Aircraft Aerodynamic Design

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®, Python and Rhinoceros® 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 codes

Aircraft 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.

Autorentext

András Sóbester is a Senior Lecturer in Aeronautical Engineering at the University of Southampton. Beyond aircraft geometry parameterization, his research interests include design optimization techniques (in particular, evolutionary algorithms, machine learning systems and surrogate model-assisted search heuristics), high altitude flight (on fixed wings or balloon-borne) and the use of additive manufacturing techniques in aircraft design.
In terms of applying these technologies, his main focus is on the design of high altitude unmanned air vehicles for scientific applications. He leads the ASTRA (Atmospheric Science Through Robotic Aircraft) initiative, which aims to develop high altitude unmanned air systems for meteorological and Earth science research. Previous work includes research into reducing the environmental impact of passenger airliners through unconventional airframe geometries, undertaken as part of a Royal Academy of Engineering (RAEng) Research Fellowship.
András also lectures on the University's Aeronautical Engineering undergraduate course - he leads the Aircraft Operations and Mechanics of Flight, and the Aircraft Design modules.

Alexander I. J. Forrester was born and brought up in Wirksworth, Derbyshire in the north of England. He studied for a Masters in aerospace engineering, followed by a PhD in computational engineering at the University of Southampton where he is now a Senior Lecturer.
He is a member of the Computational Engineering and Design Research Group and the Institute for Life Sciences. His research interests lie in the efficient use of simulation and experiments in design optimization.
Alex leads the teaching of engineering design across the University's Mechanical, Aeronautical and Ship Science first-year undergraduate courses. He also teaches design optimization to postgraduate level and supervises the University's undergraduate-developed human powered aircraft.

Zusammenfassung

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®, Python and Rhinoceros® 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 codes
  Aircraft 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.

Inhalt
Series Preface xi Preface xiii

1 Prologue 1

2 Geometry Parameterization: Philosophy and Practice 7

2.1 A Sense of Scale 7

2.1.1 Separating Shape and Scale 7

2.1.2 Nondimensional Coefficients 9

2.2 Parametric Geometries 11

2.2.1 Pre-Optimization Checks 13

2.3 What Makes a Good Parametric Geometry: Three Criteria 15

2.3.1 Conciseness 15

2.3.2 Robustness 16

2.3.3 Flexibility 16

2.4 A Parametric Fuselage: A Case Study in the Trade-Offs of Geometry Optimization 18

2.4.1 Parametric Cross-Sections 18

2.4.2 Fuselage Cross-Section Optimization: An Illustrative Example 22

2.4.3 A Parametric Three-Dimensional Fuselage 27

2.5 A General Observation on the Nature of Fixed-Wing Aircraft Geometry Modelling 29

2.6 Necessary Flexibility 30

2.7 The Place of a Parametric Geometry in the Design Process 31

2.7.1 Optimization: A Hierarchy of Objective Functions 31

2.7.2 Competing Objectives 32

2.7.3 Optimization Method Selection 35

2.7.4 Inverse Design 37

3 Curves 41

3.1 Conics and B´ezier Curves 41

3.1.1 Projective Geometry Construction of Conics 42

3.1.2 Parametric Bernstein Conic 43

3.1.3 Rational Conics and B´ezier Curves 49

3.1.4 Properties of B´ezier Curves 50

3.2 B´ezier Splines 51

3.3 Ferguson's Spline 52

3.4 B-Splines 57

3.5 Knots 59

3.6 Nonuniform Rational Basis Splines 60

3.7 Implementation in Rhino 64

3.8 Curves for Optimization 65

4 Surfaces 67

4.1 Lofted, Translated and Coons Surfaces 67

4.2 B´ezier Surfaces 69

4.3 B-Spline and Nonuniform Rational Basis Spline Surfaces 74

4.4 Free-Form Deformation 76

4.5 Implementation in Rhino 82

4.5.1 Nonuniform Rational Basis Splines-Based Surfaces 82

4.5.2 Free-Form Deformation 82

4.6 Surfaces for Optimization 8…