## An assessment of airfoil design by numerical optimization |

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40-percent chord station aerodynamic program AIRFOIL DESIGN airfoil geometry airfoil in figure airfoil sections airfoil thickness Ames Research Center arbitrary airfoil calculation CONMIN CONSTRAINT FUNCTIONS constraint of 0.7 constraint tolerance constraint value constraints on drag curvature constraint design space Drag minimization drag reduction drag was reduced effect of imposing Figure 17 figure 24 final airfoil flow full potential theory geometric constraints geometry and pressure Gj(x initial airfoil initial input inviscid iteration known optimum airfoil lifting airfoils linear theory method of feasible minimum wave drag Moffett Field Murman nonlinear numerical optimization objective function off-design optimiza optimization algorithms optimization problems optimization process optimization program based orthogonal polynomials parabolic arc partial differential equation percent chord Figure pressure coefficient recontour relaxation solution result shock-free airfoil shown in figure speed regimes square-root term starting airfoil subsonic supercritical thickness distribution unconstrained vector violated volume and thickness volume constraint Volume maximization wave drag coefficient weak shock