Effects of Nonlinearities on Subsonic Aerodynamic Center

Abstract

A refined mathematical definition for the aerodynamic center of a wing or complete airplane is presented, which allows for inclusion of the trigonometric and aerodynamic nonlinearities. From this definition, analytical relations are developed for both the axial and vertical positions of the aerodynamic center at any angle of attack, independent of whether or not the nonlinearities are included. Results show that, when all nonlinearities are included, the position of the aerodynamic center can change with angle of attack. Because the traditional approximation provides only a fixed axial coordinate, this analysis provides two additional pieces of information about the aerodynamic center, that is, its vertical coordinate and its movement. Two examples are presented, which separate these two effects. The first example uses computational fluid dynamics to show that, when the effects of the nonlinearities are combined with wing sweep at high angles of attack below stall, the aerodynamic center of a planar wing moves significantly aft and below the wing. The second example, which uses an approximate closed-form solution for two lifting surfaces, emphasizes the importance of knowing the vertical position of the aerodynamic center and shows that, in the absence of sweep, its movement with angle of attack is slight.