- Gravity should only influence the vertical component of the rocket's velocity.
- The thrust should impact both the vertical and horizontal components of the rocket's velocity.
- During the descent phase, the horizontal component of the velocity should remain constant as there are no forces acting in that direction.
Plotting range for a model rocket
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Im trying to plot the range (x-axis) and altitude (y-axis) of a model rocket at a 5 degree launch angle but cannot get a correct plot. So far ive gto the correct trajectory for the burn ohase and the coast phase of the rocket, however it looks like the rocket drifts quite significantly (~7000 m) during the descent phase, and i cannot figure out why that is. It should drift only slightly at a 5 degree launch angle (roughly a couple meters or so), so im not sure why this is the case. Any help is appreciated. Thanks!
clear,clc;
launch_angle = 5;
dt = 0.001;
t_delay = 6; %delay time [s]
d_v = 0.0532; % vehicle diameter [m]
A_v = (pi/4)*(d_v).^2; % vehicle area [m^2]
d_p = 0.771144; % parachute diameter [m]
A_p = (pi/4)*(d_p)^2; % parachute area [m^2]
CD_V = 0.72; % vehicle drag coefficient (Will confirm after CFD)
CD_P = 1.5; % parachute drag coefficient
g = 9.81; %[m/s^2]
density = 1.225; %[kg/m^3]
I_tot = 62.2; % total impulse [Ns]
m_prop = 0.0431; %propellant mass [kg]
w_prop = m_prop*g; % propellant weight [N]
Isp_avg = I_tot/w_prop; % average specific impulse [s]
for j = 1
time = 0;
mass = 0.456; % initial mass [kg]
if thrust(time) > 0
t_burn = 2.3; % burn time [s] *provided by manufacturer*
end
V_0 = 0; %velocity
Y_0 = 0; %altitude
Vx_0 = 0;
X_0 =0;
i = 1;
cont = true;
while cont
if time == 0
Y(i) = Y_0;
V(i) = V_0;
Vx(i) = Vx_0;
X(i) = X_0;
end
% burn phase
if thrust(time)>0
mdot = thrust(time)/(9.81*Isp_avg); %propellant mass flow rate [kg/s]
mass = 0.456 - mdot*dt; %updating mass
D = CD_V(j)*0.5*density*(V(i)^2)*A_v; % drag [N]
dv = (thrust(time)/mass)*dt - (D/mass)*dt - 9.81.*cosd(launch_angle).*dt;
dvx = 9.81*sind(launch_angle)*dt;
V(i + 1) = V(i) + dv;
Vx(i + 1) = Vx(i) + dvx;
Y(i + 1) = Y(i) + V(i)*dt;
X(i + 1) = X(i) + Vx(i)*dt;
end
% coast phase
if thrust(time)<=0 && (time < t_delay+t_burn)
D = CD_V(j)*0.5*density*(V(i)^2)*A_v;
if(V(i) > 0 )
D = -D;
end
mass = 0.456-m_prop; % initial mass - prop mass [kg]
dv = (D/mass)*dt - 9.81.*cosd(launch_angle).*dt;
dvx = 9.81*sind(launch_angle)*dt;
V(i + 1) = V(i) + dv;
Vx(i + 1) = Vx(i) + dvx;
Y(i + 1) = Y(i) + V(i)*dt;
X(i + 1) = X(i) + Vx(i)*dt;
end
% descent phase
if (time > t_delay+t_burn)
D = CD_P(j)*0.5*density*(V(i)^2)*A_p;
if(V(i) > 0 )
D = -D;
end
dv = (D/mass)*dt - 9.81.*cosd(launch_angle).*dt;
dvx = 9.81*sind(launch_angle)*dt;
V(i + 1) = V(i) + dv;
Vx(i + 1) = Vx(i) + dvx;
Y(i + 1) = Y(i) + V(i + 1)*dt;
X(i + 1) = X(i) + Vx(i + 1)*dt;
end
if(Y(i)<0)
cont = false;
end
i = i + 1;
time = time + dt;
end
t = 0:dt:(i - 1)*dt;
end
figure(1)
sgtitle ('Simulated Rocket Range')
set(gcf,'position',[500 200 1000 600])
plot(X,Y)
%xlim([-50 50])
set(gca,'XMinorTick','on','YMinorTick','on')
grid on,xlabel('Range [m]')
ylabel('Altitude [m]')
% Data on AeroTech F26-6FJ
function T = thrust(time)
temp = [ 0.041 38.289
0.114 36.318
0.293 34.347
0.497 32.939
0.774 32.376
1 31.25
1.254 28.716
1.498 25.338
1.743 22.241
2.003 17.737
2.077 15.484
2.304 5.349
2.484 1.689
2.61 0];
T = interp1(temp(:,1),temp(:,2),time,'linear','extrap');
end
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Antworten (1)
Pratik
am 16 Nov. 2023
Hi Garrett,
As per my understanding, you want to plot the range vs altitude plot of a model rocket. However, there is a huge drift in the range of the model during the descent phase of the rocket.
Upon reviewing the code, I noticed that there is an issue with how the force is being applied to the model rocket. To ensure the range of the rocket is accurate, you may revisit the following points.
Please consider the modifications to the 'dv' and 'dvx' variables for different phases, in the code snippet below.
% burn phase
dv = (thrust(time)/mass)*cosd(launch_angle)*dt - (D/mass)*dt - 9.81*dt;
dvx = (thrust(time)/mass)*sind(launch_angle)*dt;
% coast phase
dv = (D/mass)*dt - 9.81*dt;
dvx = 0;
% descent phase
dv = (D/mass)*dt - 9.81*dt;
dvx = 0;
Hope this helps!
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