Asked by Nasser Ramsis
on 21 Dec 2016

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

Answer by KSSV
on 22 Dec 2016

Accepted Answer

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

KSSV
on 26 Dec 2016

that is a version problem...the same error is discussed there in the link, you can correct it.

Nasser Ramsis
on 27 Dec 2016

yeah that was me who posted. unfortunately I'm not good enough at matlab to do so.

KSSV
on 28 Dec 2016

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