Theory and Practice of Aircraft Performance

CHAPTER 4Equations of Motion for a Flat Stationary Earth

4.1 Overview

A conventional fixed wing aircraft must have some motion, a minimum velocity to sustain flight (see Section 2.6). Aircraft motion has six degrees of freedom (see Section 1.15), and high‐performance combat aircraft motion can be very complex. This chapter is devoted to deriving pertinent equations of motion for use in aircraft performance. Aircraft with a large aspect ratio show elastic deformation and are designed in such a way that deformation at normal cruise conditions does not penalize the aircraft performance to significant extent. Deformation affects structural and control issues.

The mathematical relationships are established using vector/matrix algebra (the basics are reviewed in Appendix C). This chapter adheres closely to the well‐established textbook Dynamics of Atmospheric Flight by Bernard Etkin [1], meant for aircraft stability and control analysis. Since this book is meant for aircraft performance, some changes are incorporated to suit the context.

Terrestrial flights take place over the round and rotating Earth. Introducing equations of motion for a round and rotating earth during the first course of aircraft performance to undergraduates may prove to be an arduous task; these equations include terms for Coriolis and centripetal forces resulting from the Earth’s shape and motion [1]. The following reasoning justifies that aircraft rotational and curvature effects can be approximated to a ...