KármánTsien

The Kármán–Tsien method is a technique used in aerodynamics to estimate the lift and drag of airfoils at transonic speeds. It was developed by Theodore von Kármán and Hsue-Shen Tsien in the late 1930s and early 1940s. The method is based on the idea of transforming a known airfoil's properties to predict the behavior of a different airfoil.

Essentially, the Kármán–Tsien method applies a compressibility correction to the incompressible flow solution. It uses a mathematical transformation that relates the flow properties around a thin airfoil in incompressible flow to the flow properties around a different airfoil in compressible flow. This transformation is particularly useful for transonic speeds, where the flow is a mixture of subsonic and supersonic regions.

The method's accuracy is generally good for thin airfoils and moderate transonic Mach numbers. However, its effectiveness can decrease for thicker airfoils or at higher Mach numbers where non-linear effects become more pronounced. Despite its limitations, the Kármán–Tsien method provided a valuable early tool for aerodynamicists to predict airfoil performance in a challenging speed regime before the widespread availability of computational fluid dynamics (CFD). It laid important groundwork for further developments in transonic aerodynamics.