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2nd Edition

Elementary Flight Dynamics with an Introduction to Bifurcation and Continuation Methods



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ISBN 9780367562076
September 10, 2021 Forthcoming by CRC Press
406 Pages 179 B/W Illustrations

 
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Book Description

This book uses an optimal mix of physical insight and mathematical presentation to illustrate the core concepts of professional aircraft flight dynamics. This 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. The Second Edition covers wind effect on aircraft modal dynamics and offers case studies of airship dynamics with the effect of morphing characteristics on the dynamic modes of a model rigid fixed-wing UAV with added data and solved examples.

  • 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

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.

Table of Contents

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 The 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 Box 1.A: Aerostatic versus Aerodynamic Lift Box 1.B: Non-dimensional Parameters of Interest to Aircraft Flight Dynamics Box 1.C: Aerodynamic forces and moments Box 1.D: Standard Atmosphere (refer Fig. 1.31) Box 1.E: Dimensional analysis Box 1.F: Aerodynamic coefficients captured from Wind Tunnel tests Box 1.G: Velocity measurement in flight 2 Stability Concept 2.1 Linear first-order system 2.2 Linear second-order system 2.3 Nonlinear second-order system 2.4 Pitch dynamics about level flight trim 2.5 Modeling small-perturbation aerodynamics 2.6 Pitch dynamics about level flight trim (continued) 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 Box 2.A: A summary of first- and second-order system dynamics and stability. Box 2.B: A history of the dynamic derivatives. Box 2.C: Definition of wind axes. Box 2.D: Downwash lag effect 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 Center of entire airplane  3.6 Replacing  VH with V|H 3.6.1 Revised expressions for NP 3.6.2 NP as aerodynamic center 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  curves – nonlinearities Exercise Problems Box 3.A: Alphonse Pénaud (1850-1880) Box 3.B: Modeling wing downwash Appendix 3.1 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 maneuvers 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 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 modeling 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 The derivative CmMa 5.10 The derivative Cmq1 in pitching motion 5.11 The Derivative Cmq1 in phugoid motion 5.12 Flow curvature effects Exercise Problems Box 5.A: Lanchester’s analysis of the Phugoid motion (1908) Box 5.B: The derivative CTMa 6: Lateral-Directional Motion 6.1 Review 6.2 Directional disturbance angles 6.3 Directional vs. 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 dynamics modes 6.10.1 Roll (rate) mode 6.10.2 Dutch roll mode 6.10.3 Spiral Mode Exercise Problems 7 Lateral-Directional Dynamic Modes 7.1 Roll (Rate) Mode 7.2 Roll damping derivative 7.2.1 Special Case of Trapezoidal Wing 7.2.2 Due to vertical tail 7.3 Roll control 7.4 Aileron control derivative 7.4.1 Other roll control devices 7.4.1.1 Roll control with Spoilers 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 The directional derivatives CYβ and Cnβ 7.8.1 Other contributors to yaw stiffness 7.8.2 Loss of Vertical Tail effectiveness 7.9 The Lateral Derivative – Clβ 7.9.1 Wing Dihedral 7.9.2 Other sources of 7.9.2.1 Wing sweep 7.10 The damping derivatives – Cnr1 and Clr1 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 The Cnr2 and Clr2 derivatives 7.12.2 Spiral mode stability 7.13 Real-life airplane data Exercise Problems Box 7.A Lateral handling or flying qualities Box 7.B: The Cnβ,dyn criterion 8 Computational Flight Dynamics 8.1 Aircraft Equations of Motion 8.2 Derivation of Aircraft Equations of Motion 8.2.1 Equations for the translational motion 8.3 The 3-2-1 rule 8.3.1 Euler angles and transformation 8.3.2 Kinematic equations (Attitude and position dynamics) 8.3.3 Relation between body and wind fixed coordinates (Rotation triplet) 8.3.4 Force equations summed up 8.4 Derivation of Aircraft Equations of Motion (contd.) 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 8.6 Standard Bifurcation Analysis (SBA) 8.6.1 Application of SBA to F-18/HARV Dynamics 8.7 Extended Bifurcation Analysis (EBA) 8.7.1 Straight and level flight trim 8.7.2 Co-ordinated (zero sideslip) level turn trim 8.7.3 Performance and Stability Analysis Exercise Problems Appendix 8.1: Linearized Aircraft Equations of Motion Appendix 8.2: F-18 data Appendix 8.3: Equations and aircraft data used for roll-maneuver 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

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Author(s)

Biography

Dr. Nandan K Sinha is on the faculty of the Department of Aerospace Engineering at the Indian Institute of Technology (IIT) Madras, India, where he is currently serving as professor since July 2014. Dr. Sinha has Bachelors, Masters, and PhD degrees in Aerospace Engineering, all from IITs. Post-PhD, he worked as a visiting scholar in the applied dynamics group at the TU-Darmstadt, Germany for three years, before joining IIT Madras in 2006. Dr. Sinha has over one and half decade experience of teaching courses in flight mechanics, vibrations, controls, and nonlinear dynamics. His research interests evolve around design, dynamics, control and guidance of aerospace vehicles working on several funded projects from various agencies. He is known for his popular video lecture series on Flight Dynamics available on youtube and web-based lecture series on Introduction to Space Technology, both via NPTEL resources, an initiative of MHRD, Govt of India. He has co-authored books "Elementary Flight Dynamics with an Introduction to Bifurcation and Continuation Methods" and "Advanced Flight Dynamics with Elements of Flight Control" with Dr. N Ananthkrishnan both published by CRC press, USA in 2014 and 2017, respectively. In recognition of his contribution to the field of aerospace engineering, Dr. Sinha was nominated to and has been a participant of the International Visitors Leadership Program (IVLP) organized by the Department of State, USA in the year 2018. Dr. Sinha is a senior member of the AIAA and has served as reviewer and associate editor for many reputed journals and conferences. Dr N Ananthkrishnan is an Independent Consultant presently based out of Mumbai (India) with over twenty-five years’ experience in academia and industry in multi-disciplinary research and development across a wide spectrum from Combustion Systems to Airplane Aerodynamics to Flight Control & Guidance. Over the past decade and a half, he has largely worked with businesses in the Mumbai/Pune area and Bangalore in India, and in Daejeon (South Korea), and with a few select academic institutes. His recent work has focused on the broad area of Aerospace Systems Design & Integration with emphasis on Atmospheric Flight Mechanics & Control and Air-breathing Propulsion Systems. He has previously served on the faculty of Aerospace Engineering at the Indian Institute of Technology, IIT Bombay at Mumbai (India) and as a Visiting Faculty Member at the California Institute of Technology at Pasadena, CA (USA) and at KAIST (South Korea). He received the “Excellence in Teaching” award at IIT Bombay in the year 2000. He has authored two books (with NK Sinha), Elementary Flight Dynamics with an Introduction to Bifurcation and Continuation Methods (2014), and Advanced Flight Dynamics with Elements of Flight Control (2017), both published by CRC Press, Taylor & Francis, USA. He received his education in Aerospace Engineering at the Indian Institutes of Technology majoring in Flight Mechanics & Control, Aerodynamics, Aircraft Design, and Nonlinear Systems. He is Associate Fellow, American Institute of Aeronautics & Astronautics (AIAA) and has served a term as a member of the AIAA Atmospheric Flight Mechanics Technical Committee.