From: http://www.djaerotech.com/dj_askjd/d.../wingfin1.html

A finite span wing in upright flight has more pressure on the bottom of
the wing than on top. Lift is always measured perpendicular to the local
airflow direction, and drag is always parallel to it. Once you know
these two bits of information, it's not hard to understand how winglets
work.

The higher pressure air under the wing wants to spill around the wingtip
to try to fill in the low pressure area on top. This flow results in a
tip vortex trailing aft from the wingtip, like a horizontal tornado. You
can see these vortices at the wingtips of a jet fighter during a high
lift maneuver in sufficiently humid air, or at the tips of an airliner's
flaps during a landing approach in wet weather. The energy extracted
continuously from the aircraft to make the air swirl like that is what
we call induced drag.

As you probably recall from our previous discussions of induced drag,
it's at its worst when we're trying to make lots of lift with relatively
little airflow. This means that slow flight (low speed, low mass flow,
high lift coefficient) is one of the worst cases. This also means that
the intensity of the tip vortices will be highest at these kinds of
flight conditions.

Now we need to talk about "helix angle". If you understand the pitch of
a prop, you're already familiar with it. Helix angle is one way to
measure how far something rotates compared to how far it travels forward
in the same time. The blade angle of a propeller blade is nearly the
same (minus its efficiency effects and local angle of attack) as its
helix angle. A wingtip vortex has a helix angle as well. This angle will
be nearly parallel to the airplane's direction of flight when induced
drag is low, but twist up into increasingly greater angles relative to
the flight direction as we slow down or pull more "G".

If we have a significant amount of induced drag, and a correspondingly
stronger tip vortex, then the flow at the wingtip will not be parallel
to it, but rather at an inward angle on top and an outward angle on the
bottom. This is where the winglets come in.

If we park a lifting surface in the middle of this angled air flow, it
will develop lift perpendicular to the angled air flow. The resulting
lift will be angled forward, and the forward component of that lift will
be producing thrust. The lifting surface (i.e.: "winglet") will also be
producing drag of its own, including both parasite and induced drag.

If the drag the winglet produces is less than the forward component of
its lift, then there will be a net thrust applied from the winglet to
the aircraft. This thrust actually represents some of the energy in the
tip vortex, harvested from the vortex by the winglet and given back to
the aircraft. That's it. That's all there is to it. It's so simple!

OK, now the catch. How do we maximize that thrust? This is where it gets
complicated. If you increase the angle of attack of the winglet by
increasing the "toe-in" angle, then it makes more lift force (which
should theoretically increase the forward component of that lift), but
it also makes more drag force. Depending on the specific situation, this
could increase, decrease, or not change the net thrust of the winglet.
It's going to depend on a lot of factors, including the flight condition.

This last item is particularly critical. Because the amount of induced
drag, and the helix angle of the vortex decrease as you increase
airspeed, the energy available for "harvesting" by the winglet decreases
as you fly faster. Meanwhile, the parasite drag of the winglet is
increasing. Eventually you get to a point where the total drag of the
winglet is equal to the forward component of its lift, and at that point
the winglet produces zero thrust. This is called the "crossover
velocity". At airspeeds higher than the crossover velocity, the winglet
adds to the aircraft's total drag, and you would be better off without it.


Cheers