Optimal aircraft design is impossible without a parametric representation of the geometry of the airframe. We need a mathematical model equipped with a set of controls, or design variables, which generates different candidate airframe shapes in response to changes in the values of these variables. This model's objectives are to be flexible and concise, and capable of yielding a wide range of shapes with a minimum number of design variables. Moreover, the process of converting these variables into aircraft geometries must be robust. Alas, flexibility, conciseness and robustness can seldom be achieved simultaneously.Aircraft Aerodynamic Design: Geometry and Optimization addresses this problem by navigating the subtle trade-offs between the competing objectives of geometry parameterization. It beginswith the fundamentals of geometry-centred aircraft design, followed by a review of the building blocks of computational geometries, the curve and surface formulations at the heart of aircraft geometry. The authors then cover a range of legacy formulations in the build-up towards a discussion of the most flexible shape models used in aerodynamic design (with a focus on lift generating surfaces). The book takes a practical approach and includes MATLAB(r), Python and Rhinoceros(r) code, as well as 'real-life' example case studies.Key features:* Covers effective geometry parameterization within the context of design optimization* Demonstrates how geometry parameterization is an important element of modern aircraft design* Includes code and case studies which enable the reader to apply each theoretical concept either as an aid to understanding or as a building block of their own geometry model* Accompanied by a website hosting codesAircraft Aerodynamic Design: Geometry and Optimization is a practical guide for researchers and practitioners in the aerospace industry, and a reference for graduate and undergraduate students in aircraft design and multidisciplinary design optimization.

Series Preface xiPreface xiii1 Prologue 12 Geometry Parameterization: Philosophy and Practice 72.1 A Sense of Scale 72.1.1 Separating Shape and Scale 72.1.2 Nondimensional Coefficients 92.2 Parametric Geometries 112.2.1 Pre-Optimization Checks 132.3 What Makes a Good Parametric Geometry: Three Criteria 152.3.1 Conciseness 152.3.2 Robustness 162.3.3 Flexibility 162.4 A Parametric Fuselage: A Case Study in the Trade-Offs of Geometry Optimization 182.4.1 Parametric Cross-Sections 182.4.2 Fuselage Cross-Section Optimization: An Illustrative Example 222.4.3 A Parametric Three-Dimensional Fuselage 272.5 A General Observation on the Nature of Fixed-Wing Aircraft Geometry Modelling 292.6 Necessary Flexibility 302.7 The Place of a Parametric Geometry in the Design Process 312.7.1 Optimization: A Hierarchy of Objective Functions 312.7.2 Competing Objectives 322.7.3 Optimization Method Selection 352.7.4 Inverse Design 373 Curves 413.1 Conics and B¿ezier Curves 413.1.1 Projective Geometry Construction of Conics 423.1.2 Parametric Bernstein Conic 433.1.3 Rational Conics and B¿ezier Curves 493.1.4 Properties of B¿ezier Curves 503.2 B¿ezier Splines 513.3 Ferguson's Spline 523.4 B-Splines 573.5 Knots 593.6 Nonuniform Rational Basis Splines 603.7 Implementation in Rhino 643.8 Curves for Optimization 654 Surfaces 674.1 Lofted, Translated and Coons Surfaces 674.2 B¿ezier Surfaces 694.3 B-Spline and Nonuniform Rational Basis Spline Surfaces 744.4 Free-Form Deformation 764.5 Implementation in Rhino 824.5.1 Nonuniform Rational Basis Splines-Based Surfaces 824.5.2 Free-Form Deformation 824.6 Surfaces for Optimization 845 Aerofoil Engineering: Fundamentals 915.1 Definitions, Conventions, Taxonomy, Description 915.2 A 'Non-Taxonomy' of Aerofoils 925.2.1 Low-Speed Aerofoils 935.2.2 Subsonic Aerofoils 935.2.3 Transonic Aerofoils 935.2.4 Supersonic Aerofoils 945.2.5 Natural Laminar Flow Aerofoils 945.2.6 Multi-Element Aerofoils 955.2.7 Morphing and Flexible Aerofoils 985.3 Legacy versus Custom-Designed Aerofoils 985.4 Using Legacy Aerofoil Definitions 995.5 Handling Legacy Aerofoils: A Practical Primer 1015.6 Aerofoil Families versus Parametric Aerofoils 1026 Families of Legacy Aerofoils 1036.1 The NACA Four-Digit Section 1036.1.1 A One-Variable Thickness Distribution 1046.1.2 A Two-Variable Camber Curve 1056.1.3 Building the Aerofoil 1056.1.4 Nomenclature 1066.1.5 A Drawback and Two Fixes 1076.1.6 The Distribution of Points: Sampling Density Variations and Cusps 1076.1.7 A MATLAB(r) Implementation 1096.1.8 An OpenNURBS/Rhino-Python Implementation 1116.1.9 Applications 1126.2 The NACA Five-Digit Section 1136.2.1 A Three-Variable Camber Curve 1136.2.2 Nomenclature and Implementation 1166.3 The NACA SC Families 1186.3.1 SC(2) 1187 Aerofoil Parameterization 1237.1 Complex Transforms 1237.1.1 The Joukowski Aerofoil 1247.2 Can a Pair of Ferguson Splines Represent an Aerofoil? 1257.2.1 A Simple Parametric Aerofoil 1257.3 Kulfan's Class- and Shape-Function Transformation 1277.3.1 A Generic Aerofoil 1287.3.2 Transforming a Legacy Aerofoil 1307.3.3 Approximation Accuracy 1327.3.4 The Kulfan Transform as a Filter 1357.3.5 Computational Implementation 1377.3.6 Class- and Shape-Function Transformation in Optimization: Global versus Local Search 1397.3.7 Capturing the Shared Features of a Family of Aerofoils 1407.4 Other Formulations: Past, Present and Future 1428 Planform Parameterization 1458.1 The Aspect Ratio 1458.1.1 Induced Drag 1488.1.2 Structural Efficiency 1508.1.3 Airport Compatibility 1508.1.4 Handling 1518.2 The Taper Ratio 1528.3 Sweep 1538.3.1 Terminology 1538.3.2 Sweep in Transonic Flight 1558.3.3 Sweep in Supersonic Flight 1578.3.4 Forward Sweep 1588.3.5 Variable Sweep 1598.3.6 Swept-Wing 'Growth' 1618.4 Wing Area 1628.4.1 Constraints on the Wing Area 1628.5 Planform Definition 1678.5.1 From Sketch to Geometry 1678.5.2 Introducing Scaling Factors: A Design Heuristic and a Simple Example 1688.5.3 More Complex Planforms and an Additional Scaling Factor 1698.5.4 Spanwise Chord Variation 1719 Three-Dimensional Wing Synthesis 1759.1 Fundamental Variables 1759.1.1 Twist 1759.1.2 Dihedral 1769.2 Coordinate Systems 1779.2.1 Cartesian Systems 1779.2.2 A Wing-Bound, Curvilinear Dimension 1819.3 The Synthesis of a Nondimensional Wing 1819.3.1 Example: A Blended Box Wing 1839.3.2 Example: Parameterization of a Blended Winglet 1879.4 Wing Geometry Scaling. A Case Study: Design of a Commuter Airliner Wing 1899.5 Indirect Wing Geometry Scaling 19610 Design Sensitivities 19910.1 Analytical and Finite-Difference Sensitivities 19910.2 Algorithmic Differentiation 20110.2.1 Forward Propagation of Tangents 20110.2.2 Reverse Mode 20310.3 Example: Differentiating an Aerofoil from Control Points to Lift Coefficient 20410.4 Example Inverse Design 21211 Basic Aerofoil Analysis: AWorked Example 21711.1 Creating the .dat and .in files using Python 21811.2 Running XFOIL from Python 21912 Human-Powered Aircraft Wing Design: A Case Study in Aerodynamic Shape Optimization 22312.1 Constraints 22512.2 Planform Design 22512.3 Aerofoil Section Design 22612.4 Optimization 22612.4.1 NACA Four-Digit Wing 22712.4.2 Ferguson Spline Wing 22912.5 Improving the Design 23013 Epilogue: Challenging Topological Prejudice 237References 239Index 243