Help creating a graph

%% Question 1 %%
% A two stage, solid-propellant sounding rocket %
clc
clear
format ShortG
% Cosntants %
g       =   9.81;     % Gravity (m/s^2)
Dp      =   2.2;      % Parachute Diamter (m)
Cdp     =   0.8;      % Parachute Drag Coefficent 
rho0    =   1.225;    % Density (Kg/m^3)
% Stage 1 Properties %
m0_1    =   600;      % Inital Mass (Kg)  
mf1     =   350;      % Final Mass (Kg)
T       =   6500;     % Thrust (N)
Isp1    =   270;      % Specific Impulse (s)       
% Stage 2 Properties %
m0_2    =   100;      % Initial Mass (Kg)
n2      =   1.6;      % Mass Ratio
me2     =   0.5;      % Mass Flow Rate (Kg/s)
Isp2    =   290;      % Specific Impulse (s)    
% Stage 1 Calculations
C1      =   Isp2*g;                                                                     % 1st Stage Effective Exaust Velocity (m/s)
me1     =   T/C1;                                                                       % 1st Stage Mass Flow rate
TB1     =   (m0_1-mf1)/me1;                                                             % Time Since T+0 at Burnout
VB1     =   C1*log(m0_1/mf1)-(g*TB1);                                                   % Velocity at Burnout
HB1     =   C1*((-(mf1/me1))*log(m0_1/mf1)+TB1)-((g*TB1^2)/2);                          % Height at Burnout
% Stage Separation
Time    =   10;                                                                         % Time Delay
V_S     =   VB1-(g*Time);                                                               % Velocity at End of Stage Sep 
ChangeH =   VB1+0.5*g*Time^2;                                                           % Change in height during Stage Sep
Height  =   HB1+ChangeH;                                                                % Height of Rocket At End of Stage Sep 
% Stage 2 Calculations
mf2     =   m0_2/n2;                                                                    % Final Mass
C2      =   Isp2*g;                                                                     % Effective Exaust Velocity (m/s)
TB2     =   (m0_2-mf2)/me2;                                                             % Time Taken During Burn
VB2     =   V_S+(C2*log(m0_2/mf2)-(g*TB2));                                             % Velocity Increase During Burn
HB2     =   Height+(C2*((-(mf2/me2))*log(m0_2/mf2)+TB2)-((g*TB2^2)/2));                 % Height Increase During Burn
% Total Time After Final Stage
TotalT  =   TB1+Time+TB2;                                                 
% Coast Phase
Tmax    =   TotalT+(VB2/g);                                                             % Time Since T+0
Hmax    =   HB2+((VB2^2)/(2*g));                                                        % Max altitude Reached at end of flight
% V ends up being 0 in the upward direction as that is when H is Maximum
fprintf('During first stage, the velocity reached was %f m/s, \n', VB1)                 % Printing Velocity and Height at Stage 1 ECO (Engine Cut Off)

During first stage, the velocity reached was 459.988491 m/s, 

fprintf('and the Height achived was %f meters. \n',HB1)

and the Height achived was 17665.851905 meters. 

fprintf('\n')
fprintf('After the 10 second wait inbetween 1st Stage ECO, and Stage 2 ignition,\n')    % Printing to console the Velocity and Height at the end of the 10 Coast Phase inbetween stages

After the 10 second wait inbetween 1st Stage ECO, and Stage 2 ignition,

fprintf('the Velocity was %f m/s,\n',V_S)

the Velocity was 361.888491 m/s,

fprintf('and the Height achived was %f meters\n',Height)

and the Height achived was 18616.340396 meters

fprintf('\n')
fprintf('At Stage 2 ECO, the Velocity was %f m/s \n',VB2)                               % Printing to console the Velocity and Height at Stage 2 ECO (Engine Cut Off)

At Stage 2 ECO, the Velocity was 963.251816 m/s 

fprintf('and the Height achived was %f meters.\n',HB2)

and the Height achived was 37254.049791 meters.

fprintf('\n')
fprintf('At the end of the Coast Phase Velocity = 0,\n')

At the end of the Coast Phase Velocity = 0,

fprintf('as this is where the Maximum Height of %f meters is reached\n',Hmax)

as this is where the Maximum Height of 84545.286329 meters is reached

fprintf('To reach maximum Height it took %f seconds\n',Tmax)

To reach maximum Height it took 292.610038 seconds

% Creating the graphs
% Stage 1 Velocity
% m    =   m0_1-me1*t; 
% V    =   C1*log(m0_1/m)-(g*t);
% Use above equations when time is between 0 and 109
% Stage Separation, lasts for 10 seconds so from 110-120
% V   = VB1-(g*t); % time needs to go from 1-10 here
% Stage 2 velocity, From 121-195
% m2    =   m0_2-me2*t; 
% V    =   C2*log(m0_2/m2)-(g*t);
% Coasting Phase, from 196 to 293
% V   = VB1-(g*t); 

% These need to be plotted agagint time ranging from 0-Tmax (292.61)
% Also each phase needs a different line colour, and a marker at the start and end of each [hase

[Rik]

Have a read here and here. It will greatly improve your chances of getting an answer. What specifically is your question?

[Sam Griffiths]

Sorry for not making it clear, i have to create a graph using these equations that are commented out, and am struggiling on how to achive that, as t changes, as in the first eq t is 0-109, at stage sep it is 0-10, stage 2 it is 0-75, and finally us 0-96, meaning i cannot use a simple array for t. but has to be ploted against time going from 0-293. I could very easily be stupid and cannot see the simple solution.

Answer 1

[Cameron]

m0_1 = 600;
g =   9.81; 
T = 6500;
Isp2 = 290;
C1 = Isp2*g;
me1 = T/C1;        
mf1 = 350;   
TB1 = (m0_1-mf1)/me1; 
VB1 = C1*log(m0_1/mf1)-(g*TB1);    
me2 = 0.5;
m0_2 = 100;
C2 = Isp2*g;  

t1 = 0:109;
m1 = m0_1-me1*t1;
V1 = C1*log(m0_1./m1)-(g*t1);
t2 = 110:120;
V2 = VB1-(g*t2);
t3 = 121:195;
m3 = m0_2-me2*t3;
V3 = C2*log(m0_2./m3)-(g*t3);
t4 = 196:0.01:292.61;
V4 = VB1-(g*t4);
t = [t1,t2,t3,t4];
V = [V1,V2,V3,V4];
plot(t,V)