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Old Oct 08, 2012, 03:02 AM
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Local AoA and Dihedral Effect

Alright I found myself contributing to a thread where the assertions and explanations were overly simplistic in my opinion, but presented as authoritative, so thought I'd offer the topic to the much more aerodynamically learned. The discussion started with a question about how a rudder turns a plane. I offered my initial explanation that the rudder is a lever and the advancing wing rotates and creates a higher AoA which translates to higher lift and roll is the result.

My claim is that dihedral effect isnt limited to the angle of the wing, but comes from a few places like CG, high wing, planform, vortex distorting. I claimed the local angle of attack of the advncing wing is higher and that creates more lift on that wing and rolls the plane. My claim is that as the one wing advances, even a flat one, that wing has a higher local and effective angle of attack. Sweep would make this more pronounced when a yaw is applied and a yaw is a rotation.

It's not as simple as the advancing wing has a higher airspeed, or that the advancing wing is effectively longer.

Can anyone explain local AoA and how that might vary due to yaw and contribute to a dihedral effect?
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Old Oct 08, 2012, 03:50 AM
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you also have to consider the interaction between wing and fuselage. A perfectly flat wing, with no fuselage to interact with and with just a vertical fin will simply sideslip without rolling. But as soon as there's a fuselage or winglets in the mix things do change. The fuselage will act like a wing in the vertical plane, pressure will build up on one side and drop on the other. in extreme cases the airflow will separate and part of the wing inside the turn will be blanketed by the fuselage wake (this happened in the V1 flying bombs), but even without such an extreme effect part of one wing will fly in a higher pressure area than the other, and since they are both producing lift to keep the plane airborne there will be some dissimmetry of lift that will make the plane roll. The advancing wing in a sudden yaw will have an higher speed than the retreating wing (and this can cause trouble in long AR wings) but generally it's a transient effect, it will initiate a roll, but should not be a big enough effect to sustain it. And if you think about it, the advancing wing will have a lower AOA compared to the retreating wing, though a higher air speed.
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Old Oct 08, 2012, 04:28 AM
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It is definitely not as simple as the advancing wing has a higher airspeed. Suppose you deflected the rudder and the plane wanted to roll. If the plane had ailerons, you could counter the roll due to the rudder deflection with aileron deflection. By setting the right bank angle and aileron deflection, you could establish the airplane in a constant bank angle with a steady heading. Test pilots call this a "steady heading sideslip" other pilots just call it a slip. In this condition, the rudder deflection is causing a rolling moment even though both wings are moving at the same speed.

The mechanism that causes an airplane to want to roll in a steady heading sideslip is "apparent dihedral effect". Several things can contribute to this. The most common thing for models is geometric dihedral. A wing with geometric dihedral in a sideslip sees more local AOA on the wing that is deflected upwind, and less local AOA on the wing that is deflected downwind. This local AOA mismatch makes the airplane want to roll away from the upwind wing.

As noted by Brandano, a high wing can have significant apparent dihedral effect even without geometric dihedral. In this case, the interaction between the wing and fuselage again causes higher local AOA on the upwind than downwind wing (this is sometimes called the "armpit effect"). Wing sweep also contributes to apparent dihedral effect.

Just to complicate things further, a sailplane in a tight turn with no rudder deflection will have lower airspeed on the inside wing. This will often cause the sailplane to want to roll into the turn. This effect is different from apparent dihedral effect because it can happen even with no rudder deflection.

Bottom line: You can have rolling moment due to sideslip with no turn rate. You can have rolling moment due to turn rate with no sideslip (although in this case the sideslip value depends on where you measure it). You can also have rudder deflection in a tight turn without sideslip. This can get complicated in a hurry, so it's helpful to clearly specify the condition you are talking about.
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Old Oct 08, 2012, 06:07 AM
greg
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Quote:
Originally Posted by HELModels View Post
Can anyone explain local AoA and how that might vary due to yaw and contribute to a dihedral effect?
for a wing with absolutely no dihedral yawed at some angle, consider the the flow across the wing which is no longer perpendicular to the wing because it is yawed.

the the AOA is zero, it should be easy to see that the effective angle of attack on both halves remains zero. consider the line the air takes across the wing, and the relative heights of the leading and trailing edges of the wing along that path, and that the path the air takes across the wing is longer.

if the AOA is not zero, you can hopefully see that the heights at the LE and TE are the same as when not yawed, but the effective AOA is less because of the greater distance between them.

now consider dihedral, the both halves of the wings are at a small and equal angle to fuselage. because of dihedral angle, the heights at the LE and TE of the path the air takes across the wing are not the same as in the un-yawed case.

on the more aft wing, the LE height is less (because it is close to the fuse) and the TE height is greater, reducing the AOA. on the more forward wing, the reverse is true, and the effective AOA is greater.

i see shoe just posted. these comments make help you see the geometric relationships

greg
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Old Oct 08, 2012, 08:14 AM
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I usually find these trig relations are usually easiest to visualize when you go to the extremes. In this case, that would be a yaw angle of 90 degrees. Here's a terrible attempt at an ascii representation of the side view of the wing in the case of a 90 degree sideslip (the triangles depict the shape of the wing with dihedral):

Code:
                           <                 >
                              <           >
   Incoming air --->             <     >
                                   < >
On the "front" wing (the right wing yawed 90 degrees in a left turn) the incoming air can be broken up into components along the wing and normal to the wing. The normal component is upward and causes an increase in angle of attack on that wing. On the left wing, the opposite is true and there is a downward normal component due to the yaw angle and dihedral.

The same effect occurs for yaw angles less than 90 degrees, but it's just not as extreme.

The increased airspeed on the right wing while a yaw rate is present probably has some small effect as well, but this effect is only active during the period while the wing is still yawing. If that were the only way to induce roll from yaw, it wouldn't work once the steady yaw angle was reached.

EDIT: For the flat swept wing, the right wing in a left-turn yaw has a greater component of air flow normal to the sweep line. You can actually use the same visualization (above) for this case but consider it as the top view of a swept wing with no dihedral.
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Old Oct 08, 2012, 09:48 AM
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That's a lot to chew on, but is what I had in mind and appreciate the effort in answering.

I built a small high wing model that had a straight taper wing and accidentally ended up with almost zero dihedral. That model still turned with rudder. I recently built another small high wing model and again the wing didnt have enough dihderal. It wouldnt turn with rudder, but it would skid. I later added more dihedral and that fixed it. The main difference in the two planes was the first had a full fuselage that ran from nose to tail while the second is a pod and boom and most of the fuselage is in front of the wing.
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Old Oct 08, 2012, 03:21 PM
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Pod and boom vs full fuselage won't really matter. At least not in any appreciable manner. What is more important for the "high wing" placement and roll with yaw is the height above the true location of the CG. And likely the side area above the CG and under the wing comes into play as well. If your "high wing" pod and boom was a slender glider like design then likely the fuselage is/was very slim compared to your full fuselage style high winger.

Other factors can add to this as well. Beveled wing tips such as often found on Clark Y'ish airfoil wings that extend up and out from the lower surface act to some extent like tip dihedral. In fact there was an electric powered sport model many years ago out of MAN that had a short stubby Clark Y'ish wing with no dihedral other than the rather prominant beveled wing tips and no ailerons. It turned and even rolled in a slow but positive manner as long as there was positive G on the wings. But when inverted if I tried to hold it inverted the effect was gone and the model simply yawed. To call the flight charactaristics "peculiar" was being kind....

The rolling effect from wing sweeping has long been known. But it tends to be a far less effective manner of yaw/roll coupling. A rule of thumb I saw in more than one old pulication was that 30 degrees of sweep per panel was roughly equivalent to 5 degrees of regular dihedral. The odd time I've played with sweep this seems to be about right.
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Old Oct 09, 2012, 07:10 PM
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All good stuff. One might consider all effects, that as a sum total of their effect, contribute to the final force effects.

Several minor contributions come to mind, especially for the strait and square wing platform.

Slip/skid forces and the 3-dimentional balance point of the airframe verse the 3-dimentional center of lift . If the 3-dimentional vertical CG is under the 3-dimentional center of lift, the same forces that cause a slip/skid ball in a turn coordinator to one side will be applied to the entire airframe. This would cause a torque relationship between the 2 3-D locations. For example, looking at the airframe from inside the cockpit, a right-slid ball on the turn coordinator (caused by stepping on the left rudder) indicated a side force to the right. If the vertical CG is under the CL, this will impart a left hand torque rolling action. This effect is totally physical and removes any lift component from the equation, assuming the CL doesn't move vertically (not likely). The direction of the roll would change and will reverse if the vertical CG is higher than the CL (low wing design)Again, I'm just looking at other open-minded contributions to the overall roll effect with a slip/skid (rudder input). How big is it? It probably depends on lots of things, but it should be calculable as a result of simple force and leverage arm.

The other thought is aerodynamic in nature...

Again, assuming a strait square wing, the lift patterns seen at our Reynolds Numbers near the tips gets real messed up with span-wise air flows and in very low RNs bubbles and reverse flows have been demonstrated. By changing the airflow in a skid/slip, the ascending (forward reaching span) will see less adverse effects normally associated with the span-wise airflow and may produce more lift, while the receding span may see an exaggeration of the poor airflow/lift seen near the tips. Again, just trying to keep an open mind to all possible reasons a model airplane might exhibit rolling in a slip/skid. Span wise airflow near the tips is something I haven't considered before.

Thanks for the brain twisting tonight! I've never considered these two items in explaining the rudder/roll thing.
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Old Oct 10, 2012, 10:38 AM
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Andy Clancy's little Lady Bug was a high-wing model. The wing was thick, flat-bottomed, and had no dihedral on the top of the wing. But the bottom surface was bent upward, beginning about 75% out from the wing center line, to meet the upper wing skin, to form a thin taper. I hope the picture makes some of that clear.

The Lady Bug flew fine with no ailerons, only rudder to turn. In fact, not trusting Clancy's design, the first wing I built for the LB did have dihedral (polyhedral?), for the top of the wing, as well as the bottom, also beginning about 75% out from wing center. It was a handful for me to fly. So I switched to a proper Clancy wing.

Later, I made a low-wing fuselage for that "mistaken" wing, and this combo flew fine.

Jim R.
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Old Oct 10, 2012, 10:08 PM
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Jim, that's sort of the idea behind that sport electric from MAN magazine that I described in my last post.

The reason this beveled tip works is that the wings are both low in aspect ratio and the flyers are not demanding a high rate of roll. Also there is no requirement for inverted response. At least I'm guessing that a Lazy Bee or Honey Bee if flown inverted and level would lose the roll couple like that one I flew managed to do.
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