Curve fitting to airfoil coordinates

[Larry Goddard]

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

[Jan Carlsson]

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
>
>
>

[Scott Correa]

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

[Udo Rumpf]

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
>
>
>

[Martin Gregorie]

>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 are:

- 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 :

[Mark Drela]

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 are:
>
> - 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.

[Neal Pfeiffer]

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.
>
>
>
>

[Mark Drela]

>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.

[Martin Gregorie]

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 :

[Swiftel]

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
>
>
>

[Steve]

Since the good Doctors are done explaining how it should be done in
the electronic world, here is a bit of advice for you to ponder,
Larry.

It was good enough for NACA to have the leading edge be above and
ahead of the origin of the coordinates system (Remember, Aero
specialists. Leading edge radius and slope on the old sections, hmm?)
Spline it that way, from upper surface to lower surface, right on
around the old leading edge. Use a point at 0,0. See how far above
and ahead the "actual" leading edge is in percent. Then, look at how
much this is on the 36 inch or so root chord of your wing. And then
look at it on the 14 or so inch tip chord.

You could mislocate a template by twice that much if they only go as
far back as you showed in your drawing!

Get it close and make it as smooth as possible. If only it was as
easy to smooth a wing (and maintain the desired contour) as it is to
smooth a curve to give a desired pressure distribution in the world of
electronics!

BTW, I spent hours smoothing the 67K150 section coordinates. Making
changes at the thrid and fourth decimal point. Made HUGE changes in
the plot of spline curvature. When looked at on the wing sized
templates, less than .001 inches.

Steve Leonard

[plasticguy]

Steve....
Excellent points...
Thats why I said to grab compufoil, the selig website data
and plot it on their pc printer. Game over and you
don't have to worry about all the corrective actions.....

Scott Correa.


"Steve" > wrote in message
om...
> Since the good Doctors are done explaining how it should be done in
> the electronic world, here is a bit of advice for you to ponder,
> Larry.
>
> It was good enough for NACA to have the leading edge be above and
> ahead of the origin of the coordinates system (Remember, Aero
> specialists. Leading edge radius and slope on the old sections, hmm?)
> Spline it that way, from upper surface to lower surface, right on
> around the old leading edge. Use a point at 0,0. See how far above
> and ahead the "actual" leading edge is in percent. Then, look at how
> much this is on the 36 inch or so root chord of your wing. And then
> look at it on the 14 or so inch tip chord.
>
> You could mislocate a template by twice that much if they only go as
> far back as you showed in your drawing!
>
> Get it close and make it as smooth as possible. If only it was as
> easy to smooth a wing (and maintain the desired contour) as it is to
> smooth a curve to give a desired pressure distribution in the world of
> electronics!
>
> BTW, I spent hours smoothing the 67K150 section coordinates. Making
> changes at the thrid and fourth decimal point. Made HUGE changes in
> the plot of spline curvature. When looked at on the wing sized
> templates, less than .001 inches.
>
> Steve Leonard

[Larry Goddard]

Many thanks to everyone who has (will?) responded!!!! The technical info
is great. I now have a copy of Xfoil and am trying to figure out how to
use it. The "realistic" advice is also well taken.


Steve wrote:

> Since the good Doctors are done explaining how it should be done in
> the electronic world, here is a bit of advice for you to ponder,
> Larry.
>
> It was good enough for NACA to have the leading edge be above and
> ahead of the origin of the coordinates system (Remember, Aero
> specialists. Leading edge radius and slope on the old sections, hmm?)
>

Steve, et. al., did NACA _actually_ intend that the leading edge be above
and ahead of coordinate origin?? Or is that simply how we choose to
conveniently spline it currently? Seems like that messes up the whole
"chord" reference mechanism...

Thanks again to all... this is really interesting!

Larry Goddard
"01" USA

[Gary Osoba]

Hello Larry:

It's hard to add anything to the expert advice given by Dr.'s Drela &
Pfeiffer, and the practical value of an experienced
pilot/builder/engineer like Steve Leonard.

However, you might glance at :
http://www.appledor.net/tsillas/soaring/pikt7/pikt7.htm

As is so often the case, Dick Johnson has "been there, done that". A
couple of key points from this work with the related FX 17% section:

1) The practical eyeball approach yielded two serious failures when
Dan Somers found pressure waves in the NASA Langely tunnel
2) The final results give you some idea of what you *might* gain for
the work involved.

I enjoyed meeting and flying with you at Hobbs in '98. One of these
days, I might enter another contest.

Best Regards,
Gary Osoba


Larry Goddard > wrote in message >...
> Many thanks to everyone who has (will?) responded!!!! The technical info
> is great. I now have a copy of Xfoil and am trying to figure out how to
> use it. The "realistic" advice is also well taken.
>
>
> Steve wrote:
>
> > Since the good Doctors are done explaining how it should be done in
> > the electronic world, here is a bit of advice for you to ponder,
> > Larry.
> >
> > It was good enough for NACA to have the leading edge be above and
> > ahead of the origin of the coordinates system (Remember, Aero
> > specialists. Leading edge radius and slope on the old sections, hmm?)
> >
>
> Steve, et. al., did NACA _actually_ intend that the leading edge be above
> and ahead of coordinate origin?? Or is that simply how we choose to
> conveniently spline it currently? Seems like that messes up the whole
> "chord" reference mechanism...
>
> Thanks again to all... this is really interesting!
>
> Larry Goddard
> "01" USA