The quest for a truly parsimonious airfoil parameterisation scheme

The conceptual phase of the aircraft design process demands a parsimonious description of the airframe geometry. While there is no hard and fast upper limit on the affordable number of variables, the so-called 'curse of dimensionality' must always be kept in mind: if a thorough, conceptual level search of a one-variable space can be accomplished by the evaluation of n candidate designs, the same level of thoroughness (however one chooses to define this) will demand nk evaluations in k-dimensional space. Therefore, to make the design search tractable and the complexity of the geometry definition at a level where the effect of the variables can be readily understood by the designer, the number of airframe definition variables should be minimized. This has an impact on all of the components, perhaps most importantly on airfoil-type section definitions that feature on all 'wing-like' surfaces. It is therefore imperative to define these sections as parsimoniously as possible. In this paper we examine a series of parameterization schemes, whose chief conception criterion was conciseness in terms of the number of design variables. Another constraint we are considering is the ease of implementation in a commercial off-the-shelf Computer Aided Design engine