# Modeling of Complex Systems: Application to Aeronautical Dynamics

ISBN: 978-1-84821-448-4
326 pages
November 2013, Wiley-ISTE

## Description

In the field of aeronautical dynamics, this book offers readers a design tool which enables them to solve the different problems that can occur during the planning stage of a private project. The authors present a system for the modeling, design and calculation of the flying qualities of airplanes and drones, with a complete mathematical model by Matlab/Simulink. As such, this book may be useful for design engineers as well as for keen airplane amateurs.
The authors expound the various phases involved in the design process of an airplane, starting with the formulation of a design tool, under the form of a 0D mathematical model (dimensionless, time dependent), before moving on to explore the behavior of the airplane under certain circumstances and offering insights into the optimization of airplane flying qualities. As validation of this model, they present a numerical result, drawn from data collected on an existing plane – the Concorde.
The dimensional process is then explored and applied to a realistic drone project. Recommendations on the development of the principal characteristics of the plane (i.e. mass distribution, air load, wing span) are given.

Contents

1. 0D Analytical Modeling of theAirplane Motions.
2. Design and Optimizationof an Unmanned Aerial Vehicle (UAV).
3. Organization of the Auto-Pilot.

This book provides a description of the modeling, design, and calculation of the aeronautical qualities of airplanes and drones. Divided into several parts, this book first summarizes all the necessary theoretical developments about the equations of motions and trajectory calculations of the machine. It then goes on to describe practical building processes and considers piloting methods. The last part makes a comparison between theoretical calculations and measured recorded data of the real flying machine.
Accompanied by a complete mathematical model in MATLAB/SIMULINK
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Introduction vii

Chapter 1. 0D Analytical Modeling of the Airplane Motions 1

1.1. References: axis systems on use 2

1.1.1. Galilean reference: R0 2

1.1.2. Airplane reference: RB (body) also called “linked reference” 2

1.1.3. Resultant angular velocity 6

1.2. Equations of motion of the airplane 9

1.2.1. Expression of Newton’s principle 10

1.2.2. Expression of the dynamic momentum 11

1.3. Description of external forces and torques 14

1.3.1. Aerodynamic forces and torques 14

1.3.2. Sign rules 17

1.4. Description of aerodynamic coefficients 18

1.4.1. Drag coefficient: Cx 19

1.4.2. Side lift coefficient CY 19

1.4.3. Vertical lift due to attack angle: CZα 20

1.4.4. Lift due to pitch angular velocity: CZq 21

1.4.5. Roll coefficients (due to β, δl , p) 22

1.4.6. Pitch coefficients (due to α, δm , q , static curvature) 25

1.4.7. Yaw coefficients (due to β, δn, r) 27

1.5. Aerodynamic data of a supersonic airliner for valuation of the software 32

1.6. Horizontal flight as an initial condition 33

1.7. Effect of gravitational forces 36

1.8. Calculation of the trajectory of the airplane in open space 39

1.9. Validation by comparison with ONERA Concorde data 47

1.10. Definitions of aerodynamic coefficients and derivatives 51

1.10.1. Aerodynamic coefficients 51

1.10.2. Total lift coefficient 51

1.10.3. Drag characteristics: (dimensionless) 55

1.10.4. Side lift coefficient: CY (dimensionless) 58

1.10.5. Roll coefficients 59

1.10.6. Pitch coefficients 62

1.10.7. Yaw coefficients 66

Chapter 2. Design and Optimization of an Unmanned Aerial Vehicle (UAV) 69

2.1. General design of the drone 71

2.2. Weight estimation 72

2.3. Size estimation 73

2.4. Mass and inertia evaluation 76

2.4.1. Mass evaluation 76

2.4.2. Measurement of the roll inertia (A) 77

2.4.3. Measurement of pitch inertia (B) 79

2.4.4. Measurement of yaw inertia (C) 80

2.5. Convergence toward the target 82

Chapter 3. Organization of the Auto-Pilot 91

3.1. Position of the drone in open space 93

3.2. The Dog Law 95

3.3. Flight tests 98

3.4. Altitude control system 100

3.5. Altitude measurement on an actual drone 102

Bibliography 111

Index 113

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