wrote:
an excellent post...thanks,

For any given application of an airfoil there is an appropriate level
of accuracy needed. A biplane strut will not need much accuracy as a
canard that may be sensitive to disruptions in the laminar flow. At
some point the accuracy of the points used to plot an airfoil will
affect the desired aerodynamic performance. While working for a
contractor at NASA Ames once I needed to plot some airfoils for a
shrouded air probe to fly on a science mission on the NASA DC-8. In the
process I learned about the sensitivity of the surface of an airfoil to
the accuracy of the plotted points. I also developed a simple and crude
method of improving the accuracy of plotted points which may be useful
in some cases.

As I was about to put a few hours into some drawings which would then
direct the shop to cut metal and the mission was to fly in a few months
I did not want to find out later that the final product ended up with
noticable and unwanted waviness in the surface so the first thing I did
was take a careful look at the airfoil points provided by the
aerodynamicist based on his CFD design.

I was using Autocad to plot the points and the various spline functions
to generate the curve. The data was provided to three decimal places
and I typed in the points and used the spline to generate the curve.
Since the points came from the aerodynamicist's program I fully
expected the curve to form the airfoil, no problem. As I took a close
look I was suprised to find bumps as the spline function tried to do
what I asked and apply the polynomials to the points. But there were
the bumps. Neither spline for curve fit would yield a smooth shape. I
called him and asked 'are your sure'? He checked and verified yes the
points are correct.

I played around with the points and curves and came up with a crude
method to try to interpolate more digits of accuracy. Part of the mehod
involved keeping the percent cord exact. Then I used two adjacent
points, skip the third point, and the fourth point to draw a circle.
Then I intersected the circle with the percent cord to estimate the
third point. Using this mehtod I worked down the 30 or so points a few
times until the curves became more accurate. When the spline finally
smoothed out I regenerated a new set of data points and sent the set
back to the aero to be checked. It was good. The resulting parts were
smooth.

Two decimal places is usually good enough for low speed applications.
Abbot and Von Doenhoff TOWS gives standard NACA data to three decimal
places; the industry standard. To get a smoother airfoil a few hours of
Autocad can help achieve a little better performance for applications
like laminar flow. Of course the composite layup and the sanding of the
gel coat will smooth out the curve but why not start with better data?
Airflow likes smooth shapes and any deviation from smooth will only
detract from the optimum recovery of pressure and result in earlier
separation. All I am saying is as long as you are going through the
trouble to lay out an airfoil, take a close look at the curve until you
are satisfied with the shape for your applicaton. Three decimal places
on a 100 inch cord is 0.1 inches, not too bad. But what concerned me
was the possibility that the Autocad spline function might bulge out
the curve between points in unknown ways and start to affect
performance.

Here is a website with an image of the shroud probe.

http://www.espo.nasa.gov/sonex/pages/photos.html

About halfway down the page is a photo of the shroud which is still
flying missions once in a while. It is the barrel hanging below the
viewport which looks like a mini jet engine. I still can't believe that
they let us do stuff like this to the aircraft. We had to be very
careful to make sure the structure was strong enough. To be very
conservative we would over design it for loads such as full speed flow
from the side times a Cd of 1.0, and even then multiplied by a factor
of three because we had to achieve airworthiness by analysis and a test
flight.

James