Bifurcation and Stability Analysis of Aircraft Turning on the Ground

Abstract

During ground manoeuvres a loss of lateral stability due to the saturation of the main landing gear tyres can cause the aircraft to enter a skid or a spin. The lateral stability is governed not only by aspects of the gear design, such as its geometry and tyre characteristics, but also by operational parameters, for example, the weather and taxiway condition. In this paper we develop an improved understanding and new presentation of the dynamics of an aircraft manoeuvring on the ground, ultimately aimed at optimisation and automation of ground operations. To investigate turning manoeuvres we apply techniques from dynamical systems theory to a modified version of a nonlinear computer model of an A320 passenger aircraft developed by the Landing Gear Group at Airbus UK. Specifically, we present a bifurcation analysis of the underlying solution structure that governs the dynamics of turning manoeuvres with dependence on the steering angle and thrust level. Furthermore, a detailed study of the behaviour when lateral stability is lost focuses on how the tyre saturation at different wheel sets lead to qualitatively different types of overall behaviour. The presented bifurcation diagrams identify parameter regions for which undesirable behaviour is avoidable and, thus, they form a foundation for defining the safe operating limits during turning manoeuvres.

Numerical continuation analysis of a three-dimensional aircraft main landing gear mechanism

“…Several recent applications of dynamical systems methods have demonstrated the advantages that they can offer in an aerospace context; this includes the analysis of aircraft ground dynamics [7,8], the study of nose landing gear shimmy [9] and NLG mechanism modelling [2]. To be able to use these dynamical systems methods for analysing landing gear mechanisms, the mechanism configuration and internal force distribution is formulated as a system of coupled equations, which are inherently nonlinear due to various geometric constraints.…”

Operational Parameter Study of an Aircraft Turning on the Ground

“…The aircraft then moves off under constant thrust, repeating the motion periodically relative to the unstable turning solution with a maximum and minimum velocity of 20m/s and−10m/s, respectively. A detailed description of this undesirable behaviour that persists between H 1 and H 2 is given in [7]. Between H 2 and L 4 high steering angle, small radius turns can be observed, and between L 3 and the end point at the top right high steering angle, large radius turns can be observed for which the nose gear is almost perpendicular to the direction of motion and, hence, is effectively dragged along the ground.…”

“…This type of solution with a small steering angle, large radius turn persists from the initial point up to the bifurcation L 1 ; the radius of the turn decreases as L 1 is approached. At the bifurcation the turning moment generated by the nose gear tyres overcomes the stabilising aerodynamic force generated by the tail fin of the aircraft [7]. When the steering angle is increased beyond L 1 , the aircraft loses velocity rapidly over a transient period and starts to follow a solution in the region between the Hopf bifurcations H 1 and H 2 .…”

“…In previous work a combination of flight test data and low-order computer bicycle models were used to study the ground handling properties of aircraft [4,5], including the effect of tyre pressure on ground handling [3]. A previous study by the authors utilised a SimMechanics model to study the dynamics of aircraft on the ground under variation of thrust [7]. In this paper we use continuation analysis to perform a parameter study of a mathematical model of a passenger aircraft.…”

Numerical Continuation Analysis of a Dual-sidestay Main Landing Gear Mechanism

“…Tools from Bifurcation Theory, [9,10,11] including numerical continuation, have been used to help understand nonlinear problems in Aerospace applications before [12,14,13]. For all of these applications, numerical continuation was shown to provide significant advantages over alternative analysis methods.…”