# What's the theoretical background of the critical angle of attack?

The critical angle of attack seems to be at all (most?) airfoils around 15-20°. Why is that? Why is it in this range and not lower or higher? Is it just the result of optimizing airfoils? Or is it some inherent property of the air an airfoil is moving through that determines it? (Let's limit the question to subsonic flight.)

PS: I read the answer to "Does airspeed affect the critical angle of attack on an airfoil?" and don't think that this is a duplicate since the other one was more generally about "what are the factors that determine the critical AoA" while I'm asking why the critical AoA seems to be always in this range for most airfoils on planes flying nowadays.

• Not an expert, But I imagine that the designer chooses a line somewhere between perfomance v drag, ability to flare and land too little, inability to fly slow, possibly not be able to climb well, too much, and it flys like a brick – jeff the tall Mar 15 '19 at 23:02
• Adding my two cents... You can optimize airfoils for higher angles of attack but this does mean the airfoil becomes garbage for normal flight. As Jeff said, it's a compromise. The reason that we see 15 to 20 degrees probably comes from the regulations, especially max allowed stall speed for your aircraft weight category. If stall speed is dictated and your weight is maxed out for your weight category then - with your chosen flap design and optimal wing area - you will probably need those 15 to 20 degrees of AOA to reach the demanded low stall speed. – Jan Mar 17 '19 at 20:10

Both the airfoil shape and inherent properties of the air contribute to the stall angle of attack. You asked for a theoretical background, but I will list the factors that influence stall because there is no simple formula for it.

The most important factor is the suction peak which develops right behind the stagnation point on the upper side of the leading edge. High suction means high speed and that in turn means high friction, so the air loses energy which it needs further downstream to regain its pressure. If too much energy is lost, the flow separates. Enough separation and lift suffers, so here you have the most immediate reason for a stall.

What can be done to shift that point to a higher angle of attack?

1. Pitch up faster. That way, the flow over the rear part of the wing has a boundary layer from lower angles of attack and will not separate when the leading edge passes through the angle of attack at wich it stalls in normal conditions. This can shift the stall angle of attack up by 50%.
2. Increase the leading edge radius. This spreads out the suction peak and makes it less pointy. A blunt leading edge is especially helpful with higher wing loadings when Mach effects play into the stall angle of attack mechanics. Once the local suction peak at the nose of an airfoil reaches a local Mach number of slightly less than 1.6, no lift increase could be observed in experiments.
3. Increase wing camber, either by nose and/or trailing edge flaps or by cambering the airfoil. This helps to reach high lift coefficients already at low angles of attack, and especially nose devices (slats, Krüger flaps) shift the stall angle of attack up as well.
4. Use a well-designed airfoil with a long laminar run and a Stratford pressure distribution past the turbulent transition point on the upper side. This helps to reduce boundary layer losses and maximizes energy reserves for the steepest possible pressure rise. But you need a clean, smooth and well built wing for that to really happen.
5. Increase wing loading. This will shift the stall speed to a higher Reynolds number where friction losses are smaller relative to the inertial energy of the air. Of course this will increase stall speed, but is will also shift the stall angle of attack higher. A bit.
6. Increase wing chord (while maintaining the same area). This has actually two effects: The smaller one is again from the increase in Reynolds number, but the more powerful is from the reduction of the wing's aspect ratio. At a smaller aspect ratio the lift curve slope is flatter, so the same lift coefficient (and suction peak) is reached at a higher angle of attack.
7. Increase wing sweep. The pressure changes over the wing are now proportional to the cosine of the sweep angle, so all effects are shifted to higher angles of attack accordingly. But beware of a combination of high sweep and high aspect ratio: Stall will become outright nasty. If you combine 6 and 7, you will at some point arrive at a delta wing which flies well even with fully separated upper side flow (vortex lift). Now your limit angle of attack will be defined either by the vortex bursting or loss of directional stability.
8. Fly in hotter, less dense air. This also helps to increase the Reynolds number because you need to move faster for the same dynamic pressure. However, much of that advantage is eaten up by the increase of the air's viscosity with temperature.

This observation is only partially correct. If you take a generic, General aviation airfoils (moderately high Raynolds number; ie > 5 Million) this observation appears to be correct.

Why is this correct? Because most GA airplanes Fly between a limited maximum speed and stall speed which correspond to lift coefficients say 0.01 to 1.5-2.00. CL is (approximately) linearly correlates to the angle of attack (CL ~ 0.1 alpha with respect to zero lift angle) and this, in turn, implies most of our airfoils operate up to 15-20 degrees.

Above said, that angle of attack range is not the only regime where airfoils operate. If you take a highly pointed airfoil (shart leading edge) it will stall within a few degrees. I would suggest studying about few RC airfoils to better understand this. Ex: Indoor duration and indoor hand launch ones.

What determines the operatable angle of attack range of an airfoil is mostly determined by the boundary layer equations and how the edge velocity distribution affects the boundary layer. What is characterized as a stall is a massive boundary layer separation caused by steep adverse pressure gradients.