2 things:
- reduces induced drag
- adds a small amount to the thrust of the aircraft
reduces induced drag
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Conventional wings, as said before, create vortices at the wingtips due to the pressure differential on the top & bottom of the wing & the opposite spanwise flow top & bottom. The bigger the spanwise flow, the bigger the vortices. The biggest spanwise flow is at low speeds, which explains why wake turbulence is biggest at low speed.
These vortices create a downwash behind the wing and this has an effect on the airflow over the wing. In fact, it reduces the effective angle of attack on the wing and gives induced drag. Induced drag is the vector parrallel to drag when comparing effective lift force & theoretical lift force.
Winglets create smaller vortices & also more upwards as you can see in the picture posted by Lord Spandex Masher. This gives less downwash thus less induced drag.
Thrust
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When looking at a winglet from above it is a small wing. The reactionary force created by the winglet is directed towards the fuselage of the aircraft with a small vector helping aircraft thrust.
Sorry if my English is not perfect but I'm not a native speaker. Corrections and remarks always welcome ofcourse