Etienne Coetzee

Bifurcation Analysis of the NASA GTM with a View to Upset Recovery

The loss of control in-flight of civil airliners is a matter of great concern to the aviation industry. Loss of control in-flight often involves so called ‘upset’ conditions and, hence, the ability to recover from upset will reduce the frequency of loss of control incidents. This paper presents the use of bifurcation analysis, complemented by time-history simulations, to understand the flight dynamics of the open loop NASA Generic Transport Model with a view to identifying the attractors of the dynamical system that underlie upset behaviour. A number of drivers for potential upset conditions have been discovered which include non-oscillatory spirals and oscillatory spins. Time-histories of the upset conditions yield the response characteristics associated with these upset scenarios.

Upset Dynamics of an Airliner Model: A Nonlinear Bifurcation Analysis

Despite the significant improvement in safety linked to the fourth generation of airliners, the risk of encountering upset conditions remains an important consideration. Upset, which may arise from faults, external events, or inappropriate pilot inputs, can induce a loss-of-control incident if the pilot does not respond in the correct manner. Any initiative aimed at preventing such events requires an understanding of the fundamental aircraft behavior. This paper presents the use of bifurcation analysis, complemented by time-history simulations, to understand the flight dynamics of the open-loop NASA generic transport model by identifying the attractors of the dynamical system that govern upset behavior. A number of drivers for potential upset conditions have been identified, including nonoscillatory spirals and oscillatory spins. The analysis shows that these spirals and spins are connected in two-parameter space and that, by an inappropriate pilot reaction to the spiral, it is possible to enter the oscil...

Bifurcation and Stability Analysis of Aircraft Turning on the Ground

During ground maneuvers a loss of lateral stability due to the saturation of the main landing gear tires 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 tire 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 maneuvering on the ground, ultimately aimed at optimization and automation of ground operations. To investigate turning maneuvers, we apply techniques from dynamic systems theory to a modified version of a nonlinear computer model of an A320 passenger aircraft developed by the Landing Gear Group at Airbus in the United Kingdom. Specifically, we present a bifurcation analysis of the underlying solution structure that governs the dynamics of turning maneuvers with dependence on the steering angle and thrust level. Furthermore, a detailed study of the behavior when lateral stability is lost focuses on how the tire saturation at different wheel sets leads to qualitatively different types of overall behavior. The presented bifurcation diagrams identify parameter regions for which undesirable behavior is avoidable, and thus they form a foundation for defining the safe operating limits during turning maneuvers.

Operational Parameter Study of Aircraft Dynamics on the Ground

The dynamics of passenger aircraft on the ground are influenced by the nonlinear characteristics of several components, including geometric nonlinearities, aerodynamics, and interactions at the tire-ground interface. We present a fully parameterized mathematical model of a typical passenger aircraft that includes all relevant nonlinear effects. The full equations of motion are derived from first principles in terms of forces and moments acting on a rigid airframe, and they include implementations of the local models of individual components. The overall model has been developed from and validated against an existing industry-tested SIMMECHANICS model. The key advantage of the mathematical model is that it allows for comprehensive studies of solutions and their stability with methods from dynamical systems theory, particularly, the powerful tool of numerical continuation. As a concrete example, we present a bifurcation study of how fixed-radius turning solutions depend on the aircrafts steering angle and center of gravity position. These results are represented in a compact form as surfaces of solutions, on which we identify regions of stable turning and regions of laterally unstable solutions. The boundaries between these regions are computed directly, and they allow us to determine ranges of parameter values for safe operation. The robustness of these results under the variation in additional parameters, specifically, the engine thrust and aircraft mass, are investigated. Qualitative changes in the structure of the solutions are identified and explained in detail. Overall our results give a complete description of the possible turning dynamics of the aircraft in dependence on four parameters of operational relevance.

Nonlinear Analysis of Lateral Loading During Taxiway Turns

determined by the maximal lateral loading conditions identified in published studies of instrumented in-service passenger aircraft. The performance of the turn can be assessed over the entire operational range in terms of the actual loads experienced at individual landing gears. Recent studies by the Federal Aviation Administration of instrumented aircraft have been limited to investigating the lateral loads experienced at the aircraft’s center-ofgravity position. The results presented here show that this information is insufficient to predict the actual loads experienced by individual landing gears, especially for the nose gear, which is found to experience considerably higher lateral loads than predicted by the corresponding loads at center of gravity. These findings are shown to be robust with respect to changes in the aircraft’s mass and the criterion used to define the limits of the operating regions.

Numerical continuation and bifurcation analysis in aircraft design: an industrial perspective

Bifurcation analysis is a powerful method for studying the steady-state nonlinear dynamics of systems. Software tools exist for the numerical continuation of steady-state solutions as parameters of the system are varied. These tools make it possible to generate ‘maps of solutions’ in an efficient way that provide valuable insight into the overall dynamic behaviour of a system and potentially to influence the design process. While this approach has been employed in the military aircraft control community to understand the effectiveness of controllers, the use of bifurcation analysis in the wider aircraft industry is yet limited. This paper reports progress on how bifurcation analysis can play a role as part of the design process for passenger aircraft.

Application of bifurcation methods for the prediction of low-speed aircraft ground performance

The design of aircraft for ground maneuvers is an essential part in satisfying the demanding requirements of the aircraft operators. Extensive analysis is done to ensure that a new civil aircraft type will adhere to these requirements, for which the nonlinear nature of the problem generally adds to the complexity of such calculations. Small perturbations in velocity, steering angle, or brake application may lead to significant differences in the final turn widths that can be achieved. Here, the U-turn maneuver is analyzed in detail, with a comparison between the two ways in which this maneuver is conducted. A comparison is also made between existing turn-width prediction methods that consist mainly of geometric methods and simulations and a proposed new method that uses dynamical systems theory. Some assumptions are made with regard to the transient behavior, for which it is shown that these assumptions are conservative when an upper bound is chosen for the transient distance. Furthermore, we demonstrate that the results from the dynamical systems analysis are sufficiently close to the results from simulations to be used as a valuable design tool. Overall, dynamical systems methods provide an order-of-magnitude increase in analysis speed and capability for the prediction of turn widths on the ground when compared with simulations.

Shimmy of an Aircraft Main Landing Gear With Geometric Coupling and Mechanical Freeplay

The self-sustained oscillation of aircraft landing gear is an inherently nonlinear and dynamically complex phenomenon. Although such oscillations are ultimately driven from the interaction between the tyres and the ground, other effects, such as mechanical freeplay and geometric nonlinearity, may influence stability and add to the complexity of observed behaviour. This paper presents a bifurcation study of an aircraft main landing gear, which includes both mechanical freeplay, and significant geometric coupling, the latter achieved via consideration of a typical side-stay orientation. These aspects combine to produce complex oscillatory behaviour within the operating regime of the landing gear, including longitudinal and quasiperiodic shimmy. Moreover, asymmetric forces arising from the geometric orientation produce bifurcation results that are extremely sensitive to the properties at the freeplay/contact boundary. However this sensitivity is confined to the small amplitude dynamics of the system. This affects the interpretation of the bifurcation results; in particular bifurcations from high amplitude behaviour are found to form boundaries of greater confidence between the regions of different behaviour given uncertainty in the freeplay characteristics.

Influence of Tire Inflation Pressure on Nose Landing Gear Shimmy

This work investigates shimmy oscillations in the nose landing gear of a passenger aircraft and studies how they depend on changes in the tire inflation pressure. To achieve this, a mathematical model of a landing gear is considered that includes the influence of the tire pressure via different tire properties, such as cornering force and contact patch length. Experimental data obtained from two radial tires are used as a basis for modeling the influence of inflation pressure on tire properties. Bifurcation analysis of the mathematical model is then performed. It yields stability diagrams in the plane of velocity and vertical force for different values of the tire inflation pressure. Specifically, two-parameter bifurcation diagrams for five different inflation pressures are presented. This allows the conclusion that for the type of tires considered, the landing gear is less susceptible to shimmy oscillations at higher than nominal inflation pressures.

Nonlinear Ground Dynamics of Aircraft: Bifurcation Analysis of Turning Solutions

During ground manoeuvres, particularly at high velocity when exiting the runway, 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 variables, for example, the weather and taxiway condition. In this paper we develop an improved understanding and a new presentation of the dynamics of an aircraft manoeuvring on the ground, ultimately aimed at optimisation and automation of ground operations. Using a modified version of a nonlinear computer model of an A320 passenger aircraft developed by the Landing Gear Group at Airbus in the UK, we apply numerical continuation to investigate turning manoeuvres. We present a bifurcation analysis to describe the underlying structure that governs the dynamics of turning manoeuvres across the steering angle-thrust parameter space. There is a detailed description of the behaviour when lateral stability is lost using a novel diagrammatic approach to explain the dynamic tyre ground interactions. The bifurcation diagrams identify parameter regions for which this undesirable behaviour is avoidable and, thus, they form a foundation for defining the safe operating limits during turning manoeuvres.