Autorotation of many-sided bodies in an airstream

Abstract

AUTOROTATION is the rotation of an object in an airstream in the absence of any other driving force¹. It is important in the fall characteristics of some tree fruits, the growth of hailstones, and the trajectories of objects separating from aircraft and spacecraft. Previous studies have concentrated on thin, flat plates rotating about an axis normal to the airstream, but in many applications— those relating to the free fall of bodies through air—the behaviour of bodies of more complex geometry is of interest. When these autorotate, a lift force is generated which can significantly alter the body's trajectory. Here I examine the autorotation of prisms whose cross-sections are regular polygons. Prisms of triangular section rotate fastest, but generate less lift than a flat plate. Only bodies with less than eight sides are found to show autorotational behaviour. In all of these cases, the lift forces generated are larger than those obtained from a spinning cylinder driven externally at the same rotation speed. Many devices have been proposed in the past that use as a propulsion mechanism the lift force developed on a driven rotating cylinder, perhaps the most spectacular being the Flettner rotorship which crossed the Atlantic in 1926². The use of polygonal bodies would have application in these cases, not only because of the higher lift generated but also because the energy required may be derived simply from the relative wind. There are thus also clear implications for wind-power devices.