PBL;
Thank you for your elaboration on the history of the Prandtl-Glauert transformation which I found very interesting while largely confirming what I would have imagined. I discovered Wikipedia only recently, and was surprised by the extent of coverage and mostly excellent quality. By the nature of it, needs to be used with discretion.
Originally Posted by PBL
Different AoA, different c_L, different lift; you're accelerating up or down now.
Not really. For a given airplane configuration, weight, Mach, and 1g, c_L is inversely proportional to ambient pressure, so it increases with altitude. With increasing AoA the shape of the pressure distribution over the chord changes, in many cases it becomes more 'peaky'.
regards,
HN39