Tumbling Dynamics of Passive Flexible Wings

Tam, Daniel; Bush, John W. M.; Robitaille, Michael; Kudrolli, Arshad

doi:10.1103/physrevlett.104.184504

Cited by 21 publications

(25 citation statements)

References 7 publications

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“…Measurements of the air flow produced around autorotating samaras identify a leading edge vortex that is primarily responsible for the production of a positive lift force [11,40]. The seemingly simple configuration of having a single wing that generates a stable rotary descent has been widely studied [21][22][23], where recent work has shown that also the wing elasticity can influence the flight pattern [24] and may enhance lift [25,27]. Fossils from voltzian conifers dating back to the late early to middle Permian (ca.…”

Section: Introductionmentioning

confidence: 99%

Effect of wing fold angles on the terminal descent velocity of double-winged autorotating seeds, fruits, and other diaspores

2019

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Wind dispersal of seeds is an essential mechanism for plants to proliferate and to invade new territories. In this paper we present a methodology that combines 3D-printing, a minimal theoretical model, and experiments to determine how the curvature along the length of the wings of autorotating seeds, fruits and other diaspores provides them with an optimal wind dispersion potential, i.e., minimal terminal descent velocity. Experiments are performed on 3D-printed double winged synthetic fruits for a wide range of wing fold angles (obtained from normalized curvature along the wing length), base wing angles and wing loadings to determine how these affect the flight. Our experimental and theoretical models find an optimal wing fold angle that minimizes the descent velocity, where the curved wings must be sufficiently long to have horizontal segments, but also sufficiently short to ensure that their tip segments are primarily aligned along the horizontal direction. The curved shape of the wings of double winged autorotating diaspores may be an important parameter that improves the fitness of these plants in an ecological strategy.Autogyrating motion is also widely observed in multiwinged diaspores and seeds. These are commonly known as whirling fruits or helicopter fruits, which can be found in plant families such as Dipterocarpaceae [28,30,32], Hernandiaceae, Rubiaceae [34] and Polygonaceae, occurring in Asia, Africa and the Americas. These fruits are equipped with a leaf like structure (persistent and enlarged sepals), which acts as wings in their rotary descent, illustrated in their Greek name, i.e., di = two, pteron = wing and karpos = fruit. Compared to the single bladed maple fruits, these have a more complex wing shape which curves upwards and outwards [35]. Only a limited sub-set of tropical whirling fruits are described in terms of their terminal descent velocity as illustrated by the data from 34 neotropical trees [7], 53 recodings by [8] and recently extended by 16 entries of Paleotropic trees [32], which clearly limits predictions of dispersal distance. These flight recordings [7,32] suggest that the arXiv:1811.12221v2 [physics.flu-dyn]

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Section: Introductionmentioning

confidence: 99%

Effect of wing fold angles on the terminal descent velocity of double-winged autorotating seeds, fruits, and other diaspores

2019

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“…The motion of a falling flat plate has been researched extensively in the context of insect flight, falling leaves, and falling paper [16][17][18][19]30]. It provides a simple shape which can exhibit a wide range of behaviors from varying only a few parameters.…”

Section: Falling Flat Platementioning

confidence: 99%

“…Prior experimental studies have identified several canonical behaviors exhibited by falling disks, plates, and plant seeds characterized by different couplings between rotation and translation in space [2,15]. In all of these behaviors, an inherently high-dimensional system, which must consider velocities, angles, and angular velocities in 3D space, converges to a low-dimensional behavior, whether traveling in a single plane or going through a cycle of velocities [15][16][17][18][19][20].Mathematical models have offered many insights into passive descent. Ideal flow theory has been used to study the motion of a body both through a steady fluid and interacting with shed vortices [13,[21][22][23].…”

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confidence: 99%

Global phase space structures in a model of passive descent

Nave

Ross

2019

Communications in Nonlinear Science and Numerical Simulation

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Even the most simplified models of falling and gliding bodies exhibit rich nonlinear dynamical behavior. Taking a global view of the dynamics of one such model, we find an attracting invariant manifold that acts as the dominant organizing feature of trajectories in velocity space. This attracting manifold captures the final, slowly changing phase of every passive descent, providing a higher-dimensional analogue to the concept of terminal velocity, the terminal velocity manifold. Within the terminal velocity manifold in extended phase space, there is an equilibrium submanifold with equilibria of alternating stability type, with different stability basins. In this work, we present theoretical and numerical methods for approximating the terminal velocity manifold and discuss ways to approximate falling and gliding motion in terms of these underlying phase space structures.in the work of Maxwell and Zhukovskii [12][13][14]. Prior experimental studies have identified several canonical behaviors exhibited by falling disks, plates, and plant seeds characterized by different couplings between rotation and translation in space [2,15]. In all of these behaviors, an inherently high-dimensional system, which must consider velocities, angles, and angular velocities in 3D space, converges to a low-dimensional behavior, whether traveling in a single plane or going through a cycle of velocities [15][16][17][18][19][20].Mathematical models have offered many insights into passive descent. Ideal flow theory has been used to study the motion of a body both through a steady fluid and interacting with shed vortices [13,[21][22][23]. The Zhukovskii problem or phugoid model, which assumes that the wing travels with constant angle-of-attack, is a two-dimensional ordinary differential equation for flight from which phugoid oscillations, which couple forward velocity with pitch angle, arise [14]. Andersen et al. developed a phenomenological model based on experiments and simulations which produce fluttering, tumbling, and even chaotic behavior through a 4D differential equation [17,18]. To focus specifically on gliding animal flight and compare the gliding capabilities of different animals, Yeaton et al. [24] introduced a two-dimensional model for non-equilibrium gliding of animals. It is a modification of this model which we will consider in the present work. In this model, the authors decoupled translational and rotational dynamics in order to take a deeper view of the translational behavior and shape dependence based on lift and drag characteristics alone. To do so, inspired by the motion of gliding animals, the authors treat pitch angle as fixed with respect to the ground, assuming that the glider has some amount of control to hold this angle. Lift and drag are treated as functional parameters in this model, which is used to capture the differences in glider shapes. This model works especially well for gliding animals, but may be extended to general passive descent. Yeaton et al. [24] analyzed a variety of animal gliders and found tha...

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“…Most of the theoretical models are proposed based on Kirchhoff equations for inviscid fluid using quasi-steady assumptions (Tanabe & Kaneko 1994;Mahadevan 1996;Belmonte et al 1998;Pesavento & Wang 2004;Andersen, Pesavento & Wang 2005a;Andersen et al 2005b;Tam et al 2010;Fabre, Assemat & Magnaudet 2011). Different falling patterns were realized by solving the dynamical equations.…”

Section: Introductionmentioning

confidence: 99%

Influence of aspect ratio on tumbling plates

Wang

et al. 2013

J. Fluid Mech.

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The tumbling motion of freely falling plates with aspect ratio ranging from 2 to 10 is studied using both experimental measurement and simplified lifting line theory. The trajectories of plates are recorded by high-speed video camera and analysed to obtain instantaneous and average kinematic and aerodynamic parameters, including the descent angle, rotating speed, descent velocities, lift and drag coefficients, and their fluctuation spectrums. A double period rotation with period doubling is observed here for some range of aspect ratio and the double frequency is determined from a Fourier analysis. By adding a correction from the inducing effect of trailing vortices and wing-tip vortices to the corresponding two-dimensional force and torque expressions, a simplified kinematic model is obtained which successfully predicts the qualitative influence of aspect ratio on the averaged kinematics, that the descent angle and the vertical descent velocity component are decreasing functions of the aspect ratio, while the rotation speed and horizontal velocity component are increasing functions of the aspect ratio. For decreasing aspect ratio, the induced drag due to the trailing and tip vortices reduces the lift to drag ratio and thus increases the descent angle, while the dissipative torque due to translational induced drag decreases the rotation speed.

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Tumbling Dynamics of Passive Flexible Wings

Cited by 21 publications

References 7 publications

Effect of wing fold angles on the terminal descent velocity of double-winged autorotating seeds, fruits, and other diaspores

Effect of wing fold angles on the terminal descent velocity of double-winged autorotating seeds, fruits, and other diaspores

Global phase space structures in a model of passive descent

Influence of aspect ratio on tumbling plates

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