Aerodynamics and right-left symmetry in wind dispersal of maple, dipterocarps, conifers and some genera of apocyanaceae and magnoliaceae

The wind dispersing seeds have evolved remarkable aerodynamic optimisation to minimise the speed of descent on detachment from the tree, so that they could be carried away by the wind and deposited a distance away from the parent. An efficient physical mechanism that enables slowing down the descent is rotation, which reduces the translational kinetic energy. Rotation and translation always define a right or left-handedness. The present work examines the aerodynamics of the dispersal of seeds of many species in relation to right-left asymmetry, giving examples to show that in nature this symmetry is broken either spontaneously or intrinsically. In the former situation, seeds have no geometrical right-left asymmetry, but an initial instability chooses one sense of rotation (right or left). Whereas in the latter, geometrical asymmetry dictates the sense of rotation. Seeds of the maple familiy belongs to the first category and a theortical model is presented to explain the motion. Seeds of dipterocarps, conifers and some genera of apocyanaceae and magnoliaceae are found to possess a handedness, which determines the rotation during seed fall. In dipterocarps, conifers and magnoliaceae, both right-handed and left-handed seeds are produced in the same tree but correlated to the handedness of the sprial phyllotaxy of the branch that bears the fruit. Apocyanaceae is found to be unique and seeds of all genera have the same handedness. The details of extensive field observations, experiments and theoretical interpretations are presented to illustrate the relationship of right-left asymmetry to the aerodynamics of seed wind dispersal, pointing out the implications of evolutinary optimisation in practical aerodynamics.


Dipterocarpus zeylanicus
The angular speeds of falling fruits through height of after imprinting the vein structure on paper by pressing to determine the geometry of sepal arrangement. Wing morphology.

Maple samara characteristics
The maple fruit is a bilaterally symmetric structure distinctly separated from each other and the stalk as the begins in late summer and continues into autumn, and the and dimensions of a maple samara varies from species to species and perhaps climate conditions. Typically, a by the seed and the thick ridge of vein supporting the dimensions; length ~ 3.8 cm, maximum breadth ~ 1 cm.
thick ridge (Figure 1). A distinctive characteristic of the densely populated than in the depiction. The texture and pattern of distribution on either side being identical as they originate from veins embedded in the middle of could not be performed effectively.

A theoretical formulation of maple seed motion
A maple samara falling under the gravity starts spinning, located near the seed very close to the centre of gravity, during descent involve intricately complex aerodynamics energy conservation. When a samara of mass m falls h and acquire translational and angular velocities v and potential energy DV = mgh, than the kinetic energy acquired DT = 1/2 (mv 2 + I 2 ), I = moment of inertia of about a vertical axis through the centre of mass. This is because, a part of potential energy transforms into kinetic energy of air set into motion, and a part dissipated as heat generated due gh) is the velocity acquired in the absence of spinning action and air resistance. Rapid rotation, large moment of inertia and smaller mass analysis of the problem requires an understanding of motion and drag. These forces depend on the dimensions, shape, and nature of the surface, mass and its distribution and elastic properties.
The structural architecture makes a samara mirror are mirror images of each other. This symmetry implies that they do not possess handedness. Imagine a samara plane. One could argue that in this situation it cannot auto-rotate during falling, because in the absence of a again preserved. Frequently, the symmetries in nature are respected in this manner; although individual symmetry violations exist, they occur in equal probabilities. This centre of the mass reaches a critical value (v C ). The transition process needs to conserve energy, and angular and linear momenta. If a distributed and massive body takes up linear and angular momenta (in this case stream and vortices of air), the kinetic energy transferred to it instantaneous and resistive loss is minimal, conservation energy yields, Here an unstable initially symmetric state suddenly The i and associated lift and drag forces complicates the motion of falling maple seeds defying rigorous analysis for application has been arrived, incorporating empirical the next paragraph explains the salient features of this intriguing system.
Forces acting on an air foil can be related to force the magnitude of the couple remains independent of the angle of attack (Carlton, 2007;Pope, 2010). Forces acting on a falling maple samara are: the aerodynamic force A components A Z = lift force, A generating force and A r = radial component, all acting mg. For equilibrium of rotation, a centrifugal force F r = 2 , acting at the centre of a b and l = length span) needs to be provided aerodynamically. The centre of rotation O is not exactly about centre of gravity. The torque necessary A . to the vertical axis) by these forces.
forces are proportional to the square of the radius of the blade and square of velocity, so that, A r in the form in equation (5)   opposing rotation rather than translation, the vertical motion experience little drag force and dissipation results mainly from rotation. In this situation C zL l 2 2 > C zLD v 2 and equation (9) can be approximated as, ... (10) Thus a necessary condition for equilibrium of the object ... (11) If the cone angle is perturbed by a small amount , inserting = q 0 + equation of the form d 2 2 = -(k > 0) indicating that equilibrium resist perturbations. Equation (11) explains that auto-gyration could occur only if the angular velocity exceeds a critical value. This is experimentally observed; samara starts spinning only after falling through some distance h. From equation (2), the maximum angular velocity attainable is (2mgh/I ) 1 Motion in the vertical direction is described by, Thus the equation of motion for rotation can be expressed as, ... (13) I = I Cos 2 seed about the axis of rotation. The falling seed soon approaches the terminal translation and angular velocities v = v T , = giving, A question also arises regarding the stability of the of Maple samara is symmetrical), the point of action of the position of the aerodynamic centre remains unaltered irrespective of changes in the attack angle. Therefore that the move about axis is in neutral equilibrium. Thus, the system could adjust to maintain the angle of attack optimally.

The importance of right-left asymmetry in wind dispersal of seeds
that enables optimising this strategy is generation of rotation so that transitional velocity of the centre of mass is continuously reduced. The additional advantage further reduces the rate of fall. Rotation and the direction Such a handedness can be achieved either spontaneously or intrinsically. In the former situation, the object (seed) possesses no geometrical right-left asymmetry, but one sense of rotation is chosen as a consequence of the aerodynamics resulting from the design of the seed. In the latter case the seed itself possesses a geometrical right-left asymmetry giving preference to one sense of

Right-left symmetry of falling maple seeds
Most symmetries in living and non-living systems including elementary constituents of matter, are not perfectly realised giving rise to frequent instances of biasing. The same feature is seen in the sense of rotation of maple samaras. As discussed earlier maple seeds possess nevertheless they auto-rotate as a result of spontaneous breaking of the R-H symmetry. The required symmetry height, a large number of times, a higher probability of corresponds to a normal distribution, concluding that there universal bias. As only R-L distinguishing characters can to identify the factors that could introduce such biases.
(i) In maple samaras the embedded seed symmetrically gradually sanded the protrusion on one side and observed object (b) cannot be superposed on (a) by translations and rotations. If they are dropped from a height, during descent the sanded surface tends to remain uppermost.
degree of sanding. When the seed protrusion is fully levelled, the probability for this trend is about 60 % for  in the sense induced.
A system governed by dynamics of SBS displays very high sensitivity even to minutest biases near the point of criticality. The observed biases in individual tree has no signs of R-L asymmetries. At this scale of be understood as drying and action of light could be different on the faces of the fruit.

Right-left symmetries in plants and the fascinating Dipterocarpus
Not only the fruit and the samaras, maple trees have no macroscopic organs carrying an attribute of handedness. A majority of plant species falls into this group. Here the leaves and their phyllotaxy, the pattern of branching characters. After extensive observations of symmetries in plants, the author noticed that plants more primitive in the phylogenetic ladder and the ones that mature fast possess R-L symmetries to a higher degree. There seems to be a universal trend in all systems that, as complexity the symmetries disappear. Some plants demonstrate a unique handedness in one or more of their organs as a genetically inherited quality common to the species.  The dynamics governing rotational and translational motion of the stabilised system parallel that of the maple seed and equations (14) -(17) illustrate this. During the decelerating phase of motion, stability forces or their diversion. In nature this does not happen, unless evolution has turned retrograde due to changing to optimise the lift keeping drag to a minimum and also to acquire the terminal value as soon as possible. Just as in maple, the strategy has been to dissipate potential energy via rotation. According to equation (17), larger the terminal motion of a falling dipterocarpus nut can be described by equation (17). It has been suggested that the parameter 'l' in equation (13) We found that the average velocity for Dipterocarpus zeylanicus fruits is v T0 ~ 3 ms -1 h = 40 km, u H = 2 ms -1 , u = 5 ms -1 , u V = 1 ms -1 obtain D = 2.4 km. Dipterocarps have intricately deposition from the parent.
Longitudinal veins covering the surface are more or less straight on the vertical axis (extension of the straight line segment at also provides centrifugal force. It appears that the same mechanism operates in the case of dipterocarps. The angular momentum of the spinning seed is compensated by the vorticity. angular momentum of the spinning seed is compensated by the vorticity Fig.10. Schematic diagram illustrating the orientation of wings of a typical dipterocarp, relative to

Entertaining and intriguing motion of paper helicopters simulating dipterocarps
Despite the simplicity of construction, they display the necessity of a handedness. They can be crafted giving a and break the R-L symmetry spontaneously.
by cutting a single sheet of paper and folding; the dark are mirror images of each other and distinct, because other. Careful examination reveals a clear difference of the behaviour of (c) compared to asymmetric models the performance greatly improves. In models (d) and been cut-off, and the performance remarkably improves et al., asymmetry.

Right-left symmetry and wind dispersing conifers
right-left symmetries though not so conspicuous, but akin to the pattern seen in dipterocarps. Examination

Right-left symmetry in magnoliaceae and autogyrating samaras of the tulip tree
The R-L symmetry in magnoliaceae resembles that of pines and dipterocarps. Having examined Walsapu as the axis. R-L asymmetry provides torque for the rotational motion, creating a lift. The moment of inertia is minimum about the mid axis and motion remains stable. It has been suggested that this stability greatly helps dispersal, although the terminal velocities attained are smaller compared to maple (Mccutchen, 1977).
We have also conducted simple paper toy experiments to simulate the auto-gyration of tulip tree samaras. Figure 13 Leonardo da Vinci noted that the cross-sectional area of a tree trunk approximates to the sum of areas of experiments indicate that although individual seeds frequently violate the symmetry, globally it is respected. It is not possible to quantify the variations in maple seed attributes and correlate them to a bias in the sense distribution indicative of no preference. In contrast dipterocarpus nuts possess a natural handedness and a level more than 99 %. Here, both right and left handed fruits are produced in equal abundance, and during falling rotate in opposite directions. The investigation disclosed vertices of a pentagon. Sepals elongate to form either evolutionary reaction to the centre of gravity instabilities, aerodynamic effectiveness and the natural requirement R-L asymmetry of pine cones and samaras associate Conifers and some genera of magnoliaceae also possess R-L asymmetry characters similar to dipterocarps. In apocyanaceae, unlike dipterocarps and conifers, the the fruit and seeds. Several genera of apocyanaceae have handedness seems to be spreading of hairs of parachuting seeds by centrifugal acceleration, thereby enhancing the air drag.
families adopt auto-gyration as an effective mechanism of necessitates a breaking of the R-L symmetry. Maple has designed the seeds to achieve this as a dynamically generated SBS. In dipterocarps, magnolias and apocyanaceae, presumably a persisting accidently introduced genetic R-L disparity induce unique chirality an asymmetry to the seed appendage via a spontaneous asymmetric deformation, as a consequence of motion. It is not impossible that this method is also realised of morphogenesis, it is hard to conceive the advantage of a handedness to a plant in any of its functions other