Small Satellites

Home » Space Flight/Orbital Mechanics » Tsiolkovsky’s Rocket equation

Tsiolkovsky’s Rocket equation

The Tsiolkovsky rocket equation or ideal rocket equation, describes the motion of rocket vehicles. Rocket vehicle accelerates by expelling part of its mass(propellant) with high speed and move due to the conservation of momentum. The Tsiolkovsky’s equation relates the change of speed of the rocket(in absence of other external forces) with the effective exhaust velocity and the mass ratio(ratio of initial and final mass of a rocket).

clc;
clear all;
hold on; grid on;
% M0 - initial mass of a Rocket
% m  - current mass of a Rocket
R = 1:0.1:25;  % R = M0/m;    mass ratio
v_exit = [1000,1500,2000,3000,4000,5000];
for i = 1:6
    V(:,i) = v_exit(i)*log(R);
    scatter(R,V(:,i),'.');
end
legend('v_e = 1 km/s','v_e = 1.5 km/s','v_e = 2 km/s','v_e = 3 km/s',...
    'v_e = 4 km/s','v_e = 5 km/s');
set(gca,'XLim',[1 25]);
xlabel('Mass ratio (M0/m)');
ylabel('Rocket velocity [m/s]')
title('Tsiolkovskys rocket equation')
text(17,1000,'smallsats.org','Color',[0 0 0], 'VerticalAlignment','middle',...
	'HorizontalAlignment','left','FontSize',14 );
hold off;

Tsiolkovskys Equation

Equations from the book

Rocket and Spacecraft Propulsion Principles Practice and New Developments by Martin J.L. Turner – 3rd Edition

Advertisements

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out / Change )

Twitter picture

You are commenting using your Twitter account. Log Out / Change )

Facebook photo

You are commenting using your Facebook account. Log Out / Change )

Google+ photo

You are commenting using your Google+ account. Log Out / Change )

Connecting to %s

Recent Post

%d bloggers like this: