How to create an interpolation surface for a wing ?

So I got this assignment that says I have to build an interpolation surface for a wing that has the profile in the xOy plane with the coordinates:

x=b*[0 1.25 2.5 5 7.5 10 15 20 25 30 40 50 60 70 80 90 95 100 100.35]/100;

ye=a*[0 2.06 2.96 4.3 5.42 6.31 7.78 8.88 9.65 10.13 10.35 9.81 8.78 7.28 5.34 2.95 1.57 0.09 -0.1]/125;

yi=a*[0 -0.88 -1.11 -1.18 -1.08 -0.88 -0.36 0.17 0.69 1.12 1.65 1.86 1.92 1.76 1.36 0.74 0.35 -0.09 -0.1]/125;

in wich:

ye- coordinate for the upper surface(extrados)

yi- coordinate for the lower surface.(intrados)

Also the projection in the xOz plane of the wing profile is a trapezoid with the base angle equal to 70° and height c

the thickness profile after axis "oy" is considered to be constant.

a,b,c are constants given.

Does anyone has any idea how to solve this?? I tried using Bezier surface algorithm but cant make it work :(

Answer 1

[Jonathan Epperl]

Hi, if you have the Curve Fitting Toolbox, then it's pretty easy, call the GUI

cftool

If you don't have it, on the other hand, I can tell you that it looks like a 3rd-order polynome interpolates your ye nicely, while for the yi part you need a few sin and cos terms.

Once you have nice interpolants you can probably easily put that together as a parametrized surface, but that's something I don't know much about.

Also, please format you code properly, your post is hard to read.