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

Appendages of seeds, fruits, and other diaspores (dispersal units) are essential for their wind dispersal, as they act as wings and enable them to fly. Whirling fruits generate an autogyrating motion from their sepals, a leaflike structure, which curve upwards and outwards, creating a lift force that counteracts gravitational force. The link of the fruit’s sepal shape to flight performance, however, is as yet unknown. We develop a theoretical model and perform experiments for double-winged biomimetic 3D-printed fruits, where we assume that the plant has a limited amount of energy that it can convert into a mass to build sepals and, additionally, allow them to curve. Both hydrodynamic theory and experiments involving synthetic, double-winged fruits show that to produce a maximal flight time there is an optimal fold angle for the desiccated sepals. A similar sepal fold angle is found for a wide range of whirling fruits collected in the wild, highlighting that wing curvature can aid as an efficient mechanism for wind dispersal of seeds and may improve the fitness of their producers in the context of an ecological strategy.

Figure 1

(a) The left part shows an illustration of the double-winged fruit of a 7. N/A (Dipterocarpaceae) [33] the numbering is in correspondence with Fig. 3, where we have defined the characteristic geometrical parameters that describe its shape. We notice that the fruit is equipped with persistent and enlarged sepals of length $L$ with a curvature $K$ and thus a radius of curvature $1/K$. $c$ is the mean wing chord and ${\alpha }_p$ the wing angle breaking the fruits left-right symmetry. The right part of the image shows the computer-aided design mimicking the helicopter fruit, which is built by the aid of 3D printing [34]. (b) Examples of multiwinged autorotating fruits collected in the wild, illustrated by a subset of species; I. 4. Alberta magna E. mey (Rubiaceae) [31]), II. 25. Shorea lanceolata (Dipterocarpaceae), III. 3. Triplaris cumingiana (Polygonaceae) and IV. 22. Shorea beccariana (Dipterocarpaceae). Images are courtesy of Ref. [33]. (c) A schematic description of the motion of the double-winged synthetic fruit as it descends with a terminal descent velocity $U$ towards earth (vertical path) and makes one turn around the axis of rotation with a frequency $\mathrm{\Omega }$ making it spin in a horizontal motion.

Figure 2

(a) We use our mathematical blade element model to solve for the torque and vertical force balance where $KL=2.6$ and the differential mass $m=1.2$ grams relative to the surrounding fluid. $C_L(\alpha )$ together with a maximum value $\max C_L(\alpha )/C_D(\alpha )=7$ is in direct correspondence with values expected for $\mathrm{Re}\in {10}^3-{10}^4$ [43]. The fruit’s predicted Re number and the St number are both in agreement with the experiments shown in panels (b)–(d). The circular marker shows the point of a zero resultant force and zero moment, giving a steady vertical descent velocity $U$ and constant rotation frequency $\mathrm{\Omega }$. A positive resultant force on the fruit would accelerate it upwards reducing its decent velocity, while a negative resultant force would increase the descent velocity of the fruit. A positive moment would generate an angular acceleration, i.e., would increase the rotation rate of the fruit and vice versa for a negative moment. In either case the fruit would return to the equilibrium position. The star-shaped marker illustrates a possible initial state and the solid line that connects to the circular marker is the path the fruit would follow. Measurements are made on the 3D printed biomimetic models where we extract (b) terminal descent velocity $U$ (c) and the rotational frequency $f$, which determine the Re and St number in (d). Each data point represents the average from ten independent experiments. The error bar in $\mathrm{St}\approx \pm 5\%$ comes from the two independent measurements of $U$ and $f$.

Figure 3

We span the phase space of aerial dynamics by systematically changing the fold angle, which points to an optimal shape for production of lift force for the bioinspired double-winged fruit. Background: a stroboscopic illustration of 11 synthetic double-winged fruits that are released at the same time and descends in the water tank, where each column corresponds to a flight duration of 5.5 sec. The solid line shows the vertical descent velocity as predicted by the blade element model and the star-shaped markers correspond to the experimental measurements. The theoretical model and the experimental data are in good agreement and both point us to a specific fold angle $KL$ maximizing the flight time by minimizing $U$. We show in [35] that increasing the weight of the fruit or its wing camber only shift the curve along the $y$ axis (Reynolds numbers) and changing the wing angle shift the curve along the $x$ axis ($KL$). The numbers above the $KL$ axis are measurements of $KL$ from desiccated sepals found in the wild, where details about the species’ and measurement procedure for $KL$ is found in the Supplemental Material [44]. Images of wild fruits are courtesy of Ref. [33].