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

Abstract

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]

Curving to Fly: Synthetic Adaptation Unveils Optimal Flight Performance of Whirling Fruits

“…minimal U . The theoretical model illustrates that although A d is nearly identical for two geometries, the vertical lift force is not uniformly distributed along the curved wings [45]. To further verify our hypothesis we conduct experiments on the 3D printed double-winged fruit models, where we sweep the parameter phase space in wing loadings (mg ∈ [5 − 40]mN) and fold angles (KL ∈ [0.01 − 4]) , see Fig.…”

“…However, even taking into account that for KL = [1.7, 3.0] we have a varying wing-swept area A d = [0.0122, 0.0116]m 2 , we obtain a clearly different descent velocity U for the different fruits. This illustrates that there is an addition non-trivial effect of the curved wings, which is not fully captured by the scaling law for U [45], whereas the fruit's St number is independent of the weight and found to be constant for each model. We notice that the magnitude of St in Fig.…”

“…This forward resultant force generates autorotation of multi-winged fruits, in a similar way to what is used on a helicopter [36]. As a consequence, a moment that drives autorotation is produced close to the axis of rotation of the fruit, while a moment that opposes rotation is produced close to the wing tips where the tangential velocity, and therefore drag, is the dominant horizontal force [8,45]. The rotational frequency of the fruit is determined by a balance of the total torque on the wing obtained by a projection of F L and F D in the horizontal plane, where the angle of attack along the wing is given by the geometry and the local relative wind direction.…”

Investigating the presence of compensatory evolution in dicamba resistant IAA16 mutated kochia (Bassia scoparia)†

“…Lastly, G73N mutant seeds had longer sepals (‘winged’ seeds) and seemingly lower shattering rate, which might facilitate long‐distance seed dispersal and the spread of resistance over the landscape. Previous research found that Dipterocarpaceae species produce multiple‐winged seeds which can autorotate to maximize descent time 67‐69 . It is not known if kochia seeds are able to autorotate while tumbling, but they clearly adopt a similar multiple‐winged approach which can influence dispersal distances and germination locations.…”

Unraveling the vertical motion of Dipterocarpus alatus seed using Tracker

“…As suggested in Refs. [19,20], the magnitude of the lift force and the drag force on an element are proportional to the lift and drag coefficients, C L and C D . We therefore assume the total force exerting on the object takes the form…”