A Straight-in Approach to Flight Dynamics

Motions in two spatial dimensions

Abstract

In this Article we present a new approach to flight dynamics which unifies the perspectives and requirements of the aerospace engineer and the pilot. In the process, we also present a comprehensive course on aviation to non-specialists who are fascinated by flying and possess the mathematical training to understand it quantitatively. We begin with a Chapter describing the components of an aircraft as well as the basics of navigation and communication. In the next Chapter we use the principles of classical mechanics, combined with the momentum theory of lift and drag, to derive a closed-form nonlinear dynamical model of an aircraft. Restricting ourselves for conceptual and technical simplicity to motions in two spatial dimensions, we treat separately the planes of pitch, yaw and bank, writing a sixth order system in each plane. Among these, the pitch plane equations are of the greatest significance. In the following Chapter we analyse the model equations to obtain the modes of motion and their stabilities as well as pilot-induced oscillations. We also introduce the characteristic curves, which are plots of fixed point or steady state solutions as one or more parameters are varied. This prepares us for the climactic Chapter in which we use the model to construct a flight simulator and demonstrate a variety of manoeuvres including takeoff, landing, vertical loops, coordinated turns and flight with non-functional control surfaces. Extensive calculation and discussion show us how to maximize safety during each phase of flight, and set the simulation results against the backdrop of actual aviation accidents and incidents. Overall, the model-based simulations combine the theoretical approach of the engineer with the hands-on approach of the pilot; this combination should enhance pilots’ technical training and can potentially improve aviation safety by mitigating accidents and incidents. We hope that our work may prove as useful for the university as it does for the flying school; if in addition it opens for the eager explorer the portals to the fascinating world of aviation, then our mission in writing this Article will be wholly accomplished.