Analysis of some nonlinear features in the flight dynamics of a jet airplane
Year: 2022
Type: conference-paper
Abstract: Some issues and features related to nonlinear dynamics are examined for a classical model of jet airplane in this study. Concretely these nonlinear features may imply unexpected events and it is then important to evaluate if there are dangerous or not. Normally they are linked to the real behaviour and physics of an aircraft but may also explain how a simulator (unexpectedly) reacts in certain circumstances. Here the (mainly) analysed model is the Bizjet full-scale aircraft which is provided by Professor R. F. Stengel for study purposes (in both his homepage and classical textbook [1] with characteristics closed to a Learjet). In order to perform the nonlinear analysis, the Matcont toolbox [2] is mainly employed. Amongst others in this work, state jumps are observed and give rise to a nonzero bank angle during classical longitudinal flights. The phenomenon is described mathematically by means of a bifurcation diagram which exhibits some real (pitchfork) bifurcations. In order to cope with this problem, the dangerous zone is delimited by tracing the locus of bifurcation points (in the plane of the longitudinal control parameters). There may also be some Hopf bifurcations which create periodical orbits suddenly. All the predicted behaviours are illustrated and corroborated with time simulations. Moreover, this type of T-tail aircraft can be responsible for a deep stall phenomenon. By calculating the basin of attraction, we try to delimit the zone of initial conditions leading to such a phenomenon. More generally a diagnosis of the deep stall prone configurations is made (especially aft centred aircrafts) in order to avoid them. A loss-of-control can besides present an important transient nature. There is a need to explore the response of the aircraft with huge excitations or values far from the equilibrium taking into account unsteady aspects. In this case, the qualitative results depend no more on the local properties and other ways must be employed to diagnose correctly the situation during the upstream analysis part which improves understanding (and permits to avoid numerous time simulations). Finally, one hope is to contribute to the pre-design of a jet airplane so as to avoid such events and to diminish the associated risks. In order to be mathematically rigorous (for researchers) and meaningful (for aerospace engineers or pilots), for every addressed critical points, the mathematical analysis and the underlying physics are both exposed. The point-of-view of the pilot is also investigated and proposals of training exercises (on simulator) for loss-of-control are formulated. [1] Stengel, R. F. Flight dynamics. Princeton University Press (2004) [2] Dhooge, A, Govaerts, W., and Kuznetsov, Yu A. MATCONT: A MATLAB package for numerical bifurcation analysis of ODEs, ACM Transactions on Mathematical Software. (2003)
Source: HAL
Author: S. KOLB
Institution: Armée de l'air et de l'espace
Language: English
Subfield: Aerospace Engineering
Field: Engineering
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4366349166