5.0 Neutral Buoyancy Test

Transcription

1 5.0 Neutral Buoyancy Test Montgolfier balloons use solar energy to heat the air inside the balloon. The balloon used for this project is made out of a lightweight, black material that absorbs the solar energy. When the energy is absorbed it heats the air inside. When the air inside reaches the critical temperature where the weight of the internal air plus the weight of the balloon and canister equals the weight of the displaced air, the system is said to have reached neutral buoyancy. Buoyant forces occur when an object is placed in a fluid. The pressure gradient creates an upward force on the object. In water, submarines use tanks filled with water and/or air as ballast to control the depth of the vessel. By forcing air in and out of these tanks, the submarine will rise and sink, accordingly. The same is true for hot air balloons. Manned balloons use flames to heat the air inside the balloon. When the air inside the balloon is heated its density decreases, thus decreasing its weight and allowing the entire system to rise. In the unmanned application, there is no flame to heat up the balloon, only absorbed solar energy. Therefore, the balloon must be dropped from a sufficient altitude with enough sunlight to allow time for the balloon to inflate. If the air inside the balloon does not reach critical temperature, Initech s mission cannot be accomplished. 5.1 Previous Work In previous semesters, groups have manufactured the balloons and developed computer programs that attempted to predict the time it would take to achieve neutral buoyancy. The full-scale balloon has a volume of approximately 60 m 3, a total height of 10 m, and an approximate diameter of 3 m. The balloon fills with air as it falls by 40

2 scooping in air through a 1 meter diameter opening in the bottom. SOL Engineering performed drop tests and successfully demonstrated the inflation of the scaled balloons, but they were unable to confirm whether or not the balloons achieved neutral buoyancy. [Gist, 2001] 5.2 Determination of the Critical Temperature The calculations performed by Initech are approximations of the temperature difference needed to obtain neutral buoyancy. There are many factors that affect the buoyancy of the balloon including time of day, atmospheric conditions, thermal updrafts, and reflected solar energy off of the ground. The complexity of the problem makes development of an accurate model very difficult. However, finding the temperature difference required for neutral buoyancy can easily be done. In these calculations, only one assumption is made: air can be treated as an ideal gas. Making this assumption, the ideal gas law can be used. where P = ρrt (5.1) P = pressure (Pa) ρ = density of air (kg/m 3 ) R = gas constant (287 Joule/kg/K) At the ambient temperature, the mass of the air inside the balloon is equal to the volume of the balloon multiplied by the density of the air at a specific altitude. Since the HAIP system weighs roughly 4 kg, the air inside the balloon must weigh 4 kg less than it would at the ambient temperature to obtain neutral buoyancy. So the density of the air required for neutral buoyancy can be calculated by dividing the necessary mass of the air 41

3 by the volume of the balloon. Then the temperature needed can be found using Equation 5.2. T needed P = (5.2) ρ R needed The difference between the ambient temperature and the temperature needed is graphed below against altitude Temperature Difference (deg C) Altitude (m) Figure 22: Temperature Difference for Neutral Buoyancy The operational range of the HAIP will be below 4000 meters during the initial launch tests, requiring that the temperature inside the balloon to be between 22 C and 24 C above the ambient air temperature for neutral buoyancy. Attempting to test these results proved to be extremely difficult because the nature of the test. An inflation test was performed inside a large room, but attempting to inflate it outside could damage the balloon because it could tear on the ground. In order to test the balloon outside without it floating away a perfect, windless day is needed. The necessary conditions for a neutral buoyancy test are nearly impossible to obtain, therefore, Initech recommends that operational tests must be conducted. 42

4 5.3 SOL Computer Program Verification Initech modeled the balloon descent in the program written by the SOL group. The dimensions of the final balloon were entered in the balloon2_function.m file. The radius of the balloon s cylinder was approximated to be 1.5 meters. The HAIP weight was estimated to be approximately 2.5 kg. The figure below shows the initial output for the balloon drop from 8000 feet. Figure 23: Incorrect SOL Output with coefficient of drag = 0.3 According to this data, the balloon will drop 8000 feet in approximately 3.25 minutes. This means an average velocity of 28 miles per hour. This output is unreasonable since the drogue chute will prevent the Montgolfier balloon and the HAIP payload to exceed 7mph. After investigating the code, an error was found. The drag 43

5 calculation for the balloon used a coefficient of drag of 0.3 for the balloon. A drag coefficient of 1.5 is much more reasonable. The figure below shows the simulated balloon drop using this drag coefficient. Figure 24: Improved SOL Program Output with coefficient of drag =