Continuity of lifting surface theory in subsonic and supersonic flow

The continuity of linear theory for lifting surfaces in subsonic and supersonic dow is discussed, The unsteady pressure kernel functions of the singular integral equation are summarized for all Mach numbers in the Laplace transform domain. The sonic kernel in the steady flow is obtained as a finite limit from both the subsonic and supersonic sides when the Mach number tends to unity. Numerical examples are given using the doublet-point method with three different kernel functions, showing continuous results through the unit Mach number. The results also show how a rectangular wing with various Mach numbers approaches to the two-dimensional airfoil as the aspect ratio increases.