The raked wingtip of the Boeing 787 is now "le denier cri" in wingtip design, but has been successfully employed by water fowl for many millennia. The use of composite structures has made the three-dimensional shaping of wingtips much easier, and the first airplanes to use increased sweep at the wingtip were indeed composite gliders such as the Schempp-Hirth Discus.
Seagull (left) Schempp-Hirth Discus 2 (right, source)
In the times of metal wings, Dornier introduced their TNT (Tragflügel Neuer Technologie, in English: Wing of new technology) on aircraft like the Do 228, Do 328 and the Dornier ATT flying boat. It used a triangular wingtip with no change in trailing edge sweep, which is easier to manufacture in aluminium.
An Air Alps Dornier 328-110 landing at Fiumicino Airport, Rome, Italy, viewed from Ostia Antica. Picture by Makaristos.
You can think of the raked wingtip as of a winglet which has been folded down. Increasing the wingspan will involve a bigger mass of air into the creation of lift, and the induced drag is reduced. This explains already most of the effect, but the increased sweep adds some more benefits.
- Higher sweep lowers the lift curve slope. This helps to reduce the lift contribution (and, consequently, the bending moment!) of the wingtip at high angles of attack. Therefore, raking the wingtip will result in a lower maximum bending moment.
- The sweep also shifts the center of pressure of the wingtip backwards, adding a negative torsion moment. This moment lowers the angle of attack over the whole outer wing in gusts and at high load factors, again helping to lower the maximum bending moment at the root.
- Especially in gliders, it allows to combine a near-elliptical circulation distribution over a wide range of angles of attack with good stall characteristics. The lower lift curve slope of the wingtip lets it stall at a higher angle of attack and reduces its lift contribution relative to its area at increasing angle of attack.
This aeroelastic tailoring, together with the low fuel consumption of modern high-bypass-ratio engines, allows the Boeing 787 to use a wing of an aspect ratio of 10 and the A350 one of up to 11.8. Previously, - apart from gliders - only special designs for extreme flying time and range like the B-24 Liberator or the Breguet Atlantique sported such high aspect ratios. Older airliner designs had to use lower aspect ratios (between 6 and 8.5) to have enough wing volume for fuel.