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%% script to asses the design of a stealth spacecraft with low thermal signature
%% detailed algorithm description
% -compute energy absorbed by spacecraft due to sunlight (spacecraft
% assumed to be fully passive, no heat generation)
% -compute quantity of coolant needed to absorb this energy (spacecraft
% dumps energy by heating and venting coolant)
% -compute volume of coolant needed to absorb this energy
%% spacecraft bus specs
% spacecraft minimizes the sunlight it catches by using a reflective
% coating and points its smallest side towards the sun
diameter = 0.3;% diameter of area exposed to sun in m
solar_reflectance = 0.94;% alpha, fraction of solar power reflected
dry_mass = 200; %dry mass (mostly payload + coolant container) in kg
%% cooling system specs
% cooling system is just an open-loop coolant that absorbs heat by liquefying
% and/or gassifying
% values are for H2
spec_th_cap = 14e3;% specific thermal capacity in J/K/kg
melt_spec_heat = 60e3;% specific latent heat of melting in J/kg
vap_spec_heat = 450e3;% specific latent heat of vaporization in J/kg
vap_temp = 20;% vaporization temperature in K
melt_temp = 14;% melting temperature in K
t_min = 4.1; % minimum coolant temperature in K (it is stored at this temperature)
t_max = 20.1; % maximum coolant temperature in K (it is vented at this temperature)
density = 86;% density of coolant in kg/m^3 %solid h2 86 liquid H2 at 20K 70
molar_mass = 2e-3; %molar mass of the coolant, in kg/mol
%% spacecraft trajectory
% values are for Earth-Mars Homann transfer
travel_time = 250;% travel time in days
mean_distance = (1+1/2.25)/2;% mean distance to sun in astronomical units
%% physical constants
sigma = 5.68e-8;% Stefan Boltzmann constant
solar_irradiance_1UA = 1377; % mean solar irradiance at 1 Astronomical Unit in W/m^2
solar_irradiance_mean = solar_irradiance_1UA*mean_distance;% mean solar irradiance on trajectory in W/m^2
bckgrd_temp = 4;% temperature of background radiation in K
R = 8.314; % perfect gas constant, in J. K-1. mol-1
%% computations
front_area = diameter^2/4*pi;% frontal area of spacecraft in m^2
power_absorbed = solar_irradiance_mean*front_area*(1-solar_reflectance);
% absorbed power
tot_spec_heat = (t_max-t_min)*spec_th_cap+(vap_temp<t_max & vap_temp>t_min)...
*vap_spec_heat+(melt_temp<t_max & melt_temp>t_min)*melt_spec_heat;
% total specific heat for coolant going to t_min to t_max with phase changes in J/kg
spec_time = tot_spec_heat/power_absorbed;% specific time it takes to consume 1kg of coolant
%in s
travel_time_s = travel_time*24*3600;% travel time in seconds
tot_conso = travel_time_s/spec_time;% total consumption of coolant over travel
%in kg
coolant_vol = tot_conso/density;% volume of coolant required in m^3
height_coolant = coolant_vol/front_area;% height of a cylinder with diameter of the spacecraft containing
%all coolant
surf_area = pi*diameter*height_coolant;
% surface area of satellite(approximated by coolant cylinder) in m^2
radiated_pow = surf_area*sigma*t_min^4;% radiated power in W
received_bckgrd_pow = surf_area*sigma*bckgrd_temp^4;% power received from cosmic background in W
exhaust_speed = sqrt(3*R*t_max/molar_mass);% exhaust speed of the coolant
thrust = exhaust_speed/spec_time; % mean thrust in newton due to coolant evaporation
min_acceleration = thrust/(dry_mass+tot_conso); % acceleration with full coolant load
max_acceleration = thrust/(dry_mass); % acceleration with empty coolant load
delta_v = exhaust_speed*log((dry_mass+tot_conso)/dry_mass); % delta-v