Determining a mean camber line

Question

Fellow programmers,

I know this is a little outside your juridistiction, but I was wondering perhaps if you have time, if you could help me with one \"procedure\". Not i

Answer 1

I'm new to stack overflow but this is a problem I have worked on quite a bit and thought I would post an alternate approach to the problem. This approach uses the concept of a Voronoi diagram: http://en.wikipedia.org/wiki/Voronoi_diagram Essentially, a map is created which divides the space into regions containing one of the input points (x,y of your airfoil). The important part here is that any point within the region is closest to the input point in that region. The nodes created by this space division are equidistant to at least three of the input points.

Here is the interesting part: three equidistant points from a center point can be used to create a circle. As you mentioned, inscribed circle center points are used to draw the mean camber line because the inscribed circle measures the thickness.

We are close now. The nature of the voronoi diagram in this application means that any voronoi node inside of our airfoil region is the center point of one of these "thickness circles." (This runs into some issue very close to the LE and TE depending on your data. I usually apply some filtering here).

Basic Structure:

Create Voronoi Diagram
Extract Voronoi Nodes
Determine Nodes Which Lie Within Airfoil
Construct Mean Camber Line From Interior Nodes

Most of my work is in Matlab which has built in voronoi and inpolygon functions. As such, I'm not a huge help in developing those functions but they should be well documented elsewhere.

Trailing Edge/Leading Edge Issues

As I am sure you have experienced or know, it is difficult to measure thickness well when close to the LE/TE. This approach will contruct a fork in the nodes when the thickness circle is less than the edge radius. A check of the data for this fork will find the points which are false for the camber line. To construct the camber line all the way to the edge of the foil you could extrapolate your camber line (2nd or 3rd order should be fine) and find the intersection.

Answer 2

Is the mean camber line the set of points equidistant from the upper line and the lower line? If that's the definition, it's different from Sanjay's, or at least not obviously-to-me the same.

The most direct way to compute that: cast many rays perpendicular to the upper line, and many rays perpendicular to the lower line, and see where the rays from above intersect the rays from below. The intersections with the nearest-to-equal distances approximate the mean camber line (as defined here); interpolate them, with the differences in distance affecting the weights.

But I'll bet the iterative method you pasted from comments is easier to code, and I guess would converge to the same curve.

Answer 3

From what I can gather from your diagram, the camber line is defined by it being the line whose tangent bisects the angle between the two tangents of the upper and lower edges.

In other words, your camber line is always the mean point between the two edges, but along a line of shortest distance between the top and bottom edges.

So, given the y-coordinates y=top(x) and y=bot(x), why don't you:

<pseudocode>
for each x:
  find x2 where top(x)-bot(x2) is minimized
  camber( mean(x,x2) ) = mean( top(x),bot(x2) )
</pseudocode>

and then interpolate etc.?

edit

Sorry! On second thought I think that should be

  find x2 where ( (top(x)-bot(x2))^2 + (x-x2)^2 ) is minimised

obviously you should be minimising the length of that perpendicular line.

Is that right?

Answer 4

I think the best way for drawing the camber line of an airofoil is to load the profile in CATIA. After that in CATIA we can draw circles that are tangent to the both side of profile (suction side and pressure side. Then we can connect center of these circles and consequently we find the camber line accurately.