It is my understanding that while a longer wing would give more of a benefit than winglets giving the same weight penalty, winglets are used since it is more difficult to retrofit a wing with an extended tip. You'd have to reinforce the wing to handle the added lift at the tip while a winglet mainly reduces the drag load on the wing. I have not meddled with such designs myself, but that is how I’ve had it explained to me.
HD, I’d love a source for that for a more thorough explanation than what I can get on a web forum?
I’d assume that a raked wing tip would gain some of the benefits of a delta wing, with the vortex shedding along the entire leading edge of the raked section and providing lift on top of the airfoil.
Doublechecking my definition of a Hoerner wing tip: A relatively straight (square) wing tip with the outer edge cut off at an angle to the vertical, leaning out from the aircraft?
Cheers,
Fred