How does aspect ratio affect the stalling angle of the wing?

Question

I have been trying to find a clear answer for this but haven't been able to do so. From what I understand this is linked to induced drag but I'm not able to link it.

Could someone shed some light on this ?

Answer 1

Any finite span wing creates a wingtip vortex which causes an induced downwash profile that is maximum at the wingtips, and gets less as you move further inboard (towards the wing root). This is due to the vorticity causing a upwashing outboard of the wing tip, and a downwash inboard of the wing tip. If we took a theoretical wing where the aspect ratio is high enough that the span is 'near-infinite', there will be no tip-effect (vortex) induced downwash at the center (root).

Lower aspect ratio means that there is more induced downwash further inboard, and this local downwash actually helps to keep the airflow attached becuase the local flow is already flowing downwards along the later surface of the wing. You can also think of it as reducing the local incidence angle because the air is already flowing downwards.

Most wings are designed to stall first at the wing root, and for rectangular wings this is inherit due to the downwashing profile described above. For other wing shapes, designers will include "wash-out" to ensure that the root stalls first (Why does a rectangular wing stall first at the root?). Because the root is separated first, if we take away the section of the wing near the root (hence decreasing aspect ratio), the area that would have already separated is now removed, and the wing will be able to operate at a higher angle of attack.

Therefore the stall angle would increase if aspect ratio is decreased (ceteris paribus!). This is assuming that the wing is operating in the longitudinal plane only. Any asymmetrical movement (rolling and yawing), will mean that the wing could possibly stall at the tip.

Answer 2

The basic principle is that most subsonic lift is created near the nose of the airfoil and making the wing less wide but longer means that the added area in the rear has less effect than adding it at both tips of the wing.

To quote a quite indisputable source, S. Hörner writes in the introduction to Chapter XVII of his book "Fluid Dynamic Lift":

[In low aspect ratio wings] … the chord and curvature are large so that the ratio of the chord [to] the radius of the stream curvature is also large. As a consequence, the airfoil sections lose lift, their sectional lift-curve slope is less than in two-dimensional flow and the lift angle of the average section is increased. Of course, the induced angle is also increased corresponding to C$_L$/A as in larger aspect ratios.

Next, lift curve slope is no longer linear with low aspect ratios. A bit before, S. Hörner says:

The lift curve slope of low aspect ratio wings increase with angle of attack up to the stall angle rather than remaining linear as in the case of conventional wings. The increase in slope is a secondary effect that takes place over and above the basic circulation lift slope.

If you follow the logic explained in this answer, lift curve slope increases with angle of attack because the higher frontal area of the wing at increasing angles of attack will capture more air for creating lift, increasing its efficiency in the process.

With lower lift curve slope, the stalling angle is higher for wings of smaller aspect ratio. NACA Report 1091 contains test results on low aspect ratio wings, and while lift curve slope increases with aspect ratio, maximum lift is roughly constant and even shows larger values at very small aspect ratio.

Since this report is about lateral control characteristics of low aspect ratio rectangular wings, an unusual way of plotting lift coefficient over angle of attack was chosen. See below, also from NACA Report 1091:

The wing with the highest lift coefficient is the one with 45° sweep. Sweep delays the stall angle in addition to the effect of low aspect ratio.

EDIT:

Now for the theory that downwash reduces lift. This is true for the downwash of a wing flying ahead of the wing concerned (as in case of a horizontal tail) but not for the main wing of a standard configuration airplane. What happens past the wing is a consequence of the flow conditions ahead of and over the wing, not vice versa. Causality flows with the air.

What is probably meant by such a theory is that a reduced aspect ratio reduces the vorticity when flow is described as potential flow. I always find it easier and more instructive to use physically tangible phenomena to describe what happens instead of mathematics, so I will not resort to potential flow theory, even though it produces correct explanations, too.

Lift is produced by a wing by deflecting the air in its vicinity downwards. This deflection happens mostly in the forward part of the wing's chord; that is why the neutral point of an airfoil sits at its quarter chord. With smaller aspect ratios this location moves forward until the neutral point approaches the leading edge (better, in that case, the leading point) of slender bodies. These are objects where chord is much higher than span; fuselages or external tanks already behave much like a slender body.

The reason is simple: The pressure difference between both sides of the wing is reduced by flow around the wing tips: Reduce aspect ratio, and this effect becomes relatively larger and reduces lift especially in the rear part of this wing. The neutral point moves forward and the lift curve slope shrinks. Note that this is not the tip vortex but only the equalisation of pressure at the tip. This movement induces a circular flow which will form the tip vortex further downstream, and saying that the tip vortex reduces lift is similar to saying that wet streets cause rain. But I digress …

A reduced pressure difference also means that the pressure rise after the suction peak near the leading edge of the wing is shallower at the same angle of attack than it is for a wider wing of higher aspect ratio. Consequently, it needs a higher angle of attack until the pressure gradient is steep enough to cause the flow to separate on low aspect ratio wings. Since stall is caused by a sufficiently large growth of flow separation so lift stops to increase with angle of attack, a lower aspect ratio wing will reach this stall angle of attack later than one with a higher aspect ratio.

Answer 3

A little bit of logic here from what has been learned (generally):

1. Low aspect wings have lower stall speeds than higher aspect wings.
2. Rectangular wings stall at the roots.
3. Tapered wings are prone to "tip stall"
4. Inboard downwash from wing tip vortex helps delay tip stall
5. Rectangular (lower aspect) wings (with larger wing tip vorticies) are less prone to tip stall (but would produce more drag than tapered tips in cruising flight).

For equal weight and wing area we have:

1. Lower aspect wings produce larger wingtip vorticies, requiring more thrust for the same airspeed and AOA. Higher aspect wings are more efficient.
2. Larger vortices reduce tendency to tip stall.
3. Because vorticies delay tip stall, with sufficient warning from root stall "buffet", a pilot could go to a slightly higher AOA and still safely maintain control of the plane but...

It is doubtful lengthening the same airfoil would have a major effect on its stall AOA for a straight wing, without designing something hopelessly chunky with no cruise efficiency (but maybe a good fighter jet).

Then why do lower aspect wings have a lower stall speed? The answer (as in parachutes) is with improved utilization of "bottom" lift. Better here to use a square (or circle) as did the sailing clippers of old.

And how does the delta continue producing lift at a higher AOA? By actually harnessing its vortices along the top of the entire wing, which maintains organized airflow and lift. Vortex generators are used to the same effect on a straight wing.