A design method for transonic shock-free aerofoils using hodograph theory is sketched. The method is based on the approximate solution of Tricomi boundary value problems for the elliptic-hyperbolic hodograph equations of transonic aerofoil flows on a two-sheeted hodograph surface. Special attention is paid to a numerical approximation method generating nearly always closed aerofoils. The use of the computer programs in an aerodynamic design process is illustrated by an example. Several examples of computed aerofoils (some of them advanced) demonstrate that the method is flexible and powerful.
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