Nonlinear geometric decomposition of airfoils into the thickness and camber contributions

In the thin airfoil theory, the camber line and the thickness distribution of general airfoils are mainly extracted by a linear combination of the upper and lower surfaces, giving rise to geometric distortions at the leading edge. Furthermore, despite the recent effort to obtain analytic expressions for the zero-lift angle of attack and quarter-chord moment coefficient, analytic generalizations are needed for the camber line component in the trigonometric series coefficients. In this sense, the present paper proposes a straightforward algorithm to extract the camber line and thickness distribution of general-shaped airfoils based on a finite difference method and the Bézier curve fitting. Integrals in the thin airfoil theory involving a Bernstein basis are performed, leading to series coefficients related to Gegenbauer polynomials. The algorithm is validated against analytical expressions of the NACA airfoils without introducing or adapting geometric parameters, and the results demonstrate good accuracy. In addition, the proposed algorithm indicated a significantly different geometric behavior for the SD7003 and E387 airfoils’ camber slope at the leading edge in contrast with the classical linear approximation. Moreover, the method can be coupled conveniently in recent unsteady aerodynamic models established on the thin airfoil theory to obtain closed-form expressions for general airfoils.