Mathematical Modeling of the Motion of an Axisymmetric Autorotating Body of Complex Configuration in a Quasi-Static Environment
Abstract
In this paper, a mathematical model of a body of complex configuration consisting of two orthogonal rods and four rectangular plates is constructed. The design in question is a working element of a Darye wind turbine with four blades. The body makes a plane-parallel descent under the influence of gravity and aerodynamic forces. The aerodynamic forces applied to the plates are assumed in accordance with the empirical theory of stationary flow around a flat plate. The question of the existence of stationary descent modes is investigated. The greatest interest in the work is the autorotation mode, in which the body rotates rapidly and descends vertically or in an inclined straight line like a freely rotating main rotor. Using the averaging method, estimates of the average angular velocity, the average velocity of the center of mass and the average planning angle of the body in the autorotation mode are obtained; it is proved that the autorotation mode is attractive. It is shown that the descent in the autorotation mode occurs at the lowest speed compared to other modes, which makes it possible to use this design as a descent system or an aerodynamic braking device, or as a planning system. Programs have been written in which numerical integration of the equations of motion of the body under consideration is carried out and the results of numerical integration are compared with the theoretical estimates obtained to assess the accuracy of the methods under consideration.
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