Theory of Lift

Preface xvii Series Preface xxiii PART ONE PLANE IDEAL AERODYNAMICS 1 Preliminary Notions 3 1.2 Aircraft Geometry 5 1.3 Velocity 8 1.4 Properties of Air 8 1.5 Dimensional Theory 13 1.6 Example: NACA Report No. 502 18 1.7 Exercises 19 1.8 Further Reading 22 2 Plane Ideal Flow 25 2.1 Material Properties: The Perfect Fluid 25 2.2 Conservation of Mass 26 2.3 The Continuity Equation 26 2.4 Mechanics: The Euler Equations 27 2.5 Consequences of the Governing Equations 30 2.6 The Complex Velocity 35 2.7 The Complex Potential 41 2.8 Exercises 42 2.9 Further Reading 44 3 Circulation and Lift 47 3.1 Powers of z 47 3.2 Multiplication by a Complex Constant 53 3.3 Linear Combinations of Complex Velocities 54 3.4 Transforming the Whole Velocity Field 56 3.5 Circulation and Outflow 57 3.6 More on the Scalar Potential and Stream Function 61 3.7 Lift 62 3.8 Exercises 64 3.9 Further Reading 65 4 Conformal Mapping 67 4.1 Composition of Analytic Functions 67 4.2 Mapping with Powers of zeta 68 4.3 Joukowsky's Transformation 71 4.4 Exercises 75 4.5 Further Reading 78 5 Flat Plate Aerodynamics 79 5.1 Plane Ideal Flow over a Thin Flat Plate 79 5.2 Application of Thin Aerofoil Theory to the Flat Plate 87 5.3 Aerodynamic Moment 89 5.4 Exercises 90 5.5 Further Reading 91 6 Thin Wing Sections 93 6.1 Thin Aerofoil Analysis 93 6.2 Thin Aerofoil Aerodynamics 98 6.3 Analytical Evaluation of Thin Aerofoil Integrals 101 6.4 Numerical Thin Aerofoil Theory 105 6.5 Exercises 109 6.6 Further Reading 109 7 Lumped Vortex Elements 111 7.1 The Thin Flat Plate at Arbitrary Incidence, Again 111 7.2 Using Two Lumped Vortices along the Chord 114 7.3 Generalization to Multiple Lumped Vortex Panels 117 7.4 General Considerations on Discrete Singularity Methods 117 7.5 Lumped Vortex Elements for Thin Aerofoils 119 7.6 Disconnected Aerofoils 123 7.7 Exercises 125 7.8 Further Reading 125 8 Panel Methods for Plane Flow 127 8.1 Development of the CUSSSP Program 127 8.2 Exercises 137 8.3 Further Reading 139 8.4 Conclusion to Part I: The Origin of Lift 139 PART TWO THREE-DIMENSIONAL IDEAL AERODYNAMICS 9 FiniteWings and Three-Dimensional Flow 143 9.1 Wings of Finite Span 143 9.2 Three-Dimensional Flow 145 9.3 Vector Notation and Identities 145 9.4 The Equations Governing Three-Dimensional Flow 149 9.5 Circulation 150 9.6 Exercises 154 9.7 Further Reading 155 10 Vorticity and Vortices 157 10.1 Streamlines, Stream Tubes, and Stream Filaments 157 10.2 Vortex Lines, Vortex Tubes, and Vortex Filaments 159 10.3 Helmholtz's Theorems 159 10.4 Line Vortices 160 10.5 Segmented Vortex Filaments 161 10.6 Exercises 166 10.7 Further Reading 167 11 Lifting Line Theory 169 11.1 Basic Assumptions of Lifting Line Theory 169 11.2 The Lifting Line, Horseshoe Vortices, and the Wake 169 11.3 The Effect of Downwash 173 11.4 The Lifting Line Equation 174 11.5 The Elliptic Lift Loading 178 11.6 Lift-Incidence Relation 180 11.7 Realizing the Elliptic Lift Loading 182 11.8 Exercises 182 11.9 Further Reading 183 12 Nonelliptic Lift Loading 185 12.1 Solving the Lifting Line Equation 185 12.2 Numerical Convergence 188 12.3 Symmetric Spanwise Loading 189 12.4 Exercises 192 13 Lumped Horseshoe Elements 193 13.1 A Single Horseshoe Vortex 193 13.2 Multiple Horseshoes along the Span 195 13.3 An Improved Discrete Horseshoe Model 200 13.4 Implementing Horseshoe Vortices in Octave 203 13.5 Exercises 206 13.6 Further Reading 207 14 The Vortex Lattice Method 209 14.1 Meshing the Mean Lifting Surface of a Wing 209 14.2 A Vortex Lattice Method 212 14.3 Examples of Vortex Lattice Calculations 216 14.4 Exercises 220 14.5 Further Reading 221 PART THREE NONIDEAL FLOW IN AERODYNAMICS 15 Viscous Flow 225 15.1 Cauchy's First Law of Continuum Mechanics 225 15.2 Rheological Constitutive Equations 227 15.3 The Navier-Stokes Equations 228 15.4 The No-Slip Condition and the Viscous Boundary Layer 228 15.5 Unidirectional Flows 229 15.6 A Suddenly Sliding Plate 230 15.7 Exercises 234 15.8 Further Reading 234 16 Boundary Layer Equations 237 16.1 The Boundary Layer over a Flat Plate 237 16.2 Momentum Integral Equation 241 16.3 Local Boundary Layer Parameters 243 16.4 Exercises 248 16.5 Further Reading 249 17 Laminar Boundary Layers 251 17.1 Boundary Layer Profile Curvature 251 17.2 Pohlhausen's Quartic Profiles 252 17.3 Thwaites's Method for Laminar Boundary Layers 254 17.4 Exercises 260 17.5 Further Reading 261 18 Compressibility 263 18.1 Steady-State Conservation of Mass 263 18.2 Longitudinal Variation of Stream Tube Section 265 18.3 Perfect Gas Thermodynamics 266 18.4 Exercises 270 18.5 Further Reading 271 19 Linearized Compressible Flow 273 19.1 The Nonlinearity of the Equation for the Potential 273 19.2 Small Disturbances to the Free-Stream 274 19.3 The Uniform Free-Stream 275 19.4 The Disturbance Potential 275 19.5 Prandtl-Glauert Transformation 276 19.6 Application of the Prandtl-Glauert Rule 279 19.7 Sweep 284 19.8 Exercises 285 19.9 Further Reading 285 Appendix A Notes on Octave Programming 287 A.1 Introduction 287 A.2 Vectorization 287 A.3 Generating Arrays 290 A.4 Indexing 291 A.5 Just-in-Time Compilation 291 A.6 Further Reading 292 References 292 Glossary 293 Nomenclature 305 Index 309