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% Program:
% rocket-trajectory-simulation.m
% Multi-stage rocket dynamics and trajectory simulation.
%
% Description:
% Predicts multi-stage rocket dynamics and trajectories based on the given
% rocket mass, engine thrust, launch parameters, and drag coefficient.
%
% Variable List:
% Delta = Time step (s)
% t = Time (s)
% Thrust = Thrust (N)
% Mass = Mass (kg)
% Mass_Rocket_With_Motor = Mass with motor (kg)
% Mass_Rocket_Without_Motor = Mass without motor (kg)
% Theta = Angle (deg)
% C = Drag coefficient
% Rho = Air density (kg/m^3)
% A = Rocket projected area (m^2)
% Gravity = Gravity (m/s^2)
% Launch_Rod_Length = Length of launch rod (m)
% n = Counter
% Fn = Normal force (N)
% Drag = Drag force (N)
% Fx = Sum of forces in the horizontal direction (N)
% Fy = Sum of forces in the vertical direction (N)
% Vx = Velocity in the horizontal direction (m/s)
% Vy = Velocity in the vertical direction (m/s)
% Ax = Acceleration in the horizontal direction (m/s^2)
% Ay = Acceleration in the vertical direction (m/s^2)
% x = Horizontal position (m)
% y = Vertical position (m)
% Distance_x = Horizontal distance travelled (m)
% Distance_y = Vertical travelled (m)
% Distance = Total distance travelled (m)
% Memory_Allocation = Maximum number of time steps expected

clear, clc      % Clear command window and workspace

% Parameters
Delta = 0.001;                  % Time step
Memory_Allocation = 30000;      % Maximum number of time steps expected

% Preallocate memory for arrays
t = zeros(1, Memory_Allocation);
Thrust = zeros(1, Memory_Allocation);
Mass = zeros(1, Memory_Allocation);
Theta = zeros(1, Memory_Allocation);
Fn = zeros(1, Memory_Allocation);
Drag = zeros(1, Memory_Allocation);
Fx = zeros(1, Memory_Allocation);
Fy = zeros(1, Memory_Allocation);
Ax = zeros(1, Memory_Allocation);
Ay = zeros(1, Memory_Allocation);
Vx = zeros(1, Memory_Allocation);
Vy = zeros(1, Memory_Allocation);
x = zeros(1, Memory_Allocation);
y = zeros(1, Memory_Allocation);
Distance_x = zeros(1, Memory_Allocation);
Distance_y = zeros(1, Memory_Allocation);
Distance = zeros(1, Memory_Allocation);

C = 0.556;                              % Drag coefficient
Rho = 1.204;                            % Air density (kg/m^3)
A = 6.76*10^-2;                         % Rocket projected area (m^2)
Gravity = 9.81;                         % Gravity (m/s^2)
Launch_Rod_Length = 5;                  % Length of launch rod (m)
Mass_Rocket = 239.034;                  % Mass with propllant (kg)
Mass_Rocket_Empty = 138.384;            % Mass without propllant (kg)
Mass_Propellant = 100.65;               % Mass of propellant (kg)
Mass_Flow_Rate = 14.4;                  % Mass Loss of propellant (kg/s)
Burn_Time = 6.985;                       % Rocket Burn Time (s)
Engine_Max_Thrust = 29130;              % Max Thrust of rocket (N)

Theta(1) = 70;                  % Initial launch angle (deg)
Vx(1) = 0;                      % Initial horizontal speed (m/s)
Vy(1) = 0;                      % Initial vertical speed (m/s)
x(1) = 0;                       % Initial horizontal position (m)
y(1) = 0.1;                     % Initial vertical position (m)
Distance_x(1) = 0;              % Initial horizontal distance travelled (m)
Distance_y(1) = 0;              % Initial vertical distance travelled (m)
Distance(1) = 0;                % Initial  distance travelled (m)
Mass(1) = Mass_Rocket;          % Initial rocket mass (kg)

n = 1;                          % Initial time step

while y(n) > 0                  % Run until rocket hits the ground
    n = n+1;                    % Increment time step
    t(n)= (n-1)*Delta;          % Elapsed time

    % Determine rocket thrust and mass based on launch phase
    if t(n) <= 0.1                                     % Rocket Startup
        Thrust(n) = (Engine_Max_Thrust*10)*t(n);
        Mass(n) = Mass_Rocket;
    elseif t(n) >= 0.1 && t(n) < Burn_Time             % Rocket Boost Phase
        Thrust(n) = Engine_Max_Thrust;
        Mass(n) = Mass_Rocket - (t(n)*Mass_Flow_Rate);
    elseif t(n) >= Burn_Time                           % Rocket Shutdown
        Thrust(n) = 0;
        Mass(n) = Mass_Rocket_Empty;
    end

    % Normal force calculations
    if Distance(n-1) <= Launch_Rod_Length       % Launch rod normal force
        Fn(n) = Mass(n)*Gravity*cosd(Theta(1));
    else
        Fn(n) = 0;                              % No longer on launch rod
    end

    % Drag force calculation
    Drag(n)= 0.5*C*Rho*A*(Vx(n-1)^2+Vy(n-1)^2); % Calculate drag force

    % Sum of forces calculations
    Fx(n)= Thrust(n)*cosd(Theta(n-1))-Drag(n)*cosd(Theta(n-1))-Fn(n)*sind(Theta(n-1)); % Sum x forces
    Fy(n)= Thrust(n)*sind(Theta(n-1))-(Mass(n)*Gravity)-Drag(n)*sind(Theta(n-1))+Fn(n)*cosd(Theta(n-1)); % Sum y forces

    % Acceleration calculations
    Ax(n)= Fx(n)/Mass(n);                       % Net accel in x direction
    Ay(n)= Fy(n)/Mass(n);                       % Net accel in y direction

    % Velocity calculations
    Vx(n)= Vx(n-1)+Ax(n)*Delta;                 % Velocity in x direction
    Vy(n)= Vy(n-1)+Ay(n)*Delta;                 % Velocity in y direction

    % Position calculations
    x(n)= x(n-1)+Vx(n)*Delta;                   % Position in x direction
    y(n)= y(n-1)+Vy(n)*Delta;                   % Position in y direction

    % Distance calculations
    Distance_x(n) = Distance_x(n-1)+abs(Vx(n)*Delta);      % Distance in x
    Distance_y(n) = Distance_y(n-1)+abs(Vy(n)*Delta);      % Distance in y
    Distance(n) = (Distance_x(n)^2+Distance_y(n)^2)^(1/2); % Total distance

    % Rocket angle calculation
    Theta(n)= atand(Vy(n)/Vx(n));      % Angle defined by velocity vector

end

figure('units','normalized','outerposition',[0 0 1 1]) % Maximize plot window

% Figure 1
subplot(3,2,1)
plot(x(1:n),y(1:n));
xlim([0 inf]);
ylim([0 inf]);
xlabel({'Range (m)'});
ylabel({'Altitude (m)'});
title({'Height-Range Graph (Trajectory)'});

% Figure 2
subplot(3,2,2)
plot(t(1:n),Vx(1:n));
xlabel({'Time (s)'});
ylabel({'Vx (m/s)'});
title({'Vertical Velocity Graph'});

% Figure 3
subplot(3,2,3)
plot(t(1:n),Vy(1:n));
xlabel({'Time (s)'});
ylabel({'Vy (m/s)'});
title({'Horizontal Velocity Graph'});

% Figure 4
subplot(3,2,4)
plot(t(1:n),Mass(1:n));
xlim([0 60]);
ylim([0 240]);
xlabel({'Time (s)'});
ylabel({'Mass (kg)'});
title({'Rocket Mass Graph'});

% Figure 5
subplot(3,2,5)
plot(t(1:n),((Ax(1:n) + Ay(1:n))/2));
xlabel({'Time (s)'});
ylabel({'Acceleration (m/s^2)'});
title({'Acceleration-Time Graph'});

% Figure 6
subplot(3,2,6)
plot(t(1:n),y(1:n));
xlim([0 inf]);
ylim([0 inf]);
xlabel({'Time (s)'});
ylabel({'Altitude (m)'});
title({'Altitude-Time Graph'});

% Create a table with the data and variable names
T = table(Theta, 'VariableNames', {'Rocket Angle'} )

% Write data to text file
writetable(T, 'MyFile.txt')
disp(Theta(n))