Abstract: Class-shape-transformation (CST) is a new shape parameterization method which represents the geometries of aircraft shapes with a class function and a shape function. Based on the condition numbers of linear systems and the representation residuals in the parameterization process, a study is performed on the influence of the bernstein polynomial order (BPO) on the numerical uniqueness and the precision of the CST method. Comparisons of parameter number and representation precision between the CST method and B-spline, Hicks-Henne and parametric section(PARSEC) methods are represented in this paper, as well as a supersonic wing shape optimization case using the far-field composite-element (FCE) wave drag optimization method which yields a 61% reduction of wave drag. It is suggested that the CST parameterization is chara-cterized by high precision and low parameter number. In order to achieve sufficient precision and avoid ill-conditioned parameterization, the shape function should be defined by bernstein polynomials of at least 4th order, but no more than 10th order.

Key words: class-shape-transformation, linear system, parameterization, polynomial, drag reduction, shape optimization