I wanted to make a CAD model of Archimedean spiral wind turbine. I am new to MATLAB so wanted your help. To generate the profile of 3d plot of blade could you please help?

d = 1500 mm

d/L = 1.5

the equation governing the plot is r = ae^(b*theta)

r= impact width

theta=tip angle (theta=15 degree)

b= this value impact curvature

h= impact height

[Geetansh]

any help would be appreciated mates

Answer 1

[Gautam]

Hello Geetansh,

I understand from your question that you want to plot profiles of a 3D model of an Archimedean wind turbine.

Assuming that the “tip angle” mentioned in the question refers to the angle between the plane of rotation of the turbine and the bottom end of the blade, the MATLAB code below generates a 3D plot of the turbine.

a = 0.125;      % initial radius (offset from center) 
b = -0.255;    % distance between arms (increase in radius per radian) 
theta = linspace(0, 2*pi, 360); % 360 points per turn 
theta2 = theta+120*pi/180; %turns for the second blade at at offset of 120 degrees from the first 
theta3 = theta2+120*pi/180; %turns for the second blade at at offset of 120 degrees from the first and second blade 
thickness = 5e-3; %Thickness of each blade assumed to be constant 

 
height = 2*1.7; %height of the turbine 
height_change = height/(2*pi); %change in height of the turbine per change in angle 

 
% Creating a mesh for the radius of the two blade surfaces according to the 
% equation 

RadiusGrid_top = []; 
RadiusGrid_bottom = []; 

 
for i = linspace(0, 2*pi, 360) 
    rt = linspace(0,a*exp(b*i + thickness/2),360); 
    rb = linspace(0,a*exp(b*i - thickness/2),360); 
    RadiusGrid_top = [RadiusGrid_top;rt]; 
    RadiusGrid_bottom = [RadiusGrid_bottom;rb]; 
end 

RadiusGrid_top = RadiusGrid_top'; 
RadiusGrid_bottom = RadiusGrid_bottom'; 
 

%Creating a grig for the angular values 

ThetaGrid = meshgrid(theta); 
ThetaGrid2 = meshgrid(theta2); 
ThetaGrid3 = meshgrid(theta3); 

 
%Converting the value of grid points from polar to cartesian co-ordinates 
%for all three blades of the turbine 
XGrid_top = RadiusGrid_top.* cos(ThetaGrid); 
YGrid_top= RadiusGrid_top.* sin(ThetaGrid); 
XGrid_bottom = RadiusGrid_bottom.* cos(ThetaGrid); 
YGrid_bottom= RadiusGrid_bottom.* sin(ThetaGrid); 


XGrid_top2 = RadiusGrid_top.* cos(ThetaGrid2); 
YGrid_top2= RadiusGrid_top.* sin(ThetaGrid2); 
XGrid_bottom2 = RadiusGrid_bottom.* cos(ThetaGrid2); 
YGrid_bottom2= RadiusGrid_bottom.* sin(ThetaGrid2); 

 
XGrid_top3 = RadiusGrid_top.* cos(ThetaGrid3); 
YGrid_top3= RadiusGrid_top.* sin(ThetaGrid3); 
XGrid_bottom3 = RadiusGrid_bottom.* cos(ThetaGrid3); 
YGrid_bottom3= RadiusGrid_bottom.* sin(ThetaGrid3); 

 
hinit = 0.5+RadiusGrid_top(end,1)*sin(15*pi/180); %initial height of the blade  

 
ZGrid_top = []; 

for i = linspace(0, 2*pi, 360) 
    z = linspace(0,hinit+(height_change*i),360); 
    ZGrid_top = [ZGrid_top;z]; 
end 

 
%Creating a grid for the height of the turbine 

ZGrid_bottom = []; 

for i = linspace(0, 2*pi, 360) 
    z = linspace(0,hinit+(height_change*i),360); 
    ZGrid_bottom = [ZGrid_bottom;z]; 
end 

ZGrid_top = ZGrid_top'; 
ZGrid_bottom = ZGrid_bottom'; 

 
%Plotting the model 

surf(XGrid_top, YGrid_top, ZGrid_top, 'FaceColor', 'g', 'EdgeColor', 'none'); 
hold on; 
surf(XGrid_bottom, YGrid_bottom, ZGrid_bottom, 'FaceColor', [0.4 0.4 0.4], 'EdgeColor', 'none'); 
hold on; 


surf(XGrid_top2, YGrid_top2, ZGrid_top, 'FaceColor', 'b', 'EdgeColor', 'none'); 
hold on; 
surf(XGrid_bottom2, YGrid_bottom2, ZGrid_bottom, 'FaceColor', [0.4 0.4 0.4], 'EdgeColor', 'none'); 
hold on; 

 
surf(XGrid_top3, YGrid_top3, ZGrid_top, 'FaceColor', 'm', 'EdgeColor', 'none'); 
hold on; 
surf(XGrid_bottom3, YGrid_bottom3, ZGrid_bottom, 'FaceColor', [0.4 0.4 0.4], 'EdgeColor', 'none'); 
hold off; 

 
xlabel('X'); 
ylabel('Y'); 
zlabel('Z');

The figure below shows the output generated

You can use the “view” function to adjust the viewing angle to view specific profiles.

You can extract the X, Y and Z coordinate data and export the data to a file in a format that can be converted to a standard 3D model format to be imported to CAD or other 3D modelling software.

For more information on 3D plots, kindly refer to the following MathWorks documentation:

1. meshgrid: https://www.mathworks.com/help/matlab/ref/meshgrid.html?searchHighlight=meshgrid&s_tid=srchtitle_support_results_1_meshgrid
2. surf: https://www.mathworks.com/help/matlab/ref/surf.html?searchHighlight=surf&s_tid=srchtitle_support_results_1_surf
3. view: https://www.mathworks.com/help/matlab/ref/view.html?searchHighlight=view&s_tid=srchtitle_support_results_1_view

Thank You

Gautam Murthy