Originally answered on Quora on April 28 2015.

Longer, thinner wings are more efficient, but the further the wing extends outwards,the more bending is experienced at the wing root as the wing lifts, and the heavier the wing root has to be built to counter this bending. If we can make the wing act as if it is longer without increasing the bending at the root, we wouldn’t have to make the root stronger and heavier.

Without the winglet (the sticky-up bit), as other people have mentioned the high pressure air on the bottom of the wing leaks around the wingtip to the top of the wing, reducing the lift on the top of the wingtip and leaving a swirling vortex of air behind the wingtip. Looking at the wingtip in the photo from in front of the plane this vortex would be travelling in a clockwise direction, centred on the wing tip.

The winglet is attached in an upwards direction from the wingtip and designed so that it is trying to lift inwards towards the viewer sitting in the aircraft (if you think of the aircraft as a skier, and the winglets as skis, the winglets are being used to do a “snow plough”). There is higher pressure air on the far side of the winglet and low pressure air on the near side of the winglet. Like the main wingtip, the tip of the winglet has a clockwise vortex trailing behind it, proportionally smaller than the main wingtip vortex but centred higher, at the tip of the winglet. In your imagination If you superimpose the two vortices on each other you will see them running into each other half way up the winglet, like two wheels turning the same direction whose tyres are touching each other. Like the rubbing tyre surfaces, the winglet vortex pushes against the air sneaking around the wingtip from the bottom of the wing, which has the effect of “unwinding” the main vortex slightly, convincing the air near the wing tip that the wing is longer than it actually is and increasing the efficiency of the wing near the tip.

Because the winglet is trying to fly inwards towards the fuselage it compresses the wing towards the fuselage but does not increase the bending moment about the wing root, which is what would have happened if we’d added more wing instead of a winglet. This means the root does not need  beefing up to handle more bending and can be built lighter. If you hold your arms out to the side with your palms facing outwards, this is the difference at your shoulder between two people trying to lift you up by your wrists, or pushing your palms towards your head with the same force.

Birds have already solved this problem, but wing root bending moments aren’t their main worry. If efficiency was the only aim all birds would have long wings like an albatross, however manoeuvrability and fitting between obstacles is a conflicting evolutionary pressure, particularly for birds of prey. The wide spread out pinion feathers or “fingers” on the tips of the wings of eagles, hawks, kites etc each have their own discrete wingtip vortices which interfere with each other to reduce the loss of efficiency near the tip. This allows them to have shorter wings while still retaining most of the efficiency required to soar long distances or hover over a field looking for lunch.

This answer is based on an explanation on pages 133-134 of The Design of the Aeroplane by D Stinton 1983. The analogies are my own.