## How do i find geometry properties of triangles?

### Nasser Ramsis (view profile)

on 21 Dec 2016
Latest activity Commented on by KSSV

on 28 Dec 2016

### KSSV (view profile)

I want to write a code to find the polar moment of inertia of an airfoil. Being a complex shape, a friend suggested a numerical estimate. I wrote a code to create the airfoil geometry and split it up into triangles using delaunay. I now need to find the moment of inertia about x and y for each triangle and use the parallel axis theorem to relate those to the centroid.
I have the delaunay triangulation complete but how can i find the Ix and Iy of each triangle? I don't even know where to start.
here's the code i have:
chord = 0.25; %chord of airfoil
nacanum = 12; % NACA XX## number for the airfoil
t = nacanum/100; %max thickness of airfoil
x=0:0.005:chord; %points along x axis from 0 to chord length
distratio = x/chord; %ratio of points along x to the chord
% function generating top half of airfoil
yt = 5*t*(0.2969*sqrt(distratio)-0.126*distratio-0.3516*distratio.^2+0.2843*distratio.^3-0.1015*distratio.^4);
ytneg=yt*-1; %generatingg bottom half of airfoil
yfull= [yt ytneg]; % full points for y axis of airfoil
y=yfull';
x2=flipud(x);
xfull=[x x2];%full points for x axis of airfoil
x=xfull';
TR=delaunayTriangulation(x,y); %triangulation of the airfoil
triplot(TR,x,y) %plotting the triangulation

### KSSV (view profile)

on 22 Dec 2016

You can access x,y coordinates of each triangle like below:
nodes = TR.ConnectivityList ; % nodal connectivity matrix
coor = TR.Points ; % coordinates
ntri = size(nodes,1) ; % number of triangles
% loop for each triangle
for i = 1:ntri
xi = coor(nodes(i,:),1) ; % x coordinates of i'th rriangle
yi = coor(nodes(i,:),2) ; % y coordinates of i'th triangle
% do what you want
end
But let me tell you, your mesh of air foil is very bad. I suggest you to go through the following meshing package: https://in.mathworks.com/matlabcentral/fileexchange/25555-mesh2d-automatic-mesh-generation

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KSSV

### KSSV (view profile)

on 26 Dec 2016
that is a version problem...the same error is discussed there in the link, you can correct it.
Nasser Ramsis

### Nasser Ramsis (view profile)

on 27 Dec 2016
yeah that was me who posted. unfortunately I'm not good enough at matlab to do so.
KSSV

### KSSV (view profile)

on 28 Dec 2016
tsearch problem, can be sorted by minor editing the code. I have done it very long ago, if I get time I will check it. Mean while go through the above link.