Plot using array for different plot lines?

I'm trying to figure out how to make a reusable formula that will plot different lines based on a value set stored in an array. Right now I'm manually running this. The last portion of the equation has a ratio that I'd like to change and add a new plot for each value.

x = 0:1:90; %plot theta 0-90 in 1 degree increments
V = 5; % Use 5 for V since that's what's given in p.75
D = .1; % Use .1m for D since that's what's given in p.75

       % Plot 0 d/D ratio. No, hole.
  y0 = 1000 * V ^ 2 * (pi / 4) * D ^2 * (1 + sind(x)) * (1 - (0) ^ 2);
       % Plot .25 d/D ratio. 25mm hole.
  y1 = 1000 * V ^ 2 * (pi / 4) * D ^2 * (1 + sind(x)) * (1 - (0.25) ^ 2);
       % Plot .5 d/D ratio. 50mm hole.
  y2 = 1000 * V ^ 2 * (pi / 4) * D ^2 * (1 + sind(x)) * (1 - (0.5) ^ 2);
       % Plot .75 d/D ratio. 75mm hole.
  y3 = 1000 * V ^ 2 * (pi / 4) * D ^2 * (1 + sind(x)) * (1 - (0.75) ^ 2);
       % Plot 1 d/D ratio. 100mm hole.
  y4 = 1000 * V ^ 2 * (pi / 4) * D ^2 * (1 + sind(x)) * (1 - (1) ^ 2);

plot(x,y0,x,y1,x,y2,x,y3,x,y4);

So, I'm looking for something like this.

x = 0:1:90; %plot theta 0-90 in 1 degree increments
V = 5; % Use 5 for V since that's what's given in p.75
D = .1; % Use .1m for D since that's what's given in p.75
r = 0:.25:1

y = 1000 * V ^ 2 * (pi / 4) * D ^2 * (1 + sind(x)) * (1 - (r) ^ 2);

Then have MATLAB plot the 5 different values of the r array as separate plot lines. I'm new to MATLAB but not to programming. Any literature or a point in the right direction would be great. Thanks!

Answer 1

[David Goodmanson]

A vectorized Matlab technique is to use meshgrid:

[xx rr] = meshgrid(x,r)

this makes two matrices each of size { length(r) x length(x) }, the first with the x vector repeated in rows and the second with the r vector repeated in columns as you can check. Then you can create the matrix y

y = 1000*V^2*(pi/4)*D ^2*(1+sind(xx)).*(1 - rr.^ 2);

Note that you need .* and .^, where the periods indicate that the calculation is done for the matrix entries term-by-term, as opposed to some kind of matrix multiplication. You can plot the y matrix with

plot(x,y)

Matlab plots the matrix according to which dimension matches up with x, so in this case you plot out the rows of y with r as the parameter.

Answer 2

[KSSV]

You have to make y a matrix.

x = 0:1:90; %plot theta 0-90 in 1 degree increments
V = 5; % Use 5 for V since that's what's given in p.75
D = .1; % Use .1m for D since that's what's given in p.75
r = 0:.25:1 ;
y = zeros(length(r),length(x)) ;  % initialization 
for i = 1:length(r)
    y(i,:) = 1000*V^2*(pi/4)*D ^2*(1+sind(x))*(1 - r(i)^ 2);
end
plot(x,y) ;

[Emiliano Jordan]

Thanks! That's exactly what I was looking for.