Question

1. A picture of a solar tower is shown below (figure 1). You can see that there are plenty of mirrors located in different positions. Each of these mirrors tracks the sun over time and project the sunlight to the tower. The tower gets very hot and the heat is used to generate electricity (or to evaporate water). To make this problem easier for you, I changed this problem to a 2D example. 4 Figure 1 Solar Tower Figure 2 demonstrates a 2D case. The yellow line is the location of the sun over time, the mirror is located at the position [x,y]tower = [0,400] (meter). The mirror is locate at (x,y)mirror = [7000,0] (meter). The angle ß between the vector connecting the origin to the sun and the positive x axis is described with (it is assumed that sun rises from the positive x axis) B=2*pi/24*60*60*t where t is the time of the day (reported in second) t=0:60:12*60*60 We assume that we have sunlight for 12 hours during the period of t = [0 12*60*60 (sec). It is assumed that sun moves in a circle around the origin with the radius of 10,000 meter. The x and y location of sun at any time can be found as x = r cos(B) z=rsin()

Answer 1

clc
clear
hold on
box on
r =10000;
k=0:1:12*60;
beta=2*pi/(24*60)*k;
x=r*cos(beta);
y=r*sin(beta);

anglT =pi- atan(400/7000); %angle perpendicular to the mirror surface
theta= (beta+anglT)/2-pi/2;

plot(x,y,'yo');
plot(0,400,'kd');
text(-2500,800,'this is the tower')
plot(7000,0,'bd');
text(5000,400,'this is the mirror');
xlabel('X (meter)');
ylabel('Y(meter)');
l=1500; %take length of mirror just for plotting and visibility

for k=1:12*60
    thet=theta(k);
    lx=l/2*cos(thet);     %x position of mirror end
    ly=l/2*sin(thet);     %y position of mirror end
    sun=plot(x(k),y(k),'ko'); %sun plotting
    sunLight=line([x(k) 7000],[y(k) 0],'Color','r'); %sunlight plotting
    reflection=line([0 7000],[400 0],'Color','r');   %reflection plotting
    plt=line([-lx+7000 7000+lx] ,[-ly ly],'LineWidth',3); % plotting the mirror
    bt=text(-3000,4500,sprintf('Beta in degree %.6f',beta(k)*180/pi)); %beta values
    t=text(-3000,4000,sprintf('Theta in degree %.6f',thet*180/pi));    %theta values shown
    pause(0.02);                  %to show the graph
    set(plt,'Visible','off');     % to update make current graphs invisible
    set(sun,'Visible','off');
    set(sunLight,'Visible','off');
    set(t,'Visible','off');
    set(bt,'Visible','off');
  
end
set(plt,'Visible','on')

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10000 8000 6000 Y meter) Beta in degree 54.750000 Theta in degree 25.739756 4000 2000 this is the tower this is the mirror -2000 X (meter)

Above is the animation's one screen shot..

Beta and theta values at the incident has been shown. It is taken at a minutes interval.

Thanks