Flight Mechanics Modeling and Analysis

567 Pages·2023·35.032 MB·English

by  Jitendra R. Raol, Jatinder Singh

Flight Mechanics Modeling
and Analysis
Flight Mechanics Modeling and Analysis comprehensively covers flight mechanics
and flight dynamics using a systems approach.
This book focuses on applied mathematics and control theory in its discussion of
flight mechanics to build a strong foundation for solving design and control prob-
lems in the areas of flight simulation and flight data analysis. The second edition has
been expanded to include two new chapters and coverage of aeroservoelastic topics
and engineering mechanics, presenting more concepts of flight control and aircraft
parameter estimation.
This book is intended for senior undergraduate aerospace students taking Aircraft
Mechanics, Flight Dynamics & Controls, and Flight Mechanics courses. It will also be
of interest to research students and R&D project-scientists of the same disciplines.
Including end-of-chapter exercises and illustrative examples with a MATLAB®-
based approach, this book also includes a Solutions Manual and Figure Slides for
adopting instructors.
Features:
• Covers flight mechanics, flight simulation, flight testing, flight control, and
aeroservoelasticity.
• Features artificial neural network- and fuzzy logic-based aspects in modeling
and analysis of flight mechanics systems: aircraft parameter e stimation and
reconfiguration of control.
• Focuses on a systems-based approach.
• Includes two new chapters, numerical simulation examples with MATLAB®-
based implementations, and end-of-chapter exercises.
• Includes a Solutions Manual and Figure Slides for adopting instructors.

Flight Mechanics Modeling
and Analysis
Second Edition
Jitendra R. Raol
Jatinder Singh
MATLAB® is a trademark of The MathWorks, Inc. and is used with permission. The MathWorks
does not warrant the accuracy of the text or exercises in this book. This book’s use or discus-
sion of MATLAB® software or related products does not constitute endorsement or sponsorship by
The MathWorks of a particular pedagogical approach or particular use of the MATLAB® software.
Second edition published 2023
by CRC Press
6000 Broken Sound Parkway NW, Suite 300, Boca Raton, FL 33487-2742
and by CRC Press
4 Park Square, Milton Park, Abingdon, Oxon, OX14 4RN
CRC Press is an imprint of Taylor & Francis Group, LLC
© 2023 Jitendra R. Raol and Jatinder Singh
First edition published by CRC Press 2008
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cannot assume responsibility for the validity of all materials or the consequences of their use. The authors and
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Library of Congress Cataloging‑in‑Publication Data
Names: Raol, J. R. (Jitendra R.), 1947- author. | Singh, Jatinder, 1964- author.
Title: Flight mechanics modeling and analysis / Jitendra R. Raol, Jatinder Singh.
Description: Second edition. | Boca Raton, FL : CRC Press, [2023] |
Includes bibliographical references and index. |
Identifiers: LCCN 2022038871 (print) | LCCN 2022038872 (ebook) |
ISBN 9781032276090 (hbk) | ISBN 9781032276106 (pbk) | ISBN 9781003293514 (ebk)
Subjects: LCSH: Flight control–Simulation methods. | Aerodynamics–Mathematics. |
Airplanes–Control systems–Mathematical models.
Classification: LCC TL589.4 .R36 2023 (print) | LCC TL589.4 (ebook) |
DDC 629.132/3011–dc23/eng/20221018
LC record available at https://lccn.loc.gov/2022038871
LC ebook record available at https://lccn.loc.gov/2022038872
ISBN: 9781032276090 (hbk)
ISBN: 9781032276106 (pbk)
ISBN: 9781003293514 (ebk)
DOI: 10.1201/9781003293514
Typeset in Times
by codeMantra
Access the Support Material: www.routledge.com/9781032276090
This edition is dedicated
to Dr. S. Balakrishna
who had pioneered the activity in the late 60’s in the country,
and for his immense contributions to mainly the experimental
(as well as theoretical) flight mechanics and control, one of the
most thriving, formidable and difficult disciplines in India;
And
in loving memory to
Dr. S. Srinathkumar
who dedicated his life time in pursuit of flight control,
and was a main architect for the LCA Control Laws.

Contents
Preface.....................................................................................................................xix
Acknowledgements .................................................................................................xxi
Authors .................................................................................................................xxiii
Introduction ..............................................................................................................1
I.1 Modeling ....................................................................................2
I.2 Flight Simulation .......................................................................3
I.3 Flight Control ............................................................................4
I.4 Artificial Neural Networks (ANNs) in Control .........................4
I.5 Fuzzy Logic-Based Control .......................................................5
I.6 Evaluation of Aircraft Control-Pilot Interactions ......................6
I.7 Chapter Highlights ....................................................................8
References ..........................................................................................10
Chapter 1 Aerodynamic Principles and Fundamentals .......................................13
1.1 Aerodynamic Concepts and Relationships ...............................13
1.1.1 Air Pressure .................................................................13
1.1.2 Air Density ..................................................................14
1.1.3 Air Temperature ..........................................................15
1.1.4 Altitudes ......................................................................15
1.1.5 Airspeeds-IAS, CAS, EAS, TAS ................................16
1.1.6 Bernoulli’s Continuity Equations ................................18
1.1.7 Mach Number .............................................................20
1.1.8 Reynold’s Number ......................................................20
1.1.9 Viscosity ......................................................................21
1.2 Aircraft Force Parameters ........................................................21
1.2.1 Lift ...............................................................................21
1.2.2 Weight ........................................................................23
1.2.3 Thrust .........................................................................23
1.2.4 Drag ............................................................................23
1.2.5 Load Factor.................................................................25
1.2.6 Drag Polars .................................................................25
1.3 Aerodynamic Derivatives – Preliminary Determination ........25
1.4 Aircraft Propulsion and Its Performance ................................26
1.5 Aircraft Sensors-Instrumentation Systems .............................27
1.5.1 Air-Data Instruments .................................................27
1.5.2 Pressure Altimeter ......................................................28
1.5.3 Air Speed Indicator ....................................................28
1.5.4 Mach Meter ................................................................28
1.5.5 Vertical Speed Indicator .............................................28
1.5.6 Accelerometers ...........................................................29
vii
viii Contents
1.6 Energy Awareness, Convergence, and Management ...............29
1.7 Angle of Attack Awareness and Management ........................29
Appendix 1A Airflow ........................................................................30
1A.1 Boundary Layer ...........................................................31
Appendix 1B Aircraft Engines ..........................................................31
1B.1 Engine Thrust Computations ......................................32
1B.2 F or Turbojet-Type Engine ............................................33
Epilogue .............................................................................................33
References ..........................................................................................33
Chapter 2 Engineering Dynamics .......................................................................35
2.1 Introduction .............................................................................35
2.2 Kinematics ...............................................................................36
2.2.1 Rectangular Cartesian Coordinates ...........................36
2.2.2 Curvilinear Coordinates .............................................37
2.3 Relative Motion .......................................................................38
2.3.1 Displacement and Time Derivatives ..........................38
2.3.2 Angular Velocity and Acceleration ............................42
2.3.3 Velocity and Acceleration Using a Moving
Reference Frame ..........................................................43
2.4 Kinematics of Constraint Rigid Bodies ...................................44
2.4.1 General Equations ......................................................44
2.4.2 Eulerian Angles ..........................................................45
2.5 Inertial Effects .........................................................................46
2.5.1 Linear and Angular Momentum ................................46
2.5.2 Inertial Properties .......................................................50
2.5.3 Rate of Change of Angular Momentum .....................51
2.6 Newton–Euler Equations of Motion ........................................51
2.6.1 Fundamental Equations and Planar Motion ...............51
2.6.2 N-E Equations for a System .......................................53
2.6.3 Principles of Momentum and Energy ........................54
2.7 Analytics Mechanics ...............................................................55
2.7.1 Generalized Coordinates and Kinematical
Constraints...................................................................55
2.7.2 Virtual Displacements ................................................56
2.7.3 Generalized Forces .....................................................58
2.7.4 Lagrange’s Equations .................................................59
2.8 Constraint Generalized Coordinates .......................................61
2.9 Alternative Formulations .........................................................62
2.9.1 Hamilton’s Principle ...................................................62
2.9.2 Generalized Momentum Principles ...........................64
2.10 Gyroscopic Effects ..................................................................66
2.10.1 Free Motion of Axisymmetric Body ..........................66
Epilogue .............................................................................................69
Exercises .............................................................................................69
References ..........................................................................................69
Contents ix
Chapter 3 Equations of Motion ...........................................................................71
3.1 Introduction .............................................................................71
3.2 Rigid Body Equations of Motion (EOM) ................................72
3.3 Resolution of Inertial Forces and Moments ............................78
3.4 Resolution of Aerodynamic, Gravity, and Thrust Forces ........80
3.5 Complete Sets of EOM ............................................................86
3.5.1 Rectangular Form .......................................................86
3.5.2 Polar Form ..................................................................87
3.6 Missile Dynamic Equations ....................................................90
3.7 Rotorcraft Dynamics ...............................................................91
3.7.1 Momentum Theory ....................................................92
3.7.2 Blade-Element Theory ...............................................93
3.7.3 Rotorcraft Modeling Formulations ............................94
3.7.4 Limitations of Rigid Body Model ..............................95
Appendix 3A Aircraft Geometry and Coordinate Systems ..............96
3A.1 Aircraft Axis and Notations .......................................97
3A.2 Axes-Coordinates Transformations and Quaternions ....97
3A.3 Transformation from Body to Earth Axis ..................99
3A.4 Transformation from Stability Axis to Body Axis ....99
3A.5 Transformation from Stability Axis to Wind Axis (w) ......100
3A.6 Transformation from Body Axis to Wind Axis .......100
Appendix 3B Helicopter Aerodynamics .........................................100
Appendix 3C Types of Helicopters and Controls ...........................102
3C.1 Rotor Systems ...........................................................102
3C.1.1 Fully Articulated Rotor.............................102
3C.1.2 Semi-Rigid/Teetering Rotor and
Rigid Rotor ...............................................102
3C.2 Helicopter Controls ..................................................103
Epilogue ...........................................................................................104
Exercises ...........................................................................................104
References ........................................................................................105
Chapter 4 Aerodynamic Derivatives .................................................................107
4.1 I ntroduction ...........................................................................107
4.2 B asic Aerodynamic Forces and Moments .............................108
4.3 A erodynamic Parameters ......................................................110
4.3.1 Definition of Aerodynamic Derivatives ...................111
4.3.2 Longitudinal Derivatives ..........................................113
4.3.2.1 Effect of Forward/Axial Speed u along
the X-Axis: (X , Z , M) ..............................113
u u u
4.3.2.2 Effect of Change in Vertical Speed w
(Equivalently AOA) along the Vertical
Z-Axis (X , Z , M ) ....................................117
w w w
4.3.2.3 Effect of Change in Pitch Rate q:
(X , Z , M) .................................................119
q q q