Flight Dynamics

Here, SUNANDAN MALVIYA (IISER Bhopal), SARTHAK GIRDHAR (IIT Bombay) and myself present a new approach to flight dynamics. The entire work is a pdf of almost 200 pages, whose abstract we give below. Please see lower down this page for the published versions.

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.

Get the Article HERE

We wholeheartedly welcome your comments, criticisms, suggestions for improvement and any other feedback. The Article is free to download, distribute and read. For other uses, please see the Copyright and Other Statements on page 10. For a list of errata, click here. The errors, at least the ones discovered so far, are minor.

Published versions

For publication, we have to split the whole work into several pieces (on account of their size we don't think of them as salami slices). The first piece introduces the concept of model-based manoeuvre analysis. We present the model with derivation (Subdivision 3B of the pdf) and use it to analyse the Immelmann manoeuvre (Subdivision 5C) and also a vertical dive, which does not exist in the pdf. The reference is Frontiers in Aerospace Engineering 3, #1308872 (2024).
Paper 1