Is an airfoil's critical angle of attack measured using "geometric angle of attack" or "effective angle of attack?"

Question

One of the first things we learn about stalls is that they occur when a wing exceeds a certain critical angle of attack, which depends on the specific design of the wing. But if a given wing has a critical AoA of, say, 20 degrees, which definition of AoA are we using?

As shown in the image below, geometric angle of attack is measured between the wing chord and the undisturbed relative airflow.

Effective angle of attack takes into account the induced downwash caused by wingtip vortices and is therefore smaller than geometric angle of attack.

These definitions of AoA come up in explaining induced drag, but I never see them referenced in discussions of critical AoA. I am assuming that critical AoA is measured using geometric AoA, but is this correct?

As a follow up question / comprehension check: Induced drag occurs because lift is produced perpendicular to relative wind. When the airflow is deflected downwards, the lift vector is in turn deflected rearwards, contributing to drag. Would it also be correct to say that the magnitude of the lift vector is decreased, since the effective AoA is shrunk, compared with geometric AoA?

Answer 1

In general, measuring something in respect to something which is inherently variable doesn't give a good measure: induced angle changes continuously according to the lift distribution and it is actually not even well definable at stall. Using it to represent the aerodynamic characteristics of a wing would just make the measurements difficult. The geometric chord line must therefore be used. Furthermore, induced angle is just a more or less correct (less than more) logical/mathematical construct to help understand and visualise induced drag, it is not exactly something real.

A wing stall is also different than a single airfoil stall: wings (at least the ones of a GA or jetliners) are made to be as much resistant to stall as possible. Wing twist, aspect ratio, spanwise chord distribution and other parameters are all chosen (also) to retard and give a stall as smooth as possible. Typically, the stall begins at the root of the wing so that its turbulent wake impinges on the tailplane making it vibrating and warning the pilot of the imminent stall.

The following plot (red squares) shows the lift coefficient of a Cessna 172 (source - I couldn't find the origin of this plot, but it comes up quite often searching it around and it looks plausible):

Maximum lift coefficient is some 1.6 at 16°. Now compare it with the plot for the NACA 2412 which is used as basis airfoil for its wing:

As you can see the maximum lift and the relevant AoA are the same as for the whole wing but look how much smoother the stall region is for the wing in comparison to the the airfoil.

Answer 2

When we talk about stall and other things, the angle of attack is the angle between some geometric reference line (the chord for an airfoil, some datum line for a whole aircraft) and the freestream velocity. I.e. your 'geometric' angle of attack.

The stall AoA for a wing will not be the same as the stall AoA for an airfoil (even if the wing is constructed from that airfoil) because of 3D effects including downwash and the effective angle of attack.

Consequently, a 3D stall AoA for a wing essentially "builds in" the effect you're seeing.

Of course, most wings do not stall all at once. Stall may start at the wing tips (or the root) and will progress as the angle of attack is increased. Precisely defining when 'stall' happens for a wing can be complex -- is it when the first signs of stall are deteced? is it when the lift coefficient attains its maximum value?