## Application of numerical optimization to the design of low-speed airfoils |

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achieved active or violated additional constraints adverse pressure gradient aerodynamic analysis program airfoil contour airfoil design airfoil geometry airfoil in figure airfoil sections algorithm Ames Research Center angle of attack constraints are active constraints on thickness constraints were satisfied design of low-speed design problem design variables Figure 17 final airfoil exhibits final design flow flow separation Gj(x increase in lift inviscid theory leading edge Legendre polynomials Lift maximization loss in lift low-speed airfoils maximum lift coefficient method of feasible minimization subject Moffett Field nonlinear nosedown pitching numerical optimization objective function optimization process optimization program optimum design partial differential equation pitching-moment coefficient Pitching-moment minimization Pitching-moment minimization;M pressure distribution pressure gradient minimization pressure peak procedure reduced shown in figure steepest descent subject to constraints surface adverse pressure theory with viscous thickness and trailing-edge trailing-edge bluntness transonic unloading the trailing Upper surface adverse upper-surface pressure coefficient vector viscous theory volume x/c Figure