How to plot this equation in MATLAB? Keep getting matrix dimension errors

Question

The code I have is:

T=[0:0.1:24];
omega=((12-T)/24)*360;
alpha = [0:1:90];
latitude=35;
delta=[-23.45:5:23.45];
sind(alpha)=sind(delta).*sind(latitude)+cosd(delta).*cosd(latitude).*cosd(omega)
cosd(phi)=(sind(alpha).*sind(latitude)-cosd(delta))./(cosd(alpha).*cosd(latitude))

alpha represents my y-axis and is an angle between 0 and 90 degrees. phi represents my x-axis and is an angle between say -120 to +120. The overall result should look something like a half sine-wave.

Whenever I try to input that last line I get the error stating inner matrix dimensions must agree. So I tried to use reshape on my matrices for those variables I defined so that they work. But then I get '??? ??? Subscript indices must either be real positive integers or logicals.'

It seems very tedious to have to reshape my matrix every time I define a new set of variables in order to use them with an equation. Those variables are used for defining my axis range, is there a better way I can lay them out or an automatic command that will make sure they work every time?

I want to plot alpha and phi as a graph using something like

plot(alpha,phi)

but can't get past those errors? can't I just use a command that says something like define x-axis [0:90], define y-axis [-120:120] or something? I have spent far too much time on this problem and can't find a solution. I just want to plot the graph. Somebody please help! thanks.

Thanks

There is something fundamentally wrong with the commands sind(alpha) = *stuff* and cosd(phi) = *stuff*. The terms on the left of the = sign are not something that you can assign a value to. Also, you are trying to do element-wise multiplaction of things that are many different sizes, which is not allowed. Perhaps it would help if you posted some math or pseudocode to explain what you are trying to accomplish. — nispio
I am trying to plot a sun path diagram which is basically a chart showing the path of the sun throughout the year. The chart has two axes. The y-axis is represented by the solar altitude angle (alpha), the x-axis is represented by the solar azimuth angle (phi) The equations are: sin alpha = sin(delta)*sin(L) + cos(delta)*cos(L)*cos(omega) - solar altitude equation cos(phi) = sin(alpha)*sin(L)-sin(delta) / (cos(alpha)*cos(L)) Where L is the latitude of the location (can be considered a constant value). omega is the hour angle and is defined as omega = ((12-T)/24 *360) where T is time — loco
The chart looks like this: solardat.uoregon.edu/download/temp/37340782.pdf I've basically just tried to assign reasonable ranges to those variables such as T (0-24 as in 24 hours), omega etc and then define the equations so that I can plot them. That's ALL I want to do. I've been trying to do this for 2 days and it's very frustrating. This link also explains the math in a better format: pvresources.com/siteanalysis.aspx — loco

nispio nispio · Accepted Answer · 2013-10-16T15:11:51

Here is a start for you:

% Latitude
L=35;

% Hour Angle
h = [-12:5/60:12];
w = 15*h;

% Initialize and clear plot window
figure(1); clf;

% Plot one day per month for half of the year
for N = 1:30:365/2
    % Declination
    d = 23.45*sind(360*(284+N)/365);

    % Sun Height
    alpha = asind(sind(L)*sind(d) + cosd(L)*cosd(d)*cosd(w));

    % Solar Azimuth 
    x = ( sind(alpha)*sind(L)-sind(d) )./( cosd(alpha)*cosd(L) );
    y = cosd(d)*sind(w)./cosd(alpha);
    phi = real(atan2d(y,x));

    % Plot
    plot(phi,alpha); hold on;
end

hold off;
grid on;
axis([-180, 180, 0, 90]);
xlabel('Solar Azimuth')
ylabel('Solar Elevation')

The function asind is inherently limited to return values in the range of -90 to 90. That means that you will not get a plot that spans over 240 degrees like the one you linked to. In order for the plot to not have the inflection at +/- 90 degrees, you will need to find a way to infer the quadrant. Update: I added the cosine term to get an angle using atan2d. Matlab Plot

Hopefully this will be enough to give you an idea of how to use Matlab to get the kind of result that you are after.

How to plot this equation in MATLAB? Keep getting matrix dimension errors

3 Answers