There are several sources available that state that when an airfoil is fully supersonic, the Aerodynamic Center will move to the 50% chord location. Some of these sources, the ANA shown above being just one of them, use a rhombic airfoil to display how pressures build up after various types of shocks. The rhombic airfoil is simple to analyze and makes intuitive sense why the AC would be at 50% chord.
But what about an airfoil with complex curves, such as the shown Biconvex airfoil? ANA has a table, shown above, that gives a basic overview of airflow behavior as it passes through various types of shocks. Under this explanation, it would seem the biconvex airfoil, with its continuous expansion wave set across both surfaces, would continually speed up airflow and lower static pressure all the way toward the trailing edge, thus causing more lift in the rear of the airfoil than the front.
Specifically, I am curious how all airfoils, when subjected to fully supersonic flow, manage to all have their AC at 50% chord, despite variances in airfoil shape.
Perhaps a distinction between the supersonic affects on center of lift vs center of pressure would be helpful as well.
