Does thin airfoil theory work at very high angles of attack?

Thin airfoil theory says that lift coefficient is directly proportional to the angle of attack in radians. I haven't been able to find any limit, short of stall, for applying this theory. It would give us a huge lift coefficient at 90 degrees, where lift is actually zero, and double even that at 180 degrees, where again the lift is zero. This is basic reasoning. So, what am I missing?

• What makes you think there should be another limit than stall? That seems like a pretty definitive limit to me. Jun 7, 2020 at 12:08

Of course not. Thin Airfoil Theory produces a beautiful result that relates the zero-AOA lift to the mean camber of the airfoil, as well as the lift slope vs AOA of any thin airfoil is $$2\pi$$. But that's assuming:
3. AOA and camber are small: such that all angles are linearized ($$\sin\theta \approx \tan\theta \approx \theta$$); obviously at large angles, this assumption breaks down and the results are worthless