Assumptions: Vertical trajectory,constant gravitational acceleration and atmospheric drag is neglected
clc; clear all; g0 = 9.81; % [km/s^2] Constant at its sea-level value m0 = 30000; % [kg] Initial mass n = 13; % Mass ratio Isp = 320; % [s] Specific impulse T = 900000; % [N] Thrust mf = m0/n; % The burnout mass md = T/(Isp*g0); % Propellant mass flow rate t_burn = (m0 - mf)/md; % The time until burnout V_ex = Isp*g0; % Exhaust velocity h_burn = V_ex/md*(mf*log(mf/m0) + m0 - mf) - 0.5*t_burn^2*g0; v_burn = V_ex*log(m0/mf) -g0*t_burn; h_max = 0.5*V_ex^2/g0*log(n)^2 - V_ex*m0/md*(n*log(n)- n + 1)/n; fprintf('The time until burnout %4.2f [s] \n', t_burn); fprintf('The burnout altitude %4.2f [km] \n', h_burn/1000); fprintf('The burnout velocity %4.2f [km/s] \n', v_burn/1000); fprintf('TThe maximum altitude %4.2f [km] \n', h_max/1000); % Look for the next post where we will present more acurate calculations % considering the gravity effects and atmospheric drag.
The time until burnout 96.59 [s] The burnout altitude 192.64 [km] The burnout velocity 7.10 [km/s] TThe maximum altitude 2765.10 [km]
Equations from Orbital Mechanics for Engineering Students,Second Edition,Aerospace Engineering
Small Satellites 