Elementary Flight Dynamics with an Introduction to Bifurcation and Continuation Methods

Description

Elementary Flight Dynamics with an Introduction to Bifurcation and Continuation Methods, Second Edition is aimed at senior undergraduate and graduate students of aerospace and mechanical engineering. The book uses an optimal mix of physical insight and mathematical presentation to illustrate the core concepts of professional aircraft flight dynamics. An updated version of the aerodynamic model is presented with the corrected definition of rate (dynamic) derivatives, supported with examples of real-life airplanes and related data and by open-source computational tools. It introduces bifurcation and continuation methods as a tool for flight dynamic analysis. FEATURES Covers an up-to-date, corrected, ‘clean’ presentation of the elements of flight dynamics Presents a blend of theory, practice and application with real-life practical examples Provides a unique viewpoint of applied aerodynamicists and aircraft designers Introduces bifurcation and continuation methods as a tool for flight dynamics analysis Includes a computational tool with real-life examples carried throughout the chapters The book is enriched with case studies of flight dynamics of a bird’s flight, of a six-seater rigid-wing airplane from a design perspective, and airship dynamics to highlight the modal behaviour of similar-looking vehicles that are distinct from each other. Excerpts from reviews of the first edition: "Flight dynamics is a topic that can cause difficulties to aerospace engineering students. This text leads the reader gently through the material with plenty of practical examples and student exercises. As such, it is easy to follow the material and to gradually develop a deep understanding of a demanding topic. The book is ideal for undergraduate students and is a good text for graduate students."––James F. Whidborne, Cranfield University, United Kingdom "The book covers all the aspects of flight dynamics traditionally found in such texts interspersed with examples of the treatment of features of current air vehicles....In my opinion, this book covers the subject comprehensively and is a desirable reference source for undergraduates and graduates alike."––R.J. Poole, MRAeS, The Aeronautical Journal, June 2014 "The book design and the methodology of interpretation are directed to a wide range of target audience/population interested in studying the dynamics of flight. Given the scale and organization of information, the book will also be a useful tool in the analysis of flight dynamics for professionals in this field. The book is sure to appeal to anyone interested in the dynamics of flight."––Jaroslav Salga, Advances in Military Technology, June 2014 Cover Half Title Title Page Copyright Page Contents Preface Authors Chapter 1: Introduction 1.1. What, Why And How? 1.2. Aircraft As A Rigid Body 1.3. Six Degrees Of Freedom 1.4. Position, Velocity And Angles 1.5. Aircraft Motion In Wind 1.6. Longitudinal Flight Dynamics 1.7. Longitudinal Dynamics Equations 1.8. A Question Of Timescales 1.9. Longitudinal Trim 1.10. Aerodynamic Coefficients CD, CL, Cm 1.10.1. Aerodynamic Coefficients with Angle of Attack (α) 1.10.2. Aerodynamic Coefficients with Mach Number (Ma) 1.11. Wing–Body Trim Exercise Problems References Chapter 2: Stability Concept 2.1. Linear First-Order System 2.2. Linear Second-Order System 2.3. Non-Linear Second-Order System 2.4. Pitch Dynamics about Level Flight Trim 2.5. Modelling Small-Perturbation Aerodynamics 2.6. Pitch Dynamics about Level Flight Trim (Contd.) 2.6.1. Numerical Example 2.7. Short-Period Frequency and Damping 2.8. Forced Response 2.8.1. First-Order System 2.8.2. Second-Order System 2.9. Response to Pitch Control 2.9.1. Pitch Dynamics about Level Flight Trim with Elevator Control Exercise Problems Chapter 3: Longitudinal Trim and Stability 3.1. Wing–Body Trim and Stability 3.2. Wing–Body Plus Tail: Physical Arguments 3.3. Wing–Body Plus Tail: Math Model 3.3.1. Airplane Lift 3.3.2. Airplane Pitching Moment 3.4. Role of Downwash 3.5. Neutral Point 3.5.1. Static Margin 3.5.2. NP as Aerodynamic Centre of Entire Airplane 3.6. Replacing VH with V/H 3.6.1. Revised Expressions for NP 3.6.2. NP as Aerodynamic Centre of the Entire Airplane 3.6.3. Trim and Stability, Again! 3.7. Effect of CG Movement 3.8. Rear CG Limit due to Airplane Loading and Configuration at Take-Off 3.9. Cm, CL Curves–Non-Linearities Exercise Problems Appendix 3.1 Chapter 4: Longitudinal Control 4.1. All-Moving Tail 4.2. Elevator 4.3. Tail Lift with Elevator 4.4. Airplane Lift Coefficient with Elevator 4.5. Airplane Pitching Moment Coefficient with Elevator 4.6. Elevator Influence on Trim and Stability 4.6.1. Change in Trim Lift Coefficient 4.6.2. Another Viewpoint of Stability 4.7. Longitudinal Manoeuvres with the Elevator 4.8. Most Forward CG Limit 4.8.1. Using Elevator to Compensate for CG Shift 4.8.2. Typical Elevator Deflection Limits 4.8.3. Forward-Most CG Limit due to Elevator Up-Deflection Limit 4.9. Np Determination from Flight Tests 4.10. Effect of NP Shift with Mach Number Exercise Problems References Chapter 5: Long-Period (Phugoid) Dynamics 5.1. Phugoid Mode Equations 5.2. Energy 5.2.1. Normal Acceleration 5.3. Phugoid Mode Physics 5.4. Phugoid Small-Perturbation Equations 5.5. Aerodynamic Modelling with Mach Number 5.6. Phugoid Dynamics 5.7. Phugoid Mode Frequency and Damping 5.8. Accurate Short-Period and Phugoid Approximations 5.8.1. Short-Period Mode Dynamics 5.8.2. Phugoid Mode Dynamics 5.9. Derivative CmMa 5.10. Derivative Cmq1 in Pitching Motion 5.11. Derivative Cmq1 in Phugoid Motion 5.12. Flow Curvature Effects Exercise Problems References Chapter 6: Lateral-Directional Motion 6.1. Review 6.2. Directional Disturbance Angles 6.3. Directional versus Longitudinal Flight 6.4. Lateral Disturbance Angles 6.5. Lateral-Directional Rate Variables 6.6. Small-Perturbation Lateral-Directional Equations 6.7. Lateral-Directional Timescales 6.8. Lateral-Directional Aerodynamic Derivatives 6.9. Lateral-Directional Small-Perturbation Equations (Contd.) 6.10. Lateral-Directional Dynamic Modes 6.10.1. Roll (Rate) Mode 6.10.2. Dutch Roll Mode 6.10.3. Spiral Mode Exercise Problems Reference Chapter 7: Lateral-Directional Dynamic Modes 7.1. Roll (Rate) Mode 7.2. Roll Damping Derivative Clp2 7.2.1. Special Case of Trapezoidal Wing 7.2.2. Owing to Vertical Tail 7.3. Roll Control 7.4. Aileron Control Derivative, Clδa 7.4.1. Other Roll Control Devices 7.4.1.1. Roll Control with Spoilers 7.4.1.2. Roll Control by Differential Tail 7.4.1.3. Roll Control by Rudder 7.5. Yaw Due To Roll Control 7.5.1. Yaw due to Aileron 7.5.2. Yaw due to Spoilers 7.5.3. Yaw due to Differential Tail 7.5.4. Yaw due to Rudder 7.6. Aileron Input for a Bank Angle 7.7. Dutch Roll Mode 7.8. Directional Derivatives CYβ and Cnβ 7.8.1. Other Contributors to Yaw Stiffness 7.8.2. Loss of Vertical Tail Effectiveness 7.9. Lateral Derivative: 7.9.1. Wing Dihedral 7.9.2. Other Sources of Clβ 7.9.2.1. Wing Sweep 7.9.2.2. Wing Vertical Position on Fuselage 7.9.2.3. Vertical Tail 7.10. Damping Derivatives: 7.10.1. Wing Contribution to Cnr1 and Clr1 7.10.2. Vertical Tail Contribution to Cnr1 and Clr1 7.11. Rudder Control 7.11.1. Crosswind Landing 7.11.2. Other Rudder Trim Cases 7.12. Spiral Mode 7.12.1. Cnr2 and Clr2 Derivatives 7.12.2. Spiral Mode Stability 7.13. Real-Life Airplane Data Exercise Problems References Chapter 8: Computational Flight Dynamics 8.1. Aircraft Equations of Motion 8.2. Derivation of Aircraft Equations of Motion 8.2.1. Equations of the Translational Motion 8.3. 3–2–1 Rule 8.3.1. Euler Angles and Transformation 8.3.2. Kinematic Equations (Attitude and Position Dynamics) 8.3.2.1. Relation between Body Rates (p, q, r) and Euler Rates (ɸ, θ, ψ) 8.3.2.2. Relation between Inertial Velocity and Body-Axis Velocity Components 8.3.2.3. Relation between Body-Fixed and Wind-Fixed Coordinates 8.3.2.4. Relation between the Body-Axis and Wind-Axis Euler Angles 8.3.2.5. Relation between the Body-Axis and Wind-Axis Angular Rates 8.3.3. Force Equations Summed Up 8.3.3.1. Derivation of Force Equations in Wind-Fixed Axis System 8.4. Derivation of Aircraft Equations 8.4.1. Equations for the Rotational Motion 8.4.2. Symmetry of Aircraft 8.4.3. Sources of Nonlinearity 8.5. Numerical Analysis of Aircraft Motions 8.5.1. Generalized Airplane Trim and Stability Analysis 8.5.1.1. Local Dynamic Behaviour: Trim and Stability Analysis 8.6. Standard Bifurcation Analysis 8.6.1. Application of SBA to F-18/HARV Dynamics 8.6.1.1. Stall and Post-Stall Solutions 8.6.1.2. Roll Manoeuvres 8.7. Extended Bifurcation Analysis (EBA) 8.7.1. Straight and Level Flight Trim 8.7.2. Coordinated (Zero Sideslip) Level Turn Trim 8.7.3. Performance and Stability Analysis 8.7.3.1. Straight and Level Flight Trim 8.7.3.2. Level Turn Manoeuvre 8.7.3.3. Maximum Roll Rate in a Roll Manoeuvre Exercise Problems Appendix 8.1: Small-Perturbation Equations (At Longitudinal Trim State) Appendix 8.2: F-18 Data Aerodynamic Data Geometric and Other Data for F-18 Appendix 8.3: Equations and Aircraft Data Used for Roll Manoeuvre References Chapter 9: Appendix: Case Studies 9.1. Example of GA Airplane 9.1.1. Aero Data Estimation 9.1.2. First-Order Form of the Small-Perturbation Longitudinal Dynamics Equations 9.1.3. Lateral-Directional Aerodynamics Parameters 9.1.4. Lateral-Directional Perturbation Dynamics Model 9.2. Airship Dynamics 9.2.1. Airship Equations of Motion 9.2.2. Longitudinal Small-Perturbation Equations 9.2.3. Small-Perturbation Equations for Lateral-Directional Modes 9.2.4. Useful Empirical Relations 9.2.5. Numerical Example References Index