Simulation Model of Releasing a Symmetric Auto-rotating Body in the Air
Abstract
The article presents the creation of a mathematical model of a body with a complex configuration, 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 salient simplest modes of translational motion are indicated. A volplaning mode at an angle of eighty-seven degrees is found. The most interesting point in this article is the autorotation mode, when the body rotates rapidly and decreases vertically or in an inclined straight line like a freely rotating rotor. Using the homogenization method, estimates of the average angular velocity, the average velocity of the mass center and the average glide angle of the body in the autorotation mode are obtained; it is proved that the autorotation mode is attracting. 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; the functional relationship between the glide angle and the rigging angle and functional relationship between the vertical projection of speed on the rigging angle are constructed. Programs are written that numerical integrate the equations of the body motion and the results of numerical integration are compared with the theoretical estimates to evaluate the accuracy of the methods under consideration.
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