# Why does Aerodynamic Center move to 50% chord when supersonic?

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.

• Just to understand better your doubt: is it clear for you that at supersonic speeds the airflow exactly (more or less) follows the shape of the airfoil? And that this doesn't happen at subsonic speeds? Nov 10, 2023 at 7:16
• As long as the contour lines of the airfoil meet at the trailing edge, what happens between leading and trailing edge is inconsequential for lift and only determines lift-independent wave drag (and shock losses from a round leading edge). We cannot explain it better than your literature does already. Nov 10, 2023 at 7:46
• Yes the supersonic airflow exactly following the shape of the airfoil is made clear through all basic explanations of supersonic airflow, and that this is different from subsonic. When using the basics of each shock wave type one can easily relate the oblique and expansion waves of a rhomboid airfoil to the relative pressures they create on the surfaces following the shocks. My confusion lies in how to apply this to the continuous curves of the biconvex airfoil. Would the pressure distribution be similar to a rhomboid airfoil except for a smooth gradient between high and low pressures? Nov 12, 2023 at 4:53
• Am I to understand that besides for the effect on wave drag, airfoil shape is irrelevant for lift generation, all other variables being equal, during supersonic flight? Nov 12, 2023 at 4:57
• Ok, if it's clear that the flow is always perpendicular to the surface then the rest is pure maths. Being the aerodynamic force perpendicular to the surface, being at supersonic speeds the intensity of this force proportional to the local slope of the airfoil and being the airfoil a closed surface then the consequence is that the aerodynamic moment lies always in the middle of the airfoil. Maybe this answer helps you too. Nov 12, 2023 at 12:32