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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. 

Abstract In this article, we study the characteristics of steady autorotation of a tethered autogyro. The phenomenon of autorotation refers to the natural spinning of a rotor in a wind field. We explore the viability of tethered autogyros as unmanned aerial vehicles (UAVs) for long-duration and energy efficient hovering applications, such as in monitoring or surveillance. The tether provides mooring and can be used to power the rotor and to transmit wind power to the ground when suitable. This is a novel application of autorotation. It requires a generalized formulation and modeling of autorotation, beyond what is reported in the literature. We adopt a model-based approach where the blade element momentum (BEM) method and catenary mechanics are used to model the aerodynamics and the tether, respectively. The resulting model is highly nonlinear and numerical methods are proposed to solve for the equilibria. The model is validated against existing simulation and experimental results in the literature. It is extended to incorporate new features that are pertinent to our application, such as low rotor speeds, regenerative torque for power generation, combining catenary mechanics with aerodynamics, and varying atmospheric conditions with altitude. We characterize the autorotational equilibria over a range of operating conditions involving multiple independent variables. The analysis reveals an optimal operating range of the tip speed ratio of the autogyro under equilibrium. It also indicates the possibility of power generation in large autogyros stationed at high altitudes.