Re: How Important Is Cross-section Shape Of Wing?

Date:         09 Apr 2001 15:36:57 
From:         "Matthew Willshee" <matthew@amber-matt.freeserve.co.uk>
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Gord Beaman <gbeaman@pei.sympatico.ca> wrote in message
news:airliners.2001.124@ditka.Chicago.COM...
> cp@panix.com wrote:
>
> Sure...the 'path' over the top of the wing is longer than the
> path under it so the pressure has to be lower on the top
> inflight. So as the AOA increases the pressure 'under' the wing
> increases while the pressure on top decreases therefore the wing
> wants to move up. As you say, this pressure differential is
> basically the result of displacing air mass downward but it's the
> pressure differential that provided lift.

Here's my take on this one.

Bernoulli's principle says that faster flowing air has lower pressure.  This
is because as the air flow accelerates some of the pressure energy is
converted to movement energy.  Bernoulli's principle is a law of physics.
You can use Bernoulli's equation itself in incompressible flow (water or
very low Mach number air) but you must use compressible flow equations to
get accurate results at higher speeds.

Where every "popular science" text gets it wrong is that they say the air
must move faster over the top section of the wing because it has farther to
go (therefore pressure is lower hence net force on wing).  The problem is
that the air on the top doesn't know that it has to take the same time to
get across the wing as the air on the bottom.  It doesn't even know what the
air on the bottom is doing.  It might get to the trailing edge at the same
time, earlier or later.

What is going on then?  Newton's Third Law says that every action must have
an equal and opposite reaction.  In the vertical sense there are two forces
acting on the plane.  First gravity - the Earth pulls the plane down
(reaction - plane pulls earth up).  Second lift - the air is pushing the
plane up to counteract gravity.  There must be a reaction - the air must be
pushed downwards.  So any successful lift device displaces air downwards.
We could use wings, a rotor or some sort of jet.  At the wing itself this
exchange of forces is via pressure differences.  The wing feels higher
pressure on the bottom than the top.  The air on the top feels a pressure
gradient from ambient away from the wing to the lower pressure on the wing
surface - and so is deflected downwards.  The air on the bottom feels a
pressure gradient from the higher pressure on the wing surface to ambient
below the wing - and is also deflected downwards.

Other posters have already talked about different ways of achieving this
situation with a wing design - either a symmetrical wing at an angle of
attack or a curved wing.

Regards,
Matthew Willshee