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William Yeong Liang Ling 2/27/2008 Propulsion Analysis of Balloon Rise Time

This paper discusses the analysis of the rise time of a balloon to an altitude of 30,000m, considering various factors such as drag, acceleration, and velocity. The results compare well with high altitude balloon rise times.

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William Yeong Liang Ling 2/27/2008 Propulsion Analysis of Balloon Rise Time

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  1. William Yeong Liang Ling2/27/2008PropulsionAnalysis of Balloon Rise Time AAE 450 Spring 2008 Propulsion

  2. Determination of rise time • Assumptions • Constant sphere • Constant CD = 0.2 • Barometric formula • Kinematic viscosity variation with temperature • Constant acceleration over timesteps of 1 second Lift Mass Drag AAE 450 Spring 2008 Propulsion

  3. Determination of rise time • 1 hour 36 minutes to reach 30km. • Compares well with high altitude balloon rise times • Final velocity of 19.7m/s upwards • In reality, balloon will either rupture or oscillate about 30km • Future work • Determine maximum drift radius due to wind gusts AAE 450 Spring 2008 Propulsion

  4. Thanks to Jerald Balta for modifying the balloon code to output this. AAE 450 Spring 2008 Propulsion

  5. Thanks to Jerald Balta for modifying the balloon code to output this. AAE 450 Spring 2008 Propulsion

  6. AAE 450 Spring 2008 Propulsion

  7. function Output = Balloon_Rise(GLOW) close all %Timestep = 1 second % This is fixed within the code, i.e. dt = 1 Altitude = 0; g = 9.80665; %% SUMMARY % This function determines the rise time of the balloon to an altitude of % 30,000m. As a bonus, it also determines the drag, Reynolds Number, % acceleration and velocity experienced by the balloon over the rise time. %% x = 0; v = 0; i = 1; t = 0; while x < 30000 Variables = Balloon_Model(GLOW, x); Force = Variables(1); Force = Force - GLOW.*g; Volume = Variables(2); Diameter = Variables(3); [Density_AirPressure_AirTemperature_Air] = Barometric_Formula(x); Drag = 0.2.*0.5.*Density_Air.*v.^2.*(pi./4).*Diameter^2; if Drag > Force Drag = Force; end AAE 450 Spring 2008 Propulsion

  8. Acceleration = (Force - Drag)./GLOW; x = x + v + 0.5.*Acceleration; v = v + Acceleration; Altitude(i) = x; Velocity(i) = v; Acceleration_Grid(i) = Acceleration; Drag_Grid(i) = Drag; t = t + 1; Time(i) = t; % Dynamic Viscosity determined by a best fit curve by Ierardi, James. Dynamic_Viscosity = (-1.1555.*10^-14).*Temperature_Air^3 + (9.5728.*10^-11).*Temperature_Air^2 + (3.7604.*10^-8).*Temperature_Air - (3.4484.*10^-6); Re(i) = (Density_Air.*v.*Diameter)./(Dynamic_Viscosity); i = i + 1; end figure(1) plot(Time,Altitude./1000); title('Change in balloon altitude over time') xlabel('Time (s)') ylabel('Altitude (km)') AAE 450 Spring 2008 Propulsion

  9. function [Density_AirPressure_AirTemperature_Air] = Barometric_Formula(Altitude) %% Fixed Constraints g = 9.80665; % Gravitational acceleration, assumed to be constant [m/s^2] Molar_Air = 0.0289644; % Molar mass of Earth's air [kg/mol] R = 8.31432; % Universal gas constant [N·m/(mol·K)] %% Density of Air using the Barometric Formula if Altitude < 11000 Density_b = 1.2250; Temperature_b = 288.15; Lapse_b = -0.0065; Height_b = 0; Pressure_b = 101325; elseif Altitude < 20000 Density_b = 0.36391; Temperature_b = 216.65; Lapse_b = 0; Height_b = 11000; Pressure_b = 22632.1; elseif Altitude < 32000 Density_b = 0.08803; Temperature_b = 216.65; Lapse_b = 0.001; Height_b = 20000; Pressure_b = 5474.89; elseif Altitude < 47000 Density_b = 0.01322; Temperature_b = 228.65; Lapse_b = 0.0028; Height_b = 32000; Pressure_b = 868.019; AAE 450 Spring 2008 Propulsion

  10. elseif Altitude < 51000 Density_b = 0.00143; Temperature_b = 270.65; Lapse_b = 0; Height_b = 47000; Pressure_b = 110.906; elseif Altitude < 71000 Density_b = 0.00086; Temperature_b = 270.65; Lapse_b = -0.0028; Height_b = 51000; Pressure_b = 66.9389; else Density_b = 0.000064; Temperature_b = 214.65; Lapse_b = -0.002; Height_b = 71000; Pressure_b = 3.95642; end if Lapse_b == 0 Density_Air = Density_b.*exp((-1.*g.*Molar_Air.*(Altitude - Height_b))/(R.*Temperature_b)); %[kg/m^3] else Density_Air = Density_b.*((Temperature_b./(Temperature_b + (Lapse_b.*(Altitude - Height_b))))^(((g.*Molar_Air)./(R.*Lapse_b)) + 1)); %[kg/m^3] end %% Pressure of air using barometric formula if Lapse_b == 0 Pressure_Air = Pressure_b.*exp((-1.*g.*Molar_Air.*(Altitude - Height_b))/(R.*Temperature_b)); %[Pa] else Pressure_Air = Pressure_b.*((Temperature_b./(Temperature_b + (Lapse_b.*(Altitude - Height_b))))^(((g.*Molar_Air)./(R.*Lapse_b)))); %[Pa] end %% Temperature of air using ideal gas law Temperature_Air = (Molar_Air.*Pressure_Air)./(Density_Air.*R); %[K] AAE 450 Spring 2008 Propulsion

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