dihedral roll-back affect
 

No, sorry, no and no ! Symmetrical flight means exactly that, symmetrical flight, both wings (more on that later) are at the same speed and same AOA. In a coordinated turn, the yaw is NOT induced by the rudder. If we forget about adverse yaw, a turn is possible only with ailerons to bank, an elevator. Rudder is used ONLY to counteract adverse yaw. Too much or not enough rudder trigger sideslips, but with the proper use of the rudder, there is NO yaw, or if you prefer, the airplane does not turn on the yaw axis, but on both roll and pitch axis, that is what makes a turn. Remember that, for one "action" , a plane has to move on 2 axis, all the time.

Now, to confuse things a bit more, let's talk about induced roll. I said above that in symmetrical flight both wings are at the same speed. Well, depends of the wings, the radius of the turn, and the flight speed, but there is a very well known phenomenon for gliders, where in slow spiral flight (constant turn), because of the huge wingspan, the difference in speed between the external wing and the internal wing is enough to have the EXTERNAL wing seeing a lift increase (due to speed), which tend to roll the sailplane INSIDE the turn, as, in the same time, the adverse yaw is at a maximum, a correct sysmmetrical flight require to have a bit more rudder than normal, and ailerons OUTSIDE (cross control)

Is not trying to understand aerodynamic, fun ?

Bernard

dihedral roll-back affect
 

.......Or perhaps we aren't quite that close......... :D I'd like to look at the quote below and see if we are both on the same track here.

Not necessarily depending on what you meant here, side slip is the airplane moving sideways where the airstream hits on one side of the fuselage. I've attached a quick little sketch below. In A our pattern model is level and wing lift is straight up, no problem here I hope....:D In B we've used the ailerons to tilt the model but it's still pointing in the same direction. Note the wing is now lifting at an angle and there is a side slip condition. The speed it will move sideways is the based on the force from the little arrow pointed sideways. Now it's not super clear with the size and angle here but the vertical vector is not as large as the original level lift vector. This shows that there is not now enough lift to hold the model up and so we will also get a bit of a nose down and dive along with the side slip.

Quote:

---

The lower wing "see" the relative airstream at a higher AOA ( of faster, it's the same), lift increase, it correct the roll, ok.

---

With the flat wing the AoA will not change for the two wings as there the geometry of the dihedral is not there to make the AoA change. This is shown in B with the air sliding along both wings the same Now if we substitute the dihedral wing in D then the side slipping airflow will hit the angled panels from different directions and we have different AoA's for each panel. Higher angle for the low wing and lower angle for the high wing. The difference in lift levels the wings.

Quote:

---

Now, make the same bank, but imagine we are in a perfectly symmetric flight. That is, once banked, I put aileron in neutral, and give just the correct rudder input to keep the ball centered (admit it's almost impossible on a model, talking full scale here). The plane will, by itself, go back to straight and level flight, and if there is no other input, i will be able to slowly release the pressure on the rudder, to keep symmetric all the time until I am out of the bank/turn. (Done that, more than once, on the wonderfully flying machine named ASK-13. The most delightfull harmony of controls I have ever flown. )

---

But the ASK HAS dihedral. Or if it's flat on the ground then it certainly will flex under flight loads to a nice curved dihedral. And to help clear this up if you were in a left hand turn like above and neutralized the ailerons like you say then which way do you delfect the rudder? I'm guessing that you add right rudder to bring the ASK out of a left bank. Is that right? If so then the right rudder is yawing the plane to the right while it's banked to the left. So now you've got a right yaw added to a left hand side slip so the angle of the side slip is increased and the curved dihedral of the wing will roll the plane back to level.

Quote:

---

The sideslip theory is valid in only one case, assymetric flight, while the projected surface theory is always valid, so I still believe that the sideslip is a secondary effect.

---

I think this is where all the disagreement is coming from. You say that an airplane can be banked and still be flying symetrically. I say when you bank an airplane it is NOT flying symetrically. If you bank you side slip. The only way a banked airplane will not side slip is if you are in a coordinated turn. And if you side slip with dihedral the model will level itself. Some of this will come from the projected planform of the lower wing being longer but the major part will come from the changes in AoA for the two wings as in D in the diagram.

Fun? I think I need a headache pill. And some cream for my worn out fingertips from all the typing..... :D

dihedral roll-back affect
 

OK, re-read what I say having in mind that for me symetric flight = coordinated turn, as it's not possible differently. I am saying that, even without sideslip, the plane will ALSO level itself.


As a good balsa gluer, you should try a bit of CA on your fingertips to make them stiffer.... :)

Bernard

dihedral roll-back affect
 

OK, Bernie. I put some CA on my fingertips but I didn't wait long enough for it to cure.......... So after I got the keyboard off my finger I thought I'd write this up so we could close this off........ I hope :D

It seems to me that in a truly coordinated turn the airplane should not experience any return to normal as all forces should be balanced and the airplane should just go round and round until controls are then used to disturb this balance. Dihedral or no a coordinated turn should be stable.

But as you suggest with the need for the outside aileron to counter the wing dropping into the turn on the ASK there is often some other factor that disturbs a truly balanced turn. It might be the speed and lift difference from the inside to the outside or the aircraft may be spirally too stable or unstable causing the pilot to require rudder inputs that are not part of the coordinated turn just to maintain the proper turn bank and radius or any other number of design related factors.

BTW, you, as a full size pilot, should also remember that it's possible to be in a balanced spiral dive and have the T&B indicator show nothing other than straight flight. This was the cause of many early crashes when pilots tried to fly in clouds and got disoriented.

But all this has little to do with how dihedral works. You say it's the projected area difference and I say it's sideslipping air acting to change the angle of attack on the wings differently.

I'd like to close my part with another example. I've flown quite a few Goldberg Eagles with novice students. This model has a fairly strong tendency to return to level flight when the controls are neutrallized. I dont' have the actual numbers with me but from memory this model has about 3 inches of dihedral under each wingtip and the span is 50 inches. My trigonometry is a little rusty so I used my CAD to lift a 25 inch panel 3 inches and I get a projected span of 24.8 inches. That's only a 0.2 inch difference per panel and a 6.8 degree angle. So if we bank our model by 6.8 degrees then the low panel is 25 inch span and the raised panel is reduced by a futher 6.8 degree tilt to 24.3 inches projected. So we would have just 0.7 inch span worth of area to do all the restorative work. For our wing at 50 inch span and 10 inch chord this would be a differnce of 0.7 x 10 = 7 sq inches. Each panel has 250 sq inches so we have a total differnce at this bank angle of 7/250= 2.8 % total difference in wing area to do the work.

On the other hand lets look at the same wing if we allow a side slip of 5 degrees. This isn't much and it's probably safe to say that you'd need that much at least to see a noticable side slip from the ground. From having flown the Goldberg Eagle and neutrallizing the controls while banking I know it can be seen to sideslip noticeably. Using a side slip angle of 5 degrees then the change in AoA for each wing is 0.48 degrees or a 0.96 degree total difference between the two panels. Using the FoilSim applet HERE I "made up a wing and airfoil close to our model. Starting at 2 degree AoA I have a Cl of .675. Adding 0.96 degrees gives me an increase to 0.79 for a Cl difference between the wing panels of 0.115 or a 15.7% difference between the panels based on the average Cl of 0.733.

And just to see it from another perspective I changed the Foilsim units to lift vs angle and at 30 mph flight speed the 2.48 average degree AoA gives us just under 4 1/2 lbs of lift so we must have built a heavy model :D Factoring in the AoA differences for each wing shows a lift difference between the wings of a whopping 0.845 lbs of lift trying to force our model back to level.

As I said before I have every reason to agree that the projected span difference is certainly a factor but from the numbers above you can see that the side slip induced change to lift is a much more powerful force.

I think I'll go use that CA on the models now instead of my fingers. Cheers.