I did not understand it either and I have been an aeronautical engineer for Fifty years. The fact that when you bank the airplane the lift vector is broken down into a vertical componet and a horizontal componet with the horizontal componet causing the turn is sufficient. Anything more than that is pure crap. No, it isn't . . banking the wings has nothing to do with turning the plane. It does set the plane up to use the horizontal Vector. But until you use your elevator, a turn will not be in affect. This is why the person used the knife edge example. To show that horizontal vector is nothing until your AOA is changed with your elevator, thus producing the horizontal vector we all know about as "turning the plane" We automatically apply elevator while turning, to keep the nose up. This instigates the horizontal vector, allowing the plane to turn.
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