Quasi-Steady Effective Angle of Attack and Its Use in Lift-Equivalent Motion Design

The effective angle of attack of an airfoil is a composite mathematical expression from quasi-steady thin-airfoil theory that combines the geometric contribution to the angle of attack with pitching and plunging effects. For a maneuvering airfoil, the instantaneous effective angle of attack is a virtual angle that corresponds to the equivalent lift based on a steady, lift versus angle-of-attack curve. The existing expression for effective angle of attack depends on attached-flow, thin-airfoil, small-angle, and small-camber-slope assumptions. This paper derives a new expression for and effective angle of attack that relaxes the small-angle and small-camber-slope assumptions. The new expression includes effects from pitching, plunging, and surging motions, as well as spatial nonuniformity of the flow. The proposed expression simplifies to the existing quasi-steady expression by invoking the appropriate assumptions. Furthermore, the proposed expression leads to a replacement for the classic zero-lift angle-of-attack equation for steady flow past a thin airfoil, which is compared to experimental values for cambered NACA four-digit airfoils. The new expression is also used for lift-equivalent motion design for a maneuvering airfoil to emulate the effective angle of attack of a nonmaneuvering airfoil encountering a transverse gust under a quasi-steady assumption. Computational fluid dynamics simulations support the use of the proposed effective angle-of-attack expression for lift-equivalent motion design, subject to an attached-flow assumption.