How do raked wingtips reduce induced drag?

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Hi all,

I understand that both winglets and raked wingtips are for the same function (from what I have read) - to reduced the amount of induced drag.

I understand the principles behind winglets, however I am uncertain how raked wingtips actually achieve this? Could anyone please explain the aerodynamics behind it.

Thanks
 
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The term raked wingtips was unfamiliar to me, so I looked it up. These images may help others provide an answer.

Raked wingtips
Delta Air Lines airliner in flight, seen from below against a blue sky with cumulus clouds, showing its swept wings, extended landing gear and winglets on the wingtips.


Winglets
NASA slide titled Winglets comparing two airplanes: without winglets, strong vortices trail from the wingtips; with winglets, the vortices are labelled weaker. Caption reads Winglets reduce induced drag component.
 
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  • Delta Air Lines airliner in flight, seen from below against a blue sky with cumulus clouds, showing its swept wings, extended landing gear and winglets on the wingtips.
    1024px-Delta_Air_Lines_767-400ER_%40LHR.jpg
    38.7 KB · Views: 1,207
  • NASA slide titled Winglets comparing two airplanes: without winglets, strong vortices trail from the wingtips; with winglets, the vortices are labelled weaker. Caption reads Winglets reduce induced drag component.
    winglets.jpg
    33.5 KB · Views: 1,474
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Raked wingtips have more sweep compared to the rest of the wing.
But how they reduce induce drag?
I can not find explanantion...boeing dreamliner
Boeing 787 Dreamliner parked on an apron under a clear blue sky, viewed from low angle, with its raked wingtip rising sharply upward in the foreground.


albatros
Photo of a white-headed seabird with long, narrow dark-tipped wings spread wide in flight against a blue sky with clouds at the upper left.
 
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  • Boeing 787 Dreamliner parked on an apron under a clear blue sky, viewed from low angle, with its raked wingtip rising sharply upward in the foreground.
    boeing-787-10-pas-12.jpg
    41.6 KB · Views: 1,254
  • Photo of a white-headed seabird with long, narrow dark-tipped wings spread wide in flight against a blue sky with clouds at the upper left.
    journal.pone.0004016.png
    15.6 KB · Views: 880
http://www.aerospaceweb.org/question/aerodynamics/q0148.shtml
Says that they create an aerodynamic washout.

http://www.aerospaceweb.org/question/dynamics/q0055.shtml
First we will cover wing twist, of which there are two kinds, geometric twist and aerodynamic twist. A technical definition of geometric twist would go something like this: "an actual change in the airfoil angle of incidence, usually measured with respect to the root airfoil." (Raymer, Aircraft Design) In other words, if you were to look at a wing from the side, the airfoil (cross section) of the wing would rotate as you moved away from the aircraft fuselage. In most aircraft, the airfoil twists down as we move along the wing further from the fuselage. This is referred to as "washout."
Line drawing of a wing with its tip twisted down, with an angle marked between the chord line at the tip and the root, labelled Wing tip twisted down (Washout).
 
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  • Line drawing of a wing with its tip twisted down, with an angle marked between the chord line at the tip and the root, labelled Wing tip twisted down (Washout).
    twist.jpg
    9.3 KB · Views: 855
https://en.wikipedia.org/wiki/Wingtip_device#Raked_wingtip said:
[...] they increase the effective wing aspect ratio and diminish wingtip vortices, decreasing lift-induced drag. [...] While an increase in span would be more effective than a same-length winglet, its bending moment is greater. A 3 ft (91 cm) winglet gives the performance gain of a 2 ft (61 cm) span increase but has the bending force of a 1 ft (30 cm) span increase.
I would say that they basically reduce the effect of a sharp parallel edge at the tip where the air can 'escape' and create vortices.
 
Just by comparing the second illustration in Post #2 with the one in Post #4, I would say that wingtip vortices start with an upward motion of the air escaping from beneath the wing, and the downward angle at the tip of the wing opposes this motion, impeding the formation of the vortex.
 
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