Maples rely on wind, upward currents, and gusts to spread their seeds over long distances that can reach several kilometers. Maple seeds are able to autorotate because their center of gravity, determined by the position of the nut, is located at the base of the wing-shaped seed. It has been observed that, despite their small size and slow velocities, these seeds are able to generate high lift, being able to remain in the air for longer times than other non-rotating seeds. The aerodynamic mechanisms that produce such high lift are, however, unknown. The experimental work carried out by Lentink et al. 1 on three different maple seeds (m1, m2, m3 in Fig. 1 B) and a hornbeam seed (h in Fig. 1 B) shows that the generation of a stable Leading-Edge Vortex (LEV) similar to that observed in hovering insects, bats and some birds is responsible for such high lift force.
Kinematics and morphology of autorotating seeds
The function of stable autorotation in maple seeds is to create lift to prolong their descent. This depends on the interaction between the inertial and aerodynamic properties of the seeds, which are not fully understood. The free-flight parameters and the shape of the studied seeds are displayed in Fig.1 A and B, respectively.
Formally, the angle of attack is defined as the angle between a body’s reference line (often the chord line) and the vector representing its relative motion respect to the oncoming flow. In the paper, the authors distinguish between the wing’s local geometric angle of attack, defined as the arctangent of descent speed, Vd, divided by horizontal speed, Vh; and the aerodynamic angle of attack, which is equal to geometric angle of attack minus the pitch angle. Even though the pitch angle is approximately constant along the span of the seed, for the study the values measured at 75% span of the four types of seed have been adopted: m1 (−1.17°), m2 (−1.39°), m3 (−0.90°), h (−2.16°).
In conventional wings and helicopter blades, the lift force increases with the angle of attack up to a critical value. An increase of the angle of attack beyond this critical point causes the air to separate from the wing, losing lift. This situation is known as stall. However, it is known that hovering insects generate very high lift even when operating at larger angles of attack, thanks to the generation of a leading-edge vortex (LEV). The main hypothesis of the paper is that this mechanism occurs also on the descent of autorotating seeds.
Leading Edge Vortex (LEV)
As mentioned above, stall occurs at high angles of attack due to flow separation, reducing the lift. In some specific wing geometries like those of insects or delta wings, separation occurs near the leading edge of the wing and the flow rolls up forming a vortex that lies on the wing surface. This vortex, commonly known as Leading Edge Vortex, increases both the lift and drag forces acting on the wing. Its structure depends on the shape of the wing, the angle of attack and the Reynolds number. The Reynolds number is a dimensionless number that gives the ratio of inertial to viscous forces in a flow (, where and stand for the density and viscosity of the fluid, respectively; and V and L for the characteristic velocity and linear dimension of the flow), and it has been estimated to be on the order of 1000 for autorotating seeds.
To test the hypothesis of LEV generation, Lentink et al. built a dynamically scaled model. That means that both flight parameters and the Reynolds number of the model seeds were scaled such that they are identical to real seeds descending in air. Hence, for larger and faster model seeds used in the experiments, it was necessary to adopt a more viscous fluid, namely mineral oil.
Stereo digital particle image velocimetry (DPIV) was used to measure the 3D velocity field at different spanwise slices of the model seeds moving through a tank of mineral oil. This optical technique involves illuminating a plane of the flow with a laser sheet and capturing the light scattered by small seeded particles on a pair of frames. Then, the images are divided in small “interrogation areas” and a velocity vector is extracted by performing mathematical correlation analysis on a cluster of particles within each interrogation region between the two frames.
Measurements prove the generation of LEVs near the base of all the studied seeds (Fig. 2). Toward the tip, the LEV merges with the tip vortex, resulting in a trail of vorticity in the wake of the seeds. Due to the rotation of the wing, the maximum angle of attack appears at the wing root (nearly 90°), and the minimum at the wing tip (Fig. 1D). Based on prior free-flight measurements, the minimum angle of attack was obtained for the four types of seeds: m1 (16°), m2 (25°), m3 (26°) and h (28°). The difference in these angles can explain why the LEV is well attached to the wing’s surface of the three types of maple seeds, and more separated on the hornbeam seed (Fig. 2). The chordwise flow around the maple seeds reattaches behind the LEV near the trailing edge, whereas the flow around the hornbeam seed is more separated at the wing tip and fails to reattach.
To validate the findings from the large-scale model, Lentink et al. built a vertical wind tunnel to study freely flying maple seeds. By matching the velocity of the flow in the tunnel with the descent rate of the seed, it was possible to film seeds spinning at a stationary height. The seeds also flew at Reynolds numbers ~ 1000. These free-flight experiments confirmed that:
- autorotating seeds generate a stable LEV near their base, like hovering insects’ wings (Fig. 3).
- the LEV is more compact at lower angles of attack.
- the strong spanwise flow stretches the LEV from the base to the tip of the wing, preventing it to grow too large that it becomes unstable and separates from the surface.
It has been mentioned previously that the generation of an LEV increases the lift over the wing. To find out how significant this influence is, the spanwise lift distribution was calculated by integrating vorticity within each wing section. In Fig. 4A it can be seen that the lift is maximum at 40 to 60% span for maple seeds m1 and m2, whereas it is rather constant for maple seed m3 and hornbeam seed h. It was also observed that the sectional lift coefficient (Fig. 4C) reaches very high values at the 25% span location where the LEV is attached, ranging from 2 for hornbeam to almost 5 for maple seeds.
In order to determine how well autorotating seeds perform respect to gliding and straying seeds, their descent times as a function of wing loading were compared (Fig. 5A). The descent time (T) is inversely proportional to the square root of wing loading (W/S, weight per unit surface area) and directly proportional to the square root of the descent factor (DF), a dimensionless number that represents the seed’s aerodynamic efficacy for a given descent speed and wing loading. The descent factor is highest for maple m1 and decreases for m2, m3, and hornbeam h, which operate at higher angle of attacks. Gliding and straying seeds achieve long descent times despite having low descent factors because of their small wing loading. Autorotating seeds have higher descent factors so, in order to achieve similar descent times, they need much greater wing loading.
The experiments performed by Lentink et al. show that the generation of a LEV extends the descent time of autorotating seeds, allowing them to reach further distances. The aerodynamic efficacy of these seeds increases with decreasing angle of attack, because at lower angles the LEV is more compact.
- D. Lentink, W. B. Dickson, J. L. van Leeuwen, and M. H. Dickinson, Leading-Edge Vortices Elevate Lift of Autorotating Plant Seeds, Science 324, 1438-1440 (2009) ↩