Transonic Shock-Free Aerofoil Design by an Analytic Hodograph Method

Abstract

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.

Lifting-line theory for a swept wing at transonic speeds

“…4.1 shows the boundary value problem for </>" • For a given airfoil shape the boundary value problem for 0O cannot, in general, be solved analytically. Instead, one of the standard computational schemes for resolving shock waves is used ( [2,9]). Alternatively one could consider shock-free transonic flows and the corresponding airfoils generated from the hodograph solutions, for example Garabedian [8] However, there is a downwash at infinity toward the flat plate, as determined by matching (3.17), (3.18).…”