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The question comes from the Arup designs, and the engineer who turned it into blueprints, Hoffmann, ('A Novel All Wing Airplane', Raoul J Hoffman, Popular Aviation, March 1935, pp 163 and 196), they said adding dihedral would cause Dutch Roll and worsen lift to drag ratio. In low wing machines, dihedral could reduce 'Ground effect', sometimes undesirable. Blessings +

Urquiola
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    You seem to be asking a question about towing a trailer on the road -- rather than one specifically about aviation. If that's incorrect, you should [edit] your question to make it clear what you're asking about. – Zeiss Ikon Jul 07 '21 at 13:49
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    The trailer yawing, and rolling a little bit due to spring compression, behind a car is nothing like Dutch Roll, which is an oscillation about all 3 axes and all 3 motions feeding each other. Not a good analogy. – John K Jul 07 '21 at 16:27
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    @JohnK the Dutch roll is normally described as not containing pitch oscillations, just roll and yaw – Federico Jul 07 '21 at 20:46
  • It's a yaw/roll coupling oscillation and energy system, but there are also pitch movements with the nose rising and falling somewhat during the roll/yaw motion. – John K Jul 08 '21 at 01:28
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    Voting to keep this open. The basic question is very relevant to this site: what are the design parameters for dutch roll stability in aeroplanes. – Koyovis Jul 08 '21 at 03:06
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    It is a shame some folks focus on "dihedral" as the source of Dutch Roll when there is that huge tail sticking up in the back. Doesn't it make one wonder what a change in relative wind does to rolling forces there. Dihedral gets blamed when there are other design fixes for the issue. Vertical CG must be considered. There are ways of reducing "dihedral effect" without reducing dihedral. Oh, and please reference Hoffman's blueprints. – Robert DiGiovanni Jul 08 '21 at 23:08
  • The question was about Dihedral effect on Aircraft's Dutch Roll, and calculations about this, the mention of the Car towing an small trailer was there just to point something similar to Dutch Roll can happen also in road vehicles, but question is about Aviation, as only Airplanes have 'Dihedral'. Would you please reconsider posting it? Thanks Blessings + – Urquiola Jul 09 '21 at 09:48

1 Answers1

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Dutch Roll is a 2-dimenional dynamic stability issue in aeroplanes. A little trolley towed by a car can be used to illustrate what happens, but the small amount of roll is purely an effect of directional instability, it is a one-dimensional issue.

From prof. Gerlach's paper copy uni book

The pic above shows a damped dutch roll. The graph shows the two coupled variables, roll rate and yaw rate, and an unstable dutch roll occurs when the time delay between the peaks is such that they amplify each other.

Another pic from same book

The dutch roll is not the only multi-dimensional asymmetrical stability issue to be considered, the other one being the spiralling descent. Both the dutch roll and the spiral descent motions need to experience positive damping.

  • For positive damping of the spiral movement, stability matrix E must be > 0, with $$E = C_L(C_{l,\beta} \cdot C_{n,r} - C_{n,\beta} \cdot C_{l,r})$$
  • For positive damping of the dutch roll, the Routh-Hurwitz discriminant R must be > 0, with R being a conglomeration of partial linear equations such as equation E above.

So both E and R must be >0, and both are determined to a large extent by:

  • dihedral coefficient $C_{l,\beta}$, larger for larger dihedral angle
  • static directional stability $C_{n,\beta}$, larger with larger tail volume

enter image description here

But changing the tail volume also changes other stability parameters, such as $C_{n,r}$ and $C_{Y,\beta}$. Effects of varying $C_{l,\beta}$ and $C_{n,\beta}$ on E and R are represented in the side stability diagram above, showing the area where both E > 0 and R > 0.

From the diagram it can be seen that when dihedral $C_{l,\beta}$ is increased, $C_{n,\beta}$ must be increased as well. A larger tail volume achieves this, but requires further analysis on the remaining a-symmetrical dynamic equations.

Koyovis
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