Preface

In July 1978 the Journal of Aircraft published a paper titled 'Wing design by numerical optimization'. The authors, Raymond Hicks of the NASA Ames Research Center and Preston Henne of the Douglas Aircraft Company, had identified a set of functions with 'aerofoil-like' shapes, which, when added to a baseline aerofoil in various linear combinations, generated other 'sensible' aerofoil shapes.

This, as a principle, was not new. After all, the National Advisory Committee for Aeronautics was already experimenting with parametric aerofoils in the 1930s. The formulation described by Hicks and Henne (1978) was a new aerofoil family generated in a novel way - building an aerofoil out of weighted shapes, much like one might build a musical sound from multiple harmonics. But this was not the real novelty; how they proceeded to use it was.

Combining the incipient technology of numerical flow simulation (they used a two-dimensional model) with a simple optimization heuristic and their new parametric geometry they performed an automated computational search for a better aerofoil shape.

Here is the idea that thus began to take shape and commence its ascent along the technology readiness level (TRL) ladder of the aerospace industry. A parametric geometry is placed at the heart of the aircraft design process. The design variables influencing its shape are adjusted in some systematic, iterative way, as dictated by an optimization algorithm. The latter is guided by a design performance metric, resulting from a physics-based simulation run on an instance of the parametric geometry.

The TRL rise was to be a slow one, for two reasons. First, because in a world largely reliant on drawing boards for years to come, this was a disruptive idea that would encounter much resistance in this notoriously risk-averse industry. Second, none of the links in the chain of tools required (numerical flow analysis, computational geometry and efficient optimization techniques) would be really ready for some fast optimization action until well into the 1990s.

There is a maxim known by most practitioners of the art, which states that an optimization algorithm will find the slightest flaws in the analysis code (usually comprising a mesher and a partial differential equation solver) and in the geometry model; that is, it will steer the design process precisely towards their weak areas.

This is not (only) due to Sod's law - more fundamental effects are at play. Most computational analyses have a domain of 'safe' operation, outside of which they will either predict unphysically good or unphysically bad performance. Straying into the latter type of area will thus be a self-limiting deviation, but the former will lure the optimizer into 'discovering' amazingly good solutions that do not actually exist in 'real' physics. Sometimes these are obvious (what rookie optimization practitioner has not 'discovered' aerofoils that generate thrust instead of drag?), but more subtle pitfalls abound, and highlighting these remains a challenge in the path of the ubiquitous use of this technology.

Along similar lines, parametric geometry modelling has its own pitfalls, deceptions and hurdles in the path of effective optimal design, and how to avoid (at least some of) them is the subject of this book.

Some of the principles discussed over the pages that follow can be applied to the geometry of any engineering product, but we focus on those aspects of geometry parameterization that are specific to external aircraft surfaces wetted by airflow. Some of the ideas are therefore linked to aerodynamics, and so we will touch upon the relevant aspects of aircraft aerodynamic design - from an engineering perspective. However, this is not a book on aircraft aerodynamics, and, for that matter, nor will it provide the reader with a recipe on how to design an aeroplane. Instead, it is an exposition of concepts necessary for the construction of aircraft geometry that can exploit the capabilities of an optimization algorithm.

The reader may wish to peruse the text simply to gain a theoretical appreciation of some of the issues of aircraft geometry parameterization, but there is plenty to get started with for the more practically minded too. All key concepts are illustrated with code, which can be run 'as is' or can form a building block in the reader's own code. After lengthy deliberations we selected two software platforms to use for this: Mathworks MATLAB® and Python. Some of the Python code calls methods from the OpenNURBS framework, which can be accessed through Robert McNeel & Associates Rhino, a powerful, yet easy to use, lightweight CAD package. Some of the code is reproduced in the text to help illustrate some of the formulations - in each case we selected one of the platforms mentioned above, but in most cases implementations in the others are available too on the website [www.wiley.com/go/sobester] accompanying the book.

Here is a brief sketch of the structure of this book.

After discussion of the general context of aircraft shape description and parameterization (Prologue), in the following chapter (Geometry Parameterization: Philosophy and Practice) we discuss the place of parametric geometries in aircraft design in general and we start the main threads that will be running through this book: the guiding principles of parametric geometry construction and their impact on the effectiveness of the optimization processes we might build upon them.

We next tackle the fundamental building blocks of all aircraft geometries, first in two dimensions (the chapter titled Curves), then in three (Surfaces). Two-dimensional sections through wings (and other lifting surfaces) are perhaps the most widely known and widely discussed aerodynamic geometry primitive, and we dedicate three chapters to them: a general introduction (Aerofoil Engineering: Fundamentals), a review of some of the key Families of Legacy Aerofoils and, arriving at the concept at the heart of this book, Aerofoil Parameterization.

Another classic two-dimensional view of aerodynamics is tackled in the chapter titled Planform Parameterization, thus completing the discussion of all the primitives needed to build a three-dimensional wing geometry - which we do in the chapter Three-Dimensional Wing Synthesis.

The ultimate point of geometry parameterization is, of course, the optimization of objective functions that measure the performance of the object represented by the geometry. Recent years have seen a strong push towards making this process as efficient as possible, and one of the enablers is the efficient computation of the sensitivities of the objective function with respect to the design variables controlling the shape. A number of ways of achieving this are discussed in the chapter titled Design Sensitivities.

The most important concepts are illustrated via examples throughout the book, but there are two more substantial such examples, which warrant chapters of their own: Basic Aerofoil Analysis: A Worked Example and Human-Powered Aircraft Wing Design: A Case Study in Aerodynamic Shape Optimization.

We then bring matters to a close by looking ahead and discussing the area where geometry parameterization is most acutely in need of further development - this is the chapter titled Epilogue: Challenging Topological Prejudice.

Parametric geometry is a vast subject, and a book dedicated even to one of its subsets - in this case, the parametric geometry of the external shape of fixed-wing aircraft - is unlikely to be comprehensive. We hope that, beyond a discussion of the formulations we felt to be the most important, this book succeeds in setting out the key principles that will enable the reader to 'discover', critically evaluate and deploy other formulations not discussed here. Moreover, it should assist in creating new models - essential building blocks of the design tools of the future.

Finally, we would like to acknowledge some of those who helped shape this text through discussions and reviews: Jennifer Forrester, Brenda Kulfan, Andy Keane, Christopher Paulson, James Scanlan, Nigel Taylor, David Toal and Sebastian Walter. We are also indebted to Tom Carter and Eric Willner at Wiley, whose patience and support made the long years of writing this book considerably easier.

Disclaimer: The design methods and examples given in this book and associated software are intended for guidance only and have not been developed to meet any specific design requirements. It remains the responsibility of the designer to independently validate designs arrived at as a result of using this book and associated software. To the fullest extent permitted by applicable law John Wiley & Sons, Ltd. and the authors (i) provide the information in this book and associated software without express or implied warranties that the information is accurate, error free or reliable; (ii) make no and expressly disclaim all warranties as to merchantability, satisfactory quality or fitness for any particular purpose; and accept no responsibility or liability for any loss or damage occasioned to any person or property including loss of income; loss of business profits or contracts; business interruption; loss of the use of money or anticipated savings; loss...