The first-and second-order problems for a uniform shear flow past an airfoil have been formulated and solved. It has been assumed that the stream shear, when properly nondimensionalized, must be of order 1. Expressions for the first-and second-order pressure coefficients have been obtained. The lift and moment coefficients are given in integral form. Once the airfoil shape is known, the force coefficients can be obtained by integration. Numerical calculations have been carried out to obtain lift coefficients on a symmetric Joukowsky airfoil, a circular arc, and a cambered Joukowsky airfoil for different values of stream vorticity. It is found that, in general, if the nondimensional stream vorticity (with respect to the airfoil chord and a reference velocity) is limited to 1 or less, the second-order theory will give lift coefficients within 5% of the exact theory up to 30° angle of attack. The uniformly valid pressure distributions correct to the second order along a symmetric Joukowsky airfoil at 10° incidence are presented to exhibit the effect of stream shear.

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