Mad Flt Sci Fi boy
You clearly have too much time on your hands old chap, someone very succcinctly said it correctly a few post back! Winglets reduce induced drag, by reducing the severity of wing tip vortices and reducing spanwise flow along the wing. This reduction in induced drag will clearly make the engines more effective at any given power setting hence reducing fuel burn etc etc etc.
I think you have to be careful saying that winglets produce thrust, they merely make it more effective.
