynamic behaviors of samara descent. Using this approach, we identified four distinct samara-inspired flight modes: Autorotation (AR), Spiral Tumbling (ST), Chaotic (CH), and Falling (FA) (Fig. 2a). The corresponding mass distributions closely aligned with those observed in natural samaras exhibiting similar flight patterns (see Supplementary Note 1). Notably, our results demonstrate that the variations of COM can induce transitions between periodic flight modes and trigger chaotic behaviors.

By reconstructing the trajectories from experimental kinematic data, we provided a quantitative analysis of the aerodynamic characteristics associated with each mode. Measurements of descent velocities and horizontal propagation distances revealed that the periodic modes (i.e., AR and ST) exhibit relatively stable flight performance, suggesting a potential reason for their prevalence in natural samara dispersal. Further scaling analysis identified average surface density as a key factor influencing the descent velocity of periodic modes.

We also conducted numerical simulations to investigate the 3D vortical structures associated with samara-inspired descent. Analysis of flow structures and pressure distributions underscored the critical roles of LEVs, TEVs, and TVs in generating lift and torque. Interesting features such as rib-like TVs in the AR mode and intertwined Ω-shaped vortices in the ST mode were observed, both contribute to maintaining their respective flight patterns. Additionally, our theoretical analysis (see Supplementary Note 2) suggests that the aerodynamic differences between the AR and ST modes arise from the displacement between the center of lift and the COM.

Overall, our findings emphasize mass distribution as a key determinant of samaras flight patterns. By strategically tuning mass distribution, it is possible to actively modulate flight behaviors, thereby enhancing the maneuverability and reliability of aerial devices. This flight pattern control paradigm could be integrated with several existing microflier control technologies, such as origami structures³⁵ and 3D electrothermal actuators³⁶, offering a new perspective for the design of biomimetic microfliers.

While our study primarily focused on the role of mass distribution in samara flight dynamics, other factors such as surface texture⁶⁴ and 3D curvature⁶⁵ were not considered. Nevertheless, the core insights into how mass distribution governs flight patterns and vortical structures remain well-supported. The approach proposed here can be extended to investigate a broader range of 3D samara flight behaviors, laying a foundation for future explorations into the complex aerodynamics of these natural systems.

Methods

Samara-inspired framework

To mimic the aerodynamic structure of samaras, we developed a framework using a rectangular thin plate^27,37–41 to represent the wing-like structure, with attached weights simulating the seed and the naturally uneven mass distribution of real samaras (Fig. 1c). Two metallic weights were affixed to the plate: a heavier weight ($m_h$) positioned along the longer symmetrical axis and a lighter weight ($m_l$) along the shorter symmetrical axis. By adjusting the distance of $m_h$ and $m_l$ from the plate’s centerline (denoted as $x\prime$ and $y\prime$, respectively), we precisely controlled the mass distribution, thereby altering the center of mass (COM) location ($x_c$, $y_c$), which is calculated as follows:

$$x_c=m_h\cdot x^{\prime }/m_{total}$$ 1-1

$$y_c=m_l\cdot y^{\prime }/m_{total}$$ 1-2

Observations show that samaras typically have wing aspect ratios ranging from 3.0 to 5.0 to enhance flight stability^66,67. Accordingly, we primarily employed a thin rectangular plate with an aspect ratio of 3.0 to model the wing-like structure. For mode identification and kinematic measurements, we used a $60mm\times 20mm$ plate, precisely cut from kraft paper, with a mass of $92.8mg$³³. The heavier and lighter weights were $102.9mg$ and $51.4mg$, respectively. During free-falling experiments, the weights remained fixed to ensure a consistent mass distribution. All models used in this study maintained an average surface density within the range of real samaras analyzed ($0.02-0.47kg/m^3$), with physical scales ($45-75mm$) generally consistent with the natural size range ($20-60mm$).

Experimental setup

Experiments were conducted inside an enclosed 4m-height platform with a $2m\times 2m$ cross-section, under controlled environmental conditions of 15 ± 1 °C and standardized air density (Figs. S4, S5). The flight dynamics of the plate were captured using two high-speed cameras (Phantom VEO-640L) positioned at the top of the platform, recording at 1000 frames per second. A remotely controlled servo motor clamp was used for the plate release mechanism, ensured consistent release conditions (cone angle $\theta =0$ and self-rotation angle $\psi =\pi /2$) in different test cases. Example high-speed videos of the periodic modes exhibited by the samara-inspired framework and real samaras are provided as Movie S3 and S4, respectively.

Kinematics measurement technique

The motion of the falling plate was tracked using a stereoscopic vision system^30,68,69, which recorded the plate’s trajectory via two synchronized cameras. The system was calibrated using a chessboard pattern, enabling accurate 3D spatial reconstruction. Key reference points on the plate were identified and tracked across frames to dynamically determine its position in real-time (Fig. S6). The Levenberg-Marquardt algorithm was utilized to optimize the six degrees of freedom (translational and rotational) kinematic data, substantially reducing re-projection errors and enhancing the accuracy of motion analysis^27,64. In instances where the plate moves perpendicularly to the camera’s field of view, a second-order interpolation of motion parameters was performed to reconstruct the plate’s trajectory and flight attitude effectively.

Scaling relationship of terminal velocity

For periodic descent modes, several factors may influence the terminal velocity of samaras. These include the characteristic length ($L$) and average surface density ($\sigma$) of the sample (encompassing both artificial samara-inspired models and real samaras), as well as air density ($\rho$), viscosity ($\nu$), and geometric properties. Through dimension analysis, the terminal velocity ($V_d$) can be expressed as:

$$V_d=\sqrt{\frac{\sigma g}{\rho }}\cdot f\left(Re,{\sigma }^{*},Ge{o}^{*}\right),$$ 2

where $\mathrm{Re}$ is the Reynolds number, ${\sigma }^{*}=\sigma /\rho L$ represents the non-dimensional average surface density, and $Ge{o}^{*}$ includes geometric parameters such as the aspect ratio and the COM position.

Simulations

CFD simulations were conducted using the immersed boundary (IB) method, a technique widely applied in biomimetic flow studies^70–73. The IB method defines the flow field on a background Eulerian grid and the immersed boundary (i.e., the plate) on a Lagrangian mesh to facilitate efficient resolution of the unsteady flow-structure interaction (FSI) (Fig. S7). The Navier-Stokes equations for incompressible Newtonian flow are solved at the Reynolds number $\mathrm{Re}=L{u}_0/\nu =560$ with the characteristic velocity $u_0=\sqrt{gL}$. Due to the challenge of complex FSI simulation at high $\mathrm{Re}$²⁹ and the limitation of experimental materials (deformation, stereo imaging resolution etc.), the $\mathrm{Re}$ in the simulation is lower than the experiment in the present study. In spite of this, the previous studies of similar falling plate problem^26,27 and other unsteady biomimetic scenarios^74,75 have shown that the vortices and the flow properties are consistent at different $\mathrm{Re}$ within a similar range of this work (see Supplementary Note 3). All results presented were obtained after a duration of $10\times L/u_0$ when the plate reaches a periodically steady state. The forces and torques presented in this study are all non-dimensionalized by ${\rho }_f{u}_0^2{L}^2$ and ${\rho }_f{u}_0^2{L}^3$, respectively.

Peer review

Peer review information

Communications Engineering thanks Lifang Zeng, and the other, anonymous, reviewer for their contribution to the peer review of this work. Primary Handling Editors: [Rosamund Daw]. Peer review reports are available.

Data availability

All data needed to evaluate the conclusions in the paper are present in the paper and/or the Supplementary Information.

Code availability

The authors verify that the codes for data processing can be obtained from the corresponding author, W.-X. H, upon reasonable request.

Competing interests

The authors declare no competing interests.

Supplementary information

The online version contains supplementary material available at 10.1038/s44172-025-00465-8.