The following is taken from an article published in the Putnam Aeronautical Review in May 1989 :-
Wing tip drag has been known about since the early days of flight. This drag can be reduced by increasing the wingspan, however this has the negative effect of increasing the bending moment at the wing root. To overcome this you have to build a heavier structure which counterbalances the benefit of reducing the vortex drag.
Interest in Vortex drag didn't really happen until the late 1940's when the US found the solution by fitting simple end plates to the wing tips. Unfortunatly it was found that to be efficient these end plates had to be quite large which induced drag of their own which once again negated the reduction in vortex drag.
Interest then waned again until the oil crisis focused everyones attention on fuel consumption. At this time NASA took a look at the subject and developed what are now known as winglets
As we know, the winglet operates in the circulation field around the wingtip. Airflow in this area is spanwise with the air below the wing spilling round to the upper surface. The winglet tends to produce a large side force and because the side force vectors are approx perpendicular to the local flow, the side forces produced have a forward (thrust) componant which reduces the a/c trailing edge vortex. This is similar to the principle that enables sailing boats to travel upwind by tacking.
The side force produced by a winglet, and so the thrust generated, depends on the strength of the circulation flow around the wingtip. Now since the circulation strength is a product of the amount of lift in the wing tip area, winglets are most effective on a/c requireing high lift such as exec jets & heavy commercial transports.
Some practical figures.
Fitting winglets to the Cessna 421C produced a payload increase of 50 Lbs and a 25% increase in max ROC. Cruise speed is increased by 10 kts and the a/c is more stable.
On a Cessna 414A Chancellor the drag reduction gives an 300 Lbs payload increase with no loss of climb or cruise performance. Alternatively with a standard payload the time to climb to 18000 Ft is reduced by 25%. Additionally winglets have been found to reduce the tendancy to dutch roll.
Moving up the scale to the 747-400 the 6 Ft winglets on this a/c can either provide a fuel burn improvement of 2% or, if extra range is required, a range increase of 1%.
On a A300-600 the tip fence gives a fuel saving of 1% @ cruise speed and on the A310-300 1.5%. The 1% fuel saving equates to 36,000 galls over a 1 year period.
The addition of tip fences to the A320 produces a fuel reduction of 1.5%