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 basic s of navigation and communication . In the next Chapter w e 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 dimen sions, w e treat separately the planes of pitch, yaw and bank, writing a sixth order system in each plane. Among these, t he pitch plane equations are of the greatest significance. In the following Chapter w e analyse th e model equation s to obtain the modes of motion and their stabilities as well as pilot - induced oscillations . We also introduce the characteristic curve s, 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 backdr op of actual aviation accidents and incidents. Overall, the model -based simulation s combine the theoretical approach of the engineer with the hands -on approach of the pilo t; this combination should enhance pilots’ technical training and can potentially impro ve 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. ---- o ---- 3 TABLE OF CONTENTS We have opted for quite detailed Section headings , so that a glance through the contents can give you an idea of the topics which we will cover . We have further implemented the entire Table of Contents as bookmarks in the pdf – please use those for easy navigation. Title . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 Table of contents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 List of symbols . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 List of abbreviations and acronyms . . . . . . . . . . . . . . . . . . . . . . . . . 8 Numbering conventions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 Copyright and other statements . . . . . . . . . . . . . . . . . . . . . . . . . . 10 Chapter 1 : Aims and Scope O. This Chapter has no Subdivisions . . . . . . . . . . . . . . . . . . . . . . . . 12 §01 The Literature . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 §02 Flight dynamics Quiz . . . . . . . . . . . . . . . . . . . . . . . . . 14 §03 Outline, novelty, learning objectives and prerequisite requirements . . . . . . . 18 §04 Presentation style, c hange of narrative voice . . . . . . . . . . . . . . . . 20 Chapter 2 : Aviation, Navigation and Communication A. Aircraft components, operating variables and units . . . . . . . . . . . . . . . . . 21 §05 Primary components of an aircraft . . . . . . . . . . . . . . . . . . . . 21 §06 Additional components . . . . . . . . . . . . . . . . . . . . . . . . 29 §07 Operational quantities, system of units . . . . . . . . . . . . . . . . . . 30 §08 Types of pilot , roles of the two pilots . . . . . . . . . . . . . . . . . . . 35 §09 Environmental impact of aviation . . . . . . . . . . . . . . . . . . . . 35 B. Introduction to navigation . . . . . . . . . . . . . . . . . . . . . . . . . . . 36 §10 VFR or visual flight rules – course maintenance . . . . . . . . . . . . . . 36 §11 VFR – departures and arrivals . . . . . . . . . . . . . . . . . . . . . 37 §12 IFR or instrument flight rules – course maintenance . . . . . . . . . . . . . 38 §13 IFR – departures and arrivals . . . . . . . . . . . . . . . . . . . . . . 41 §14 STAR and SID example – John F Kennedy International A irport . . . . . . . 44 C. Rudiments of communication . . . . . . . . . . . . . . . . . . . . . . . . . 49 §15 Spelling alphabet, airport and airline codes . . . . . . . . . . . . . . . . 49 §16 Good communication practices . . . . . . . . . . . . . . . . . . . . . 51 Chapter 3 : The Aircraft Dynamic Model A. Axes and angles, lift and drag . . . . . . . . . . . . . . . . . . . . . . . . . 54 §17 Axis and angle conventions – full treatment . . . . . . . . . . . . . . . . 54 §18 Axis and angle conventions – simplified treatment . . . . . . . . . . . . . 56 §19 Different theories of lift . . . . . . . . . . . . . . . . . . . . . . . . 59 §20 Momentum theory of lift , drag . . . . . . . . . . . . . . . . . . . . . 61 §21 Aerodynamic stall . . . . . . . . . . . . . . . . . . . . . . . . . . 66 B. Pitch plane equations of motion . . . . . . . . . . . . . . . . . . . . . . . . 67 §22 Geometry, variables and paramet ers . . . . . . . . . . . . . . . . . . . 67 §23 The horizontal tail or elevator (stabilator) . . . . . . . . . . . . . . . . . 67 §24 Forces and torques . . . . . . . . . . . . . . . . . . . . . . . . . . 70 §25 The xyz model . . . . . . . . . . . . . . . . . . . . . . . . . . . 73 4 §26 The qdo model . . . . . . . . . . . . . . . . . . . . . . . . . . . 73 §27 The space vector model . . . . . . . . . . . . . . . . . . . . . . . . 74 §28 Interpretation of the space vector model . . . . . . . . . . . . . . . . . 74 §29 Model in some special situations . . . . . . . . . . . . . . . . . . . . 76 C. Yaw and banking plane equations of motion . . . . . . . . . . . . . . . . . . . . 78 §30 Yaw plane equations of motion . . . . . . . . . . . . . . . . . . . . 78 §31 Banking plane equations of motion . . . . . . . . . . . . . . . . . . . 80 D. Chapter conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81 §32 Limitations of yaw and banking plane models, c oncluding remarks to Chapter 3 . 81 Chapter 4 : Stability and Characteristic Curves O. This Chapter has no Subdivisions . . . . . . . . . . . . . . . . . . . . . . . . 82 §33 Static stability, difference between one - and two -piece tails , CM position limits . 82 §34 Modes of motion and their stabilities . . . . . . . . . . . . . . . . . . 84 §35 Pilot -induced oscillation . . . . . . . . . . . . . . . . . . . . . . . 89 §36 Characteristic curves and their interpretation , normal and reversed command . . 93 Chapter 5 : Flight Simulations A. The Academic flight simulator . . . . . . . . . . . . . . . . . . . . . . . . 100 §37 Description of the simulator . . . . . . . . . . . . . . . . . . . . . . 100 §38 Characterization of the short period and phugoid modes . . . . . . . . . . 101 §39 Structure of the follow ing Subdivisions . . . . . . . . . . . . . . . . . . 103 B. Takeoff . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105 §40 Description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105 §41 Planning – calculation of the V -speeds . . . . . . . . . . . . . . . . . . 105 §42 Execution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109 §43 Further discussion , accidents and incidents . . . . . . . . . . . . . . . . 113 C. Immelmann turn . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116 §44 Immelmann turn . . . . . . . . . . . . . . . . . . . . . . . . . . 116 D. Landing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120 §45 Description . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120 §46 Planning – calculation of the approach and flare . . . . . . . . . . . . . . 121 §47 Execution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124 §48 Perfecting the approac h – velocity ratio . . . . . . . . . . . . . . . . . 128 §49 Types of flare, bounce and shimmy . . . . . . . . . . . . . . . . . . . 133 §50 Further discussion , accidents and incidents . . . . . . . . . . . . . . . . 140 E. Coordinated turns . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 144 §51 Turn coordination . . . . . . . . . . . . . . . . . . . . . . . . . . 144 F. Simple stall . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 148 §52 Approach to the stall . . . . . . . . . . . . . . . . . . . . . . . . . 148 §53 Stall . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151 §54 Recovery from stall . . . . . . . . . . . . . . . . . . . . . . . . . 153 §55 Further discussion , accidents and incidents . . . . . . . . . . . . . . . . 155 G. Banking plane dynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . 161 §56 Why don’t we feel a banked turn ? . . . . . . . . . . . . . . . . . . . 161 §57 Further discussion . . . . . . . . . . . . . . . . . . . . . . . . . . 163 H. Pugachev cobra . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 164 §58 Description . . . . . . . . . . . . . . . . . . . . . . . . . . . . 164 §59 Design of the aircraft . . . . . . . . . . . . . . . . . . . . . . . . 165 §60 Execution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 166 5 J. Elevator fault . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 168 §61 Description . . . . . . . . . . . . . . . . . . . . . . . . . . . . 168 §62 Planning – basics of approach and flare . . . . . . . . . . . . . . . . . 169 §63 Planning – calculation of waypoints on the flight path . . . . . . . . . . . 172 §64 Execution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 176 §65 Further discussion , accidents and incidents . . . . . . . . . . . . . . . 181 K. Chapter conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 183 §66 Concluding remarks to Chapter 5 . . . . . . . . . . . . . . . . . . . 183 Chapter 6 : Conclusion and Future Directions O. This Chapter has no Subdivisions . . . . . . . . . . . . . . . . . . . . . . . 185 §67 Summary of contributions . . . . . . . . . . . . . . . . . . . . . . 185 §68 Future directions . . . . . . . . . . . . . . . . . . . . . . . . . . 186 §69 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . 188 Answers to the quiz questions . . . . . . . . . . . . . . . . . . . . . . . . . . 189