Asked by Amit
on 2 Apr 2013

I am currently doing a school project where i have to plot the trajectory of a projectile launched from the ground with initial speed V0, and angle theta above the horizontal. The projectile has to hit a target distance D=10000m away once it has reached the ground. I have used an initial guess of theta=pi/30 as the angle, so that the projectile does not reach D. The program should then automatically pick a new value of theta. I am doing this by increasing theta from pi/30 in steps dtheta=0.1 until the target is overshot. However, after plotting, I keep getting a wrong and wild graph. Here is my code:

%contants D=10000; u=600; m=50; g=9.81;

%initial conditions theta=pi/30; x=0; i=0; t=0; y=0; dtheta=0.1; dt=0.1;

while x(i+1)<D

for i=1:1000

xdot(i)=u*cos(theta); ydot(i)=u*sin(theta); v(i)=sqrt(xdot(i).^2+ydot(i).^2);

x(i+1)=(t.*xdot(i)); y(i+1)=(t.*ydot(i))-(0.5*g*(t.^2));

xdbldot(i)=0; ydbldot(i)=-g;

vel_x(i+1)=xdot(i)+(t.*xdbldot(i)); vel_y(i+1)=ydot(i)+(t.*ydbldot(i));

t=t+dt;

if y(i+1)<0 break end end

if x(i+1)<D theta=theta+dtheta; if x(i+1)>D break end end

end

plot(x,y),grid xlabel('Distance/[m]') ylabel('Height/[m]')

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Answer by the cyclist
on 2 Apr 2013

Accepted answer

I think maybe you want this:

x(i+1)=x(i) + (t.*xdot(i)); y(i+1)=y(i) + (t.*ydot(i))-(0.5*g*(t.^2));

when you update x and y.

Show 6 older comments

Amit
on 11 Apr 2013

Thank you so much! That worked perfectly! Also allowed me to actually visualise how the trajectory changes as the angle changes. I really appreciate it.

Amit
on 13 Apr 2013

If you have some time, could you please help with one final thing? Now, I have incorporated the part where a parachute is deployed at t_pchute=15 seconds. My initial guess for theta is now pi/12 and dtheta=theta/100. At the moment, the trajectory falls short of the D=10000m target. Once again, I would like to know how I can increase the angle theta iteratively in steps dtheta?

I was told to use theta(i+1)=atan(vy(i)/vx(i)) but I have no idea why.

%Constants D=10000;%m u=600;%m/s m=50;%kg t_pchute=15;%s g=9.81;%m/s^2 a_proj=0.01;%m^2 a_pchute=0.05;%m^2 C_proj=0.4; C_pchute=1.2; p0=1.207;%kg/m^3 theta=pi/12; dtheta=theta/100; %initial conditions x=0; i=0; t=0; y=0; dt=0.1; p=p0; vx=u*cos(theta); vy=u*sin(theta); v=sqrt(vx.^2+vy.^2); for i=1:1000 Fa(i+1)=0.5*p(i)*C_proj*a_proj*v(i); Fp(i+1)=0.5*p(i)*C_pchute*a_pchute*v(i); if t<t_pchute ax(i+1)=-((Fa(i)*cos(theta(i)))/m)*vx(i); ay(i+1)=-g-(((Fa(i)*sin(theta(i)))/m)*vy(i)); else ax(i+1)=-((Fp(i)*cos(theta(i)))/m)*vx(i); ay(i+1)=-g-(((Fp(i)*sin(theta(i)))/m)*vy(i)); end vx(i+1)=vx(i)+(dt.*ax(i)); vy(i+1)=vy(i)+(dt.*ay(i)); v(i+1)=sqrt(vx(i).^2+vy(i).^2); x(i+1)=x(i)+(dt.*vx(i)); y(i+1)=y(i)+(dt.*vy(i)); p(i+1)=p0*(1-2.333e-5*y(i+1)).^5; theta(i+1)=atan(vy(i)/vx(i)); t=t+dt; if y(i+1)<0 break end end plot(x,y),grid xlabel('Distance/[m]') ylabel('Height/[m]') title('Projectile Trajectory')

Amit
on 13 Apr 2013

I believe that, at the moment, theta changes at each iteration. I would like it to increase by dtheta from the beginning, where x=0 and plot the graph until x(end) and y=0. Whilst x(end) is less than D (10000 metres), theta should increase by dtheta, and the graph should be re-plotted from the the start where x=0. When x(end) reaches D, theta should stop increasing. Not sure how I do this though? Thanks

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## 1 Comment

## Amit (view profile)

Direct link to this comment:http://www.mathworks.com/matlabcentral/answers/69552#comment_140723

Basically, what I am trying to do is increase the angle, theta, in steps dtheta, until the target, D=10000m, is overshot. I have tried doing this by implementing an if loop, as can be seen above.

However, it just doesn't work, any help will be greatly appreciated.