Creating a Function to Plot Projectile with Drag

Hello, I've recently been tasked with creating a program for a course regarding plotting projectile motion with drag (air resistance). The problem i have run into is regarding overwriting of variable (Vx and Vy) but whenever i replace them and put them back into the function so they don't overwrite themselves the program either does nothing or crashes matlab. since i don't have matlab at home i've been using freelab and convert back and forth as i work at uni and home.

The process i followed can be found here http://wps.aw.com/wps/media/objects/877/898586/topics/topic01.pdf

Another problem i have had is that i am unable to plot the y axis for the function without drag.

 clear 
 close all
 disp('Welcome to the Projectile Motion Plotter');
 disp('This projects the motion for a tennis ball with and without air resistance');
 Vx = input('Please input the horizontal velocity [m/s]: ');            
 Vy = input('Please input the vertical velocity [m/s]: ');              

 %Sets up intial conditions
  V = sqrt(Vx^2 + Vy^2);   %Determines V by combining v of both axes 
  G = 9.80665;             %m/s^2 Acceleration due to Gravity       
  DC = 0.8;                %Drag coefficient
  Area = 0.0033;           %m^2 cross section area of a tennis ball
  Mass = 0.057;            %Kg mass of tennis ball
  x(1) = 0;                %intial x postion
  y(1) = 0;                %inital y postion
  xf(1) = 0;               %inital xf postion
  yf(1) = 0;               %intial yf postion
  AP = 1.2;                %kg/m^3 Air Density @ Sea  Level
  D = AP*DC*Area/2;        %constant needed for drag calculations created    
  t(1) = 0;                %sets intial time
  dt = 0.01;               %s set the intervals at which time will be evalutated
  i = 1;                   %sets counter/index

 %Starts a loop for Projectile Motion with Drag    
    while min(y)> -0.01;                                          
       t = t + dt;                                               
       i = i + 1;                                                
       xf(i) = xf(i-1)+ Vx.*dt;                                  
       AxD = - ( D / Mass ) * V * Vx;                            
       AyD = -G - ( D / Mass ) * V * Vy;                         
       Vx = Vx + AxD * dt;                                       
       Vy = Vy + AyD * dt;                                       
       x(i) = x(i-1) + Vx * dt + 0.5 * AxD * dt^2;               
       y(i) = y(i-1) + Vy * dt + 0.5 * AyD * dt^2;               
   end;

 plot(x,y,'b'), hold on;               %plots the Projectile Motion with Drag
 plot(xf,y,'r'), hold off;             %plots the Projectile Motion without Drag
 xlabel('Horizontal Distance (m)');    %labels the x axis "Horizontal Distance (m)"
 ylabel('Vertical Distance (m)');      %Labels the y axis "Vertical Distance (m)"
 title('Projectile Motion Paths');     %Gives a Title "Projectile Motion Paths"

so this is the latest and furthermost i have got, this was done in freeMat 4.2 so some small changes need to be done to make it work in matlab. Other things i have yet to do is add the y axis for projectile motion without drag and a legend for the graph. if you spot anything odd or can tell me how to stop getting those variables overwriting themselves i would be very thankful.

Bryce

[José-Luis]

A possible solution: create two differently named variables

 V_old, V_new

and replace where it corresponds.

[Sara]

what do you mean that Vx is overwritten? Do you mean that:

Vx = Vx + AxD * dt;

should use Vx inputted by the user on the right side?

[Bryce]

Sara: i tried using what Jose-Luis said by replacing the Vx on the left hand side with Vx_New and and the Vx on the right hand side with Vs_Old and changing all associated variables. The problem i had was that after the point where:

Vx = Vx + AxD * dt;

was written the Vx was not the original value, so afterwards it was unusable as the variable which the user inputted. I changed it to now:

Vx_New = Vx_Old + AxD * dt;
Vy_New = Vy_Old + AyD * dt;              
x(i) = x(i-1) + Vx_New * dt + 0.5 * AxD * dt^2;
y(i) = y(i-1) + Vy_New * dt + 0.5 * AyD * dt^2;

the new problem is now it doesn't work, whereas before if i just let it overwrite Vx it would work but after that Vx could not be used anymore as it was a different value. The problem it comes up with now is that it fails "array indexing scalar values...", "index out of range"

[José-Luis]

Please try using the debugger.

 dbstop if error
 your_script.m

And look at the variables in your workspace. It would be much more efficient than us trying to debug remotely.

[Bryce]

well thanks for all your help, very much appreciated

[Douglas Leaffer]

Substitute V for Vx in this loop: xf(i) = xf(i-1)+ Vx.*dt;

Answer 1

[Sara]

You can replace your while loop with:

while min(y)> -0.01;                                          
       t = t + dt;                                               
       i = i + 1;                                                
       xf(i) = xf(i-1)+ Vx.*dt;                                  
       AxD = - ( D / Mass ) * V * Vx;                            
       AyD = -G - ( D / Mass ) * V * Vy;                         
       Vx_new = Vx + AxD * dt;                                       
       Vy_new = Vy + AyD * dt;                                       
       x(i) = x(i-1) + Vx_new * dt + 0.5 * AxD * dt^2;               
       y(i) = y(i-1) + Vy_new * dt + 0.5 * AyD * dt^2;         
       Vx = Vx_new;
       Vy = Vy_new;
   end;

It plots something without errors.

[Bryce]

Thanks a Bunch for fixing that part!!!! Now it works perfectly and i can keep the original values for later functions :)

[Sara]

Note that Vx and Vy are still overwritten at each iteration. To keep the user inputted values, define two new variables, e.g., V0 = Vx before the while loop.