A supercritical wing is, by definition, designed to operate in a
compressible flow regime. You can throw Bernoulli out the window for such
wings.
They still generate lift the same way as all other wings; they induce a
circulation in the airflow. They have a "fat" shape to control adverse
transonic effects and prevent shock separation on the upper surface from
occuring too far forward.
As a side benefit, you can fit more fuel in there and use deeper chords, but
it's not strictly necessary...the 747 doesn't have a supercritical wing and
does just fine.
Tom.
Late Professor Richard S. Shevell, Stanford Uni, chief aerodynamist for
making the DC-9, MD-80 and DC-10, once wrote in a private mail, "Dont
explain Lift using Bernoulli equation, but use it for the calculation
in connection with the Potential/ Circulation Theory model"! Shevell
described how the Potential theory model was use less for 150 years
(after Euler and others), but in 1904 the superpositioning of the
manually applied Circulation solved the problem of calculation Lift.
Today Newton based CFD (Navier-Stokes) calculates the best
aerodynamics.
Professor e.m John D. Anderson, Maryland Uni, writes in one of his
books about the venturi pipe:
"Strictly speaking Bernoulli equation can only be valid along the
centerline of the venturi, and then we have disregarded the
compressibility effects"!
A senior CFD aerodynamist once told me, that "the continuity equation"
only is a mathematical model, not a physical law.
Since the venturi pipe is a restriction in the pipe, it will increase
the drag, so to overcome that a increase in pressure infront of the
venturi is needed. The 1953 Piper Colt has as venturi pipe a
speedsensor without the convergent entrance part! Why? The front part
is not needed, only the divergent backpart makes the jobb by help of
the Coanda effect!
Jan-Olov Newborg
Everybody seems to want to be an aerodynamicist, and explain
Bernoulli's Theorem. See today's "Overboard" comic strip:
http://www.uclick.com/client/smc/ob/2006/08/13/