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function [Rho,P,T] = Atmosphere(Alt)

% This function takes input 'altitude' [km] and interpolates using

% tables of atmospheric data to find parameters

% Find value from tables

load 'atmospheric.mat'

j=1;

while Alt > density(j,1)

j=j+1;

end

Rho = ((Alt-density(j,1))/(density(j+1,1)-density(j,1)))*(density(j+1,2)-

density(j,2)) + density(j,2);

P = ((Alt-density(j,1))/(density(j+1,1)-density(j,1)))*(density(j+1,3)-

density(j,3)) + density(j,3);

T = ((Alt-density(j,1))/(density(j+1,1)-density(j,1)))*(density(j+1,4)-

density(j,4)) + density(j,4);

%Name: Balloon size & Cost

%Goal: Determine a first approximation of the balloon size and associated cost to

launch at a given altitude. Plot variation of cost and balloon size w.r.t desired

altitude.

%Created by: SERGIU PETRE ILIEV. Date: 10.06.2015

%Imperial College London | Aeronautical Engineering | GDP | Coursework

close all; %clean workspace

clc;

clear all;

%% Assumptions

% consider just the limiting case, when the balloon reaches desired altitude and

has to sustain all mass; neglect ascent time, drag on envelope and A/C

%% Initialize parameters

fprintf('Inputs \n');

h=[20,0:0.1:30]; %first value is the input height,

following values are from 0 to 30km in steps of 100m

h(1,1)=input('Desired altitude to be reached by the balloon (km): ');

m=input('Aircraft total mass (kg): ');

k=2.77; %$/kg of liquid H2 (cost)

%% Researched Data, source: www.redbullstratos.com/technology/high-altitude-

balloon/

t=2.03200*10^-5; %m thickness of balloon envelope skin

(based on Red Bull Stratos)

%Polyester-fiber reinforced load tapes are incorporated for weight bearing

%Balloon mass = of skin + estimated mass of reinforcements wires, parachute,

balloon avionics, release valve nylon "destruct line" will release the helium so

that the balloon returns to Earth. Then, the team will gather the envelope into a

large truck, to be inspected at the base and reused.

q_material=889.6; %kg/m3 smeared density of balloon

V_stratos=849505.398; %m3

R_stratos=(849505.398*3/4)^(1/3); %m

m_balloon_stratos=q_material*t*4*pi*R_stratos^2; %kg mass of the entire balloon

%knowing the actual mass of the Red Bull Stratos as 1680kg, a loop was done to

find the smeared density above that would give m_balloon_stratos=1680kg

%% Initialize

% find the AIR atmospheric parameters for all heights using a function that

interpolates experimental data NB: better results can be obtained is the

interpolation is not done between 1km height values

for i=2:302 %from 2 (to skip the input value) to 302 (size of h)

[Rho(i),P(i),T(i)] = Atmosphere(h(i)); % air density, pressure and temperature

end

%% Loop to stabilize mass of the system for all possible altitudes

%acceptable error of 100 grams

% find the H2 atmospheric parameters as a function of AIR atmospheric parameters

(assume H2 and AIR behave the same (same Cp)

% using H2 because it has a lower density, is cheaper, but has the

disadvantage of escaping the envelope over a long time

m_total(1)=m + 15+50+54.57+2+50; %15kg wires and quick release system, 50kg

vaporiser, 54.57±0.1kg of H2, 10kg recovery parachute and 2kg control unit

m_balloon(1)=0; %assume massless balloon initially

eps(1)=20;

for j=2:302

c=2;

while eps(c-1)>0.01 && c<100 %within 10 g not more than 100 iterations

rho_h2(j)=0.0899*( (P(j)/P(2))*(T(2)/T(j)) );%kg/m3 hydrogen density at sea

level * from perfect gas law ratios = hydrogen density at various heights;

assuming it adapts perfectly to temperature and pressure of the exterior

R(j)=((3*m_total(c-1) )/( 4*pi*(Rho(j)-rho_h2(j)) ))^(1/3); %m balloon

radius at altitude

V(j)=(4*pi/3)*R(j)^3; %m3 volume of balloon at altitude

m_balloon(c)=1.5*q_material*t*4*pi*R(j)^2;%50% safety margin

m_total(c)=m_total(1)+m_balloon(c);

eps(c)=m_total(c)-m_total(c-1);

m_balloon_save(j)=m_balloon(c); %remember balloon mass

c=c+1;

Cost(j)=k*V(j)*rho_h2(j)*50; %$ H2 cost associated with 50 Everplanes

end

m_total(j)=m_total(c-1);

end

%% Plot

figure

subplot(1,2,1)

plot(m_balloon_save(2:end), h(2:end), 'b') %plot the experimental response

xlabel('Baloon Mass (kg)'); %label the vertical axis

ylabel('Desired insertion (i.e. neutral buoyancy) altitude (km)'); %label the

horizontal axis

% plot(R(2:end), h(2:end), 'b') %plot the experimental response

% xlabel('Balloon Radius (m)'); %label the vertical axis

% ylabel('Desired insertion (i.e. neutral buoyancy) altitude (km)'); %label the

horizontal axis

subplot(1,2,2)

plot(Cost(2:end), h(2:end), '--r') %plot the reference signal

xlabel('Fleet launch cost ($)'); %label the vertical axis

ylabel('Desired insertion (i.e. neutral buoyancy) altitude (km)'); %label the

horizontal axis