In reply to the original question, yes ailerons do provide lift just because they are a part of the wing area, and especiallyΒ*when they are deflected down.Β* But not when deflected up, then they reduce lift, but....this has already been discussed enough.
Draw yourself an airplane fuse, going away, wing, tail, just a circle with lines extended to emulate wings and stab and vertical stab. Draw an arrow straight up over the fuse.. That is ''Lift'' in straight flight. Draw another line straight down of equal length. That is weight (gravity, whatever) Now draw another line of same length in a bank angle, let's use 60 degrees. Notice the straight down line will be the same
Below is a drawing such as the one Hossfly is talking about....have a good look at it.
Now I am going to pick on poor Top_Gunn for a bitΒ*Β* (sorry Top)Β* (NOTE:Β* For the following, it is important to remember, the WEIGHT of the airplane does not change....fuel burn during a simple turn is negligible)
That's true. But it's also true that up elevator is needed to turn when banked. It does two useful things in turns, not just one. As you said, the banked wing ''pushes'' the plane sideways. Some up elevator helps convert that push to a turn
This is not totally correct.Β* While there is a sideways ''push'' do to the banked wing, which you can see in the drawing below, the tail surfaces, in particular the vertical fin, causes the airplane to turn when it trys to fly ''sideays''.Β* You do not need elevator to convert that ''push'' into a turn, the design of the airplane tail will do it by itself.Β* On many aircraft a touch or rudder is needed to help it turn, but that is usually do to adverse yaw...a whole seperate turning issue.Β* In actual practice, the elevator is used to keep the nose up and prevent altitude loss, not to ''turn'' the airplane.
This isn't just a trivial point about how airplanes fly; it has a practical application. If you are making a tight turn and you need to make it tighter (to stay in front of the flight line, for instance), you tighten the turn by using more up elevator. Beginners sometimes try to do it by adding aileron or rudder, and the usual result is to add to the roll, sometimes leading to an unintentional split S. Planes get broken that way.
In your example of tightening the turn to stay on front of the flightline, simply adding elevator as you say is also going to cause a broken airplane.Β* In a steady turn at a set bank angle, adding elevator will cause the aircraft to pitch up...NOT turn tighter, and may lead to a stall.Β* In reality, if you want to turn tighter, you need to increase bank angle.Β* Of course, the increase in bank angle will require more elevator as well, but again, it is to keep the aircraft from losing altitude, and not to turn.Β* We will see why in my next point.
NASA disagrees: ''During a banked turn, elevator inputs can increase the lift and cause a tighter turn. That is why elevator performance is so important for fighter aircraft.'' http://www.grc.nasa.gov/WWW/k-12/airplane/elv.html
And Langewiesche, p. 198: ''An airplane is turned by laying it over on its side and lifting it around through back pressure on the stick.'' (In ''Stick and Rudder,'' this whole sentence is in italics.)
You are of course right to say that you need elevator in a turn to keep the nose from dropping. But you also use elevator to tighten a turn.
While these are both correct statements, you are missing an important statement there, the ''increase the lift'' part.Β* Lets look at why that is important.
Now, go and have another look at the diagram.Β* You will see that when the airplane is straight and level, the lift equals the weight.Β* AlsoΒ*note that the lift is always perpendicular to the wings.Β* But, when the airplane is put into a bank, the lift vector tilts to the same angle as the bank angle.Β* Now, the lift vector can be split into two vectors, one vertical and one horizontal.Β* The vertical one is what is opposing the weight of the aircraft, and the horizontal one is what is giving that ''sideways push'' discussed earlier.Β* Here is the issue though:
Because the total lift is ''split'' between the two vectors, the vertical lift vector is reduced.Β* That means that the weight now exceeds the amount of lift holding the airplane up, remember, the weight doesn't change.Β* In order to get that lift back, we need to increase either airspeed or angle of attack.Β* Increasing angle of attack is the most practical, especially in full size aircraft that do not have gobs of extra power.Β* So, we increase angle ofΒ*attack, Β*and the way to do that is to pull back on the stick (up elevator).Β* This increases the total
lift vector, which allows the vertical component to again equal the weight.Β* Now, looking at that diagram again, you can see how in a set angle of bank, simply applying up elevator will cause the airplane to climb.Β* There will be a small increase in the horizontal component too, but in a ''normal'' turn, not enough to even notice the increase in turn radius.
BUT, look what happens if we steepen the bank further.Β* Now, the total
lift vector is still being split, but the steeper the bank, the more of the lift is given to the horizontal vector.Β* This will cause a tighter turn.Β* (Remember, the tail area will cause the airplane to ''yaw'' when that horizontal lift ''pushes'' us sideway, thus turning the airplane.)Β* So, now we havea large portion of our lift going to the horizontal vector and less to the vertical vector, now the airplane really wants to drop, so we need to increase the total
lift a lot more.Β* So, to do this we need to pull back some more to increase the angle of attack enough to increase the total lift to increase the vertical component to keep us up in the sky.Β* Whew, lots going on here isn't there.Β*
So, as we can see, the more we increase the bank, the quicker we will turn.Β* But at the same time, the faster we will drop unless we pull back more to mainain enough lift to hold the airplane up.Β* We can also visualise that for a set bank angle, and a set airspeed, there will be a set angle of attack that the wings need in order to produce enough lift to hold the airplane up while some of the lift is being ''stolen'' to turn the airplane.Β* There will come a point where the elevator will become the primary ''turning'' control, but not until a nearly vertical bank.Β* Until then, we still need to hold the airpalne in the air, and that is the job of the wings.Β* They need to continue to produce enough ''vertical'' lift to overcome the weight.
Sorry if I ''stepped on your toes'' Top_Gunn.Β* Just hoping to help with a bit of understanding.