Projectile motion with drag:

if true
  % code
clear all
%Drag Parameters
Cd = 0.47;
p = 1.1225;     %Air density at 15degrees
D = 0.043 ;     %Diameter of Golf Ball
A = pi*(D/2)^2; %Cross Sectional area
D = (Cd*p*A)/2; %Drag Constant
%Projectile Parameters
alpha = 45;    %Launch Angle
m = 0.045;     %Mass of Golf Ball/kg
g = 9.81;      %Acceleration Due to Gravity/m/s^2
w = m*g;       %Weight of the Golf Ball/N
v = 40;        %Initial Velocity/m/s
vxi = v*cos(alpha);    %Initial Velocity Resolved in x
vyi = v*sin(alpha);    %Initial Velocity Resolved in y
%Arrays
n = 100;
xdisp = zeros(1, n+1);  %x-displacment Array
ydisp = zeros(1, n+1);  %y-displacment Array
vx = zeros(1, n+1);     %x-velocity Array
vx(1) = vxi;
vy = zeros(1, n+1);     %y-velocity Array
vy(1) = vyi;
t = zeros(1, n+1);       %Time Array
%Iteration
dt = 0.01;
i=1;
while i<n
  ax=-(D/m)*v.*vx;
  ay=-g-(D/m)*v.*vy;
  vx=vx+ax*dt;
  vy=vy+ay*dt;
  xdisp(i+1)=xdisp(i)+vx(i)*dt+0.5*ax*dt^2;
  ydisp(i+1)=ydisp(i)+vy(i)*dt+0.5*ay*dt^2;
  t(i+1)=t(i)+dt;
  v(i+1) = sqrt(vx(i).^2 + vy(i).^2);
  i=i+1;
end
plot(x,y)

end

On the line xdisp(i+1)=xdisp(i)+vx(i)*dt+0.5*ax*dt^2;

i get the error In an assignment A(:) = B, the number of elements in A and B must be the same.

Any help would be greatly appreciated

[Giulio Giovannetti]

Pay attention to the vxi and vyi initialization, you should use cosd(*) instead of cos(*) since the angle has been defined in deg.

vxi = v*cosd(alpha);    %Initial Velocity Resolved in x
vyi = v*sind(alpha);    %Initial Velocity Resolved in y

Answer 1

[Star Strider]

As you have written your code, you need to subscript all your vectors:

while i<n
  ax(i)=-(D/m)*v(i).*vx(i);
  ay(i)=-g-(D/m)*v(i).*vy(i);
  vx(i+1)=vx(i)+ax(i)*dt;
  vy(i+1)=vy(i)+ay(i)*dt;
  xdisp(i+1)=xdisp(i)+vx(i)*dt+0.5*ax(i)*dt^2;
  ydisp(i+1)=ydisp(i)+vy(i)*dt+0.5*ay(i)*dt^2;
  t(i+1)=t(i)+dt;
  v(i+1) = sqrt(vx(i).^2 + vy(i).^2);
  i=i+1;
end

I cannot figure out what you want to plot. I leave that for you to sort.

[Conor Stevenson]

Thank you for your input, since posting i have reproached and solved the issue

[Star Strider]

My pleasure.

I’m glad you sorted it.