On evaluating load aerodynamic effect on free oscillations of parachute system with pivotally suspended load

Аuthors

Churkin V. M.

Moscow Aviation Institute (National Research University), 4, Volokolamskoe shosse, Moscow, А-80, GSP-3, 125993, Russia

e-mail: churandr@mail.ru

Abstract

The paper considers parachute system with pivotally suspended load movement in vertical plane. When deriving the equation of motion the parachute system is presented as a mechanical system consisting of two solid bodies connected by ideal linkage joint (deadeye), i. e. parachute and load. Parachute system free oscillations analysis is carried out with the equations of the simplified disturbed motion model, where translational movement with constant speed and constant parachute canopy and load incidence angles.

As partial movement mathematical model the equations of first approximation system are accepted, and the sought non-linear model is obtained by substituting in these equations normal components of parachute canopy and load aerodynamic forces coefficients linear dependencies from their incident angles by non-linear dependencies. The dependency of parachute canopy aerodynamic force normal component from its incidence angle herewith takes the form characteristic for the case when canopy fabric has low permeability. After harmonic linearization of these non-linear dependencies the thus obtained system of non-linear equations for simplified non-linear model falls into two systems corresponding to constant and variable components of the sought solution. Equations linking amplitudes and center displacements of the sought oscillations are derived from the equations containing constant components, while equations linking amplitudes with oscillation frequencies and inequalities, determining stability conditions of the sought oscillations are derived from the equations containing variable components. Implementation of the suggested procedure of parachute system with pivotally suspended load with allowance for aerodynamic load is illustrated by numerical example. The boundaries of canopy incidence angle initial values that provide damping oscillations mode of the considered parachute system near the specified unperturbed motion are determined with or without considering the load aerodynamics. To evaluate the results of theoretical calculations the paper presents the results of numeric integration of the initial equations of the parachute system movement.

Keywords:

parachute system, parachute system is pivotally suspended load, aerodynamic load, nonlinear analysis, harmonic linearization , free oscillations, stability

References

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