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

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. Mathematics Subject Classification: 76Z99, 70B10, 92B99 (Some figures may appear in colour only in the online journal)