# How does the angle of attack vary in turns?

I read somewhere that when the aircraft banks to turn, its angle of attack increases.Since angle of attack is the angle between the relative wind and chord line, how does turning increase it? Is it because the relative wind is now from different direction or is it because the wing that goes higher meets the air at a higher angle?

• Given the variety of answers this is getting, I suggestyou try to clarify exactly what it is you're asking. Jul 21, 2016 at 17:41
• Added one more tag since question was at top of stack anyway due to another recent answer... Apr 5, 2020 at 1:50

Just to avoid some confusion that I feel in your question:

## It doesn't!

That is, it doesn't happen by itself. The pilot or autopilot must actively pitch up (and possibly do other adjustments, e.g. increase thrust). Without active control, the angle of attack will stay about the same (initially), and the airplane will start descending if it enters a turn, because the lift becomes insufficient for level flight (see pictures in other answers).

• yes that was confusion - I thought AOA varies when aircraft enters into a turn. So I understand that it only varies when pilot or autopilot pitches it up to increase the lift Jul 23, 2016 at 16:54
• As soon as the aircraft descends, AoA will increase from the change in the flight path angle. No pitching needed, but now drag will increase and the aircraft both slows down and pitches down in order to stay at its trim point. Apr 4, 2020 at 1:26

The aircraft turns to change its speed vector. The absolute value of the vector stays the same, but its direction is changed. A force is needed to change the direction of movement of any mass, and the wing is used to provide this force in addition to the lift force. This is why lift is increased in a turn.

For turning, the aircraft needs to add a force in the direction of the red vector in the sketch above. This it can either do by pointing its nose to the right, and then the fuselage will create a small lateral force, albeit at a heavy price in drag. Or the airplane uses its wing to provide this force, which is a much cleverer way of creating the desired force because the wing is by far the most efficient "force generator" of an aircraft.

Note that as the turn progresses, the red vector will point in the opposite direction of the initial (blue) speed vector, which means that the speed in the initial direction is reduced to zero when a 90° turn is completed. The horizontal component of the lift force accelerates the aircraft in the new, desired direction and decelerates it in the old direction.

Lift can be increased either by speeding up, by flying in denser air or by increasing the angle of attack. The first two options are not very practical, so it is the angle of attack change which gives the aircraft the additional lift for turning. This angle of attack increase is controlled by pulling the stick gently back, thereby reducing lift on the horizontal tail so the aircraft can pitch up.

If you need more formulas to calculate the precise angle of attack change, look at this answer for flight mechanics in banked flight and this answer for how lift depends on angle of attack.

• can you explain what does this mean "speed in the initial direction is reduced to zero when a 90° turn is completed" Jul 23, 2016 at 16:57
• @user2927392: Yes. After turning 90°, all initial speed is gone. Instead, the aircraft has gained the same speed value in the perpendicular direction, and all the acceleration to reduce the initial speed and build up the new speed has been provided by the wing's lift. Think of speed as a vector here - the scalar quantity does not change in a turn. Jul 24, 2016 at 0:36

The AoA in a turn will be higher than in level flight IF the same airspeed and level is maintained. Reason being, in a turn some of the "upwards" (relative to the lateral axis) force generated by the wing is used to turn the aircraft around, so more lift needs to be generated to maintain altitude. To generate more lift at the same airspeed, the angle of attack has to increase.

This image illustrates it nicely:
source: http://avstop.com/ac/flighttrainghandbook/forces.html

(consider the "Total Lift" vs. the "Vertical Component of Lift")

• So if you do not pitch up during a turn, will the angle of attack remain same even though aircraft pitches down a bit during the turn Jul 20, 2016 at 17:50
• This does not explain how the AoA is increased. Jul 20, 2016 at 18:11
• @user2927392 Yes, you can maintain the same AoA, but you would have to sacrifice some altitude. Jul 20, 2016 at 18:14
• @Simon The question is not "how does the angle of attack increase?", it is "how does the angle of attack vary?" Jul 20, 2016 at 18:15
• @RyanMortensen Intuitively I would agree, that for a constant airspeed and G-load, the AoA should remain the same. I don't have the formulas to support it, though. Jul 20, 2016 at 18:34

How does the angle of attack vary in turns?

While many of the answers focus on the need for the angle-of-attack to be higher in a turn than in wings-level-flight if altitude is to be maintained with no change in power setting (or alternatively if altitude is to be maintained with increased power but no change in airspeed), your question seems to be asking about something else.

I read somewhere that when the aircraft banks to turn, its angle of attack increases.Since angle of attack is the angle between the relative wind and chord line, how does turning increase it? Is it because the relative wind is now from different direction or is it because the wing that goes higher meets the air at a higher angle?

You seem to have the impression that the angle-of-attack is inherently tends to increase as we enter a turn.

Of course when considering this whether this is true and why, an important question is "is the pilot in the loop, making pitch control inputs as needed to achieve some given goal, such as maintaining altitude without changing the thrust or power setting, or such as maintaining both airspeed and altitude (which will require more thrust and power)?

Many of the other answers to this question assume that the pilot is in the pitch control loop, manipulating the controls as needed to to achieve parameters such as the ones stated above. In this case, the angle-of-attack usually will indeed be higher in the turn than in wings-level flight, for reasons given in other answers such as this one.

Of course, there are exceptions. Here is an example of a situation where the angle-of-attack would ideally not be higher while turning than in wings-level flight, even when the pilot is in the pitch control loop: a glider is soaring in weak but smooth and widespread ridge lift, flying at the angle-of-attack that yields the minimum sink rate in steady-state linear flight. In this case, as long as the roll rate is kept low, it would be a disadvantage rather than an advantage to increase the angle-of-attack when entering a turn.

But generally speaking, especially in the context of powered flight, a pilot will increase the angle-of-attack when entering a turn. In fact, if you know you prefer to travel in some other direction than the one you are currently going in, in some cases you might want to do a little zoom climb as you roll into the turn, to convert some kinetic energy into altitude and get the turn accomplished quicker as well.

On the other hand, if we assume that the pilot is not in the pitch control loop, then your impression that the angle-of-attack tends to increase as we enter a turn is mistaken. Here's why:

First of all, it's worth noting that if we start with the aircraft in a somewhat nose-up pitch attitude relative to the flight path-- i.e. a somewhat positive "angle-of-attack of the fuselage"-- than any rolling motion toward a steeper bank angle converts angle-of-attack into sideslip angle, so that the angle-of-attack tends to decrease. This happens because an aircraft generally rolls about its longitudinal axis, not its velocity vector (flight path vector). So the angle-of-attack tends to decrease, as if we were pushing the control stick forward, while applying some top rudder at the same time. If this is hard to visualize, imagine starting at an extreme angle-of-attack, like 15 degrees or more, and rolling to very steep bank angle. Since the aircraft's natural pitch stability dynamics are constantly trying to return the aircraft to the "correct" angle-of-attack for the elevator position (with one caveat that we'll note below), this dynamic will be most pronounced when the roll rate is very high and the aircraft's pitch stability dynamics are relaxed, i.e. the CG is so far aft as to give near-neutral pitch stability. You aren't going to detect this dynamic as you practice maneuvers for the private pilot or commercial flight test in a typical general aviation trainer.

But what if we are not beginning the maneuver at a high "angle-of-attack of the fuselage", and/or we are rolling slowly enough that the above dynamic is trivial? For example, what if we are making a typical turn entry in a general aviation light airplane, or perhaps a sailplane? It turns out that if we leave the control stick or yoke in a fixed fore-and-aft position as we roll (or if we allow the control stick or yoke to "float" at trim in the fore-and-aft sense and apply no forward or aft pressure on it), we still find that the angle-of-attack tends to decrease as we increase the bank angle. The reason for this is that as we bank, we start to turn, and the curving flight path actually creates a curvature in the free-stream airflow or relative wind, which tends to "push up" on the horizontal stabilizer and pitch down the nose, or more precisely, tends to alter the angle-of-attack of the horizontal stabilizer in a way that causes the aircraft to transition to a lower angle-of-attack overall, including a lower angle-of-attack as measured at the wing. This effect is related to bank angle, not roll rate.

One way to see this effect first-hand in some aircraft is to trim for level flight with the stall horn just barely sounding, and then increase the bank angle without exerting any fore or aft pressure on the control yoke (or while using a special clamp to hold the yoke in a fixed position in the fore-and-aft sense while still allowing free roll control inputs), and note that the stall horn stops sounding when we slowly roll the aircraft into a moderately-banked turn, such as 45 degrees of bank. In the turn, we are further from the stall angle-of-attack than we were in wings-level flight. Be sure to try it both directions so as not to be misled by asymmetries in the angle-of-attack of the inside wing and outside wing during the turn.

Because of this effect, to maintain the same angle-of-attack in turning flight as we had in wings-level flight, we have to have the control stick or yoke further aft in the turn. Since turn radius is proportional to velocity squared, this dynamic is especially pronounced in aircraft that fly at relatively low airspeeds and also fly at relatively low "scale speeds", i.e. take a relatively long time to cover one fuselage-length. A sailplane circling in a thermal updraft would be a good example of such an aircraft, and it's not uncommon for a pilot in such a case to be circling with the stick so far aft that it would command a full stall if the wings were level rather than banked.

Another way to look at the curving relative wind induced by the turn, is to note that the aircraft is rotating around the pitch and yaw axes (and in some cases the roll axis as well), and this rotation induces a change in direction and magnitude of the local free-stream airflow as measured at various points along the length and span of the aircraft, just as different points on the blades of a pinwheel are not travelling through the airmass in exactly the same direction at any given point in time. By this point of view, the tendency of the angle-of-attack to be lower when turning than when wings-level can be viewed as a natural consequence of a "pitch damping" effect, creating a resistance to rotation about the pitch axis which requires a change in elevator position to overcome.

Now to "throw one more wrench into the gears"-- the discussion of the effect of roll rate in the first paragraph of this answer referred to the combined average angle-of-attack of both wings. It's simultaneously true that a rolling motion tends to increase the angle-of-attack of the descending wing and to decrease the angle-of-attack of the ascending wing. This is important, as in extreme cases it can lead to a stall of the descending wing. This is also an important cause of adverse yaw that it is not directly related to actual changes in the shape of the wing-- for more see https://www.av8n.com/how/htm/yaw.html#sec-adverse-yaw. Note that even a constant-banked turn involves some degree of roll rate if the altitude is not constant with respect to the surrounding airmass-- the roll rate is toward the inside wingtip in a descending turn, and toward the outside wingtip in a climbing turn, and this will tend to create a difference in angle-of-attack between the two wings that tends to destabilize a climbing turn (i.e. makes the bank angle tend to increase) and stabilize a descending turn (i.e. makes the bank angle tend to decrease). But that's probably more than you wanted to know!