Curve fitting to airfoil coordinates

I was trying to use Autocad to plot the airfoil shape for eventually
creating leading edge templates. In doing so I came up with a couple of
questions.

I started with the coordinates from the UIUC database.
http://www.aae.uiuc.edu/m-selig/ads/coord/fx67k150.dat

What I wanted to come out with was something like this:
http://www.goddard.com/soaring/info/FX67K150.gif

My attempts were to use the "spline" command in order to fair the shape
through all of the points. The problem came with the leading edge area
(doesn't it always!). My first attempt was to simply use the spline
command for the top surface and then the bottom surface. But this left
me with a hard point at the leading edge (0,0). Clearly, one needs to
create some sort of 'fairing' around the leading edge. Intuition told
me that I should start the spline at the trailing edge and continue it
around the leading edge and along the other surface.\

But that approach came out with a leading edge like this:
http://www.goddard.com/soaring/info/spline-full.gif
This gave a very nice faired curve but it extends too far forward (into
negative X territory) and puts the actual leading edge above the
centerline.

So then I plotted it with the top surface and bottom surface splines
separately forcing each of them to a tangent with a vertical line at
(0,0). That produced the following:
http://www.goddard.com/soaring/info/spline-normal.gif

Now that looks about like what I thought it would... but the questions
occurred to me... What is the "official" method of creating accurate
plots from the data? How was the coordinate system designed in order to
be able to accurately recreate the shapes? How did they calculate this
stuff before the advent of computers and CAD programs? I know they had
an arsenal of 'french curves' but there seems like there would be a lot
of "eyeball judgement" in that approach.

Just wondering...

Larry Goddard
"01" USA

The Italian "Profili" program can export dxf files that is usefull in
autocad, maybe it have to many coordinates!? but..

Jan Carlsson
www.jcpropellerdesign.com

"Larry Goddard" skrev i meddelandet
...
I was trying to use Autocad to plot the airfoil shape for eventually
creating leading edge templates. In doing so I came up with a couple of
questions.

I started with the coordinates from the UIUC database.
http://www.aae.uiuc.edu/m-selig/ads/coord/fx67k150.dat

What I wanted to come out with was something like this:
http://www.goddard.com/soaring/info/FX67K150.gif

My attempts were to use the "spline" command in order to fair the shape
through all of the points. The problem came with the leading edge area
(doesn't it always!). My first attempt was to simply use the spline
command for the top surface and then the bottom surface. But this left
me with a hard point at the leading edge (0,0). Clearly, one needs to
create some sort of 'fairing' around the leading edge. Intuition told
me that I should start the spline at the trailing edge and continue it
around the leading edge and along the other surface.\

But that approach came out with a leading edge like this:
http://www.goddard.com/soaring/info/spline-full.gif
This gave a very nice faired curve but it extends too far forward (into
negative X territory) and puts the actual leading edge above the
centerline.

So then I plotted it with the top surface and bottom surface splines
separately forcing each of them to a tangent with a vertical line at
(0,0). That produced the following:
http://www.goddard.com/soaring/info/spline-normal.gif

Now that looks about like what I thought it would... but the questions
occurred to me... What is the "official" method of creating accurate
plots from the data? How was the coordinate system designed in order to
be able to accurately recreate the shapes? How did they calculate this
stuff before the advent of computers and CAD programs? I know they had
an arsenal of 'french curves' but there seems like there would be a lot
of "eyeball judgement" in that approach.

Just wondering...

Larry Goddard
"01" USA

Gentlemen....
Why don't you guys do it the easy way and just plot from compufoil??
You can downloat the airfoil coordinates from the Mike Selig site, import
them into
compufoil and plot them at any chord length you desire.

http://www.compufoil.com/compufoil.html

http://www.aae.uiuc.edu/m-selig/

Scott Correa

Establish a few more coordinates between zero and the first set of
coordinates by iteration till you are happy with the results regarding that
final curve near the leading edge.( the last few to 10 thousands of an
inch).
I have done this a number of years ago on my acad and found that this
precision is only of value if the machine is able to reproduce it,
regardless of method. I prefer a template with a slight "point", when
sanding, all will be taken care off. Some one maybe of help with the finer
points on how to work the acad to get the spline right, with just
the coordinates you have.
Udo

...
I was trying to use Autocad to plot the airfoil shape for eventually
creating leading edge templates. In doing so I came up with a couple of
questions.

I started with the coordinates from the UIUC database.
http://www.aae.uiuc.edu/m-selig/ads/coord/fx67k150.dat

What I wanted to come out with was something like this:
http://www.goddard.com/soaring/info/FX67K150.gif

My attempts were to use the "spline" command in order to fair the shape
through all of the points. The problem came with the leading edge area
(doesn't it always!). My first attempt was to simply use the spline
command for the top surface and then the bottom surface. But this left
me with a hard point at the leading edge (0,0). Clearly, one needs to
create some sort of 'fairing' around the leading edge. Intuition told
me that I should start the spline at the trailing edge and continue it
around the leading edge and along the other surface.\

But that approach came out with a leading edge like this:
http://www.goddard.com/soaring/info/spline-full.gif
This gave a very nice faired curve but it extends too far forward (into
negative X territory) and puts the actual leading edge above the
centerline.

So then I plotted it with the top surface and bottom surface splines
separately forcing each of them to a tangent with a vertical line at
(0,0). That produced the following:
http://www.goddard.com/soaring/info/spline-normal.gif

Now that looks about like what I thought it would... but the questions
occurred to me... What is the "official" method of creating accurate
plots from the data? How was the coordinate system designed in order to
be able to accurately recreate the shapes? How did they calculate this
stuff before the advent of computers and CAD programs? I know they had
an arsenal of 'french curves' but there seems like there would be a lot
of "eyeball judgement" in that approach.

Just wondering...

Larry Goddard
"01" USA

Now that looks about like what I thought it would... but the questions
occurred to me... What is the "official" method of creating accurate
plots from the data? How was the coordinate system designed in order to
be able to accurately recreate the shapes? How did they calculate this
stuff before the advent of computers and CAD programs? I know they had
an arsenal of 'french curves' but there seems like there would be a lot
of "eyeball judgement" in that approach.

There are several de facto file format standards for transferring
airfoil co-ordinates between programs and many of them use 100 points
along the chord with the co-ordinates starting at the TE for the opt
surface, continuing round the LE and back to the TE. A list like this,
sucked into autocad and then joined using a cubic spline starting and
ending at the TE should give a reasonable result if you use, say, 10
line segments per point. The critical points a

- use enough co-ordinate points
- use at least 10 line segments per point
- make sure you're using a CUBIC spline, not a circular spline

You didn't say what format you're using to download the co-ordinates.
If it doesn't suit this method and/or hasn't enough points to give a
really accurate wing section you can use Martin Hepperle's ConCord
program to convert the co-ordinates into a more suitable form. His web
site is: http://www.mh-aerotools.de/airfoils/index.htm.

Click 'Software' on the index and scroll down to ConCord for a free
download.

HTH
Martin

--
martin@ : Martin Gregorie
gregorie : Harlow, UK
demon :
co : Zappa fan & glider pilot
uk :

In article , Martin Gregorie writes:

sucked into autocad and then joined using a cubic spline starting and
ending at the TE should give a reasonable result if you use, say, 10
line segments per point. The critical points a

- use enough co-ordinate points
- use at least 10 line segments per point
- make sure you're using a CUBIC spline, not a circular spline


None of this will solve the problem. The real problem
is that like with most early Wortmann sections, the original
FX67K150 coordinates are grossly too coarse at the leading edge.
A cubic spline will produce bad glitches just above and just
below the 0,0 leading edge point. There are many different
types of cubic spline parameterizations possible, but they
all produce shape glitches with various degree of severity.

What I usually do in such situations is to add points
near the LE point, and then smooth the local LE shape
by smoothing the local Cp(s) distribution in Xfoil at high
and low angles of attack, like +15 and -10 degrees.
Whether or not this produces the "correct" shape is a moot point,
because the correct shape cannot be determined from the
official coordinates. At least it produces a shape with
a well-behaved Cp spike, which is really what matters.

Mark is right.

If you have a CAD program that will allow you to impose tangency
constraints as well as point location (like CATIA or UniGraphics), you
can force the curve to be vertical at the leading edge. Now if you
spline the upper and lower surfaces separately (preferably a with a
B-spline of some form) along with the vertical constraint, the curve
should be closer to the desired shape. It will, however, likely still
produce a suction spike at the leading edge due to a jump in curvature
(2nd derivative for the mathematician) at the leading edge. But if you
distribute points on this new curve more densely near the leading edge,
you have a better starting point than the coarse tabular data.

You could then do as Mark suggests to home in on an acceptable solution.
If you have a program like CATIA though, you could try one more
smoothing by using the first 5 or 10% of the upper and lower surfaces as
a smooth curve. If you examine the curvature (2nd derivative with
respect to the arclength of the curve), you can slightly move the points
near the leading edge to make a smooth transition in curvature between
the upper and lower surfaces. This should remove the any spike from the
pressure distribution at the leading edge.

You should, however, use a code like Mark's Xfoil to check for problems
with any of your airfoils.

Good Luck!

...... Neal

Mark Drela wrote:


None of this will solve the problem. The real problem
is that like with most early Wortmann sections, the original
FX67K150 coordinates are grossly too coarse at the leading edge.
A cubic spline will produce bad glitches just above and just
below the 0,0 leading edge point. There are many different
types of cubic spline parameterizations possible, but they
all produce shape glitches with various degree of severity.

What I usually do in such situations is to add points
near the LE point, and then smooth the local LE shape
by smoothing the local Cp(s) distribution in Xfoil at high
and low angles of attack, like +15 and -10 degrees.
Whether or not this produces the "correct" shape is a moot point,
because the correct shape cannot be determined from the
official coordinates. At least it produces a shape with
a well-behaved Cp spike, which is really what matters.

If you have a CAD program that will allow you to impose tangency
constraints as well as point location (like CATIA or UniGraphics), you
can force the curve to be vertical at the leading edge.

In Xfoil you can effectively do this by placing a point just above
the 0,0 LE point, and placing another point just below. For example,
change the three points at the LE...

0.001070 0.004620
0.000000 0.000000
0.001070 -0.001450

to...

0.001070 0.004620
0.0 0.00001
0.000000 0.000000
0.0 -0.00001
0.001070 -0.001450

Xfoil's arc-length spline parameterization doesn't care
about the resulting very non-uniform point spacing,
so these new coordinates spline OK without any difficulty.

But in the case of the original FX67-150 coordinates,
this still produces overshoots, with a concavity below
the LE point (top looks better, but still wavy).
The real problem is that the necessary geometric
information is simply not present in the coarse
coordinates. An adequately-smooth interpolated shape
has to be literally "made up" in one way or another.

On 20 Jan 2004 02:28:34 GMT, (Mark Drela) wrote:

But in the case of the original FX67-150 coordinates,
this still produces overshoots, with a concavity below
the LE point (top looks better, but still wavy).
The real problem is that the necessary geometric
information is simply not present in the coarse
coordinates. An adequately-smooth interpolated shape
has to be literally "made up" in one way or another.

That's why I suggested pumping the co-ordinates through ConCord on the
grounds that its internal representation looks pretty good and I hoped
it would fix the interpolation. I just tried this trick and it doesn't
work. Apologies.

--
martin@ : Martin Gregorie
gregorie : Harlow, UK
demon :
co : Zappa fan & glider pilot
uk :

i had no problems splining airfoils,
starting at the trailing edge,
round the leading edge
and stop at the trailing edge again.
Easy with a Sinumerik numerical control.
Just user the original coordonates as X and Y,
add some parameters for speed and spline,
add the radius (0.12mm) compensation for the laser
and cut it out of stainless steel in any size using
the scaling factor - easy.

Chris

BLS
Bristow Laser Cutting Systems
Melbourne, Australia



"Larry Goddard" wrote in message
...
I was trying to use Autocad to plot the airfoil shape for eventually
creating leading edge templates. In doing so I came up with a couple of
questions.

I started with the coordinates from the UIUC database.
http://www.aae.uiuc.edu/m-selig/ads/coord/fx67k150.dat

What I wanted to come out with was something like this:
http://www.goddard.com/soaring/info/FX67K150.gif

My attempts were to use the "spline" command in order to fair the shape
through all of the points. The problem came with the leading edge area
(doesn't it always!). My first attempt was to simply use the spline
command for the top surface and then the bottom surface. But this left
me with a hard point at the leading edge (0,0). Clearly, one needs to
create some sort of 'fairing' around the leading edge. Intuition told
me that I should start the spline at the trailing edge and continue it
around the leading edge and along the other surface.\

But that approach came out with a leading edge like this:
http://www.goddard.com/soaring/info/spline-full.gif
This gave a very nice faired curve but it extends too far forward (into
negative X territory) and puts the actual leading edge above the
centerline.

So then I plotted it with the top surface and bottom surface splines
separately forcing each of them to a tangent with a vertical line at
(0,0). That produced the following:
http://www.goddard.com/soaring/info/spline-normal.gif

Now that looks about like what I thought it would... but the questions
occurred to me... What is the "official" method of creating accurate
plots from the data? How was the coordinate system designed in order to
be able to accurately recreate the shapes? How did they calculate this
stuff before the advent of computers and CAD programs? I know they had
an arsenal of 'french curves' but there seems like there would be a lot
of "eyeball judgement" in that approach.

Just wondering...

Larry Goddard
"01" USA