Dihedral Design on Lateral Stability
 

Dear all,

How is it going? Anyone out there can explain to me why the dihedral design causes the the lower wing to have a larger angle of attack than the higher one during a bank?

Cheers. :ok:

- sideslip?

sideslip not bank:

http://i636.photobucket.com/albums/u...pseaabb501.jpg

me tinks allus you experts forgetting something.
why is the stall warning on the left wing??
nothing to do with sideslips that one.:=:=

Lightning Mate: Shouldn't the angle of attack be referenced by the relative wind direction (headwind) rather than from the side? That's what I don't understand.......:ugh:

It is - 'Relative Airflow'.

What BOAC said. Relative wind is an amateur term.

The angle of attack sensors on a transport aeroplane are on the front fuselage below the office windows.

My drawing shows the relative wind component due to sideslip!

:ugh::ugh:

Geometry.
The vertical lift vector is larger in the case of the lower wing.

Busser is right. In a steady turn, the Angle of attack is the same. The lift vector is perpendicular to the wing. So if there is dihedral, the vertical component of the lift vector is greater from the lower wing which tends to roll the aircraft back level. To keep most aircraft in a turn you have to hold a small amount of aileron - if you centralise the yoke the aircraft will tend to roll back to wings level. The angle of attack is significantly different as you roll into or out of a turn because the wings are moving up or down relative to the free stream and that will tend to oppose the roll but that effect is the same whether you have dihedral or not.

I have no idea what lightenings diagram is showing.

I've never flown an aeroplane which behaves like that. The latter part of the statement refers to aerodynamic roll damping.

If you have no idea what my diagram is showing then perhaps I'll leave it at that. All my students understood it perfectly well.

Both BOAC and I have given the answer.

superb..

"I dont understand your diagram"

"well you're obviously thick"

"please explain it"

"no, you're too stupid"

Please can you explain the diagram with the yellow wedges and the blue arrows?
Its probably right, I just don't understand it.

BOAC will explain it for me... Whats that pic all about BOAC?

Lightening, if you say you have students you must be an instructor. Facilitate me mon brave...

Ok then.

I didn't mean to suggest you were thick. It's just that I grow tired of trying to explain dynamics on a thread such as this - it's easier in a classroom.

Yes - I was indeed an instructor, both as an RAF QFI and as a civilian. I am now retired.

So to the diagram.

The black arrow shows sideslip in a turn. Very little is required, but it is necessary for any dynamic stability attributes to work.

Therefore there will be a component of the relative airflow as shown by the blue arrows (very much exaggerated).

The yellow "wedges" show angle of attack, which is the angle between the relative airflow and the wing chordline. Because of dihedral the AoA of the lower wing is slightly higher than that of the upper.

Therefore if you look closely the two yellow angles are different.

Hope that helps.

edit: I have just noted that you hold a CPL.

Stop teasing me, you lot. What diagram? :}

If the problem is simply one of trying to understand the fact that dihedral causes the angle of attack of a dropped wing to become greater than that of the raised wing, a demonstration may be sufficient.

Take an A4 sheet of paper and fold it down the centre so that the two short edges come together. Now unfold it so that it looks like a pair of wings with dihedral. We will use this to represent our aircraft. It works best if you use a large dihedral angle (about 30 degrees).

Grasping the sheet at the tail end of the centre crease, hold it up about a foot in front of your face so that the crease is pointing directly at your right eye. Hold the paper so that it is in a non-banked attitude, and raise the front end of the crease to represent a nose up pitch attitude.

Close your left eye and look at the paper with your right eye. The view that you see is what the approaching air would see (assuming of course that air could see at all). You should be able to see the underside of both wings and the view of the left wing should be a mirror image of that of the right wing. This indicates that both wings are set at the same angle of attack.

Now rotate the front end of the crease so that it points at your (still closed) left eye and slightly drop the wing that is closest to your right eye. The view from your right eye now represents an aircraft that has dropped its left wing and is side slipping towards you. Once again the view that you have of each wing represents the view that the approaching air would have. You should be able to see more of the underside of the dropped wing and less of the underside of the raised wing. This means that the angle of attack of the dropped wing is greater than that of the raised wing.

If this difference is not obvious gradually increase the bank angle. You will eventually get a situation in which you can see the bottom of the dropped wing and the top of the raised wing.

The above process will not explain why the angles of attack change, but it should at least convince you that it is true.

To understand why the difference in angle of attack occurs we need to consider the relative airflow as being made up of two components. The first component is that due to forward motion of the aircraft. This component approaches the aircraft from directly ahead. The angle of attack between this component and each of the wings is identical.

The second component is the lateral airflow caused by the aircraft side slipping towards the dropped wing. As illustrated in Lightning Mate’s diagram, the dihedral angle causes the wingtip of the dropped wing to be higher than the root. The lateral airflow on this wing is from tip to root, so this means that the lateral airflow meets this dropped wing at a positive angle of attack. But for the raised wing the dihedral angle causes the wing root to be lower than the wingtip. The lateral airflow on this wing is from root to tip, so this causes the lateral airflow to meet the raised wing a lesser angle of attack.

The total angle of attack of each wing is the vector sum of the angles of attack of the two airflow components. The contribution made by the forward motion of the aircraft is the same for both wings. But the contribution made by the lateral (side slip) airflow is greater for the dropped wing that for the raised wing. The overall effect is that the dropped wing experiences a greater angle of attack than the raised wing.

I've got an ATPL and an engineering degree. But thats not all that relevent, I simply don't think the response to the original posters question addresses what he or she asked. I think they want to know if, in a balanced turn, the angle of attack is the same for both wings.
I still don't understand the reply. Do you mean the angle of attack with respect to the airflow component parallel to the lateral axis as per your diagram? Or is this a representation of the angle of attack with respect to the free stream?
If its the free stream, then I don't agree and I don't agree with the parallax demonstration by Mr Williams either. The reason the parallax arguement doesn't work is the free stream presents itself to the wing from a direction which is parallel to the trajectory of the aircraft. So if you close one eye then look from a point half way down one wing you are assuming that the free stream is approaching both wings from one point. Which it clearly isn't.
By the way, I agree that a roll torque is applied if there is a sideslip and thats what gives stability in roll about the longditudinal axis but I dont think there is a difference in the angle of attack in a balanced, zero slip turn. I'm happy to be proved wrong but not by answering a different question.

So please educate the three of us who have posted.