Does stall angle of attack in inverted flight change due to the camber of an asymmetric airfoil?

Question

What is the stall angle in an inverted flight configuration? How does it relate to the stall angle in normal flight?

As visible in the image below, in upright flight the lower pressure is on the extrados of the wing. In inverted flight the lower pressure is on the intrados.

(source)

The air stream separation at the stall will occur on a side with different characteristics. One could expect the stall will happen differently.

Equivalent representation, where the gravity is inverted and the wing orientation remains in the same direction. Flying inverted implies flying at a negative angle of attack.

The values taken into account are the airflow direction and the chord line, reflected in the angle of attack value.

As commented, while the two previous images suggest a wing in horizontal flight, the situation can be extrapolated to any stable linear trajectory with a negative AoA.

The horizontal plan or the pitch angle are not necessary to determine the stall angle (though they influence the stall speed).

Answer 1

Short answer: Asymmetric airfoils have different positive and negative stall angles, the largest absolute value of the two depends on factors like nose shape and camber. With positive camber (normal and utility aircraft), the negative stall angle can be the largest (in absolute values) but the maximum negative lift available before stall will be smaller than for the positive stall. Larger Reynolds numbers push the stall further away in both directions

It depends on the airfoil. With symmetric airfoils, the stall angle is the same for positive and negative stalls. Positively cambered airfoils (the sort mostly used) have their negative stall at a smaller absolute value of the lift coefficient compared to their positive stall, but the stall angle can well be at a higher absolute value.

Below you see a polar plot for a supercritical airfoil which I used for this answer. The positive stall angle of attack is 8°, while the negative one is around -10°.

Polar plot of the R2A airfoil at Mach 0.6 (own work)

The stall angle depends on details of the nose contour and the camber: Positive camber means that the zero lift angle is shifted to negative values, so there is some bias to negative values in the polar. However, if the lower part of the nose has very high curvature, it will create a high suction peak which leads to flow separation just aft of the nose already at a small negative angle of attack.

One extreme case would be the Göttingen 417a airfoil. Airfoiltools unfortunately plots only a range of Reynolds numbers suitable for model airplane enthusiasts, but the plot below should get the point across. The positive stall angle is 12° at the highest Reynolds number, while the negative stall angle is only around -8°.

Gö 417 lift over angle of attack. The lowest Reynolds number (blue line) is 50,000 and the highest is 1,000,000 (olive green line). Note that all curves are XFOIL predictions - real-world data might look differently.

Answer 2

You are basically comparing a situation with positive $\alpha$ (above) with a situation with negative $\alpha$ (below).

You could obtain the same situation by pitching down: see how in the second picture your flow direction arrives from above the chord line (in the reference frame of the wing).

If your airfoil would have been symmetrical, the critical positive and negative $\alpha$ would have the same absolute value, only opposite sign, but you show a cambered airfoil.

I currently do not have my aerodynamics book at hand, but google helps us:

As you can see in the image, adding camber to an airfoil shifts its $C_{L\alpha}$ line towards negative values. This is desirable because in this way you can have lift even when the angle of attack is 0 (and with no or little drag increase). Another consequence it that the maximum positive $\alpha$ will be smaller than the uncambered case and the negative one will be even more negative (but with some limitations, the Runge-Kutta condition at the trailing edge will affect the shape of the negative $C_{L\alpha}$ curve)

Answer 3

Notice inverted flight is very rare in birds, which have heavily cambered wings similar to the GO 417.

It is important to remember that inverting an asymmetric wing, in simple terms, is reversing all that is good about the lift generation "right side up". The result is a loss of lift at that speed and angle of attack. Further more, there is a very good chance the stall angle of attack of the inverted wing is lower.

In the case of a heavily undercambered wing, inversion would likely be a disaster. Wind tunnel/smoke would show heavy turbulence over the top and very little lift from pressure underneath the wing. Notice the two great virtues of thin undercambered wings have been reversed.

On the other extreme, fully symmetrical wings show little difference when inverted and are popular in aerobatic aircraft.

The flat bottom will behave better than the undercambered, but when inverted will generate less lift at a given AOA and exhibit flat plate stalling characteristics (stalling at a lower AOA).

Amazing how much interest the movie is generating. We'll have to give Denzel a symmetric wing, and Sully a good set of floats.