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0.01c INITIAL AIRF0IL a6 and bx achieved additional constraints adverse pressure gradient aerodynamic analysis program airfoil contour airfoil design airfoil geometry airfoil in figure airfoil sections Ames Research Center angle of attack CL Cm Cm V INITIAL constraints are active constraints on thickness Cpus design of low-speed design problem design variables figure 19 final airfoil exhibits final design flow separation increase in lift INITIAL AIRF0IL 0.904 inviscid theory leading edge Legendre polynomials loss in lift low-speed airfoils maximum lift coefficient method of feasible minimization subject Moffett Field nonlinear 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