Spline-based airfoil curvature smoothing and its applications

The performance of a transonic airfoil is directly related to the airfoil curvature profile and its smoothness. Whereas univariate data smoothing has been studied extensively, very little research has been conducted on curvature smoothing. Consequently, airfoil smoothing in design environments is largely based on heuristic methods, and there is an art to the generation of an unbiased smooth fit of the airfoil's curvature profile by the modification of its geometry. In this paper, the sum of squares of the third derivative jumps is used as a curvature smoothness measure for the development of a spline-based airfoil smoothing method, called constrained fitting for airfoil curvature smoothing (CFACS). CFACS can take out dramatic curvature oscillations with extremely small geometry changes and smooth an airfoil segment without creating curvature oscillations near the endpoints. Visually, CFACS. generates an unbiased smooth fit of the curvature profile. Examples demonstrating the utility of CFACS show how the smoothing can be tailored to promote desirable characteristics in performance trade studies.