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rocketSimMainV4.m
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rocketSimMainV4.m
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%% Numerical Simulation of a Sounding Rocket Flight
% Author: Karl Parks
% Class: AE 530
% Date: 2.13.19
% GitHub Repo: https://github.com/Kheirlb/rockets
clc; clear; clear all; close all;
fprintf('\n --- Numerical Simulation of a Sounding Rocket Flight ---\n\n');
fprintf('Author: Karl Parks\n');
fprintf('Class: AE 530\n');
fprintf('Date: 2.13.19\n\n');
% Used this for help:
% https://mintoc.de/index.php/Gravity_Turn_Maneuver
% https://carlospereyradotus.wordpress.com/independent-projects/drag-simulation/
%% Dependent Functions
% rocketSimODE_Real
% rocketSimODE_Ideal
% valueAt
% findrho
% findTemp
% valueOfMach
% findCd
% simpleInterp
% yzero
% All the above functions can be found on the github repository.
% https://github.com/Kheirlb/rockets
%% Initial Variables
global Mo g0 drag0 beta0 thrust0 burntime m_dot r0 atmosphereData CdvsMach frontArea;
%% Choose Initial Conditions
rocketType = 1;
%rocketName = '';
% 1 = HW2
% 2 = FAR/MARS
% 3 = GAH
% 4 = HW1
% 5 = BASE11
% 6 = COMPARISON_1
% otherwise = LR101 Rocket
railLength = 18.288; %18.288 m = 60 feet
switch rocketType
case 1
%% Initial Values - HW2
fprintf('rocketType: HW2\n');
rocketName = 'HW2';
beta0 = 0; %deg launch angle
thrust0 = 20000; %Newtons
burntime = 60; %seconds
frontArea = 0.196; %m^2
Mo = 750; %kg total weight
Ms = 240; %strucure mass
Ml = 10; %payload mass
case 2
%% Initial Values - FAR/MARS
fprintf('rocketType: FAR/MARS\n');
rocketName = 'FAR/MARS';
beta0 = 0.0; %deg launch angle
thrust0 = 2224; %Newtons
burntime = 20; %seconds
frontArea = 0.031; %m^2
Mo = 75-3.5; %kg total weight
Ms = 45; %strucure mass
Ml = 0; %payload mass
case 3
%% Initial Values - GAH
fprintf('rocketType: GAH\n');
rocketName = 'GAH';
beta0 = 1; %deg launch angle
thrust0 = 4500; %Newtons
burntime = 60; %seconds
frontArea = 0.071; %m^2
Mo = 150; %kg total weight
Ms = 90; %strucure mass
Ml = 0; %payload mass
case 4
%% Initial Values - HW1
fprintf('rocketType: HW1\n');
rocketName = 'HW1';
beta0 = 1; %deg launch angle
thrust0 = 25162; %Newtons
burntime = 75; %seconds
frontArea = 0.196; %m^2
Mo = 1000; %kg total weight
Ms = 240; %strucure mass
Ml = 85; %payload mass
case 5
%% Initial Values - BASE11
fprintf('rocketType: BASE11\n');
rocketName = 'BASE11';
beta0 = 1; %deg launch angle
thrust0 = 31400; %Newtons
burntime = 31; %seconds %31.4
frontArea = 0.2; %m^2
Mo = 640; %kg total weight %640
Ms = 418; %strucure mass
Ml = 0; %payload mass
case 6
%% Initial Values - COMPARISON_1
fprintf('rocketType: COMPARISON_1\n');
rocketName = 'COMPARISON_1';
beta0 = 2; %deg launch angle
thrust0 = 2668.93; %Newtons
burntime = 25; %seconds
frontArea = 0.032423161; %m^2
Mo = 15.51286 + 28.4856 + 1.81437; %total mass
Ms = 28.4856; %strucure mass
Ml = 1.81437; %payload mass
otherwise
%% Initial Values - LR101
fprintf('rocketType: LR101?\n');
rocketName = 'LR101?';
beta0 = 1; %deg launch angle
thrust0 = 4500; %Newtons
burntime = 15; %seconds
frontArea = 0.071; %m^2
Mo = 113; %kg total weight
Ms = 90; %strucure mass
Ml = 0; %payload mass
end
%% Propellant/Burnout
Mb = Ml + Ms; %mass at burnout (structure and payload)
Mp = Mo - Mb; %mass of propellant
%% Earth Values
g0 = 9.81; %[m/s2]
r0 = 6.371*10^6; %raduis of earth [m]
%% Excel Data
fprintf("Importing Data: This may take a moment...\n");
fileName = 'rocketSimExcel.xlsx';
%col1 = Mach 0.01 increments
%col2 = Cd Power-off
%col3 = Cd Power-on
CdvsMach = xlsread(fileName, 1, 'A2:C2502');
%col1 = Altitude [m]
%col2 = Temp [K]
%col3 = Density [kg/m^3]
atmosphereData = xlsread(fileName, 2, 'A3:C1204');
%% Some Initial Calcs
m_dot = Mp/burntime; %mass flow rate
isp = thrust0/(m_dot*g0); %isp
ueq = isp*g0; %ueq
R = Mo/Mb; %mass ratio
deltaU = ueq*log(R); %total deltaU
%% Grab Initial Values & Time Adjustments
%accel_y = (thrust0*cosd(beta0))/Mo - g0;
accel_y = (thrust0*cosd(beta0) - Mo*g0)/Mo;
accel_x = (thrust0*sind(beta0))/Mo;
tFirstStep = sqrt((2*railLength)/accel_y);
tStep = 0.1;
tFinal = 2000;
tSpan = tFirstStep:tStep:tFinal;
ux_1 = accel_x*tFirstStep;
uy_1 = accel_y*tFirstStep;
z1o=0; % x-(initial x position)
z2o=ux_1; % x-(initial x velocity)
z3o=0; % y-(initial y position)
z4o=uy_1; % y-(initial y velocity)
y=[z1o;z2o;z3o;z4o];
%% Run Numerical Simulation
options = odeset('Events',@yzero);
%fprintf("\n------- Real --------\n");
[t, x, te, ye, ie]=ode45(@rocketSimODE_Real,tSpan,y, options);
%fprintf("\n------- Ideal --------\n");
[t2, x2, te2, ye2, ie2]=ode45(@rocketSimODE_Ideal,tSpan,y, options);
x_pos = x(:,1); % x-(x position)
x_vel = x(:,2); % x-(x velocity)
y_pos = x(:,3); % y-(y position)
y_vel = x(:,4); % y-(y velocity)
%% Post Processing Using Solved Position and Velocity Values
% This section will find Acceleration, Dynamic Pressure, and Mach # vs Time
return_t = length(t);
Mach = zeros(return_t,1);
Q = zeros(return_t,1);
AccelFlight = zeros(return_t,1);
velVecFlight = zeros(return_t,1);
plotHold = te(2)/10;
fprintf('\nNOTICE: Holding some values constant on plots after t: %4.1f\n', te(2) - plotHold);
for i = 1:return_t
area_ref = frontArea; %m^2
rho = findrho(y_pos(i)); %rho = f(atl)
temp = findTemp(y_pos(i));
velVecFlight(i) = sqrt(x_vel(i)^2 + y_vel(i)^2);
%fprintf('i: %2.1f rho: %2.1f temp: %2.1f velVecFlight(i): %2.1f\n',i,rho,temp,velVecFlight(i));
Mach(i) = valueOfMach(velVecFlight(i), temp);
Cd = findCd(Mach(i));
drag = 0.5*rho*Cd*(velVecFlight(i)^2)*area_ref;
beta = asind(x_vel(i)/(sqrt(x_vel(i)^2 + y_vel(i)^2)));
g = g0*((r0/(r0+y_pos(i)))^2);
m = valueAt(t(i), 'mass'); %kg total weight
thrust = valueAt(t(i), 'thrust');
x_accel = (thrust*sind(beta))/m - (drag*sind(beta))/m; %x-accel
y_accel = (thrust*cosd(beta))/m - (drag*cosd(beta))/m - g; %y-accel
% This last few values have issues so we omit them.
if t(i) < te(2) - plotHold
Q(i) = 0.5*rho*(velVecFlight(i)^2);
AccelFlight(i) = sqrt(x_accel^2 + y_accel^2);
tempIndex = i;
else % Simply set a flat line near flight completion
velVecFlight(i) = velVecFlight(tempIndex);
y_vel(i) = y_vel(tempIndex);
x_vel(i) = x_vel(tempIndex);
Q(i) = Q(tempIndex);
AccelFlight(i) = AccelFlight(tempIndex);
Mach(i) = Mach(tempIndex);
end
end
%% Plots
labelIdeal = 'Ideal - No Drag';
labelComplex = 'Real - Drag';
plotR = 2;
plotC = 3;
[maxAltReal,maxAltIndex] = max(y_pos);
maxHorzReal = max(x_pos);
maxVertVelReal = max(y_vel);
maxHorzVelReal = max(x_vel);
%burnoutIndex = find(t == burntime);
%tIb = t(burnoutIndex); %time index at burnout
burnoutIndex = find(abs(t - burntime) < 1.0);
tIb = t(burnoutIndex); %time index at burnout
firstPlot = subplot(plotR,plotC,1);
plot(t,x(:,3),'r',t2,x2(:,3),'k')
title('Altitude vs Time')
xlabel('Time [sec]');
ylabel('Altitude [m]');
legend(labelComplex,labelIdeal)
firstPlot.YAxis.TickLabelFormat='%.f';
firstPlot.YAxis.Exponent = 0;
y1 = get(firstPlot,'ylim');
hold on
plot([tIb tIb],y1, '--m')
legend(labelComplex,labelIdeal,'Burnout')
grid on
firstPlot(2) = subplot(plotR,plotC,4);
plot(t,x(:,1),'r',t2,x2(:,1),'k')
title('Downrange Distance vs Time')
xlabel('Time [sec]');
ylabel('Horizontal Distance [m]');
firstPlot(2).YAxis.TickLabelFormat='%.f';
firstPlot(2).YAxis.Exponent = 0;
y1 = get(firstPlot(2),'ylim');
hold on
plot([tIb tIb],y1, '--m')
legend(labelComplex,labelIdeal,'Burnout')
grid on
firstPlot(3) = subplot(plotR,plotC,2);
plot(t,velVecFlight,'r',t,x_vel,'b',t,y_vel,'g')
title('Velocity vs Time')
xlabel('Time [sec]');
ylabel('Velocity [m/s]');
legend('Flight Path','Horizontal','Vertical')
firstPlot(3).YAxis.TickLabelFormat='%.f';
firstPlot(3).YAxis.Exponent = 0;
y1 = get(firstPlot(3),'ylim');
hold on
plot([tIb tIb],y1, '--m')
legend('Flight Path','Horizontal','Vertical','Burnout')
grid on
firstPlot(4) = subplot(plotR,plotC,5);
plot(t,AccelFlight,'r')
title('Acceleration vs Time')
xlabel('Time [sec]');
ylabel('Acceleration [m/s^2]');
%legend('Flight Path')
firstPlot(4).YAxis.TickLabelFormat='%.f';
firstPlot(4).YAxis.Exponent = 0;
y1 = get(firstPlot(4),'ylim');
hold on
plot([tIb tIb],y1, '--m')
legend('Flight Path','Burnout')
grid on
firstPlot(5) = subplot(plotR,plotC,3);
plot(t,Q,'r')
title('Dynamic Pressure vs Time')
xlabel('Time [sec]');
ylabel('Q [Pa]');
firstPlot(5).YAxis.TickLabelFormat='%.f';
firstPlot(5).YAxis.Exponent = 0;
y1 = get(firstPlot(5),'ylim');
hold on
plot([tIb tIb],y1, '--m')
legend('Q','Burnout')
grid on
firstPlot(6) = subplot(plotR,plotC,6);
plot(t,Mach,'r')
title('Mach Number vs Time')
xlabel('Time [sec]');
ylabel('Mach');
firstPlot(6).YAxis.TickLabelFormat='%.f';
firstPlot(6).YAxis.Exponent = 0;
y1 = get(firstPlot(6),'ylim');
hold on
plot([tIb tIb],y1, '--m')
legend('Mach','Burnout')
grid on
%sgtitle(strcat('Plots for ',rocketName)); %only works on R2018b
fprintf('\nPlots Displayed\n');
fprintf('\nf. ');
fprintf('\nBurnout Time (Real): %4.1f [sec]\n',t(burnoutIndex));
fprintf('Burnout Alt (Real): %4.1f [m] %4.1f [ft]\n',y_pos(burnoutIndex),convlength(y_pos(burnoutIndex),'m','ft'));
fprintf('Burnout Vel (Real): %4.1f [m/s]\n',velVecFlight(burnoutIndex));
fprintf('\ng. ');
fprintf('\nTime @ Apogee (Real): %4.1f [sec]\n',t(maxAltIndex));
fprintf('Apogee Alt (Real): %4.1f [m] %4.1f [ft]\n',maxAltReal,convlength(maxAltReal,'m','ft'));
fprintf('\nh. ');
fprintf('\nTime @ Impact (Real): %4.1f [sec]\n',te(2));
fprintf('Max Horiz (Real): %4.1f [m] %4.1f [ft]\n',maxHorzReal,convlength(maxHorzReal,'m','ft'));
fprintf('\nl. ');
fprintf('\nMATLAB''s ode45 numerical integrator chooses its own time step.\n');
fprintf('https://www.mathworks.com/help/matlab/ref/ode45.html#bu00_4l_sep_shared-tspan\n');
maxAltIdeal = max(x2(:,3));
maxVertVelIdeal = max(x2(:,4));
maxHorzVelIdeal = max(x2(:,2));
fprintf('\n--- Other Interesting Information ---');
fprintf("\nTotal Weight: %2.0f pounds\n", convmass(Mo,'kg','lbm'));
fprintf("Thrust: %2.0f pounds\n", convforce(thrust0,'N','lbf'));
fprintf("T/W: %2.3f \n", thrust0/(Mo*g0));
fprintf('Isp: %4.1f [sec]\n',isp);
fprintf('u_eqivalent: %4.1f [m/s]\n',ueq);
fprintf('Mass Ratio: %1.0f \n',R);
fprintf('Delta V: %4.1f [m/s]\n',deltaU);
h_max = (ueq^2*(log(R))^2)/(2*g0) - ueq*burntime*((R/(R-1))*log(R) - 1);
fprintf('\nMax Alt (Real): %4.1f [m] %4.1f [ft]\n',maxAltReal,convlength(maxAltReal,'m','ft'));
fprintf('Max Alt (Eq): %4.1f [m] %4.1f [ft]\n',h_max,convlength(h_max,'m','ft'));
fprintf('Max Alt (Ideal): %4.1f [m] %4.1f [ft]\n',maxAltIdeal,convlength(maxAltIdeal,'m','ft'));
fprintf('\nMax Vert Vel (Real): %4.1f [m/s]\n',maxVertVelReal);
fprintf('Max Horz Vel (Real): %4.1f [m/s]\n',maxHorzVelReal);
fprintf('Max Velocity (Real): %4.1f [m/s]\n',max(velVecFlight(1:maxAltIndex)));
fprintf('Max Velocity (Ideal): %4.1f [m/s]\n',sqrt(maxVertVelIdeal^2 + maxHorzVelIdeal^2));
%fprintf('Max Vert Vel (Ideal): %4.1f [m/s]\n',maxVertVelIdeal);
%fprintf('Max Horz Vel (Ideal): %4.1f [m/s]\n',maxHorzVelIdeal);