4.4.1 Aircraft trihedron (G, X1, Y1, Z1) with respect to the reference trihedron (G, X0, Y0, Z0) 39
4.4.2 Aerodynamic trihedron of the aircraft (G, Xva, Yva, Zva) with respect to the aircraft trihedron (G, Xe, Ye, Ze) 40
4.5 Relative positions of the various trihedra40
4.5.1 Position of the aircraft trihedron with respect to the local geographical trihedron 40
4.5.2 Position of the aerodynamic trihedron with respect to the terrestrial trihedron 43
4.5.3 Position of the aircraft trihedron in relation to the aerodynamic speed trihedron 46
4.5.4 Position of the aircraft trihedron in relation to the balance trihedron 48
4.5.5 Position of the terrestrial trihedron in relation to the local geographic trihedron 50
Chapter 5 Movement of a Solid 53
5.1 Rotation of a solid around a fixed point 53
5.2 Kinematics of a solid57
5.3 Reference framework60
5.3.1 Absolute reference 60
5.3.2 Relative reference60
5.3.3 Drive movement61
5.3.4 Goal 61
5.3.5 Change of reference framework 61
5.3.6 Change of reference: conclusion and summary 67
5.4 Components of the instantaneous velocity vector of the aircraft reference (O, ie, je, ke)E with respect to the local geographic reference (O, ilgt, jlgt, klgt)LGT in the aircraft reference 70
5.5 Equations of accelerations and forces in the aircraft frame (O, ie, je, ke)E 74
5.6 Determination of load factors in the aircraft reference (O, ie, je, ke)E 77
5.7 Case where the speeds and accelerations are provided at a point other than G77
5.8 Coordinates of the aerodynamic speed in aircraft axes 79
5.9 Equations of moments in the aircraft frame (O, ie, je, ke)E 80
5.10 Forces and moments applied to the aircraft85
5.10.1 Force of gravity85
5.10.2 Forces and moments of propulsion 86
5.10.3 Aerodynamic forces and moments 86
5.10.4 Forces and inertia torques86
Chapter 6 Aircraft Characteristics 87
6.1 Aerodynamics problems posed by aircraft 87
6.1.1 Drag 87
6.1.2 Lift 89
6.1.3 Reynolds number90
6.1.4 Flow velocity 90
6.1.5 Stability of an aircraft 91
6.1.6 Resistance of structures92
6.1.7 Sizing of an aircraft 93
6.2 Load factor 93
6.2.1 Definition of the load factor93
6.2.2 Definition of load factor requirements 93
Chapter 7 Aircraft Simulation Model95
7.1 Simulation model of the atmosphere 96
7.2 Propulsive coefficients 96
7.3 Mass coefficients 96
7.4 Aerodynamic coefficients 97
7.5 Equations of motion 98
7.6 Introduction of wind104
Chapter 8 Processing of Trajectography Information 107
8.1 Telemeasured parameters 107
8.2 Smoothing, first derivation and second derivation 107
8.3 Performance calculation108
8.3.1 Change of coordinates to move from the trihedron (O, Xc, Yc, Zc) to the trihedron (O, X0, Y0, Z0)108
8.3.2 Aircraft speed relative to the ground109
8.3.3 Aerodynamic speed and Mach number 109
8.4 Aerodynamic route and slope 111
8.5 Determination of the angle ψ 114
8.6 Load factors in the aerodynamic trihedron (O, Xa, Yaf, Zr) 114
8.7 Processing of data from the inertial unit (in the aircraft frame) 115
8.7.1 Load factor conversion 116
8.7.2 Calculation of accelerations at the center of gravity 118
8.7.3 Speed conversion118
8.7.4 Calculation of Ψ120
8.7.5 Recomposition of the trajectory 120
8.8 Determination of some aerodynamic parameters 120
8.8.1 Determination of the incidence α and sideslip β 120
8.8.2 Determination of ψac121
8.8.3 Determination of θ 128
8.9 Determination of load factors (nx1, ny1, nz1) in the aircraft trihedron 129
8.10 Determination of CY and Cz 131
8.11 Determination of the total incidence132
8.12 Determination of the longitudinal attitude compared to the local horizontal plane 132
8.13 Determination of drag coefficients 136
8.14 Determination of the pushing force 137
Chapter 9 Quaternion Methods 139
9.1 Goal 139
9.2 Reminder of the axis change formulas using Euler angles 140
9.3 Olinde-Rodrigues’s formulas: definition of quaternions 140
Glossary 161
List of Abbreviations 165
References 169
Index 171
Performance calculations can be classified into three main types: lift, thrust and slope. Firstly, since the lift profile is known and unmodifiable from the time an aircraft is designed, the mass at a given speed or the speed at a given mass must be determined. Then, once the thrust of the engines and the mass are known, the slope must be calculated. Finally, once the slope is known (for example, level flight) as well as the mass, it is necessary to deduce the thrust; this is the position of the throttle control lever that ensures balance. The corresponding consumption must then be defined. Performance specifications for customer aircraft, such as manoeuvrability, fuel consumption, maintenance, safety and testability, have become ever more demanding with each generation of equipment. Major technical advances have been required: wing profiles, engines, materials to reduce mass, etc. This book presents a theoretical approach to flight mechanics that makes it possible to grasp the subject and links it with the empirical approach of manufacturers.
About the Author Gilles Louis is an engineer at Polytech Nancy, France, and currently works for Thalès AVS.