Otto Lilienthal (see Section 1.5) carried out a series of aerodynamic measurements on smal...

Otto Lilienthal (see Section 1.5) carried out a series of aerodynamic measurements on small model wings using first a whirling arm and later stationary models. He tested both flat plate wings and wings with a thin curved (cambered) airfoil. For the flat plate, the resultant aerodynamic force was always inclined behind the per perpendicular to the plate, with an axial force always oriented in the backward direction. However, his data for the cambered airfoil showed that at some angles of attack the resultant aerodynamic force was inclined ahead of the perpendicular to the chord line; for these cases the axial force was oriented in the forward direction. Lilienthal called this forward component a “pushing component” and cited its existence as evidence of the superiority of cambered airfoils. (For more historical detail on this matter, see Anderson, A History of Aerodynamics, Cambridge University Press, 1998.) With the above information as background, show that the aerodynamic condition that results in a forward-facing axial force is

where α is the angle of attack.