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I've been reading Wolfgang Langewiesche's book Stick and Rudder and am a little confused about the definition of the elevator as the "Angle of Attack Control" or rather, the idea that each position of the elevator corresponds to a unique angle of attack.

I was under the impression that Angle of Attack is the angle the wing meets the relative wind. Consider a certain elevator position for straight and level flight at cruise rpm. If I then add power and climb (while holding the same attitude) isn't it true the Angle of Attack will increase because the relative wind is now coming from in front and above the plane? If this is true, then how can I reconcile this with the idea the elevator is an "angle of attack" control. Isn't the plane's Angle of Attack based on not just the position of the elevator, but the motion of the plane through the air?

If anyone could give me some advice to clear this up it would be greatly appreciated!

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Wolfgang Langewiesche is right to appropriate order of approximation. For every elevator position a statically stable airplane settles to a specific equilibrium angle of attack. That's how static stability works.

Airplane is statically stable if and only if increasing angle of attack causes higher increase in coefficient of lift on the aft airfoil (tail for normal layout). Then increasing angle of attack (by random fluctuation like turbulence) increases the lift aft more, the overall centre of pressure moves aft and the aircraft pitches nose down to return the angle of attack to the trimmed position.

By moving the elevator you adjust the coefficient of lift on the control surface, and the plane needs to assume a different angle of attack to shift the centre of pressure back to coincide with centre of gravity. Most aircraft are designed so this is quick enough that if you don't jerk the controls too much the angle of attack simply follows the elevator position.

isn't it true the Angle of Attack will increase because the relative wind is now coming from in front and above the plane?

The angle of attack is high when the relative wind is from below and low when it is from above.

If I then add power and climb (while holding the same attitude)

If you add power and leave the yoke as trimmed, the plane will start to accelerate, which increases the lift. That causes the plane to accelerate upward, which decreases the angle of attack. This decreases the lift more on the tail, so the tail sinks and the aircraft pitches up until it assumes the original angle of attack. At this point, the pitch angle is increased by the same amount as the flight path angle.

The aircraft is still moving faster than the original speed due to inertia, so the lift is still more than weight and the aircraft continues accelerating up and pitching up to maintain the angle of attack. When the speed returns to the trimmed, the aircraft is already pitched too much, so now it will slow down and pitch down again and repeat the cycle. This is called the Phugoid oscillation. In most planes it is damped, but still annoying if you don't counter it with a bit of elevator deflection. But if you don't touch the trim, just arrest the phugoid, the aircraft will settle in climb at the same speed.

It has some consequences:

  • Tendency of the plane to pitch down means it is losing airspeed.
  • If you are not pulling on the yoke, or trim aggressively nose up, you won't stall. Unfortunately pulling on the yoke to keep the nose up becomes too much of a muscle memory so it's easy to miss this clue.
  • It is how pitch for speed and power for descent rate works on descent.

See also How It Flies, specifically section 2.3 talks about trim and angle of attack, with more details further in chapter 6.

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Stick and Rudder also states on page 5 that we normally teach "theory of building the airplane rather than of flying it." Take the Lift Formula, and let's put it into terms the pilot can control in flight. Lift = coefficient of lift x 1/2 air density x true velocity squared x wing area.

When we teach this in ground school, we instantly see the eyes glaze over on over half of the class. Simplified for Pilots, the Lift formula can be shown as Lift = (better shown as proportional to) Angle of Attack x KIAS x KIAS.

Now we have only two items that enter into the formula: AoA and the Airspeed dial. (wing area can't be controlled by the pilot in flight, unless flying something like the F-111 with a wingsweep handle and huge double-slotted Fowler Flaps). True Airspeed Velocity and air density interact to get to Calibrated Airspeed (KIAS when adjusted for installation), and the Pilot's handbook of Aeronautical Knowledge (PHAK) figure 5.5 shows a straight line relationship between Coefficient of Lift and Angle of Attack.

Therefore, when in the cockpit, the only way the pilot can control lift is by adjusting either AoA or KIAS.

Note: Throttle does not enter into the lift equation, unless the pilot is trying to maintain a specific airspeed while maneuvering, which requires throttle movement to counteract changes in drag.

Note: Trim does not enter into the Lift equation. All that trim accomplishes is to reduce/eliminate stick/yoke pressure to maintain a specific hands-off angle of attack (which some equate to attitude or airspeed, but trim really just commands a hands-off AoA).

Langewische is correct about elevator position (which equates to stick/yoke position) commanding a specific AoA. But, as always there are some caveats such as:

  • Center of Gravity Location (forward vs rearward CG within range)
  • Aircraft configuration (flaps, gear, etc)
  • Power downwash over the tail.

So, we can't just paint marks on the control yoke rod "green, yellow, red." There was some talk earlier saying "what can happen if the engine abruptly quits while an aircraft is in a very steep climb". What will really happen is the airplane will rotate downward to maintain the trimmed AoA and will not stall "unless" the pilot continues to pull the yoke backward (which is what nearly always happens in this stressful situation). There were some other comments about flying a phugoid to show stability. The pitch phugoid is great to show stability, but it also shows the relationship between AoA, speed, lift, and stick/yoke position.

Here's a great demonstration, which is best accomplished in an airplane with both a G-meter and and AoA gauge. Trim the airplane for 1-G, steady speed, level flight. Slow the airplane to a range where not all of the green bars on the AoA gauge are illuminated (I do this around 80-90 KIAS). Pull the nose about 20 degrees nose up, then take your hand off the stick/yoke. Monitor the yoke position--it will revert back to the same position it was before you pulled (I've used a ruler to document stick position). Watch the AoA gauge (it will remain nearly constant), watch the stick/yoke not move, watch the G-meter go to less one when the airspeed is slow (at the top) and more than one when the airspeed is high (as the airplane pulls out). This is because the amount of lift required is constantly changing (L = AoA x KIAS x KIAS), but the AoA is not changing (or changing slightly, due to mostly to momentum).

As for maneuvering flight, the lift equation remains the same. The airplane doesn't care what attitude it is in, just how much lift is required. When you roll into that 60 degree bank (LEVEL, 2G turn, while maintaining constant speed with throttle), the airplane sees a need to generate twice the amount of lift. Since airspeed is unchanged, the AoA must increase to double the lift--this is done by pulling back on the stick/yoke a specific amount to command that AoA. Is there some lag? yes, Momentum enters into the equation a bit, but the plane still reacts pretty quickly to elevator inputs (especially when at higher speeds). Can you pull so abruptly that things get out of kilter a bit, yes.

Another great demonstration is to get a flight in an Ercoupe, especially an older one with just a one brake pedal on the floor. Slow up, pull the yoke all the way back, you will not stall (maybe you can get close with a super abrupt pull, but then the plane will stabilize out). You can get into a pretty good rate of descent, but the elevator will not travel high enough to maintain a stall. So, knowing about the physical position that the stick/yoke will reach stall AoA (in the configuration, CG, etc., that you typically fly) will give you another indication of when you are approaching a stall in either 1G or accelerated G flying. (You don't have to know that position exactly, just be aware of the approximate location, kind of like playing a trombone).

I'm sure this will be controversial, but I hope you will think about these comments and try out the maneuvers before commenting. This is not meant to be a discussion on how to build an airplane (the actual aero formulae get extremely complicated, and heck, we can't agree on whether Bernouli, Newton, or Coanda develop lift), but this is meant how to provide tools to the pilot understand what is happening in flight that they have "control" over.

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  • $\begingroup$ Re "Watch the AoA gauge (it will remain nearly constant)"-- I've done similar experiments in Cessna 152s and 172s and was consistently able to trim the airplane so that in hands-off flight, the stall horn consistently sounds at the top of each pitch phugoid oscillation but is quiet at the bottom of each pitch phugoid oscillation. Food for thought. My interpretation is that the curvature of the flight path in the pitch dimension causes a "damping" effect on the tail surfaces that tends to decrease the AOA of the wing whenever the curvature of the flight path is in "upward" direction rel to a/c. $\endgroup$ – quiet flyer Mar 23 at 16:43
  • $\begingroup$ Which I interpret as being a bit different than "momentum". Would be interesting to really try to evaluate the relative importance of pitch rotational inertia (momentum), versus "damping" effect due to curvature of flight path/ relative wind. Another way to look at "damping" is that curving relative wind is pushing "down" on tail whenever flight path is curving "upward"; this effect is very pronounced in hang gliders due to low flight speed and resulting small radius of curvature of flight path while maneuvering, even though their pitch rotational inertia is rather low. $\endgroup$ – quiet flyer Mar 23 at 16:43
  • $\begingroup$ In both hang gliders and sailplanes, the pilot typically holds a strong nose-up pitch control in a steady-state moderate-to-steep-banked turn while circling at min sink speed, such as would be sufficient to produce a full stall if the wings were level. Since the turn is a steady-state manuever, we can eliminate momentum/inertia as a consideration here. So the pitch "damping" phenomenon due to non-zero pitch rate (i.e. due to curvature of flight path in pitch axis-- two sides of the same coin, at least in a steady-state maneuver) must be the key reason that this pitch input is required. $\endgroup$ – quiet flyer Mar 23 at 16:48
  • $\begingroup$ But to a first approximation the observation that the a-o-a remains nearly constant through the phugoid is a valid one-- $\endgroup$ – quiet flyer Mar 23 at 16:52
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There is a contradiction built into the question. You write:

Consider a certain elevator position for straight and level flight at cruise rpm. If I then add power and climb (while holding the same attitude) isn't it true the Angle of Attack will increase because the relative wind is now coming from in front and above the plane? If this is true, then how can I reconcile this with the idea the elevator is an "angle of attack" control?

You've implied that you've kept the elevator position constant as you added power and climbed. You've also stated that the aircraft's attitude has remained constant. You've over-constrained the problem. The elevator is to a first approximation an angle-of-attack control, not a pitch attitude control, and it's not possible for the angle-of-attack and the pitch attitude to remain constant as the plane transitions from level flight to a climb.

No doubt if we tried hard enough we could come up with an exotic example where some particular aircraft could in fact maintain both a constant elevator position and a constant pitch attitude when power was added to transition from level flight to a climb. For example, if the nose-mounted engine had a great deal of downthrust, causing a large decrease in angle-of-attack when the power was added and the elevator position was held constant. Most pilots would consider such an aircraft to be unpleasant and unnatural to fly. To a first approximation, in most aircraft the angle-of-attack is primarily determined by the position of the elevator. That's what the elevator is designed to do-- to control the angle-of-attack of the wing.

It's often true that the power setting has some influence on angle-of-attack, for a given elevator position, but this is generally a byproduct of the thrust line location and other aspects of the aircraft's geometry, not an intentional design feature. Designers typically strive to minimize such effects.

Langewiesche's basic point is that if the control stick or yoke is not pulled too far aft, the wing cannot stall, regardless of the aircraft's pitch attitude. This isn't always exactly true-- consider what can happen if the engine abruptly quits while an aircraft is in a very steep climb, or if the towline breaks while a glider is climbing very steeply on a winch tow. But it's a good starting point. To a first approximation, the elevator controls the angle-of-attack of the wing, not the pitch attitude of the aircraft. The pitch attitude is a result of the angle-of-attack of the wing and the climb or descent angle, and the angle-of-incidence at which the wing is attached to the fuselage.

We often hear that "pitch plus power equals performance". And pilots often say things like "pitch for a climb at Vy". Statements like these may seem to carry some implication that the elevator is controlling the aircraft's pitch attitude. While it's certainly true that changing the elevator position will change the aircraft's pitch attitude, it's also true that as we vary the power setting from idle to full power, we'll find that any one particular elevator position correlates to one specific angle-of-attack much more closely than it correlates to any one particular pitch attitude. This also means that as we vary the power setting from idle to full power, we'll generally find that there's a good correlation between elevator position and airspeed, at least for any given G-loading.1

Footnotes:

  1. At really extreme climb or descent angles, the correlation between angle-of-attack and airspeed changes, which also means that the correlation between elevator position and airspeed changes. At really extreme climb or descent angles, the airspeed indicator no longer serves as an "angle-of-attack gauge" in the same way that it does when the flight path is closer to horizontal. This is discussed in more detail in this related ASE answer to a related question -- which also has some other content that you may find relevant to your question.
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It seems to me that the crux of the misunderstanding in your question is here:

If I then add power and climb (while holding the same attitude)

If you hold the elevator in a fixed position and add power, the airplane will pitch up relative to the ground, to the extent needed to preserve the original angle of attack relative to the airplane's motion through the air (i.e. "relative wind").

If by "holding the same attitude", you mean "maintain the elevator in a fixed position", then your answer is in your question. Angle of attack doesn't change if you don't change the elevator position; if in your question you mean to assert the latter, then the former results, just as the book says.

On the other hand, if you mean "maintain the airplane's orientation relative to the ground", then the only way to accomplish that after you add power is to change the elevator position, reducing actual angle of attack. This negates the premise of your question.

It's not entirely clear from your post which you mean, but either way it's interpreted, the resulting explanation is consistent with the information you're asking about.

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If you add power while holding the same attitude you will accelerate. As you accelerate you will have to hold the nose down and trim, (gradually changing your attitude) but this will actually decrease rather than increase the AOA.

Unless you want to climb. If you add power and pitch up to hold the same airspeed, you will climb at the same AOA and airspeed that you previously had during level flight.

The relative wind in a climb is coming more from above, (which would otherwise decrease, not increase AOA) but because you pitched up the angle of that relative wind to the wing chord can, and does, remain the same for a given airspeed.

Since the elevator controls pitch it is also correct to say that it directly controls AOA as well, although you are correct that it is also dependent on the aircraft's motion through the air. (think of a loop, with positive AOA at the top...)

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For a given airspeed, there is exactly one distinct angle of attack possible resulting in straight stabilized flight. If it would be higher or lower in any moment, there is excessive or insufficient lift and forces are no longer in balance. It gets "adjusted" thanks to airplane designed longitudinal stability by either readjusting change in pitch, changed airspeed or rate of climbing, likely more of these simultaneously.

So you can think -- for straight flight -- that setting AoA is the same as setting airspeed. Maybe it is more convenient way? (In steep high-G turns this relation breaks as you need higher airspeed for given AoA to provide enough lift. Here, a properly working trim should hold stable AoA and let airspeed increase.)

Another fact to keep on mind is that, in first order approximation (neglecting extreme attitudes) airplane's stability and pitch control does not care too much about horizon and attitude. It is AoA which defines forces regardless if it is affected by attitude or climb. (The change in direction of gravity force has usually negligible effect here.) Elevator or trim has no direct way to "feel" attitude w.r.t horizon, so that's why controlled value is AoA.

On the other hand, you engine does care a lot about vertical speed because of available power. If you trim for specific AoA (or speed), then depending on available power, it will result in horizontal flight, or climb with same AoA (and therefore more nose-up attitude to compensate for change in relative airflow), or sink with more nose-down attitude.

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Your understanding of AoA is correct. While the elevators do influence AoA they don’t control it, so you’re right that a particular elevator position doesn’t correspond to a particular AoA. You example is flawed though - if you increase power to climb then your AoA might not change at all, or not significantly.

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  • $\begingroup$ I'm not sure what you mean by "influence", but the elevator most definitely controls AOA. $\endgroup$ – Michael Hall Jan 3 at 1:01

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