The cost of exploring a k-dimensional design space at a sampling density n is of the order nk. In view of this “curse of dimensionality,” the paper explores the possibility of reducing the dimensionality of parametric airfoil definitions to as low as one, to minimize their cost impact on full-airframe conceptual design studies. A formulation based on nonuniform rational B-splines is introduced in which the parametric airfoil is constructed in a reduceddimensionality space defined in terms of a small number of basis geometries. These bases are airfoils themselves, selected to represent key features of their class; we use them as learning cases or case-based representations of our knowledge of what makes a nonuniform rational B-splines curve an airfoil: moreover, an airfoil belonging to a certain class. This study focuses on supercritical sections, but the template presented here can also be applied to other types of airfoils and, indeed, to other classes of curves and surfaces
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