ORIGINAL: Top_Gunn
You are right to say that adding elevator increases the total lift vector. What I don't understand is your claim that doing this does not make the turn tighter. Since the plane is banked in a turn, the lift vector is not vertical. Therefore, increasing that vector increases "lift" in two directions: upward and in the direction you are turning. The extreme case would be if you are banked 90 degrees, in which case adding lift would only tighten the turn and wouldn't raise the nose at all (possible coupling aside). To be sure, we do not usually bank that much except when we're having lots of fun. But the principle is the same even in a 45 degree bank, where about half of the added lift tends to move the plane's nose in the direction in which it is turning.
The lift vector is always opposing gravity. Gravity vector is always pointing to earth center.
"Adding elevator" means what exactly? That you added elevators to the stab? If it means moving the elevator, you have two options, "up or down". Either one "adds"
Giving a plane"up" elevator changes, increasesthe wing AOA when the plane is flying S&L or is in general upright flight mode.Increased wing AOA creates the added lift. And for many planes you can give too much "UP" elevator to the point the wing AOA is too high, then the wing stalls and dumps lift quickly
If the plane is inverted and you give it "UP" elevator, wing AOA decreases and dumps lift
Ailerons are part of the wing area. They create lift, roll and drag forces