Control Oriented Modeling, Experimentation, and Stability Analysis of an Autorotating Samara

Abstract

This paper presents a control-oriented model for describing the steady-state and dynamic behavior of a single-winged samara seed-pod in autorotative descent. A negligible lateral center of mass motion and constant, prescribed roll-angle to develop a simplified and compact model. Spanwise aerodynamic dependence is exchanged for an independent blade element representation with two tuned parameters to account for the effects of leading-edge vortex phenomena. The resulting model is a fourth-order nonlinear dynamical system. The accuracy of this model is established by validating it against our own experimental data as well as against those reported in the literature by other researchers. The validation exercise reveals that zero roll-angle is a viable assumption that significantly reduces model complexity while retaining accuracy. A necessary condition is derived for the existence of steady autorotation of the samara under free descent. Furthermore, a stability analysis is conducted suggesting that the eigenvalues of the fourth-order system, linearized about the autorotational equilibrium, can be well-represented by those of two decoupled two-dimensional systems. The analysis reveals the critical parameters that determine stability of sustained autorotation. Such stability analysis provides a platform for similar analytical exploration of future model improvements. The validity of this compact model suggests the plausibility of designing and controlling simple autorotative mechanisms based on these dynamics.