while loop nestled in a for loop

This is the first code I have ever written so there might be a simple solution or not even possible to make a code this way.

Im supposed to write a code that simulates the path of a thrown ball including airresistance. And calculate what angle gives the maximal length?

I started to simulate the path of a thrown ball including airresistance with a launch angle of 45degrees and succeded to find the maximum x for that angle. Then I thought I could just do a for loop outside and have the angle go from 0-90degrees instead and finding the maximum x that corresponds to each degree. And then plot the maximum x vs. degree graph.

But something is wrong and I cant se what.

I am very thankful for help!

 clear; close all;

 %Constants for Tennisball
  m=0.057; %mass in kg
  r=0.033; %radius in m
  C=0.47; %Drag Coefficient of a sphere
  rho= 1.2; %density of air kg/m^3 
  g=9.81; %m/s^2 (acceleration due to gravity)
  A=pi*r^2; %m^2
  D=rho*C*A/2; %
  dn=0.1;
  NT=900*dn;
for theta =1:NT;  

    %Initial Conditions
    dt=0.001; %s
    x(1)=0;
    y(1)=0;
    v=10; %m/s
    vx=v*cosd(theta);
    vy=v*sind(theta);
    t(1)=0; 
    %Start Loop
    i=1;
    while y >= 0;
        ax=-(D/m)*v*vx;
        ay=-g-(D/m)*v*vy;
        vx=vx+ax*dt;
        vy=vy+ay*dt;
        x(i+1)=x(i)+vx*dt+0.5*ax*dt^2;
        y(i+1)=y(i)+vy*dt+0.5*ay*dt^2;
        t(i+1)=t(i)+dt;
        v=sqrt(vx^2 + vy^2);
        i=i+1;
    end
        c = max(x);
        clist(theta)=c;
end 
    tlist = (1:NT)*dn;
    plot(tlist,clist)

[John BG]

similar question has already been answered here:

http://uk.mathworks.com/matlabcentral/answers/43077-numerical-approximation-of-projectile-motion-with-air-resistance?s_tid=srchtitle

[Stephen23]

Read the while documentation and it clearly explains its behavior with non-scalar inputs: "An expression is true when its result is nonempty and contains only nonzero elements".

Answer 1

[Dalibor Knis]

The issue is that you use y as an array. I don't think the while statement is defined over array. The while expects single boolean value. I do not know how exactly guys in Matlab implemented 'while' statement but my experience is that while over array evaluates as false. That's why the second iteration of theta never jumps in the while loop.

You could easily identify the problem if you placed [theta, i] printout in the innermost loop.

So what you want is something like this:

clc; clear; close all;
 %Constants for Tennisball
  m=0.057; %mass in kg
  r=0.033; %radius in m
  C=0.47; %Drag Coefficient of a sphere
  rho= 1.2; %density of air kg/m^3 
  g=9.81; %m/s^2 (acceleration due to gravity)
  A=pi*r^2; %m^2
  D=rho*C*A/2; %
  dn=0.1;
  NT=900*dn;

   for theta =1:NT;  
      %Initial Conditions
      dt=0.001; %s

      i=1;
      x(i)=0;
      y(i)=0;
      t(i)=0; 
      v=10; %m/s
      vx=v*cosd(theta);
      vy=v*sind(theta);
      %Start Loop
      while y(i) >= 0;
          ax=-(D/m)*v*vx;
          ay=-g-(D/m)*v*vy;
          vx=vx+ax*dt;
          vy=vy+ay*dt;
          x(i+1)=x(i)+vx*dt+0.5*ax*dt^2;
          y(i+1)=y(i)+vy*dt+0.5*ay*dt^2;
          t(i+1)=t(i)+dt;
          v=sqrt(vx^2 + vy^2);
          i=i+1;
      end
          c = max(x);
          clist(theta)=c;
  end 
      tlist = (1:NT);
      plot(tlist,clist)
      i=i+1;

BTW: if this is indeed the first code you have ever written then is it not so bad. :-)

[Walter Roberson]

"if" and "while" with array or vector arguments are considered true only if all the elements in the vector are non-zero. It is well defined in MATLAB, but it is bad programming practice to use it deliberately rather than explicitly calling all() on the vector to make it clear to readers what is being tested.

[Dalibor Knis]

Thank you. 👍