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The Angle of Incidence (AoI) of most GA planes is 6°. Assuming a plane with an Angle of Incidence of 6 degrees--

How do we calculate pitch attitude if we know the direction of the flight path and the Angle of Attack? This is essentially a question about whether Angle of Attack is measured in relation to the chord line of the wing, or in relation to the longitudinal axis of the fuselage.

During takeoff, the Angle of Attack (AoA) is often 11° or more. Is the 11° AoA measured in relation to the chord line of the wing, so that the pitch attitude at takeoff is 11 - 6 = 5 degrees?

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  • $\begingroup$ This question is unclear. Do you know the angle-of-attack, or don't you? It seems you do. So know the angle-of-attack, and the angle-of-incidence, and you are asking how to calculate the pitch attitude? Basically it sounds like you are saying "I know the angle-of-attack but I don't know what it means and therefore I'm not sure how to calculate the pitch attitude from it." Is that right? If not, you could improve the question. $\endgroup$ – quiet flyer Apr 3 at 15:50
  • $\begingroup$ @quietflyer If you think the question is unclear and it should be closed, why did you answer? $\endgroup$ – Bianfable Apr 3 at 17:12
  • $\begingroup$ @Bianfable well, you do the best you can to clear up the confusion of the asker. Who knows whether the question will actually be closed, and others may be led astray whether it is closed or not. If I've violated ASE etiquette in some way, let me know, and I'd appreciate a link to a page that spells out what I did wrong. Just out of curiosity, is there a way to see who submitted a close vote, or did you just make the logical assumption based on the fact that I commented? $\endgroup$ – quiet flyer Apr 3 at 17:18
  • $\begingroup$ Specifically, to try to be more constructive about improvements-- "does the 11° AoA include the initial 6° AoI in it i.e, 11 - 6 = 5"-- what is exactly is the thing that you are suggesting may be equal to 5? Pitch attitude, or something else? "does the 11° AoA include the initial 6° AoI in it i.e, 11 - 6 = 5? Meaning the deflection for takeoff will be 5° (plus 6° of incidence)?" What exactly is the thing that you are calling "deflection"? Pitch attitude. or something else? $\endgroup$ – quiet flyer Apr 3 at 17:21
  • $\begingroup$ (Ctd) ""when I say my plane is climbing with an AoA of 11°, does this 11° include the wings' AoI?" -- in exactly what calculation are you asking whether or not AoI should be "included"? Calculation of pitch attitude starting from Angle of Attack? Or some other calculation? $\endgroup$ – quiet flyer Apr 3 at 17:24
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Speaking of an aircraft, the AOA is simply the angle between the airflow and the aircraft fuselage, in the vertical plane.

The incidence is only required to calculate the wing AOA. The wing AOA is the sum of AOI and AOA_aircraft.

When talking to some aerodynamicist or another engineer, it’s a good practice to state your conventions the first time you use a term, to avoid miscommunication.

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Not really.

The angle of incidence is the angle between the chord of the wing and the longitudinal axis of the airplane. But the plane is mostly free to pitch as necessary. So if the best thing is for the wing to have an AOA of 11°, then it can pitch to that point.

Now if the angle of incidence were too different, it could increase drag on the climb-out, or the thrust angle might be less than optimal. But there's no direct relationship.

The angle of incidence is a figure about the geometry of the plane. The angle of attack is how the wing is oriented to the wind. They don't "add" together.

If you did the math the other way (AOA - AOI), you'd find the angle the wind is making with respect to the airplane axis, not a figure that you tend to need.

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  • $\begingroup$ So if I understand correctly,aoa is totally independent of the angle of incidence? $\endgroup$ – David Teahay May 18 '18 at 8:36
  • $\begingroup$ Simpler question: what is the angle between chord of wing and the ground when the plane has AOA of 11°? 11° or 17°? $\endgroup$ – SF. May 18 '18 at 13:07
  • $\begingroup$ @SF Not a simple relation. Angle to ground depends only on attitude (pitch). AOA depends on path through the air. It would be different for a climbing vs descending plane. $\endgroup$ – BowlOfRed May 18 '18 at 15:23
  • $\begingroup$ @DavidTeahay I hate to say "totally independent", but yes that's right. The angle of incidence is completely fixed while you're flying. The AOA is quite variable as you adjust attitude and path through the air. $\endgroup$ – BowlOfRed May 18 '18 at 15:27
  • $\begingroup$ @SF But if the plane is flying level and the air is still, then the AOA and the wing angle to ground are identical. $\endgroup$ – BowlOfRed May 18 '18 at 15:49
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What they all said, just basically Angle of Attack is created by the pilot pitching the airplane, Angle of Incidence is set by the manufacturer, cannot be adjusted.

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  • $\begingroup$ The asker seemed clear on what Angle of Incidence was and also seemed clear that Angle of Attack would vary if the pilot changed the elevator deflection. $\endgroup$ – quiet flyer Apr 3 at 16:54
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During takeoff, the Angle of Attack (AoA) is often 11° or more. Is the 11° AoA measured in relation to the chord line of the wing, so that the pitch attitude at takeoff is 11 - 6 = 5 degrees?

It seems odd that a pilot would know his plane's angle-of-attack in a given situation, but not know what the angle-of-attack was defined to mean. It sounds like you are saying you know the angle-of-attack is 11 degrees during takeoff, but you are not sure whether the pitch attitude is 11 - 6 = 5 degrees, or whether the pitch attitude is simply 11 degrees, or something else.

Setting aside the fact that it seems more likely that you would know the pitch attitude and not the angle-of-attack rather than vice versa, the answer to your question is --

In the world of practical piloting, flight-training guides, etc, angle-of-attack is usually defined to mean the angle between the wing's mean chord line and the free-stream airflow or "relative wind", which is equal and opposite to the direction of the flight path. At the instant of take-off, the flight path is still horizontal. (Take-off may be defined as the point where the flight path begins to curve upwards into a climb.) So if the angle-of-attack is 11 degrees at this instant, and the angle-of-incidence (as usually defined in practical aviation, especially in the American context) is 6 degrees, then the pitch attitude of the fuselage would be 11 - 6 = 5 degrees.

When we are talking about a whole aircraft rather than just a part such as just the wing or just the fuselage, then sometimes angle-of-attack is used to mean the angle of the longitudinal axis of the fuselage to the relative wind, in which case at the instant of takeoff in the example above, if the angle-of-attack were stated to be 11 degrees, then the pitch attitude of the fuselage would also be 11 degrees. But this is not the norm, especially in the world of practical piloting. Normally angle-of-attack is defined as the angle between the mean chord line of the wing and the relative wind.

When angle-of-attack is defined as the angle between the mean chord line of the wing and the relative wind, a pilot usually does not know his actual angle-of-attack at any given instant, unless he does the math by adding the angle-of-incidence (if known) to the pitch attitude (as visually estimated or as read off the attitude indicator), which is why your question seems a bit odd. Still, even the exact angle-of-attack may not be known at any given instant, all pilots should understand that it is extremely important to the flight dynamics of an aircraft at any given instant. Hence it is entirely logical and normal to talk of "increasing the angle-of-attack to maintain altitude in a turn", etc.

To a first approximation, for any given trim setting, the fore-and-aft position of the control stick or yoke serves to control angle-of-attack rather than pitch attitude. The resulting pitch attitude will be strongly dependent upon climb or descent angle, which is strongly dependent on power setting. In a sense the fore-and-aft position of the control stick or yoke actually serves as an "angle-of-attack gauge", though this effect is distorted by many different factors such as the curvature of the relative wind in turning flight, propwash effects, "bending" of the airflow over the tail by deflected flaps, etc. Still, the basic connection between the fore-and-aft position of the control yoke or stick and the angle-of-attack of the wing is one of the reasons for the frequent references to angle-of-attack by pilots, pilot training manuals, etc.

If you are talking to people who aren't Americans, you should know that there is a British usage of the phrase "angle of incidence" that means the same thing as "angle of attack", rather than meaning the angle between the mean chord line of the wing and the longitudinal axis of the fuselage. You'd more likely encounter this usage in an aerodynamics textbook or a design textbook than in a study guide for a private pilot ground school or written test.

Many other definitions of angle-of-attack exist. For example one might measure between the mean chord line of the wing and the local airflow, including the effect of the upwash coming into the wing, and any propwash that is may be present. One can speak of the angle-of-attack of the vertical fin, or the horizontal tail, in which case again one might be measuring relative to the local airflow rather than the free-stream airflow. Even if one is not considering the deflection of the local airflow by the physical presence of the aircraft, one may, or may not, be taking into account that even the undisturbed free-stream airflow or relative wind is "curved" in turning flight to follow the curvature of the flight path. In other words the rotation of the aircraft about its axes creates an additional velocity component in the undisturbed free-stream airflow which differs at different points along the length of the aircraft, and effectively makes the relative wind "bend" to follow the curving flight path. So, it's complicated. But taking the simple case of linear flight, a good starting point for practical piloting is to take the "angle-of-attack" as meaning the angle between the flight path and the mean chord line of the wing.

Useful related external links--

https://www.av8n.com/how/htm/aoa.html#sec-def-aoa

https://www.av8n.com/how/htm/aoa.html#sec-raoa-aaoa

https://www.av8n.com/how/htm/aoa.html#sec-incidence

Some related ASE questions and answers--

(Q) What is the difference between Angle of Incidence (AoI) and Angle of Attack (AoA)?

(A) What is the difference between Angle of Incidence (AoI) and Angle of Attack (AoA)?

(Q) How common is it in current British usage for the angle between the chord line of a wing and the flight path to be called the "angle of incidence"?

(A) How common is it in current British usage for the angle between the chord line of a wing and the flight path to be called the "angle of incidence"?

(Q) Is there a standard word or phrase in the English-speaking world to describe the angle between the fuselage and the flight path / relative wind?

(A) Is there a standard word or phrase in the English-speaking world to describe the angle between the fuselage and the flight path / relative wind? -- (possibly a non-standard view on the matter)

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  • $\begingroup$ It seems that using the wing angle-of-attack is more common in small aircraft, which tend to have straight untwisted wings with obvious chord line and not much of a floor to define the body axis, while using fuselage angle-of-attack is more common in large aircraft with twisted swept wings where the chord line varies along span, but they have a lot of floor that clearly defines the fuselage axis (e.g. for A320 the alpha-limit is given as 17° and critical AoA around 20°, which are unrealistic values for any airfoil, so they are clearly referenced to fuselage). $\endgroup$ – Jan Hudec Apr 3 at 19:51
  • $\begingroup$ @JanHudec -- interesting, thanks, worthy of an answer $\endgroup$ – quiet flyer Apr 3 at 19:54

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