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Feb 05, 2018, 12:58 PM
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aeronaut999's Avatar
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Is a "Dutch Roll" oscillation possible in an aircraft with zero "effective dihedral"?


Is a "Dutch Roll" oscillation possible in an aircraft with zero "effective dihedral" or mildly negative "effective dihedral"?

In other words, is positive "effective dihedral" an essential ingredient in a "Dutch Roll" yaw-roll oscillation?

By "positive effective dihedral" I mean that a sideways airflow (sideslip) generates a roll torque component in the "downwind" direction, due to the combined effects of dihedral/anhedral, sweep, high/low/mid wing placement, height of vertical fin, vertical location of CG, and any other relevant factors.

I recognize that --particularly if sweep is present-- the "effective dihedral" varies with angle-of-attack and can change from positive to negative as the angle-of-attack is decreased, so a more comprehensive phrasing of the question would be "is it possible for a "Dutch roll" oscillation to occur in a part of the flight envelope (i.e. at an angle-of-attack) where an aircraft's "effective dihedral" is zero or mildly negative?"

Inherent in the question, I guess, is another question-- is "Dutch roll" one very specific type of yaw-roll oscillation, or can the term be applied to a variety of different kinds of yaw-roll oscillations with substantially different forcing effects? I.e. substantially different phasing between the point of max deviation from average heading, the point of max sideslip, the point of max bank angle, etc. ? Are a variety of such oscillations even possible or is there only one way all the variables can fit together to drive a yaw-roll oscillation?

For simplicity let's assume we're talking about a non-elastic (non-deformable) aircraft. Let's also assume that pilot inputs are not involved, at least once the oscillation has begun.

Some of you probably know I've posted in the past about a yaw-roll oscillation (also involving a pitch "phugoid" component as well) that I've seen in one particular, rather flexible aircraft in a part of the flight envelope where the "effective dihedral" was definitely negative-- but for the moment let's assume that nothing is proved by that particular example due to the flexible nature of the aircraft.

Steve
Last edited by aeronaut999; Feb 05, 2018 at 01:17 PM.
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Feb 05, 2018, 03:03 PM
B for Bruce
BMatthews's Avatar
GOOD QUESTION!

It takes me back to a trial I did with a 2M aileron glider to determine the role of the vertical tail volume in how aileron gliders handle in turns. I had found that some needed strong outer aileron to be held in even lower bank angle turns and some needed little or no outer aileron at lower bank angles. So I did a test to see how my one model handled going from a much too high Vvt to a much too low Vvt. Also from my past posts you'll likely know that due to my free flight flying that I've also seen my share of models that dutch roll.

The glider got down to where the yaw damping was poor by any measure and the tail hung low in the turns and I was getting bad adverse yaw despite a coupled rudder and some aileron differential. Yet it never did the classic dutch roll thing with the tail swinging side to side.

It's also interesting to note that the free flight models that showed a lot of dutch roll during the powered climb did not have any dutch roll in the glide.

So it occurs to me that the dutch roll symptoms may only occur when climbing. Although there are other issues with too small a vertical tail when gliding and perhaps when cruising level.

I've read accounts of full size planes with a cyclical hunting of the tail during climbs or cruise. Some put up with it and others ended up with various fixes. Just don't ask me at the moment for specific examples. It's been a long time since I read the articles in question in magazines like Air Progress and such. But one that I believe had this issue was the B-17 where it grew the curved dorsal on the fin between the "D" and "E" versions.
Feb 05, 2018, 05:56 PM
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I think it’s absolutely possible to have a Dutch Roll mode with zero dihedral effect. When you excite the Dutch Roll in a full scale airplane, it’s interesting to watch the path traced by one of the wingtips. Some airplanes have a lot of vertical motion with almost no perceived horizontal motion. Test pilots call that a “rolly” Dutch Roll mode. At the other end of the spectrum, other airplanes have a lot of horizontal motion with almost no perceived vertical motion. Test pilots call that a “snaky” Dutch Roll mode. A plane with zero dihedral effect would represent the limiting case of a snaky Dutch Roll.

In a Dutch Roll, the airplane’s directional behavior (Izz, stiffness, and damping) couples to its lateral behavior (Ixx and damping) through dihedral effect. Note that there is no lateral stiffness in this context. Without the Spiral Mode being excited, pure lateral motion has a first-order response, whereas pure directional motion has a second-order response.

So I would say you can decouple the lateral and directional motions by removing dihedral effect and observing directional oscillation without lateral oscillation. You cannot, however, go the other way and observe lateral oscillation without directional oscillation, because it’s the directional displacement that provides the stiffness (tendency to return to original condition). Very strong dihedral effect may, however, make it appear this way.
Last edited by ShoeDLG; Feb 05, 2018 at 06:03 PM.
Feb 05, 2018, 06:45 PM
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Interesting thoughts Bruce and Shoe; thanks. I guess I was trying to think of whether there could be a case where there WAS substantial lateral (roll) oscillation, but somehow driven by something other than positive "effective dihedral"-- e.g. driven by roll-torque-due-to-yaw-rate, with direction of the roll torque presumably being toward the retreating wingtip. Would such an oscillation look substantially different than one strongly driven by positive effective dihedral, in terms of when in the cycle the different variables are hitting their max and min values?

Or, in a really possible bizarre case where the phase of the oscillation must be quite different from the normal case, could there be a yaw-roll oscillation driven in part by a "backwards" roll response to sideslip, due to negative "effective dihedral"?

Those are the things I'm mulling over--

Quote:
Originally Posted by ShoeDLG
I think it’s absolutely possible to have a Dutch Roll mode with zero dihedral effect. When you excite the Dutch Roll in a full scale airplane, it’s interesting to watch the path traced by one of the wingtips. Some airplanes have a lot of vertical motion with almost no perceived horizontal motion. Test pilots call that a “rolly” Dutch Roll mode. At the other end of the spectrum, other airplanes have a lot of horizontal motion with almost no perceived vertical motion. Test pilots call that a “snaky” Dutch Roll mode. A plane with zero dihedral effect would represent the limiting case of a snaky Dutch Roll.

In a Dutch Roll, the airplane’s directional behavior (Izz, stiffness, and damping) couples to its lateral behavior (Ixx and damping) through dihedral effect. Note that there is no lateral stiffness in this context. Without the Spiral Mode being excited, pure lateral motion has a first-order response, whereas pure directional motion has a second-order response.

So I would say you can decouple the lateral and directional motions by removing dihedral effect and observing directional oscillation without lateral oscillation. You cannot, however, go the other way and observe lateral oscillation without directional oscillation, because it’s the directional displacement that provides the stiffness (tendency to return to original condition). Very strong dihedral effect may, however, make it appear this way.
Feb 05, 2018, 07:20 PM
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ShoeDLG's Avatar
Got it. I would expect that if rolling moment due to yaw rate was significantly greater than rolling moment due to sideslip, then the phasing (and possibly damping) would be quite different.
Feb 06, 2018, 06:52 AM
Registered User
Dunno if the soon-corrected initial issue was caused by the control system per se, rather than aerodynamic, but I had a lengthy PanAm flight from Schiphol to Kennedy in one of the first (maybe the first?) 747s ... during which the tail wagged L/R (and NOT up/down nor either in a broad "U"-shaped arc as it did in several turbulent flights I had in a V-Bonanza) when flying at low speeds. My understanding is that the 747 has lots of actual as well as effective-dihedral, of course
Feb 06, 2018, 09:54 AM
Closed Account
For the theoretically minded, Slide 13 of this presentation:

https://www.princeton.edu/~stengel/MAE331Lecture19.pdf

shows the effect of varying dihedral effect on a business jet. It affects the stability of the Dutch roll mode, but the mode always exists.
Feb 09, 2018, 04:39 AM
Registered User
Hi Steve,

Quote:
Originally Posted by aeronaut999
Is a "Dutch Roll" oscillation possible in an aircraft with zero "effective dihedral" or mildly negative "effective dihedral"?
If we take out the yaw-roll coupling from the lateral system of equations, the dutch roll is analagous to the short period mode in the longitudinal case.
So the answer should be yes, its possible as per my understanding. [depending whether you can call it dutch roll]

And I felt really interested to see the contents of these articles when I read one of your early posts. [I am big fan of Prof Rawdons work]

Quote:
Originally Posted by aeronaut999
I recently re-read Blaine Beron-Rawdon's articles on dihedral in "Model Aviation"-- a 2-part series of articles called "Spiral Stability and the Bowl Effect" (September and October 1990) and a series of 4 articles entitled "Dihedral, a 4-part series" (August through November of 1988).
Can you kindly share these old Model aviation articales with me if you dont mind ?

Thanks so much
Buwa.
Feb 09, 2018, 12:17 PM
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aeronaut999's Avatar
Thread OP
I'll post url's to the articles later today--

Quote:
Originally Posted by Buwa
Hi Steve,



If we take out the yaw-roll coupling from the lateral system of equations, the dutch roll is analagous to the short period mode in the longitudinal case.
So the answer should be yes, its possible as per my understanding. [depending whether you can call it dutch roll]

And I felt really interested to see the contents of these articles when I read one of your early posts. [I am big fan of Prof Rawdons work]



Can you kindly share these old Model aviation articales with me if you dont mind ?

Thanks so much
Buwa.


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