The quest for a truly parsimonious airfoil parameterisation scheme

Description/Abstract

The conceptual phase of the aircraft design process demands a parsimo-
nious 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 di-
mensionality' 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 can-
didate 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 de-
signer, 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 pa-
per 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
of-the-shelf Computer Aided Design engine.