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We know that any aircraft will stall at its stall speed (for a specific weight, CG position, etc.) but also, that the same airplane will always stall at the same angle of attack.

I´ve read that IAS is just the easy way to control AOA, because in reality it's all about AOA and nothing to do with airspeed. That when changing IAS we are changing the relative wind and thence AOA. On the other hand, I know that the critical AOA doesn´t change with weight (it will always be the same for a given airfoil) but the stall speed will.

There are also high speed stalls... I'm confused. Can we get into a stall without reaching the critical AOA? What's exactly the relationship between AOA and IAS?

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    $\begingroup$ The angle of attack for the stall is always the same, as you already understood correctly. Depending on the load that you put on the wing, either by pulling more g's in a dive (high speed stall) or in a steep turn or by increasing the weight of the aircraft, you change the necessary speed to create enough lift. Think of it like this: Stall speed is your IAS as your angle of attack reaches the critical angle of attack. That means stall speed can be literally anything from 0 to vmax if you pull between 0gs or pull over g's or put too much load in the aircraft. $\endgroup$ – Jan Nov 15 '20 at 10:12
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"Can we get into a stall without reaching the critical AOA?" -- no.

"We know that any aircraft will stall at its stall speed (for a specific weight, CG position, etc.)"-- we need to add "G-loading" to this list of parameters. The "stall speed" we usually talk about is the 1-G stall speed. Change the weight or the G-loading, and the airspeed correlating to the stall angle-of-attack changes.

"On the other hand, I know that the critical AOA doesn't change with weight"-- correct, but for a given G-loading, such as 1 G, the airspeed correlating to that critical AOA scales according to the square root of the weight.

"What's exactly the relationship between AOA and IAS?" -- if we know the IAS where the wing reaches the stall AOA at some given weight and G-loading, then we can adjust that IAS for some other condition by multiplying by the square root of the change in weight times the square root of the change in G-loading. "Change in" meaning the ratio, i.e. new divided by initial.

The fundamental relationship between AOA and IAS is that net lift force at any given AOA is proportional to airspeed (IAS) squared.

Here's an extra complication that you may not want to worry about right now -- the "dynamic stall" -- What is the immediate cause of stall? -- scroll down to last paragraph.

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A practical answer to help you understand critical angle of attack and stall speeds would be the operation of fast jets. The quickest way to land a jet is to join for a ‘run-in and break’ this could be at any speed but typically 350kts. A high-g turn would be used from overhead the runway at circuit height to the downwind position. The aircraft would be pulled into the turn until the stall buffet was achieved. This stall and associated drag slows the aircraft quickly and easily to the approach speed. Because the aircraft is above the minimum stall and retains lots of energy a reduction of control forces at any point would reestablish normal flight. Although the aircraft would experience a ‘stall’ at high speed due to the critical AOA being exceeded, the same aircraft would stall at about 100kts straight and level.

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    $\begingroup$ Close, but there are a few errors in this: First, the break turn is typically performed 500’ above pattern altitude. Second, the aircraft does not “experience a stall at high speed due to critical AOA being exceeded”. That would be very bad. Typically the target in the break is max lift AOA to use all the induced drag available to slow down. Even pre-stall buffet is too much pull. Good point though that accelerated stall recovery is easy because you have lots of energy. With airspeed above straight and level stall speed, simply relax the pull and you are safe again. $\endgroup$ – Michael Hall Nov 15 '20 at 15:34
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The direct answer to the question as it is ("What´s the relationship between AOA and Airspeed?") is simple: none whatsoever -- that is, until you introduce context and some conditions.

Your context is: we want an airplane to fly. And not just 'fly' but to keep level, at least. For that, you need a certain amount of lift. Lift is used to counteract weight, so you need at least that much to fly level. Plus, you'll need some extra to pull most manoeuvres (such as turns).

The way airplanes create lift is by using wings. If we 'fix' the wing for simplicity (that is, forget about flaps and other devices that change the wing1), there will be only two variables under the pilot's control that effect lift:

  • Angle of attack (AoA).
  • Airspeed. (Pilots usually talk about indicated (or calibrated) airspeed rather than true airspeed. It implicitly includes air density and thus altitude).

The more of each, the more lift. The dependency is quadratic on airspeed (double airspeed, 4x the lift), and more or less linear on AoA (until you get closer to stall).

What determines stall is, in practice, solely the AoA,2 as you already understand. If you had an accurate AoA sensor, that's all you'd need to watch in order to avoid stall. (But you'd still need to have knowledge of how the airplane flies, i.e. the above dependencies, in order to know what to do to avoid it).

However, for various reasons you usually don't have such sensor. In this case you can use airspeed as a proxy. But airspeed is linked to AoA via lift, as we discussed. You need to know the current lift, too! How do you know it? Well, in a straight and level flight, lift exactly equals weight, by definition. You know your weight because you filled in the weight & balance chart prior to flight, right? You also know how much fuel you used up to this point.

So, the heavier your given airplane is (say, if you load an extra passenger), the more lift you'll need in the same conditions. And as we know, we can create this extra lift in two ways: by increasing AoA or by increasing airspeed, or both. If we just increase AoA, we'll obviously get closer to stall, and at some point we'll stall - at the same airspeed as we were perfectly able to fly with lower weight. Or, the other way round, if we 'fix' AoA (say, consider the stall AoA - which is fixed, as we know), we'll need higher airspeed for higher weight. (1.4x airspeed for double weight).

This is why your stall speed varies with weight. It also varies with G-loading, which is the case when the wing needs to create more lift than weight. (Coordinated turn is the first manoeuvre that pilots learn when this happens). When the documents (such as POH) specify 'stall speed', they also specify the weight at which it applies. (If they don't, they conservatively imply maximum permitted weight). They also often have charts how the stall airspeed increases in turns (as a function of the bank angle).

So, when we talk about 'stall airspeed', we understand it as 'airspeed at which the wing produces the required amount of lift while being at the stall AoA'. The 'required amount', in turn, depends on the conditions being considered: for the simplest case of straight and level flight, this is just the weight.


1 As well as about ice, bugs and dirt on the surface, etc.

2 In truth, true airspeed also has an effect via Reynolds number (Re), but in the context of GA this effect is very minor. The rate of change of AoA also matters, but only for very aggressive manoeuvres, like in aerobatics.

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The relationship between AOA and airspeed is beautifully explained in the Lift Equation:

$Lift$ = Air density x Wing Area x Lift Coefficient (Camber and AOA) x V$^2$.

IAS is an easy way to control AOA

Theoretically, yes. In reality, not very practical because airspeed cannot be instantaneously changed by adding thrust. This is especially true when the aircraft is bigger, like an airliner.

Inertia (mass) must be overcome to move at all, as shown by the Acceleration Equation:

$Force$ = Mass x Acceleration

Rearranging to: Acceleration = Force/Mass

It is airspeed that creates lift, so we must keep adding thrust until we are going fast enough to fly (as on the run way taking off).

can we get into a stall without reaching critical AOA

Yes! If you slow down too much, your plane will not be making enough lift to support its weight. The plane will "sink" from its line of flight, which increases the AOA on the wing. Then you stall.

This is especially true if your Center of Gravity is too far back, or (for builders), if the tail is too small.

There are also high speed stalls...I'm confused

No need to be. A stall occurs when wing AOA exceeds its limit. People stall at higher speeds because they are trying too hard to turn, for example, to reach a runway.

So the best ways to avoid stalling are to watch our airspeed (so we don't need a high AOA) and to not be too aggressive with the elevator.

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    $\begingroup$ You cannot stall without reaching the critical angle of attack. Stall is defined by airflow separating from the airfoil which happens at a certain angle which can be thought of identical in the flight envelope. It should be changed to: "No you can't. But if you slow down too much AND TRY TO MAINTAIN ALTITUDE you will have to increase angle of attack. When the angle of attack reaches your critical angle that is what we call stall speed. $\endgroup$ – Jan Nov 15 '20 at 10:08
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    $\begingroup$ @Jan no kidding. The issue, especially with larger aircraft, is the sink leads to the stall. Your second to last comment sentence is exactly the point. $\endgroup$ – Robert DiGiovanni Nov 15 '20 at 18:36
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    $\begingroup$ Yes, but it stalls because sink causes increase of the local AoA if you don't change the attitude (due to the extra vertical airspeed component). Your AoA sensor will show the increase, and if equipped with a stall warning, it will trigger. $\endgroup$ – Zeus Nov 15 '20 at 23:36

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