Имитационная модель спуска симметричного авторотирующего тела в воздушной среде

Abstract

A mathematical model of a body of complex configuration is constructed in the work, consisting of a rod and two rectangular plates orthogonal to the rod, which is a working element of the Darier wind turbine. The body makes a plane-parallel decrease under the action of gravity and aerodynamic forces. The aerodynamic forces applied to the plates are adopted in accordance with the empirical theory of stationary flow around a flat plate. The question of the existence of various stationary descent modes and their stability is investigated. First, we consider the simplest stationary modes in which the body moves translationally. The most characteristic simplest modes of translational motion are indicated. The planning mode is found at an angle of eighty-seven degrees. Of greatest interest in the work is the autorotation mode, in which the body rotates rapidly and carries out a decrease in the vertical or inclined straight line like a freely rotating 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 autorotation mode occurs at the lowest speed compared to other modes, which allows you to use this design as a descent system or aerodynamic braking device, or as a planning system. The equilibrium equations are numerically solved and the dependences of the planning angle on the installation angle and the vertical projection of speed on the installation angle are constructed. 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 obtained theoretical estimates to assess the accuracy of the methods considered.