# How to plot the range of a model rocket?

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Garrett Ponce on 21 May 2022
Edited: Parsa on 21 May 2022
Right now i have this code that plots the altitude with respect to time, but i want to plot the altitude with respect to range of the rocket (i.e. distance in the x-direction vs. distance in the y-direction) by chancing the launch angle. Any help is greatly appreciated! Here's what Ive got:
clear,clc;
launch_angle = 0;
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
i = 1;
cont = true;
while cont
if time == 0
Y(i) = Y_0;
V(i) = V_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;
V(i + 1) = V(i) + dv;
Y(i + 1) = Y(i) + V(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;
V(i + 1) = V(i) + dv;
Y(i + 1) = Y(i) + V(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;
V(i + 1) = V(i) + dv;
Y(i + 1) = Y(i) + V(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 Trajectory')
set(gcf,'position',[500 200 1000 600])
plot(t,Y)
set(gca,'XMinorTick','on','YMinorTick','on')
grid on,xlabel('Time [s]'),xlim([0 140]),ylim([0 500]),...
ylabel('Altitude [m]'),xline(t_burn,':','burn time'),...
xline(t_delay+t_burn,':','delay time'),xline(time,':','landing time')
% 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

Parsa on 21 May 2022
Edited: Parsa on 21 May 2022
Hi Garrett
According to your code, I didnt find any expression for velocity along x-direction. I think, you should define such an expression, with respect to initial horizontal position and Vx(t) for any integration time step.
I also recommend take a look at the link below, to find a comprehensive analysis of rocket motion, which contains a great Matlab code for that. Hope it will be useful.