Because the maximum camber ratio of a thin airfoil is small by definition, the moment expression for a cambered airfoil can be represented adequately by the expression derived for a symmetrical airfoil (i. e., flat plate). Then, referring to Fig. 5.21 and the development for a symmetrical airfoil:
MLle = – J(PL – PU)(x)dx = – J(pVji)(x)dx.
Applying the transformation from linear to angular measure and writing this equation in coefficient form results in:
Substituting for у (ф) = у (0) from Eq. 5.21 and integrating using basic trigonometric identities and integral tables results in:
The moment coefficient for a cambered airfoil is seen as depending on only three Fourier-series coefficients and as a function of the angle of attack and camber.