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I've been reading the FAA's Glider Flying Handbook, 2013 (FAA-H-8083-13A). In chapter 3 ("Aerodynamics of Flight"), the book is discussing stability. On page 3-12, it states:

Dihedral is the upward angle of the wings from a horizontal (front/rear view) axis of the plane. As a glider flies along and encounters turbulence, the dihedral provides positive lateral stability by providing more lift for the lower wing and reducing the lift on the raised wing. As one wing lowers, it becomes closer to perpendicular to the surface and level. Because it is closer to level and perpendicular to the weight force, the lift produced directly opposes the force of weight. This must be instantly compared to the higher and now more canted wing referenced to the force of weight. The higher wing's lift relative to the force of weight is now less because of the vector angle. This imbalance of lift causes the lower wing to rise as the higher descends until lift equalizes, resulting in level flight.

That doesn't sound right to me.

This paragraph says that there's more lift on the lowered wing and less lift on the raised wing. That's not true, is it? The amount of lift only depends on a wing's airspeed and angle of attack, not on the wing's bank angle.

The paragraph then explains that the lowered wing produces more upward lift than the raised wing. I think this is true, but it's not relevant, because upward lift isn't the only lift which contributes to rolling moment. Rolling moment depends on the total lift (and the direction of the lift).

All in all, I think that dihedral can't produce a stabilizing rolling moment in the way that the book says that it does. Any stabilizing effect must come from a difference in airspeed or angle of attack between the two wings.

Is the book's description of dihedral correct?

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    $\begingroup$ Possible duplicate of How does the dihedral angle work? $\endgroup$ – Pilothead Jul 11 '18 at 18:59
  • $\begingroup$ I agree with you. Dihedral effect requires sideslip. They seem to be describing what people call the "pendulum effect," which is due to the dihedral but is not the same thing. $\endgroup$ – TomMcW Jul 11 '18 at 19:19
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    $\begingroup$ @Pilothead I'm asking about this one particular explanation of the dihedral effect. Only one of the answers on that question addresses the FAA's explanation. That answer essentially says that the FAA's explanation is correct, but it's also downvoted, and there are comments which say that the answer (and therefore the FAA's explanation) is not correct. So, there is apparently no answer to that question which correctly answers my question. $\endgroup$ – Terran Swett Jul 11 '18 at 19:23
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    $\begingroup$ @PeterKämpf I think I'll post up a question about it later so I can figure it out. We haven't had a question specific to the "pendulum" thing. $\endgroup$ – TomMcW Jul 11 '18 at 22:13
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    $\begingroup$ I don't think this is a duplicate. Although the question is about the same topic, this question asks about understanding a particular detail which isn't really mentioned in the other question or its answers. $\endgroup$ – Dan Hulme Jul 12 '18 at 8:33
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No, the explanation is not correct.

Tanner, you are right when you say that lift does not depend on bank angle. Lift is caused by a pressure difference, and pressure can only act perpendicularly to a surface. Therefore, the lift on each wing and its lever arm to the center of gravity won't change with bank and no "correcting" rolling moment is created.

Instead, what does happen is a side force from the wing's bank angle which will accelerate the airplane sideways. This in turn will result in a sideslip condition, and only now will a dihedral effect show up: By changing the angle of attack on each side differently, the sideslip in combination with dihedral will create a correcting rolling moment.

As you correctly observe, a stabilising effect can only come from a difference in angle of attack between both wings, and that only occurs in a sideslip.

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The analysis by the asker of the question is correct, and the paragraph in the FAA's "Glider Flying Handbook" is not correct. The same is true of any "explanation" of dihedral that doesn't rely on the difference in angle-of-attack between the two wings generated by sideslip.

Furthermore, it's important to note that sideslip cannot be explained simply by noting that when an aircraft is banked, the tilted lift vector contains a sideways component, or that "from the point of view of the aircraft, lift is still acting in the plane of symmetry, but gravity does not and will cause it to sideslip", as is sometimes stated. (For example, we find something close to this in Martin Simons' well-known book "Model Aircraft Aerodynamics", as well as in many other sources.) Those are essentially Aristotelian concepts rather than Newtonian concepts. A continuous net sideways force component causes a turn, not a sideslip. Force causes acceleration, not steady sideways motion, and turning is a curvature in the flight path which is a form of acceleration.

For ideas on the actual cause of sideslip during banked, turning flight, see this related answer How does the dihedral angle work?

The "explanation" of dihedral is only one of several conspicuous errors in the FAA's "Glider Flying Handbook". For example, it doesn't even contain an accurate depiction of the L-D-W vector triangle to explain why the L/D ratio is the same as the glide ratio through still air-- such a diagram is fundamental to understanding gliding flight. It also claims that it is dangerous to slip gliders with swept leading edges due to the resulting slip-roll coupling-- totally overlooking the much larger slip-roll coupling created by dihedral (e.g. any modern glass ship other than Fox, Swift, etc) and/or high wing placement (e.g. 2-33, 2-22) in a typical sailplane.

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Yes, it is correct. Consider an airplane with a positive 5° dihedral to its wings. If the lift the airfoils generate is perpendicular to its span line, this means that in level flight the lifting force parallel to the plane’s vertical axis is L*cos(5°) for both wings. If the airplane is rolled 30° to the left, then the lift generated by the left wing parallel to the force of gravity is L * cos(25°) whereas the lift generated by the right wing is L*cos(35°). This imbalance in lift causes a moment about the plane’s CG, causing it to roll back level and providing both a positive lateral static and dynamic stability.

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    $\begingroup$ It looks to me like you're only looking at the component of lift which is parallel to the force of gravity, and not the component which is perpendicular to the force of gravity. Is that right? When you add in the component which is perpendicular to gravity, is there still an overall rolling moment, or is the rolling moment canceled out to zero? $\endgroup$ – Terran Swett Jul 11 '18 at 20:16

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