Intrinsic equilibrium of stably autorotating samaras.

Abstract

During descent, a single-winged maple seed (samara) can naturally reach a delicate equilibrium state, stable autorotation, before landing. This article reveals the intrinsic equilibrium of a particular type of samaras in terms of measurable aerodynamic and geometric parameters. To this end, we conducted a series of in situ measurements for the rate of vertical descent (exclusive of crosswind) of an autorotating samara in a natural range of samara sizes and masses. We then extended the range of size and mass by introducing artificial samaras, with discrete mass elements purposely designed to approximate the asymmetrical and nonuniform distribution of mass found with natural samaras. Based on the widened range, a fundamental nondimensional correlation of dynamic pressure and disc loading was generalized, where all stable autorotation descent profiles collapse to a single descent characteristic curve, irrespective of the size and mass of the natural and artificial samara's specimens. Results reveal that for stably autorotating (both natural and artificial) samaras, their terminal descent velocity (expressed as dynamic pressure) and disc loading attained equilibrium at a value that is inversely proportional to the coefficient of lift.