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# Lift and drag on airfoils

An airfoil  is a two dimensional cross-section of an airplane wing. Alternatively, an airfoil can be thought of as an infinite wing of constant shape. For airfoil nomenclature see Fig. 4.2.

Figure 4.2: Airfoil nomenclature. The airfoil shown is cambered; an airfoil without camber is called a symmetric airfoil.

The Magnus effect contains the essential ingredient for the generation of lift by an airfoil--that ingredient is circulation of the fluid about the airfoil. Since we are usually interested in large Reynolds number flows, the fluid outside the boundary layer may be treated as being nonviscous. With this assumption, it can be shown that the lift per unit length (or span) of the airfoil for a fluid with density and free stream velocity U, with a circulation about the airfoil is

which is known as the Kutta-Joukowsky Theorem. This is identical to the result for the cylinder, and the physics is the same. The fluid has a higher velocity on the upper surface of the airfoil than on the lower surface, and the pressure on the upper surface is less than that on the lower surface, leading to lift. What determines ? For the rotating cylinder it was simply the angular velocity of the cylinder (combined with the viscosity of the fluid). For the airfoil the answer is not so obvious.

Vittorio Celli
Tue Oct 21 21:23:27 EDT 1997