Lateral Stability

[airyana]

I've been trying to understand how dihedral contributes to lateral stability, the explanation is basically the same in
all texts I've ]managed to find. they go on to explain how the roll will incline the lift vector and the horizontal component will cause a sideslip, then the the relative airflow will be coming from the side oppsite to the direction of the sideslip. And because of dihedral, the angle of attack of the lower wing will be higher than that of the upper wing, which will cause the ac to roll to a laterally level position. Now the part i am having difficulty picturing, is how dihedral was the cause for a different AOA on both wings.

thanx . . .

[moogleman]

Try this website which might give you a better idea of the situation.

http://selair.selkirk.bc.ca/aerodynamics1/Stability/Page5.html

Just to clarify though, I think the angle of attack in question here is with reference to the sideslip velocity and not the forward velocity of the aircraft which may have been causing you confusion due to it not explicitly saying so in the text.

Hope this helps!

MM

[airyana]

Thanx this does help, but it still doesn't clearly show what dihedral has to do with it . . .

[Gillespie]

In a nut shell...

Because of the dihedral, during a turn, the down going wing will produce more lift than the up turn turning wing. This then trys to roll the aircraft out of the turn. This is positive static lateral stability.

The down going wing produces more lift due to the effect of the slip stream in a turn.

To be honest is very difficult for me to explain the answer to your question without drawing a diagram of how the dihedral effects the AOA. Sorry.

[mikehammer]

Moogleman that's an excellent website, I wish I'd known about it when I sat my exams.

[moogleman]

Airyana,

Picture the aircraft banked in a turn. If there is no dihedral present both wings will have the same angle of attack to the sideslip velocity (neglecting any factors arising from flow around the fuselage). The dihedral means that the lower wing is presented to the oncoming sideslip velocity at a different angle of attack than the higher wing.

Draw the two wings of an aircraft with dihedral (viewed from the front whilst banked), but leave a gap instead of the fuselage. Treat each wing as a flat plate and draw the direction of the velocity caused by sideslip. The higher wing has a larger negative angle of attack with reference to this sideslip direction than the lower wing does. This means the lower wing will produce more lift and pull the aircraft straight and level.

Hope this makes some kind of sense!

MM

[airyana]

to be honest moogleman, the only way i can picture dihedral having anything to do with it, is that in a turn the down going wing will effectively have a slightly longer span, thus producing more lift ... but since this is not mentioned in any of the texts it probably has nothing to do with it. now the point you mentioned in your answer about the sideslip, i did draw it like you said, but still, the relative aiflow will be hitting the wing in a spanwise direction from tip to root, so why should it produce lift at all . . .

i know its not that important to understatnd this point, but its frustrating

[Gillespie]

airyana,

I've sent you a pm with some info that might help you on this.

cheers.

[moogleman]

Yes there will be some spanwise flow which will cotribute to the restoring moment, although due to the relatively small sideslip velocities this will probably be small compared to the overall lift.

There are so many different factors affecting lateral stability, and it is obviously the sum of all these factors that dictate how the aircraft behaves. The spanwise flow is just a small one. With reference to the oncoming forward flow also remember that in a bank, due to dihedral, the lift vector will be titled further from the vertical on the higher wing than the lower wing. This will give a greater component of lift from the lower wing producing a restoring moment.

Lateral stability is always a pig to try and understand, and i get confused everytime i try and think a problem through. I think im getting myself even more muddled as I speak so it might be best to ask an instructor/mentor or anyone who is more current on it.
If you have access to a good library try getting a hold of 'Aircraft Dynamic Stability and response'(1980) by Babister, or 'Performance and Stability of Aircraft' (1998) by Russell. I seem to remember both these books will give details all the stability derivatives (particulary Lv which is the rolling moment due to sideslip) which is what you are concerned with. They are both quite 'mathy' books however, and unless you're really interested they're probably not worth bothering to find and trying to understand!

[airyana]

thanx a lot guys ... ill have a look at these books and let you know.

[Keith.Williams.]

The way in which dihedral affects the angle of attack of each wing can be demonstrated using a simple sheet of A4 paper or card.

Fold the paper over so that the two short side are together and a crease is formed down the centre. Now unfold it so that it takes up the shape of two wings with dihedral. The crease represents the fuselage and the the two halves of the sheet represent the wings.

Now close your left eye and hold the paper about 18 inches in front of your face, so that the crease points directly at your right eye. In this position the end of the crease closest to your eye represents the nose of the aircraft.

Now raise the nose to give it a slight pitch up attitude. This position represents an aircraft flying directly into wind, with no sideslip. Now imagine that the wind is blowing from your right eye towards the aircraft. This means that the view from your right eye represents the view that the air gets as it approaches the aircraft.

Looking with your right eye you will be able to see the underside of both wings. If you look carefully you will observe that your views of the two wings are identical. This means that the angles of attack of the two wings are identical.

Now to represent sideslip turn the paper slightly so that the crease is pointing towards your left eye. Looking once again with your right eye you will see that your view of the two wings has changed. You can now see more of the underside of the wing that is closest to you and less of the underside (or possibly even some of the upper side) of the wing that is furthest away from you. This means that the angle of attack of the closest wing has increased and the angle of attack of the furthest wing has decreased.

The greater the degree of dihedaral and/or the greater the angle of sideslip, the greater will be these changes in angle of attack.

Now turn the paper over so that it represents anhedral and repeat the experiment. You will see that anhedral has exactly the opposite effect.

[rusty_y2k2]

That is a bloody excellent explanation Keith - the best I have come across infact!

[airyana]

impressive keith, thanx a lot . . .

[Keith.Williams.]

Well I got it from reading PPRUNE. My earlier explanations were much more complicated.

A beer mat works much better because it is less floppy.

All of those old (and young) pilots that you see leaning against the bar late at night, with one eye closed and a mangled beer mat in their hands are not drunk.....They're just revising dihedral!