Optimization of airfoils for maximum lift

The pressure distribution which provides the maximum lift without separation for a monoelement airfoil in an incompressible flow is determined using existing boundary-layer theory and the calculus of variations. The airfoil profiles corresponding to these pressure distributions are determined using second-order airfoil theory. The results indicate maximum lift coefficients as high as 2.8 for Reynolds numbers between five and ten million, and the corresponding drag coefficients are on the order of 0.01. Compressibility has not been considered directly, however the form of the optimum pressure distributions suggests that the critical Mach numbers should be on the order of 0.35.