Revised Analytical Criteria for Aircraft Lateral - Directional Instabilities

Abstract

Following the recently revised presentation of the theory of small-perturbation flight dynamics by the authors, the present paper considers the newly corrected aircraft lateral-directional equations with trim angle of attack as a parameter. The dynamics is modeled by a set of second-order equations written in matrix form which makes it convenient to derive conditions for onset of instability. The static instability criterion is directly obtained and is seen to match entirely the condition for spiral mode instability. An approximate criterion for dynamic instability is obtained by considering the undamped lateral-directional dynamics, which happens to be a Hamiltonian system. The onset of dynamic instability corresponds to the occurrence of a Hamiltonian Hopf bifurcation which can be explicitly evaluated. This yields a new criterion for dynamic instability which is simpler and easier to use than the Routh discriminant. Also, the new criterion has the Cnβ, dyn parameter as a leading term which explains why this parameter may be used as an indicator for wing rock onset.