I'm trying to get Matlab to return the maximum range and angle for a projectile launched from a set height h and initial velocity vO.

When I put in a number for theta, my program works. But when I try to use linspace, I get the error message:

???  In an assignment  A(I) = B, the number of elements in B and I must be the same.

Error in ==> Mech14a at 19
   x(n)=vx0*tau*(1-exp(-t(n-1)/tau))+x(n-1); %X position with linear drag

I understand what this error message means. I just have no idea going about fixing it. Thank you in advance for your help! My code is below!

v0=10; theta=linspace(0,90);  g=9.8;  vterm=50; h=10; %setting initial values
t(1)=0; %setting initial time
y(1)=h; %setting intial height
x(1)=0; %setting initial range
dt=.1;

vx0=v0*cosd(theta); vy0=v0*sind(theta);tau=vterm/g; % calculating constants 

for n=2:200
    if y>=0
   t(n)=t(n-1)+dt;
   x(n)=vx0*tau*(1-exp(-t(n-1)/tau))+x(n-1); %X position with linear drag
   y(n)=(vy0+vterm)*tau*(1-exp(-t(n-1)/tau))-vterm*t(n-1)+h+y(n-1);  %Y position with linear drag  
    else 
        break
    end
end

MaximumRange=max(x)

hold on
grid on
plot(x,y)
axis([0 inf 0 inf]);
xlabel('X displacement');
ylabel('Y displacement');
title('Trajectory with Linear Drag');

Answer 1

[Walter Roberson]

You will need to think more clearly about what you would like the program to do if you have a range of theta.

There is nothing in your current program that calculates a maximum angle as referenced in your description. What do you mean by that? Do you perhaps mean that you want to find the angle at which the projectile would have the maximum range?

I do not know what your tau represents? And I do not see any linear drag term?

Your test

if y>=0

will work, but only accidentally. Remember that y is a vector, so y>=0 will construct the logical array [y(1)>=0, y(2)>=0, ...], and the "if" will be applied against that complete logical array. It so happens that in such a situation supplying an array is equivalent to wrapping the test all() around the array -- the "if" is true if and only if all the y are >= 0. Which happens to be safe for you. I recommend, though, that you consider instead testing if y(n-1)>=0

By the way, if y(n) does become 0 exactly, is there a reason to continue? Your model does not account for "plowing along the ground", so if you have reached the ground there is no point taking another step.

[coppercookie]

Yes, I am trying to find the angle at which the projectile would have the maximum range... Tau is the linear drag. So is the problem where I define my if statement?

[coppercookie]

OH! And to answer your question... This simulates a projectile launched from a height h... so by saying y(1)=0, I'm just stating that I'm at sea level rather than on a cliff about to throw my projectile. So depending on the initial angle, I would want to proceed.

Answer 2

[Jordan]

It seems like you are a bit confused with some syntax. You keep using the '*' for times, which works fine for scalers. When dealing with vectors (like the one you created with the linspace command), matlab uses '*' for matrix multiplication. If you want to do an element by element operation, which I am assuming because you pick a maximum at the end of the program, you want to use the '.*' (and './' for that matter, for essentially the same reason) in stead. hope that helps.

-Jordan

[coppercookie]

I completely missed that thank you! However, that doesn't seem to be the problem! I'm still receiving the same error message!