Modeling of Complex Systems Application to Aeronautical Dynamics

Mr Anh-Tuan PHAM graduated from the INSTITUTE OF SPACE AND AERONAUTICS (ISAE / TOULOUSE). Former research and development engineer in sectors like Aerospace (ONERA) and Automotive (Peugeot) during the period 1962-2002. Now retired and Professor of Aircraft and Automotive at ESTACA (Paris).

Mr Emmanuel GRUNN, former specialist engineer of mechanical design inside RENAULT affiliates. Now Professor of Automatics Systems at ESTACA (Paris).

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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