Jim and Steve,

Winglets work by 'flying' in the tip vortex; they are placed on the
wing with a slight 'toe out' such that their lift vector is inward and
slightly forward. They fly with a posivitve AOA at this toe out angle
because their local relative wind is the top (inward rotating) part of
the tip vortex. The forward component of their lift vector shows up as
a reduction of induced drag.

Winglets are effective only on aircraft that cruise at or near the
stall speed, where the vortex is large. This is true on most bizjets
and transport type jets; while their true airspeed is very high, their
indicated airspeed is nearly down to the stall. Most of these types of
aircraft cruise in this little 'corner' of the envelope, just above the
stall speed and just below the limiting Mach numer. A little slower
and you stall, a little faster and you get into bad Mach effects
(buffeting or Mach tuck.) It is commonly called the coffin corner.

Winglets are effective on these planes not because they are flying
fast, but rather because (in indicated airspeed) they are flying slow
(close to the stall). The low IAS means they fly at a high AOA (nearly
stalled) and create strong vortices for the winglets to fly in.

Winglets are typically of no or even negative value on light aircraft
because our cruise speed is typically about twice the stall speed.
This means we cruise with a much lower AOA, and therefore create much
weaker wingtip vorticies. Without the strong vortex, there is little
rotating flow for the winglet to fly in, and it just adds parasite
drag.

The voyager had winglets (until Dick scraped them off) because that
aircraft was designed to fly at the airspeed of maximum range, which
was near enough to the stall speed to make the winglets effective.
That the aircraft made it around the world without them attests to the
fact that the induced drag reduction is incremental (a few percent.)
Regards,

Gene