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Routes to chaos in the post-stall dynamics of higher-dimensional aircraft model

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Abstract

Aircraft dynamics are dominated by nonlinearities that may drive the aircraft into chaotic motions under certain conditions. Past studies in this area have explored several factors leading to the evolution of chaotic dynamics. However, a proper route or sequence for the evolution of chaotic dynamics has not been adequately substantiated. In this context, this paper systematically examines possible routes to chaos in the post-stall dynamics of an F-18 High-Alpha Research Vehicle model with external steady wind as the driving agent. Using tools from nonlinear dynamics based on bifurcation analysis, phase portrait, Poincaré map and amplitude spectrum analysis techniques, existence of quasi-periodic, period-doubling and intermittency routes to chaos are established. An eighth-order nonlinear aircraft model incorporating wind effects has been used for generating time responses from different post-stall flight conditions.

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Abbreviations

M :

Mach number

\(\alpha \) :

Angle of attack

\(\beta \) :

Sideslip angle

p, q, r :

Body axis roll, pitch and yaw rates, respectively

\(\phi ,\theta \) :

Euler roll and pitch angles, respectively

\(\gamma \) :

Flight path angle

X, Y, Z :

Position coordinates

u, v, w :

Body axis velocity components

\(u_{w},v_{w},w_{w}\) :

Wind velocity components along body axis

\(v_{s}\) :

Speed of sound

\(\rho \) :

Air density

\(T_{m}\) :

Maximum thrust

\(I_x\), \(I_y\), \(I_z\) :

Roll, pitch and yaw moments of inertia

\(I_{xy}\), \(I_{xz}\), \(I_{zy}\) :

Cross-moments of inertia terms

\(\eta \) :

Thrust as a fraction of maximum available thrust

\(\delta e\) :

Elevator deflection

\(\delta a\) :

Aileron deflection

\(\delta r\) :

Rudder deflection

\(C_{{L}}\), \(C_{{D}}\), \(C_{{Y}}\) :

Lift, drag and sideforce coefficients, respectively

\(C_{{m}}\), \(C_{{l}}\), \(C_{{n}}\) :

Aerodynamic pitch, roll and yaw moment coefficients, respectively

\(\alpha \), \(\beta \), p, q, r :

Derivatives with respect to \(\alpha \), \(\beta \), p, q, r, respectively

\(\delta e\), \(\delta a\), \(\delta r\) :

Derivatives with respect to \(\delta e\), \(\delta a\), \(\delta r\), respectively

\((\underline{.})\) :

Vector

\(\dot{(.)}\) :

Time derivative

\(({.})^*\) :

Equilibrium point

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Acknowledgements

We express our sincere gratitude to the anonymous reviewers who have been very patient with multiple revisions of the manuscript. Their useful comments and valuable suggestions have helped us immensely in elevating the manuscript both in quality and in presentation.

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  1. Flight Dynamics and Control Laboratory, Department of Aerospace Engineering, IIT Madras, Chennai, 600036, India

    G. Rohith & Nandan K. Sinha

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  1. G. Rohith
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  2. Nandan K. Sinha
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Correspondence to G. Rohith.

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Rohith, G., Sinha, N.K. Routes to chaos in the post-stall dynamics of higher-dimensional aircraft model. Nonlinear Dyn 100, 1705–1724 (2020). https://doi.org/10.1007/s11071-020-05604-8

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