Semi-empirical methods have been proposed to extrapolate airfoil aerodynamics at high Reynolds numbers and at transonic Mach numbers. The theory has been compared with the available wind-tunnel data for some rotorcraft airfoils, the NACA 0012, the NACA 23012, the SC1095, and the SC1095-R8. An iterative procedure around Mdd allows the calculation of the point of transonic dip. The Mdd can be calculated accurately at zero angle of attack and in some cases, at all useful angles of attack. The data required include the airfoil thickness, the reference Reynolds and Mach numbers, the Mdd at nonlifting conditions, and the corresponding aerodynamic polar. The semi-empirical relationships proposed are valid up to about M = 0.90, and cannot accurately predict nonlinear phenomena such as lift stall, Mach tuck on the pitching moment, or the drag recovery at low supersonic speeds.