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

The design of aircraft for ground manoeuvres 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, where 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 manoeuvre is analysed in detail, with a comparison between the two ways in which this manoeuvre 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 regards to the transient behaviour, where 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, compared to simulations.