.......Or perhaps we aren't quite that close.........
I'd like to look at the quote below and see if we are both on the same track here.
Originally posted by BernieG
I would tend to disagree, as the sideslip is not a cause, but a result. Ok, I am in a bank, and release the control. The flight is assymetric. Because I have less lift (projected surface), the plane tend to dive and accelerate (this IS a sideslip)
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....
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.
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.
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.
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.....