I am trying to find the gross liftoff mass of a 2 stage rocket for different values of n and plot it in MATLAB. I found the total liftoff mass for stage 1 and stage 2. Is the gross liftoff mass equal to m_i1 in the code or do you have to add m_i1 and m_i2? Also, the liftoff seems to be negative for some intial values of n? That is not feasible, right?   % Constants delta_V_ideal = 9800; % m/s f_inert1 = 0.15; f_inert2 = 0.25; Isp_1 = 325; % s Isp_2 = 380; % s g0 = 9.81; % m/s^2 m_PL = 750; n = 0.3:0.01:0.7;   % Initializing variables delta_v1 = zeros(size(n)); delta_v2 = zeros(size(n)); MR_2 = zeros(size(n)); m_prop2 = zeros(size(n)); m_inert2 = zeros(size(n)); m_i2 = zeros(size(n)); MR_1 = zeros(size(n)); m_prop1 = zeros(size(n)); m_inert1 = zeros(size(n)); m_i1 = zeros(size(n));   for i = 1:length(n) delta_v1(i) = n(i)*delta_V_ideal; delta_v2(i) = (1-n(i))*delta_V_ideal;   MR_2(i) = exp(delta_v2(i)/(g0*Isp_2)); m_prop2(i) = (m_PL*(MR_2(i)-1)*(1-f_inert2))/(1-f_inert2*MR_2(i)); m_inert2(i) = (f_inert2*m_prop2(i))/(1-f_inert2); m_i2(i) = m_inert2(i) + m_prop2(i) + m_PL*ones(size(i));   MR_1(i) = exp(delta_v1(i)/(g0*Isp_2)); m_prop1(i) = (m_i2(i)*(MR_1(i)-1)*(1-f_inert1))/(1-f_inert1*MR_1(i)); m_inert1(i) = (f_inert1*m_prop1(i))/(1-f_inert1); m_i1(i) = m_inert1(i) + m_prop1(i) + m_i2(i);     end     figure; plot(n, m_i2, '-b'); % plotting m_i_2 in blue hold on; % this will allow the next plot to be on the same figure plot(n, m_i1, '-r'); % plotting m_i_1 in red xlabel('n'); ylabel('Liftoff Mass'); legend('Stage 2', 'Stage 1'); grid on;

Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
Problem 1.1MA
Question

I am trying to find the gross liftoff mass of a 2 stage rocket for different values of n and plot it in MATLAB. I found the total liftoff mass for stage 1 and stage 2. Is the gross liftoff mass equal to m_i1 in the code or do you have to add m_i1 and m_i2? Also, the liftoff seems to be negative for some intial values of n? That is not feasible, right?

 

% Constants
delta_V_ideal = 9800; % m/s
f_inert1 = 0.15;
f_inert2 = 0.25;
Isp_1 = 325; % s
Isp_2 = 380; % s
g0 = 9.81; % m/s^2
m_PL = 750;
n = 0.3:0.01:0.7;
 
% Initializing variables
delta_v1 = zeros(size(n));
delta_v2 = zeros(size(n));
MR_2 = zeros(size(n));
m_prop2 = zeros(size(n));
m_inert2 = zeros(size(n));
m_i2 = zeros(size(n));
MR_1 = zeros(size(n));
m_prop1 = zeros(size(n));
m_inert1 = zeros(size(n));
m_i1 = zeros(size(n));
 
for i = 1:length(n)
delta_v1(i) = n(i)*delta_V_ideal;
delta_v2(i) = (1-n(i))*delta_V_ideal;
 
MR_2(i) = exp(delta_v2(i)/(g0*Isp_2));
m_prop2(i) = (m_PL*(MR_2(i)-1)*(1-f_inert2))/(1-f_inert2*MR_2(i));
m_inert2(i) = (f_inert2*m_prop2(i))/(1-f_inert2);
m_i2(i) = m_inert2(i) + m_prop2(i) + m_PL*ones(size(i));
 
MR_1(i) = exp(delta_v1(i)/(g0*Isp_2));
m_prop1(i) = (m_i2(i)*(MR_1(i)-1)*(1-f_inert1))/(1-f_inert1*MR_1(i));
m_inert1(i) = (f_inert1*m_prop1(i))/(1-f_inert1);
m_i1(i) = m_inert1(i) + m_prop1(i) + m_i2(i);
 
 
end
 
 
figure;
plot(n, m_i2, '-b'); % plotting m_i_2 in blue
hold on; % this will allow the next plot to be on the same figure
plot(n, m_i1, '-r'); % plotting m_i_1 in red
xlabel('n');
ylabel('Liftoff Mass');
legend('Stage 2', 'Stage 1');
grid on;
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