--- In wingboats@yahoogroups.com, "Williams, Deane G HS"
<deane.williams@...>
wrote:
>...
> In playing with the airfoil simulator "Foil Sim II" at
> http://www.grc.nasa.gov/WWW/K-12/airplane/foil2.html
> you see that increasing the thickness causes the lift (units=pounds) to
> rise.
> Also many of the high-lift airfoils I see are very thick....

I've uploaded some papers to the Max_Airfoils files folder that might help.
Take a look at
Figure 13 in http://tinyurl.com/5rwp8p. The higher the design lift coefficient,
the thinner
the section gets. A.M.O. Smith explains why in http://tinyurl.com/574bal.

Basically, there are two ways you can look at an airfoil. You can represent it
as a camber
line clothed in a thickness distribution, or you can view it as an upper surface
and a lower
surface. The camber+thickness method is convenient because the thickness
distribution
adds essentially no lift. You can use thin airfoil theory to calculate the lift
and moment
from the camber line. If you want the pressure distribution, you can get the
velocities
from the camber line and add to them the velocities from the thickness
distribution by
superposition.

Now the thicker the thickness distribution is, the higher the peak velocity will
be around
it. This makes sense when you think about it. If you had zero thickness - a
flat plate
aligned with the flow - you'd have the freestream velocity everywhere on it. If
you have a
circular cylinder in an inviscid flow, the peak velocity would be twice
freestream. Most
thickness distributions will be somewhere in between those two.

So when you add thickness to a given camber line the peak velocity on each side
will
increase. The difference in velocity between the windward and leeward side will
stay the
same because that's controlled by the camber line. Now in inviscid flow, of the
kind that
is calculated by Foil Sim II, the peak velocity really doesn't matter. But we
aren't interested
in how much lift we can get at a given angle of attack, because we can change
the sail
trim to get any angle of attack we want. What we care about is the maximum
lift, and Foil
Sim II doesn't say anything about that.

Maximum lift is all about the boundary layer. The velocities outside the
boundary layer
and the pressure distribution only matter in so far as they determine how the
boundary
layer develops. As the flow moves from the stagnation point at the leading edge
to the
trailing edge, it's kind of like riding across Grand Canyon on a bicycle.
Starting from rest,
there's a rapid increase in velocity, a leveling off in the speed near the
middle, and then a
gradual climb to the end. If the slope gets too steep, the bike will stop and
roll backwards
before gaining the far side, and the slope can increase rapidly soon after the
peak velocity
when the rider is fresh, but must increase more gradually toward the end as the
rider gets
tired. The boundary layer develops in much the same way, with the pressures
playing the
role of elevation. This leads to the approach of considering the lee side and
the windward
side separately.

You can imagine that at a given airspeed (Reynolds number), there's a pressure
distribution for the lee side that maximizes the development of the boundary
layer. This
is shown in Figures 24 and 25 of the A.M.O Smith paper
(http://tinyurl.com/574bal). For
a given peak velocity, lift would be a maximum if you could maintain that
velocity all the
way from the leading edge to the trailing edge on the lee side, because anything
more
would violate the assumption of a given peak speed, and anything less would
result in a
smaller difference between the lee side and whatever the velocities are on the
windward
side. If the peak velocity is too high, it takes most of the distance to the
trailing edge to
recover, which eats into the ideal block of constant velocities something
fierce. If the peak
velocity is too low, the block can be maintained farther toward the trailing
edge, but it's
not as high as it could be, so lift is lost. In between is the Goldilocks
pressure distribution
- not too high, not too low, just right.

So that's how Liebeck created his high lift airfoils. He designed the lee side
to get the
maximum the boundary layer could give him from that side. But what about the
windward
side?

The ideal windward side would have stagnation pressure from the leading edge to
the
trailing edge - zero velocity everywhere. That would maximize the difference in
velocity
between the boundary layer constrained lee side and the windward side, and
maximize the
lift of the whole airfoil. Remember how increasing the thickness distribution
for a fixed
camber increased the velocity on both the windward and lee sides? If the lee
side
velocities are fixed and you increase the thickness, you have to flatten the
camber to
compensate for the increased lee side velocity due to the thickness.

The other way to think of it is you add the thickness down from the suction side
instead of
adding it symmetrically about the camber line. That maintains the shape of the
lee side to
maintain the boundary layer development. But if you took adding the thickness
to the
extreme, you'd end up with a fat symmetrical section in which both sides had the
optimized boundary layer development, but there'd be no lift at all.

So that's why really high-lift sections tend to be thin. The Drela ML5 section
depicted in
the other files in the Max_Lift folder is a good example, as is the ultimate
Liebeck airfoil
shown in Figure 27 of A.M.O Smith's paper. If you compare it to the Liebeck
airfoil in
Figure 26, it has a very similar lee side pressure distribution and a similar
lee side shape.
But the windward side is drastically different, with the thick section having
25% less lift.
The difference is in the windward side pressure distribution. The thin section
has a much
lower velocity for the first third of the chord, while the thick section has an
immediate
increase in velocity behind the windward leading edge.

What thickness buys you from an aerodynamic point of view is a wider range of
operating
conditions. The thin section is only good for a narrow range of angles of
attack. If the
angle of attack is too high, the section stalls. If the angle of attack is too
low, the flow
separates behind the leading edge and forms a separation bubble that grows in
size as
the angle of attack moves toward the negative. This adds lots of drag.

At any given operating point, you can achieve the same lift with less drag using
a thin
section because the peak velocities are lower. However, it takes a different
thin section to
do better than the thick section at a different operating point. Hard to do
with a rigid
airplane wing. But that's what mast rotation and sail adjustments are all
about.