Abstract Planar airfoils are studied for the unsteady flow motion in two-dimensional aerodynamics. Such problems are reduced to the solution of a non-linear multidimensional singular integral equation, when the form of the source and vortex strength distribution is dependent on the history of these distributions on the NACA airfoil surface. A turbulent boundary layer model is also proposed, based on the formulation of the unsteady behavior of the momentum integral equation. Finally, an application is given to the determination of the velocity and pressure coefficient field around an aircraft by assuming constant vortex distribution. Key Word and Phrases Non-linear Aerodynamics, Two-dimensional NACA airfoil, Non-linear Multidimensional Singular Integral Equations, Constant Vortex Distribution, Aircraft, Velocity & Pressure Coefficient Field. Introduction Over the last years a continuously increasing interest has been given to the non-linear singular integral equations by which are solved very important problems of aerodynamics and fluid mechanics, especially these referred to unsteady flows. The computational methods which are used for the numerical evaluation of the non-linear singular integral equations consist of the latest high technology to the solution of general problems of solid and fluid mechanics. For this reason such computational methods are continuously improved. The aerodynamic characteristics of the NACA airfoils are too important for the design of the new generation aircrafts, with very high speeds. This new technology aerodynamic problems are therefore reduced to the solution of non-linear singular integral equations, which are used for the determination of the velocity and pressure coefficient field around the NACA airfoils. Hence, special attention should be concentrated to such computational methods used for the solution of the above mentioned aerodynamic and fluid mechanics problems of unsteady flows. The Over the last years, several other scientists made extensive calculations by using unsteady turbulent boundary layer methods. Among them we shall mention
