What is wrong with my code?

2013 4 2
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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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Amit
Amit 2013-4-2
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.

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the cyclist
the cyclist 2013-4-2

1 个投票

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.

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Amit
Amit 2013-4-2
Thanks a lot. That section of my code seems to be working fine.
I am mainly having problem with the part where my program keeps updating its angle, theta, until the target is overshot. For some reason, it doesn't work properly.
I would be really grateful if you could provide any assistance
the cyclist
the cyclist 2013-4-2
The test
if x(i+1) ...
is outside your loop over i. Is that what you intended?
Amit
Amit 2013-4-2
yes, it is. Thanks. I just have a problem with the angle. would i need a for loop for the angle to keep increasing until the point at which the target is overshot?
the cyclist
the cyclist 2013-4-2
编辑：the cyclist 2013-4-2
Your test of whether x(i+1)>D is embedded inside the test of whether x(i+1)<D, and therefore will never be satisfied. Did you mean this instead?
if x(i+1)<D
theta=theta+dtheta;
end
if x(i+1)>D
break
end
That also be written as
if x(i+1)<D
theta=theta+dtheta;
else
break
end
Amit
Amit 2013-4-8
unfortunately it still doesn't work. I've made the code slightly simpler and clearer but still i cant find a way of increasing the angle (theta) until x>D.
%constants
D=10000;
u=600;
m=50;
t_pchute=15;
g=9.81;
a_proj=0.01;
a_pchute=0.05;
C_proj=0.4;
C_pchute=1.2;
p0=1.207;
%initial conditions
theta=pi/30;
x=0;
i=0;
t=0;
y=0;
dtheta=0.1;
dt=0.1;
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));
p=p0*(1-2.333e-5*y).^5;
Fg=-m*g;
Fa=-0.5*p*C_proj*a_proj;
Fp=-0.5*p*C_pchute*a_pchute;
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
plot(x,y),grid
xlabel('Distance/[m]')
ylabel('Height/[m]')
the cyclist
the cyclist 2013-4-9
I think this does what you want. I plot once per iteration of the while loop (with a brief pause), so you can see what is happening as theta changes.
%constants
D=10000;
u=600;
m=50;
t_pchute=15;
g=9.81;
a_proj=0.01;
a_pchute=0.05;
C_proj=0.4;
C_pchute=1.2;
p0=1.207;
theta=pi/30;
dtheta = theta/100;
x=0;
figure
while x(end) < D
theta = theta+dtheta;
%initial conditions
x=0;
i=0;
t=0;
y=0;
dt=0.1;
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));
p=p0*(1-2.333e-5*y).^5;
Fg=-m*g;
Fa=-0.5*p*C_proj*a_proj;
Fp=-0.5*p*C_pchute*a_pchute;
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
plot(x,y),grid
xlabel('Distance/[m]')
ylabel('Height/[m]')
pause(0.25)
end
Amit
Amit 2013-4-11
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
Amit 2013-4-13
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
Amit 2013-4-13
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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