Model-based manoeuvre analysis: a path to a new paradigm in aircraft flight dynamics

Abstract

We propose a closed-form system of nonlinear equations for the pitch plane or longitudinal motions of a fixed-wing aircraft and use it to demonstrate a possible path to the unification of theoretical flight dynamics and practical analysis of aircraft manoeuvres. The derivation of an explicit model free of data tables and interpolated functions is enabled by our use of empirical formulae for lift and drag which agree with experiments. We validate the model by recovering the well-known short period and phugoid modes, and the regions of normal and reversed command. We then use the model to present detailed simulations of two acrobatic manoeuvres, an Immelmann turn and a vertical dive. Providing new quantitative insights into the dynamics of aviation, our model-based manoeuvre analysis has the potential to impact both the academic flight dynamics curriculum and the ground training program for pilots of manned and unmanned aircraft. Possible consequences of future model-centric pilot training may include improved safety standards in general and commercial aviation as well as expedited theoretical course completion in air transport.