Dihedral and angle of attack. Say again??

[mcg]

Today I have been collecting explanations of why dihedral provides lateral stability. Here is a typical example I found on the net:

"The dihedral angle is the angle that each wing makes with the horizontal. The purpose of dihedral is to improve lateral stability. If a disturbance causes one wing to drop, the unbalanced force produces a sideslip in the direction of the downgoing wing. This will, in effect, cause a flow of air in the opposite direction to the slip. This flow of air will strike the lower wing at a greater angle of attack than it strikes the upper wing. The lower wing will thus receive more lift and the airplane will roll back into its proper position."

Here is another one, more academic, invoking a partial differential equation:

http://www.aoe.vt.edu/~cwoolsey/Courses/AOE3134/Lectures/AOE3134.Lecture8.pdf

And finally here is an explanation written by a pilot.

http://www.av8n.com/how/htm/roll.html

I like this one best, for its direct language and approach, but I still don't understand how dihedral works.

Okay, say the left wing has dipped, owing to some sort of transient turbulence. The plane is seen to be in a sideslip to the left. This sets up a flow of air sparwise along the wings, crosswise to the normal (oncoming) flow of air.

According to the literature, here, if a dihedral angle exists, then the spanwise flow of air somehow alters (in fact, increases) the angle of attack of the dipped left wing. Simultaneously, the spanwise flow reduces the angle of attack of the upraised right wing.

Fine. Virtual ailerons. The differential lift rolls the plane back to level flight.

What I cannot seem to visualize, at all, is the way in which the spanwise flow of air is somehow interacting with the bent wing in such a way as to increase the angle of attack of the dipped left wing -- while decreasing the angle of attack of the elevated right wing.

I don't doubt that it happens. I just cannot see the mechanism.

Thanks for your insights.

Michael

[BMatthews]

It's easy. Take a dihegralled wing and look at it from the front so it's as thin a line as you can adjust it to. Now reach out and yaw the wing to one side or the other by about 10 or 15 degrees. You'll now find that you're able to see the lower surface of the panel that is closer to you and the top surface of the panel that is farther away. This is what the air sees when the wing side slips due to a disturbance or if you use the rudder to yaw the model and make it turn.

Your eyesight is the air and it's seeing the wing with the lower surface exposed at a higher angle of attack and the wing with the top surface exposed at a lower angle of attack... in this case a negative angle in fact.

Let's modify the this expample a little. Move the wing back to straight across and shim up the leading edge so you can see some of the lower surface. Now swing (yaw) the wing again. Note that now you see more of the lower side of the panel closer to you and less of the lower side of the panel further away. This is a more typical example of what the airflow sees. The airflow is seeing the leading wing (the one closer to you) at a higher angle of attack (it can see more of the lower surface) and a lower angle for the trailing wing. And since in increase in the angle of attack generates more lift thisis why the wing rolls when it side slips.

The rudder in a rudder controlled model does not turn the model. Instead it is used to yaw the model which produces a sideslip angle and it is the side slip angle working with the dihedral that rolls the model into the turn.

Howzzat?

[mcg]

Thank you Bruce, this works beautifully. I made a paper wing and eyed it from various perspectives, as you suggest.

Your explanation differs from the others in that it starts with a rotation about the yaw axis. This makes all the difference.

Start from a yaw, and the rest of the story falls right into place.

There is one persistent difficulty. Most of the explanations I have found start with an aircraft straight and level, and then introduce a perturbation in roll. The left wing dips, say, for whatever reason.

How do we get from this simple rotation about the roll axis to the necessary rotation about the yaw axis? And would this happen whether or not the wing were bent?

This is the reverse of the more familiar and readily understood yaw=> roll, as in the familiar rudder-only control system.

Here is a link to yet another in my growing collection of dihedral essays:

http://www.rubber-power.com/h/rp/Articles/ftaf3.pdf

In the second paragraph he acknowledges your central and crucial point -- that the correction in roll starts with a yaw. But maybe he sort of hurries past the problem of how this might come about.

So I am much further along, thanks to your clear reasoning and images, but still stuck on this problem: how does a roll turn into a yaw?

Sounds sort of gyroscopic.

Thank you again. Michael

[BMatthews]

...There is one persistent difficulty. Most of the explanations I have found start with an aircraft straight and level, and then introduce a perturbation in roll. The left wing dips, say, for whatever reason.

How do we get from this simple rotation about the roll axis to the necessary rotation about the yaw axis? And would this happen whether or not the wing were bent?....

This is because most of the explanations you're reading are about how dihedral is a stabilizing feature. So of course they are going to deal with how it responds to an upset.

The key is that whatever happens the result is that airflow alters from straight onto the wing to coming from one side at an angle. This angled flow can be the result of a yawing action or a side slip action due to an unwanted roll upset. Both result in the airflow direction altering to the side as far as teh wing is concerned. At that point the dihedral comes into play and rolls the aircraft and continues to roll it as long as it sees the air flowing onto the wing from an angle.

Your issue seems to be how does a rolling upset convert to yaw. The answer is that it doesn't. But the wing doesn't care. It's not the yaw or the roll that it sees. It's ONLY the airflow direction onto the wing.

So in your turbulent upset that rolls the left wing low the dihedral actually does not do anything initially until the model starts to slide slip. Only once it sees this angled airflow does it alter it's span wise lift distribution and create a rolling force of it's own.

[mcg]

Okay -- at long last I am clearly comprehending this.
Thank you for you patient logic.

The dihedral effect actually is pretty simple -- once you manage to see past the densely complicated attempts in print to explain the darn thing.

For anyone else who is having trouble seeing this, here is how I finally broke through.

I made a V-wing out of folded paper and put it on my desk, with the right wing resting flat on the desk and the left wing elevated about 30 degrees.

[You could, to exaggerate the dihedral and demonstrate the principle more clearly, bend the left wing up 90 degrees].

Then I approached the leading edge with my pencil, using the pencil to represent the "relative wind." When the pencil approaches the wing straight-on, parallel to the desktop and perpendicular to the leading edge -- both the flat and the elevated wing have the same angle of attack. Nothing happens.

But when, to represent a slip, the pencil comes in at a slant to the aircraft's forward progress (though still parallel to the desktop) something new appears. Although the angle of attack for the wing flat on the desktop is not changed -- the sideslanted incoming pencil now points to the top of the airfoil for the elevated left wing. It is in this sense that the "effective angle of attack" is reduced for the left wing. It is as though the left wing, only, had been put into a dive.

Dihedral is one of those concepts that could probably be illustrated very readily with a cartoon or in a classroom, but kind of resists an explanation in words.

One other thing that seems to be happening in the slip. The airfoil traced by two streams of atoms that diverge at the leading edge and find each other again at the TE -- is going to changed in cross-sectional shape. Stretched. Not sure if this effect is the same for both wings.

Best, Michael

[BMatthews]

Yeah the air effectively sees a wider chord but this isn't a big deal. You can ignore that effect in most cases.

However in the case of a swept wing it does matter. The air "sees" a longer wing on the leading side of the side slip than the trailing wing thanks to the angle and thus the leading wing tries to lift itself up to restore the airflow to straight ahead and balanced. This is the source of the concept of swept wings providing some dihedral effect. But the effect is minimal with a general acceptance of something like 7 to 10 degrees of sweep being about as effective as only 2 or 3 degrees of dihedral.

This is because the lift change due to angle of attack variations in a dihedral wing is far more powerful than a surface area change of a flat but swept wing.

[mcg]

Thank you again, Bruce. I appreciate your help in working through this thing.

[Peter D Rieden]

I guess the crucial thing is actually that there is no such thing as "lateral stability". Instead there is yaw-roll coupling. Where you have proverse yaw-roll coupling you will get a self-righting effect in roll as a secondary effect because a displacement in roll will produce a sideslip, which is the same thing as a yaw. But it isn't "lateral stability" because of this phase lag, so the aircraft will not return to its pre-disturbed position - it will return to wings-level, but on a different heading.

PDR

[Gene Bond]

I don't see any discussion of roll stability, so he's a thought:

I made a V-wing out of folded paper and put it on my desk, with the right wing resting flat on the desk and the left wing elevated about 30 degrees.

Now, picture the effective wing area of each side, in other words, looking straight down on the wing (or up, actually), and the side that's flat on the desk has more effective area, thus more lift, so it will want to lift, while the up-tilted wing will want to drop, viola!

[Peter D Rieden]

I don't see any discussion of roll stability, so he's a thought:



Now, picture the effective wing area of each side, in other words, looking straight down on the wing (or up, actually), and the side that's flat on the desk has more effective area, thus more lift, so it will want to lift, while the up-tilted wing will want to drop, viola!

This is the common fallacy - you'll even find it in a lot of books! Unfortunately in reality the wing that's NOT flat on the desk has a lift vector which resolves into two components. A vertical one and a horizontal one. The horizontal one is a roll moment that is equal and opposite to the perceived "extra lift" of the one that is flat on the desk, so no voila...

PDR

[Ollie]

See:
http://en.wikipedia.org/wiki/Paraglider
This aircraft is stable in pitch, roll and yaw because its low CG position relative to lift and drag forces. I has "lateral stability". The aircraft is controlled by CG position relative (or other way around) to drag and lift vectors. It holds its shape with the shrouds' and frabic tension between weight and lift vectors.

[Peter D Rieden]

See:
http://en.wikipedia.org/wiki/Paraglider
This aircraft is stable in pitch, roll and yaw because its low CG position relative to lift and drag forces. I has "lateral stability". The aircraft is controlled by CG position relative (or other way around) to drag and lift vectors. It holds its shape with the shrouds' and frabic tension between weight and lift vectors.

The lateral stability mechanism only stabilises to the local "G" vector, not to true vertical. In priciple thhis stability mechanism can stabilise the aeroplane in a constant rate turn and a constant bank angle. That's why it is not a true "lateral stability mechanism".

PDR

[Ollie]

Peter,
Thanks for correcting me. I accept your point for lateral stability.

I said "weight" and I should have said "weight and other inertial forces."