Wing dihedral

[Dallas]

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

[Jose]

> "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."

I used to think that, but it was pointed out that the issue isn't
"raising the wing" as "rotating the aircraft" and that the higher wing
still has a moment that will tend to rotate the aircraft.

Jose
--
Money: what you need when you run out of brains.
for Email, make the obvious change in the address.

[William Snow]

Give some thought to the components of lift, on both wings, and to which
direction lift acts. ;-)


"Dallas" > wrote in message
nk.net...
> 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
>
>
>
>

[Don Tuite]

On Wed, 15 Mar 2006 23:02:58 GMT, "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."
>
Try this illustration from NASA:

http://history.nasa.gov/SP-367/f144.htm

Don

[[email protected]]

That gave me some problem for a while when I read about it as well.
Here's how I deicded to understand it. (Well, it works for me whether
it's the truth or not...)

Take it to an extreme--an airplane with a 90 degree dihedral. The
fuselage in in the "corner.
Now imagine one wing horizontal, the other wing vertical. All of the
lift component is on the horizontal wing, but the fuselage is at the
corner. The wing is pushing up, the fuselage is being pulled down by
gravity, and the plane rotates. The vertical wing is attempting to
push the airplane sideways. However, the fuselage isn't fixed in space
to rotate in just one place, so the sideways force actually does push
the airplane sideways rather than just rotating towards the horizontal
wing. Therefore, the fuselage "sinks", until it is in the low point
between the two wings (which would then be both pointing upwards at 45
degree angles.

Clear as mud? Oh well, I tried.

[Dallas]

"William Snow"
> Give some thought to the components of lift, on both wings, and to which
> direction lift acts. ;-)
http://makeashorterlink.com/?B25A35DCC

I have. I see no forces presented in this illustration that would change
the components of lift on the wings or it's direction that would cause the
aircraft to roll back to horizontal.

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

This thread began in another group and some interesting points were
discussed, but I honestly expected a few belly laughs here on the absurdity
of this book's explanation.


Dallas

[Roger]

On Wed, 15 Mar 2006 23:13:03 GMT, Jose >
wrote:

>> "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."
>
>I used to think that, but it was pointed out that the issue isn't
>"raising the wing" as "rotating the aircraft" and that the higher wing
>still has a moment that will tend to rotate the aircraft.
>
Try both. The lower wing is trying to come back up as it has move
vertical component of lift than the other wing. The higher wing has
more lift in the direction of the lower wing so the plane will start
to turn that direction at the same time.

If you don't believe me, Get in the back seat of a Bonanza on a day
with lots of thermals. It doesn't have to be a V-tail, the F33 will
do the same thing. As the seat is behind the center of lift you get
some strange and exaggerated sensations and a high barf factor.

OTOH it makes the plane quite stable for the pilot even though it has
a wing loading on par, or slightly less than some Cherokees.

Cherokees which have a lot of dihedral also do pretty well on the
bumps and do not have quite the barf factor of the Bo's rear seat.

Roger Halstead (K8RI & ARRL life member)
(N833R, S# CD-2 Worlds oldest Debonair)
www.rogerhalstead.com

>Jose

[Chris Wells]

The higher wing has less AOA.

[The Visitor]

I'm not sure what the question is.

I think I do....

Lift is a vector. If a wing drops a little bit, the vertical
(lift)component of the wing is greater than the vertical component of
the raised wing. (The raised wing now also has a horizontal component.)

Having the greater vertical component helps it to raise itself. This is
just a stability aid, not a wing leveller. Some airplanes are anhedral,
to improve the "rollability" of it.

John




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
>
>
>
>

[Maule Driver]

I haven't looked at the illustration but what happens is that if the a/c
rolls to the left, it will begin to slip to the left. The left wing
will have a greater angle of attack than the right, therefore more lift
and it will tend to correct the roll.

By the same token, if it is yawed the left it will begin to skid to the
right. The right panel has a higher angle of attack and it roll left.
That's how rudder-only model a/c manage to roll and turn.

You fly enough models - especially free flight - and the value of
dihedral for stability becomes quite evident. Dihedral produces
stability in roll. Most full size a/c don't have enough to produce what
I guess would be called static roll stability. Left alone, they go into
a spiral and either hit the ground or break up. Free flight models
have enough dihedral (or polyhedral) to remain stable in roll.
Typically they are set up for stable circling flight. Take too much
dihedral out and they will spiral in.

Dihedral was key to controlling early RC models. With a properly setup
rudder-only non-proportional control model, you could not only turn, but
climb, dive, and even loop. I wonder what Jepp says about that?

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
>
>
>
>

[[email protected]]

I've often wondered how 2 channel R/C works without ailerons (obviously
well enough, right?)

I know a guy with a Yak-52, and I've noticed what looks like an almost
complete lack of dihedral on its wing. I suppose that has a lot to do
with its stability (or lack thereof?) The Chinese version (Nanchang)
has dihedral starting on approx the outer 1/3rd of its span IIRC.

[Maule Driver]

Only because the a/c is slipping - the vertical/horizontal component of
lift stuff misses the point

Chris Wells wrote:
> The higher wing has less AOA.
>
>

[Maule Driver]

I agree completely - it's about the slip created and how dihedral
responds to it.

Dallas wrote:
> "William Snow"
>
>>Give some thought to the components of lift, on both wings, and to which
>>direction lift acts. ;-)
>
> http://makeashorterlink.com/?B25A35DCC
>
> I have. I see no forces presented in this illustration that would change
> the components of lift on the wings or it's direction that would cause the
> aircraft to roll back to horizontal.
>
> Why would a horizontal wing create "more effective lift" than a banked wing?
>

[Maule Driver]

2 channel (w/o ailerons) works great. You'll never see a aileron-less
model without dihedral (I understand swept wings work too but I've never
seen that).

single channel works too - how does one do a loop with rudder-only?
Quite well thank you.

Acrobatic R/C with a normal configuration a/c are often straight winged
or close too it. That's to isolate the function of the rudder so it
causes yaw only. Works pretty well except for some effects from
fuselage blanking and such.

But that's when R/C aircraft were mosting just trying to model full
scale aircraft. That balloon was busted a long time ago. What is this?

http://youtube.com/watch?v=K6besEwoRYQ&search=rc%20hydroplane

wrote:
> I've often wondered how 2 channel R/C works without ailerons (obviously
> well enough, right?)
>
> I know a guy with a Yak-52, and I've noticed what looks like an almost
> complete lack of dihedral on its wing. I suppose that has a lot to do
> with its stability (or lack thereof?) The Chinese version (Nanchang)
> has dihedral starting on approx the outer 1/3rd of its span IIRC.
>

[Morgans]

"Dallas" >

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

Let's think of a set of wings with a dihedral angle of 10 degrees up from
horizontal, on both wings.

Now, think of the shadow the wings would make, if the sun were straight
overhead, while the plane is banked at 10 degrees. The wing that is up
would make a smaller shadow than if the plane were flying level. The wing
that is down would be making the largest shadow that is possible.

The size of the shadow is the only size that is important, because the lift
that is straight up (towards the sun, in our example) is the only lift that
will be important to the plane, as that is what is counteracting the force
of gravity. The fact that the down wing's shadow is larger, will make have
more effective area than the up wing, and will tend to bring that wing back
up.

While you are in level flight, the same thing will constantly be at work,
automatically trying to keep the plane level.
--
Jim in NC

[Maule Driver]

It's a coherent description but I think it's inaccurate. The sum of the
lift vectors is now simply tilted from the vertical aircraft will
simply turn.

I agree that dihedral will have a stabilizing effect but it's not
because more of the wing low wing is parallel to the earth. It's
because the a/c slips towards the inside of the turn (controls being
neutral). The slip gives the low wing a higher angle of attack, thus
more lift and it will tend to right itself.

Conversely, a wing with dihedral will tend to bank if the aircraft is
yawed with the rudder. Left rudder, right skid, right wing has higher a
of a in relation to relative wind and the aircraft banks left.

Fold a hersey bar sized piece of paper to simulate such a wing. Then
slip and skid it and imagine the a of a on each panel.

Morgans wrote:
> "Dallas" >
>
>>Why would a horizontal wing create "more effective lift" than a banked
>
> wing?
>
> Let's think of a set of wings with a dihedral angle of 10 degrees up from
> horizontal, on both wings.
>
> Now, think of the shadow the wings would make, if the sun were straight
> overhead, while the plane is banked at 10 degrees. The wing that is up
> would make a smaller shadow than if the plane were flying level. The wing
> that is down would be making the largest shadow that is possible.
>
> The size of the shadow is the only size that is important, because the lift
> that is straight up (towards the sun, in our example) is the only lift that
> will be important to the plane, as that is what is counteracting the force
> of gravity. The fact that the down wing's shadow is larger, will make have
> more effective area than the up wing, and will tend to bring that wing back
> up.
>
> While you are in level flight, the same thing will constantly be at work,
> automatically trying to keep the plane level.

[William Snow]

Take a look at the NASA item in the following threads. It should be apparent
what happens. L1>L2 therefore L1 wing rises until L1=L2. I can not believe
all of this discussion has ensued. This is a fundamental of aircraft design.

"Dallas" > wrote in message
ink.net...
>
> "William Snow"
>> Give some thought to the components of lift, on both wings, and to which
>> direction lift acts. ;-)
> http://makeashorterlink.com/?B25A35DCC
>
> I have. I see no forces presented in this illustration that would change
> the components of lift on the wings or it's direction that would cause the
> aircraft to roll back to horizontal.
>
> Why would a horizontal wing create "more effective lift" than a banked
> wing?
>
> This thread began in another group and some interesting points were
> discussed, but I honestly expected a few belly laughs here on the
> absurdity
> of this book's explanation.
>
>
> Dallas
>
>
>
>
>
>

[William Snow]

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

"Maule Driver" > wrote in message
m...
>2 channel (w/o ailerons) works great. You'll never see a aileron-less
>model without dihedral (I understand swept wings work too but I've never
>seen that).
>
> single channel works too - how does one do a loop with rudder-only? Quite
> well thank you.
>
> Acrobatic R/C with a normal configuration a/c are often straight winged or
> close too it. That's to isolate the function of the rudder so it causes
> yaw only. Works pretty well except for some effects from fuselage
> blanking and such.
>
> But that's when R/C aircraft were mosting just trying to model full scale
> aircraft. That balloon was busted a long time ago. What is this?
>
> http://youtube.com/watch?v=K6besEwoRYQ&search=rc%20hydroplane
>
> wrote:
>> I've often wondered how 2 channel R/C works without ailerons (obviously
>> well enough, right?)
>>
>> I know a guy with a Yak-52, and I've noticed what looks like an almost
>> complete lack of dihedral on its wing. I suppose that has a lot to do
>> with its stability (or lack thereof?) The Chinese version (Nanchang)
>> has dihedral starting on approx the outer 1/3rd of its span IIRC.
>>

[William Snow]

It is clearly explained in "Aerodynamics for Naval Aviators", NAVWEPS
00-80T-00, page 295....



"Dallas" > wrote in message
nk.net...
> 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
>
>
>
>

[Andrew Sarangan]

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.

"The most common method of obtaining lateral stability is by the use of
a dihedral angle on the main planes. Dihendral angle is taken as being
the angle betwen each plane and the horizontal, not the total angle
between the two planes, which is really the geometrical meaning of
dihedral angle. If the planes are inclined upwards towards the wing
tips, the dihedral is positive; if downwards, it is negative and called
anhedral; the latter arrangement is used in practice for reasons of
dynamic stability.

The effect of the dihedral angle in securing lateral stability is
sometimes dismissed by saying that if one wing tip drops the horizontal
equivalent on that wing is increased and therefore the lift is
increased, whereas the horizontal equivalent and the lift of the wing
which rises is decreased, therefore obviously the forces will tend to
right the airplane.

Unfortunately, it is not all quite so obvious as that.

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.

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.

Both the leading edge effect on the lower wing, and the shielding of
the upper wing by the fuselage, occur on nearly all type of aircraft,
and may well mean that an aeroplane has a sufficient degree of lateral
stability without any dihedral angle, or too much if some of the
follwing effects also apply. Even if there is no actual dihedral angle
on the wings, these other methods of achieveing lateral stability may
be described as having a dihedral effect."

[Prime]

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

That is an excellent writeup!

[Chris Wells]

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.

[Maule Driver]

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....
>

[Maule Driver]

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)

[Leonard Milcin Jr.]

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.

[David CL Francis]

On Thu, 16 Mar 2006 at 05:56:35 in message
et>, 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

[Chris Wells]

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.

[Chris Wells]

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

[Private]

"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,

[Jose]

> 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
--
Nothing takes longer than a shortcut.
for Email, make the obvious change in the address.

[Chris Wells]

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).

The point I was making is that this is not true. You can rotate the diagram any which way, but the lift vectors won't be the same. I think confusion is caused because you're looking at the diagram head-on, but the plane doesn't fly through the air that way. With dihedral, the AOA on each wing is only equal when they're level.

[Peter Duniho]

"Chris Wells" > wrote in message
...
> The point I was making is that this is not true. You can rotate the
> diagram any which way, but the lift vectors won't be the same. I think
> confusion is caused because you're looking at the diagram head-on, but
> the plane doesn't fly through the air that way.

It doesn't? I normally make every effort to fly my airplane through the air
"head-on". Granted, it's possible to fly through the air in a wide range of
attitudes, but "head-on" is the most efficient and is what most pilots use
for normal, straight-and-level flight.

> With dihedral, the AOA
> on each wing is only equal when they're level.

Only because of the resulting slip. Which is what several people have been
trying to point out already, including Jose (in his latest post).

Ignoring gravity (as Jose suggested), if you take an airplane flying
straight and level and bank it, all that changes is the net lift vector, and
all that changing that will do is change the direction of flight. It will
do nothing to return the airplane's attitude back to straight and level.

It's only when you reintroduce gravity into the equation that rolling the
airplane will *also* result in a change in the resulting vertical component
of the lift, resulting in a descent, resulting in a slip (ta da!) that
changes the actual lift on each wing.

Which is what the people pointing out the flaw in the usual presentation of
dihedral diagrams have been saying all along (including Jose, now).

Pete

[Chris Wells]

It doesn't? I normally make every effort to fly my airplane through the air
"head-on". Granted, it's possible to fly through the air in a wide range of
attitudes, but "head-on" is the most efficient and is what most pilots use
for normal, straight-and-level flight.


Your fuselage may be "head-on", but your wings aren't. The relative wind is coming from below. It's impossible to fly straight & level while the wing is head-on - you need lift to maintain level flight.



Only because of the resulting slip. Which is what several people have been
trying to point out already, including Jose (in his latest post).


Yes, and I am pointing out that this is not the main correcting force. Slip is a secondary factor, and takes a finite amount of time to develop.


Ignoring gravity (as Jose suggested), if you take an airplane flying
straight and level and bank it, all that changes is the net lift vector, and
all that changing that will do is change the direction of flight. It will
do nothing to return the airplane's attitude back to straight and level.


No, the AOA of the higher wing will be lower, due to the change in angle of the relative wind, as I have been saying all along. Besides, ignoring gravity pretty much changes everything in the equation.

You can draw the angles on a piece of paper, to help visualize it. If the angle of the wings is different (i.e. dihedral) then the AOA of the upper wing will get lower, and the AOA of the low wing will increase the closer it gets to horizontal. Past horizontal, the low wing will start to develop less lift as well, but the high wing will lose it faster.

[Jose]

> No, the AOA of the higher wing will be lower, due to the change in
> angle of the relative wind, as I have been saying all along.

Consider an airplane with 45 degree dihedral. When it is 45 degrees in
bank, one wing is horizontal and the other is vertical. To keep the
airplane from sinking, the horizontal wing will need to provide
significantly more lift, since it's the only wing supporting the plane.
But as you said above:

> It's impossible to fly straight & level
> while the wing is head-on...

you need lift. This means the horizontal wing will need a greater AOA.
How do you get a greater AOA on a wing that is horizontal due to bank?
Rudder, for one thing. You have to keep the nose up... sideways since
you are tilted.

Well, gee, that's a slip.

Jose
--
Nothing takes longer than a shortcut.
for Email, make the obvious change in the address.

[Chris Wells]

How do you get a greater AOA on a wing that is horizontal due to bank?



It's already there, as I have pointed out repeatedly. Honestly, if no one is even reading my posts, than I'll leave this discussion for when folks are interested.

[Jose]

Here's another way to think about it.

Consider straight and level flight, including gravity, for an aircraft
with dihedral. Consider the "lift" vectors of each of the wings. (They
are not pointed up, they are actually pointed slightly inward due to the
dihedral).

Now, instead of rolling the airplane, swing the entire earth arround so
that the earth (and its gravity) is coming from the right somewhere.
The lift vectors on the wings do NOT change! NO rolling moment is
produced...

until...

....the airplane starts getting dragged to the right by the newly
misplaced earth. Of course, it's being dragged sideways against the
air. ONLY THEN will the AOA change for the wings, directly due to the
sideways slipping of the airplane.

Jose
--
Nothing takes longer than a shortcut.
for Email, make the obvious change in the address.