Analysis of Stability and Control of Helicopter Flight Dynamics Through Mathematical Modeling in Matlab

AbstractThe development of the non-linear equations of motion for the hang glider from first principles is described, including the complex geometry of control by pilot ‘weight shift’. By making appropriate assumptions the linearised small perturbation equations are derived for the purposes of stability and control analysis. The mathematical development shows that control is effected not by pilot weight shift, but by centre of gravity shift and that lateral-directional control by this means is weak, and is accompanied by significant instantaneous adverse response.The development of a comprehensive semi-empirical mathematical model of the flexible wing aerodynamics is described. In particular, the modelling attempts to quantify camber and twist dependencies. The performance of the model is shown to compare satisfactorily with measured hang glider wing data obtained in earlier full scale experiments. The mathematical aerodynamic model is then used to estimate the hang glider stability and control derivatives over the speed envelope for substitution into the linearised equations of motion.Solution of the equations of motion is illustrated and the flight dynamics of the typical hang glider are described. In particular, the dynamic stability properties are very similar to those of a conventional aeroplane, but the predicted lateral directional stability margins are significantly larger. The depth of mathematical modelling employed enables the differences to be explained satisfactorily. The unique control properties of the hang glider are described in some detail. Pitch and roll control of the hang glider is an aerodynamic phenomenon and results from the pilot adjusting his position relative to the wing in order to generate out of trim aerodynamic control moments about the centre of gravity. Maximum control moments are limited by hang glider geometry which is dependent on the length of the pilot‘s arm. The pilot does not generate control moments directly by shifting his weight relative to the wing. The modelling thus described would seem to give a plausible description of the flight dynamics of the hang glider.

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Mathematical Modeling of Helicopter Dynamics with an External Sling Load

International Journal of Engineering & Technology ◽

10.14419/ijet.v7i4.38.27652 ◽

2018 ◽

Vol 7 (4.38) ◽

pp. 1112

Author(s):

Vadim Viktorovich Efimov ◽

Konstantin Olegovich Chernigin ◽

Nikolay Ivanovich Nikolaykin ◽

Vadim Vadimovich Vorob’ev ◽

Mikhail Semenovich Kublanov

Keyword(s):

Mathematical Modeling ◽

Mathematical Model ◽

Rotational Motion ◽

Flight Dynamics ◽

Systems Of Equations ◽

Coordinate Systems ◽

Theoretical Methods ◽

Helicopter Flight

The article shows the urgency of the development of theoretical methods for studying the dynamics of the flight of a helicopter with an external sling load aimed at ensuring the flight operation safety when transporting loads. A mathematical model of the helicopter flight dynamics with an external sling load is described. The assumptions made are indicated. The load coordinate systems are introduced and described. The systems of equations of acting forces and moments are presented, which are derived considering the accelerated movement of the load's slinging point on the helicopter with its translational and rotational motion.

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