The kinematics of falling maple seeds and the initial transition to a helical motion

Abstract

A maple seed falls in a characteristic helical motion. A crude analogy with autorotation of a wind turbine suggests that the torque due to the aerodynamic force would initiate the gyration of the seed. We were therefore surprised that a seed with a torn wing gyrates in a similar manner as a full-winged seed. In fact, a seed with only a sliver of leading edge can still gyrate. Thus the gyrating motion appears not to fully depend on the aerodynamic force. If, on the other hand, the aerodynamic force is completely absent, a seed would fall from rest like a rock in a vacuum.To investigate how the seed reaches its steady helical motion, we use a high-speed digital camera to film the intact and cut seeds at 1000 Hz. With a mirror, the camera records two views simultaneously so that we can extract the 3D kinematics of the wing. We tracked the centre of mass and quantified the descending speed, the azimuthal rotation, and the cone angle for seeds with wings of different shapes. We found that the initial transition from rest to a steady gyration occurs in three steps: a tumble about the span-wise direction, followed by a tilt towards the vertical axis, leading to the gyration about the vertical axis and an opening of the cone angle before settling into a steady state. We offer a new explanation for the cause of the auto-gyration that accounts for these three stages.

On the autorotation of animal wings

“…Animal wings with higher rotates at 18 Hz to descend at a speed of 1 m s 21 [3]. In spite of the major anatomical and material property differences between animal wings and samaras (for morphology details of samaras, see [1,3,7,13,[15][16][17]), both groups can perform stable autorotation at descent rates ranging from approximately 0.5 to approximately 2 m s…”

“…p10) were degraded in performance (table 1), perhaps because the small ensuing wing chord impedes formation of a stable LEV. Ablation experiments on maple seeds indicate that, by contrast with hummingbird wings, descent speed is actually reduced as area removal proceeds [13]. More generally, the study of autorotation is useful for manipulative experiments on isolated wings that otherwise are difficult to perform on alive animals, including comparative studies of the effects of feather moulting, wear and asymmetrical ablation on aerodynamic performance [34].…”

Stereoscopic particle image velocimetry measurements of the three-dimensional flow field of a descending autorotating Mahogany seed (Swietenia macrophylla)

“…The coning angle (γ) was computed from static images in which the seeds lie orthogonal to the camera direction. Because the seed's dimensions along the spanwise direction are known, the coning angle was inferred using the projected length of the seed's total length along the horizontal plane (Varshney et al, 2012). An accurate spinning rate of autorotation was inferred by measuring the elapsed time between consecutive images where the seed lies orthogonal to the camera direction.…”

Construction and control of monocopter using MEMS AHRS

“…In this circumstance, the system stability will increase in one hand and in the other hand, the system controllability will decrease. In addition, the force increase of wing, area and standing angle of winglets will be effective in determination of flying cone angle in the flyer [5]. Also, if the distribution of masses in the system is far from central gravity, the amount of gyroscopic force in the system will increase and therefore the system stability will increase [9,10].…”