Mixing
Projectile motion with non-constant air resistance
I need to simulate the projectile motion of a "Paris Cannon". I need to consider the air resistance changing according to the altitude with the following equation:
p = p0*exp(-y/y0)
where y0 = 1000m
And the drag is:
Fd = -0.5*C*p*A*v^2
So far, my code looks like this:
clc
clear
m = 94;
A = pi*(.21)^2;
C = .12;
p0 = 1.225;
g = 9.81;
%Initial Conditions
dt = .001;
x(1) = 0;
y(1) = 0;
v = 10000;
angle = 20;
vx = v*cosd(angle)
vy = v*sind(angle);
t(1) = 0 ;
i = 1;
y0 = 1000;
while min(y)> -.001
p = p0*exp(-y/y0)
Drag = p*C*A/2*v^2
ax = -(Drag/m)*(vx*vx+vy*vy)^0.5*vx;
ay = -g-(Drag/m)*(vx*vx+vy*vy)^0.5*vy;
vx = vx+ax*dt;
vy = vy+ay*dt;
x(i+1) = x(i)+vx*dt+.5*ax*dt^2;
y(i+1) = y(i)+vy*dt+.5*ay*dt^2;
t(i+1) = t(i)+dt;
i = i+1;
end
plot(x,y,'-')
xlabel('x distance (m)')
ylabel('y distance (m)')
pause(0.001);
I cannot get the correct simulation here. If I take drag as constant and place it in initial conditions, it works fine. But when I put it in the while loop, the whole simulation gives me absolute nonsense. I would appreciate your help.
matlab projectile
edited Jan 1 at 8:25
Sardar Usama
15.4k82548
asked Dec 30 '18 at 14:18
OzanTOzanT
11
add a comment |
I need to simulate the projectile motion of a "Paris Cannon". I need to consider the air resistance changing according to the altitude with the following equation:
p = p0*exp(-y/y0)
where y0 = 1000m
And the drag is:
Fd = -0.5*C*p*A*v^2
So far, my code looks like this:
clc
clear
m = 94;
A = pi*(.21)^2;
C = .12;
p0 = 1.225;
g = 9.81;
%Initial Conditions
dt = .001;
x(1) = 0;
y(1) = 0;
v = 10000;
angle = 20;
vx = v*cosd(angle)
vy = v*sind(angle);
t(1) = 0 ;
i = 1;
y0 = 1000;
while min(y)> -.001
p = p0*exp(-y/y0)
Drag = p*C*A/2*v^2
ax = -(Drag/m)*(vx*vx+vy*vy)^0.5*vx;
ay = -g-(Drag/m)*(vx*vx+vy*vy)^0.5*vy;
vx = vx+ax*dt;
vy = vy+ay*dt;
x(i+1) = x(i)+vx*dt+.5*ax*dt^2;
y(i+1) = y(i)+vy*dt+.5*ay*dt^2;
t(i+1) = t(i)+dt;
i = i+1;
end
plot(x,y,'-')
xlabel('x distance (m)')
ylabel('y distance (m)')
pause(0.001);
I cannot get the correct simulation here. If I take drag as constant and place it in initial conditions, it works fine. But when I put it in the while loop, the whole simulation gives me absolute nonsense. I would appreciate your help.
matlab projectile
edited Jan 1 at 8:25
Sardar Usama
15.4k82548
asked Dec 30 '18 at 14:18
OzanTOzanT
11
add a comment |
I need to simulate the projectile motion of a "Paris Cannon". I need to consider the air resistance changing according to the altitude with the following equation:
p = p0*exp(-y/y0)
where y0 = 1000m
And the drag is:
Fd = -0.5*C*p*A*v^2
So far, my code looks like this:
clc
clear
m = 94;
A = pi*(.21)^2;
C = .12;
p0 = 1.225;
g = 9.81;
%Initial Conditions
dt = .001;
x(1) = 0;
y(1) = 0;
v = 10000;
angle = 20;
vx = v*cosd(angle)
vy = v*sind(angle);
t(1) = 0 ;
i = 1;
y0 = 1000;
while min(y)> -.001
p = p0*exp(-y/y0)
Drag = p*C*A/2*v^2
ax = -(Drag/m)*(vx*vx+vy*vy)^0.5*vx;
ay = -g-(Drag/m)*(vx*vx+vy*vy)^0.5*vy;
vx = vx+ax*dt;
vy = vy+ay*dt;
x(i+1) = x(i)+vx*dt+.5*ax*dt^2;
y(i+1) = y(i)+vy*dt+.5*ay*dt^2;
t(i+1) = t(i)+dt;
i = i+1;
end
plot(x,y,'-')
xlabel('x distance (m)')
ylabel('y distance (m)')
pause(0.001);
I cannot get the correct simulation here. If I take drag as constant and place it in initial conditions, it works fine. But when I put it in the while loop, the whole simulation gives me absolute nonsense. I would appreciate your help.
matlab projectile
edited Jan 1 at 8:25
Sardar Usama
15.4k82548
asked Dec 30 '18 at 14:18
OzanTOzanT
11
I need to simulate the projectile motion of a "Paris Cannon". I need to consider the air resistance changing according to the altitude with the following equation:
p = p0*exp(-y/y0)
where y0 = 1000m
And the drag is:
Fd = -0.5*C*p*A*v^2
So far, my code looks like this:
clc
clear
m = 94;
A = pi*(.21)^2;
C = .12;
p0 = 1.225;
g = 9.81;
%Initial Conditions
dt = .001;
x(1) = 0;
y(1) = 0;
v = 10000;
angle = 20;
vx = v*cosd(angle)
vy = v*sind(angle);
t(1) = 0 ;
i = 1;
y0 = 1000;
while min(y)> -.001
p = p0*exp(-y/y0)
Drag = p*C*A/2*v^2
ax = -(Drag/m)*(vx*vx+vy*vy)^0.5*vx;
ay = -g-(Drag/m)*(vx*vx+vy*vy)^0.5*vy;
vx = vx+ax*dt;
vy = vy+ay*dt;
x(i+1) = x(i)+vx*dt+.5*ax*dt^2;
y(i+1) = y(i)+vy*dt+.5*ay*dt^2;
t(i+1) = t(i)+dt;
i = i+1;
end
plot(x,y,'-')
xlabel('x distance (m)')
ylabel('y distance (m)')
pause(0.001);
I cannot get the correct simulation here. If I take drag as constant and place it in initial conditions, it works fine. But when I put it in the while loop, the whole simulation gives me absolute nonsense. I would appreciate your help.
matlab projectile
matlab projectile
edited Jan 1 at 8:25
Sardar Usama
15.4k82548
asked Dec 30 '18 at 14:18
OzanTOzanT
11
edited Jan 1 at 8:25
Sardar Usama
15.4k82548
asked Dec 30 '18 at 14:18
OzanTOzanT
11
edited Jan 1 at 8:25
Sardar Usama
15.4k82548
edited Jan 1 at 8:25
Sardar Usama
15.4k82548
edited Jan 1 at 8:25
Sardar Usama
15.4k82548
15.4k82548
asked Dec 30 '18 at 14:18
OzanTOzanT
11
asked Dec 30 '18 at 14:18
OzanTOzanT
11
asked Dec 30 '18 at 14:18
OzanTOzanT
11
11
add a comment |
add a comment |
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