Wing dihedral

"Andrew Sarangan" posted the exciting message
oups.com:

That is an excellent writeup!

Once the aircraft has stopped rolling, provided it is still travelling
straight ahead, the aerodynamic forces will be influenced only by the
airstream passing over the aircraft. This will be identical for both
wings and so no restoring moment will result.

This is incorrect. The upper wing will have a lower AOA, regardless of whether the plane is slipping or not, and therefore will produce less lift. The higher relative lift of the lower wing will stabilize the plane.

Let's consider the "90 degree" dihedral wing mentioned earlier. Let's assume that when the wings are "level" they produce enough lift to fly level at the current airspeed. Let's assume that one wing is horizontal, and one vertical.

The relative wind is coming from ahead, and from slightly below. The vertical component of lift on the upper wing is now directed inwards, and is therefore no longer supporting the plane's weight, so the plane starts to descend, increasing the AOA on the lower wing even further. The AOA on the upper wing remains lower than normal, because the relative wind is hitting it diagonally. Note that due to the relative wind, the dihedral would right the plane even if it weren't descending.

Do you have a link?

Andrew included this explanation in his response which is the one I was
trying to recite (excerpt):

What, then, is the real explanation as to why a dihedral angle is an
aid to lateral stability? When the wings are both equally inclined the
resultant lift on the wings is vertically upwards and will exactly
balance the weight. If, however, one wing becomes lower than the other,
then the resultant lift on the wings will be slightly inclined in the
direction of the lower wing, while the weight will remain vertical.
Therefore the two forces will not balance each other and there will be
a small resultant force acting in a sideways and downwards direction.
This force is temporarily unbalanced and therefore the aeroplane will
move in the direction of this force - i.e. it will sideslip - and this
will cause a fow of air in the opposite direction to the slip. This ahs
the effect of increasing the angle of attach of the lower plane and
increasing that of the upper plane. The lower plane will therefore
produce more lift and a restoring moment will result. Also the wing tip
of the lower plane will become, as it were, the leading edge so far as
the slip is concerned; and just as the center of pressure across the
chord is nearer the leading edge, so the center of the pressure
distribution along the span will now be on the lower plane; for both
these reasons the lower plane will receive more lift, and after a
slight slip sideways the aeroplane will roll back into its proper
position. As a matter of fact, owing to the protetcion of the fuselage,
it is probably that the flow of air created by the sideslip will not
reach a large portion fo the raised wing at all; this depends very much
on the position of the wing relative to the fuselage.

William Snow wrote:
Take a look at "Aerodynamics for Naval Aviators" NAVWEPS 00-80T-00, Page
295....

Excellent excerpt - it was what I was trying to say. Thanks.

Andrew Sarangan wrote:
Dallas wrote:

Would anyone care to comment on the accuracy of this illustration of how
wing dihedral works from a 1981 Jeppesen Sanderson book.

http://makeashorterlink.com/?B25A35DCC

The accompanying statement reads:
"When an aircraft with dihedral rolls so that one wind is lower than the
other, the lower wing will have more effective lift than the raised wing
because it is not tilted from the horizontal as much. The imbalance in lift
tends to raise the lower wing and restore level flight."


Dallas



This is not quite correct, and most of the "pilot books" have it wrong
too. Here is a very nice explanation taken from the book titled
"Mechanics of Flight" by A.C. Kermode of the RAF. (snip)

(snipped)

T o d d P a t t i s t skrev:
Chris Wells
wrote:

Once the aircraft has stopped rolling, provided it is still travelling
straight ahead, the aerodynamic forces will be influenced only by the
airstream passing over the aircraft. This will be identical for both
wings and so no restoring moment will result.
This is incorrect.

No, it is exactly correct.

No it isn't. The cause of the restoring moment is not the actual rolling of the
aircraft but the difference of force generated by both wings when the aircraft
is not level. Someone posted link to image which is perfect description of
what is actually happening.

http://makeashorterlink.com/?B25A35DCC


--
Leonard Milcin Jr.

On Thu, 16 Mar 2006 at 05:56:35 in message
. net, Dallas
wrote:

Why would a horizontal wing create "more effective lift" than a banked wing?

I suppose the thinking is that the lower wing has more effective span
than the upper more raised wing.

However that is not wholly convincing, in any case if the only thing
that happened was a slight roll and nothing else then the lift would not
change. The lift vector would incline however and that would tend to
push the aircraft sideways. The lose of truly vertical lift at right
angles to the wing would also cause the aircraft to sink and the AoA to
increase initially before other things would happen. The initial yaw
displacement may be followed by a yaw rate which could be said to
increase the speed of the outer wing relative to the inner and increase
the roll! That is the possible beginning of a spiral dive!

Try this. Consider an aircraft rolled slightly and nothing else. If no
control inputs are made then the inclined lift and vertical weight will
tend to cause the aircraft to start a side slip as suggested above.

If the side slip continues then the lower wing will have a higher angle
of attack than the upper. Get a strip of card as a wing put dihedral on
it and look at it from various directions. A correcting roll couple is
then produced. Other things then come into play as well, like yaw
stability.

The power of dihedral can be demonstrated with rudder and elevator only
controls on a radio controlled model. I know; I used to fly one. With
plenty of dihedral apply say left rudder. The skid to the right so
produced results in a left roll and a subsequent side slip depending on
the yaw stability.. However that effect is likely to be small. Maintain
the rudder and pull back on the elevator and a nice turn results. Might
be uncomfortable for passengers but if you are controlling from the
ground who cares! :-) Quite steep turns are easily possible.

Incidentally sweep-back can have the same effect as dihedral and may
make a delta too stable in roll. Too stable? Add anhedral or turn down
the tips?

I have probably missed out several other effects but I just wanted to
indicate that all sorts of effects may come into play and it depends on
a number of factors which way it all goes. What about Dutch Roll for
example?


--
David CL Francis

Someone posted link to image which is perfect description of
what is actually happening.

http://makeashorterlink.com/?B25A35DCC



I don't believe this link is accurate. It doesn't make clear why the lower wing makes more lift, in fact it seems to reinforce the "horizontal" notion. The largest correcting force is from the difference in AOA.

I could have sworn this was covered in "Stick & Rudder".

"Andrew Sarangan" wrote in message
oups.com...
This is not quite correct, and most of the "pilot books" have it wrong
too. Here is a very nice explanation taken from the book titled
"Mechanics of Flight" by A.C. Kermode of the RAF.

I really enjoyed reading this book and would recommend it highly. I did
notice that some British terminology differed from common American usage.
The book lived on my bedside table for several months and I would often read
several pages to give me something to ponder as I fell asleep.

Happy landings,

Someone posted link to image which is perfect description of
what is actually happening.

http://makeashorterlink.com/?B25A35DCC

I agree that this link does not accurately describe what is happening.
It is what I thought too until I thought about it some more (at the
prompting of this very newsgroup). The image shows less upwards force
on the higher wing. This much is true. What the image does not show is
the horziontal forces on the wing. The lower wing, being flat to the
ground, have no net horizontal forces on them. The higher wing however
does, since the wing's lift is not actually pointing in the upwards
direction, but is normal to (at right angles to) the wing's surface.
Since the wing is tilted, there is a horizontal component of lift at
work. Ignoring gravity for a moment, you can rotate the diagram any
which way, and the lift vectors will always be normal to the wing, and
will always have a net zero =torque= (and it's torque that would, by
this explanation, return the aircraft to level). Looking at it another
way, the higher wing has a horizontal component which will tend to
rotate the aircraft along the longitudinal axis, in the opposite
direction and with equal force as the "excess lift" attributed to the
lower (horizontal) wing.

So, this explanation is incorrect.

Jose
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