Question about dutch roll.
 

I didn't find any previous thread about this matter, so I hope none strangles me if I just missed it.

I am interested to know a little bit more about the theory of the initiation of dutch roll. I have a theory but I am not sure whether it's the correct one or not. So here we go (it assumes a non swept wing aircraft):

With the fact in mind that the air is not smooth, gusts hit us all the time and if one comes from the side it will give us a side slipe angle. Let us assume we have gust from the right giving us a right side slipe angle.
- The directional stability gives a right yaw into the wind. The outer (left) wing will move faster through the air and create more lift and drag.
- The net result will be a roll to the right and a yaw to the left.
- When the aircraft now yaws left, the right wing will move faster through the air and we will have a roll to the left and yaw to right.
- The sequence is repeated.

How did that sound?

Now, your opinions :ok:

TIA

That's some but not all of the mechanism.

Dutch Roll is a combined rolling and yawing motion, so it is driven by the interaction of the rolling and yawing moments on the aircraft, and the responses to them.

Assuming that the controls are fixed (quite a big assumption in fact) and that there is no longitudinal coupling (another biggie) the main derivatives involved are:

Cn-beta - yaw due to sideslip = "directional stability"
Cn-p - yaw due to roll rate
Cn-r - yaw due to yaw rate = "yaw damping"

Cl-beta - roll due to sideslip = "dihedral effect"
Cl-p - roll due to roll rate = "roll damping"
Cl-r - roll due to yaw rate

So, taking your description (the assumption of a disturbance in sideslip is quite valid):

Let us assume we have gust from the right giving us a right side slipe angle.

The directional stability gives a right yaw into the wind and the dihedral effect gives a roll.

The outer (left) wing will move faster through the air and create more lift (Cl-r) and drag (Cn-r). More importantly, the fin will also contribute to Cn-r. It's more true to say that as a result of the roll rate and yaw rate which is generated by the sideslip, there are further rolling and yawing moments driven by various components of the airframe
- The net result will be a roll to the right and a yaw to the left. if the aircraft is stable in both axes - it's possible that one or other effect may be marginally stable or unstable and it takes the other effect to bring the aircraft back towards equilibrium
- When the aircraft now yaws left, the right wing will move faster through the air and we will have a roll to the left and yaw to right. again, as with the previous comment, it's not just the wing acting, and the wing may not in fact be stabilising
- The sequence is repeated.

You have to view the Dutch Roll as a whole-aircraft mode and consider all the effects together. A "real" DR will also see pitch-coupling, which will further complicate matters.

at least you didn't mention stalling!;)

Dutch roll and spiral dive
 

Both Dutch roll and spiral dive are caused by coupled rolling, yawing and slipping movemens. Are they the same mode - spiral dive divergence if it´s unstable, Dutch roll oscillation if it is stable - or are they completely different modes?

Seperate modes - an aircraft will have a spiral mode whether or not the Dutch roll is stable or unstable.

Excellent, thanks for your answers. Very much appreciated!!!

I guess only a diverging dutch roll (where the roll rates become greater by each oscillation) will finally result in a stall? When the wing is moving downwards the angle of attack will increase. Am I right in that sentence?

The downgoing wing does indeed experience an increase in angle of attack, and in theory, yes, if the Dutch roll oscillation were allowed to progress to a severe enough point then you could induce a local stall (starting at the tip, since the local velocity would be greatest). But it'd have to be a pretty gross Dutch Roll at that point, and I'm not sure you wouldn't see other handling non-linear behaviour (perhaps in yaw) before you reached that point. Even then, the first effect would simply be to reduce the Cl-p contribution a bit, since most of the wing flow would stay attached. To get to the point of actually seeing a "stall" that caused some form of autorotation would require huge roll rates.

Why's it Dutch roll and not French,German,or Outer Mongolian, roll?

I vaguely remember something to do with Dutch Ice Skaters.....or was I dreaming that during my DR lecture........:E

The allusion to the rolling motion of a Dutch ice skater is one of the supposed origins of Dutch Roll, but there are competing notions too, one of which was I thought something to do with Dutch merchant ships.

No doubt it's been discussed here before. - yep, here

I thought it was well known that the origin of the expression Dutch roll was from the observation of a drunken Dutchman managing to remain upright whilst his upper body gently swung to and fro and from left to right simultaneously. Why Dutch? perhaps they have a reputation for holding their drink better than the other nation we tend to use for less than flattering descriptions (the French)

Or minimal margin before stall without the Dutch roll. Logically, if the aircraft already is near stall, a small amplitude Dutch roll might bring the falling wingtip past stall?

As for yaw... I suppose the fin might stall, but perhaps not due to Dutch roll...

By the way, is it possible to tell if the initial roll will be right or left?

For the situation mentioned above, with a right side slip angle. The yaw into the wind will result in the left wing travelling faster through the surrounding air giving a right roll.

But if the aircraft has dihedral the right wing will get a higher AoA which will tend to give a left roll. Or if the aircraft has swept wings, the right wing will "see" more air giving more lift and a left roll.

So which effect is dominant or maybe it is type specific?

Please be indulgent, I am a bit newish and never learnt the principle behind dutch roll during the theory class :\

Yes.

What matters, for the case you postulate - disturbance in sideslip - is the dihedral effect, because that will immediately cause the aircraft to roll in response to the sideslip. The roll due to yaw rate won't have a chance to have an effect until the plane begins to yaw in response to the sideslip, and even then may well be less significant than the dihedral effect.

Cl-beta is almost always negative, which means I'd expect a left roll for a right sideslip disturbance.

Swept wings
 

172_driver,
I'm surprised no one has yet mentioned swept wings.
Straight wing aircraft do not suffer from dutch roll - unless you intentionally cause it by continually gently applying left and right rudder when you will get a yaw induced oscillatory rolling motion.
SOME swept wing aircraft exhibit dutch roll and the simple reason understandable to a mere Basil is as follows:
1. Aircraft yaws (eg to right).
2. Left wing sweep relative to airflow is reduced therefore:
a) Airspeed normal to leading edge is increased so V increases.
b) Camber to airflow is increased so CL increases. (remember L= CL*1/2*p*V2*S)
c) Lift on left wing increases so left wing rises (slightly assisted by sideways lift on fin).
3. Increased drag on left wing and fin lift opposing yaw now stop right yaw and aircraft yaws to left.
4. Aircraft overswings to left, right wing rises etc etc.
5. "Bu**er I!" says pilot putting down coffee and page 3 of 'The Sun' "Now what did they say to do when this happens?"

If the resulting phugoid is divergent it will continue until the aircraft departs controlled flight - unless, of course, the pilot corrects with a timely and controlled input of aileron.

Some swept wing jets, whose clever aerodynamicists and structural engineers got it just right (eg B747) do not dutch roll.

Its quite frustrating there doesn't seem to be one definitive answer to the dutch roll question. My understanding was that it was caused by stronger lateral stability and relatively weak directional stability. Aircraft yaws then rolls due to faster moving wing plus increase projected span on the outer wing, the tailfin then acts like a wind vane yawing the aircraft back to zero slip this then causes secondary roll, the aircraft rolls beyond zero slip in the opposite directon and the process is repeated. Also at play I thought was the dihedral effect of the lower wing increasing lateral stability.

Sorry, but that is completely nonsense. As long as an aircraft does not have some kind of control augmentation system (i.e. FBW) or a configuration grossly different from the standard aircraft - wing.fuselage,tail - it WILL have a Dutch Roll mode. The mode may be well damped, the mode may have a frequency different to the normally expected range, or the roll/yaw ratio may be at one extreme (so you may get a mode which is mainly yaw, or mainly roll) but it will be present.

That's just the dihedral effect - Cl-beta - and is present regardless of sweep or no sweep.

The "one definitive answer" can be found by solving the equations of motion for an aircraft, decomposing into the (assumed) independent longitudinal and lateral/directional components and then identifying the second-order roll-yaw coupled motion in the solution.

It involves all six derivatives in the roll/yaw axes to determine the frequency, damping, roll-ot-yaw ratio and the phasing of the roll and yaw motions.

You don't need one derivative to be "strong" or "weak" to have Dutch Roll - all that specific values do is change the nature of the mode, not its existence.

Mad (Flt) Scientist,

I'd draw your attention to my comment <<simple reason understandable to a mere Basil >>. I am an experienced practical pilot, ex mil with commands with two majors.

I am not disputing that you may be able to prove, in theory, that a straight wing aircraft will dutch roll however I have never flown one which does so at the flight levels normally occupied by straight wing aircraft, i.e. not Starfighter etc which had another set of roll/pitch problems.
I was referring to sweep, not dihedral and yes, sweep does cause dutch roll.
Correct me if I'm wrong but the basic reason for dihedral is to improve roll stability.
I do appreciate that many factors contribute more or less to aircraft stability however since the thread was started by a PPRuNer calling themselves 172_driver I'd guess they'd prefer a short rather than longwinded answer.

Dutch roll tends to happen when the lateral stability is greater than the directional stability - the rolling out of the sideslip force is stronger than the tendency for the aircraft to yaw towards the sideslip. So divergence in roll to the right=sideslip right. Sideslip right=roll left due to dihedral and/or sweep. Roll left=increased drag on upgoing (right) wing due to inc lift dependent drag = yaw right ie roll and yaw opposite.

If directional stabilty is higher than lateral, as usually in light/straight wing aircraft then same sideslip right=yaw right (outweighing any tendency to roll back to the left) so right yaw=right roll etc and you have a spiral dive.

Background Noise,
That, as a line pilot, is how I understand it.
Any further comment from the people between the aerodynamicists and the line pilots, i.e. the test pilots?

Just out of curiousity, do you consider the dash 8 or the Jetstream to be swept wing aircraft?

Haven't flown either.
Do they have a yaw/roll couple PROBLEM as opposed to exhibiting a tendency?
Getting back to swept wings, the B757 could exhibit a slight tendency to a roll cycle on approach (about 1 cps) which we put down to PIO.

Edited to say: M(F)S please don't think I am challenging your aerodynamic knowledge. I was probably incorrect to state <<Straight wing aircraft do not suffer from dutch roll>> but I have never flown nor heard of a straight wing aircraft going into service which suffered from dutch roll to the extent of the early swept wing aircraft of the B707 era.

I have been following this discussion for a while now. Without doubt, I follow it with interest but the more I read the more I come to the conclution that there is perhaps no simple explanation to the 'dutch roll question'. Not without a deep analysis of all aspects that affect an aircraft during a sideslip. I don't feel my aerodynamic knowledge is sufficent for such an analysis but I find your's most interesting. :ok: