Characterization of the thermal wake of a weather balloon

Research Group: Matthew Christianson, Cannon Coats, Will Engelhardt, and Chris Roberts

Launch: Whitworth Spring 2018

''Our goal was to determine the size and effect of the thermal wake that is caused by a weather balloon rising though the atmosphere. We used a series of small DS1820 temperature sensors attached to long arms reaching outside of the thermal wake. We also used a long tail to reach far enough under the wake. Unfortunately, due to problems in transportation, one of our arms was damaged which caused our experiment to not collect any data during the weather balloon's ascent and descent.''

Atmospheric Layers
To better understand the thermal wake, we thought it necessary to know the characteristics of the atmospheric layers that the weather balloon would be travelling through. The atmosphere starts with the troposphere which ranges from the surface of the earth to approximately 10 kilometers up. the temperature throughout the troposphere is warmest at the bottom and steadily decreases to approximately -80 degrees fahrenheit at the top. There are also clouds in the troposphere which can lead to a large amount of moisture build up. The tropopause ranges from 10 km to 11 km and rests right between the troposphere and the stratosphere. In this transitionary stage of the atmosphere, the temperature remains fairly constant. The stratosphere then ranges from 11 km to 50 km where the temperature gradually increases from -62 degrees Celcius to -21 degrees Celcius. The ozone also exists in the stratosphere. The remaining layers of the atmosphere are irrelevant to our project since the balloon generally rises to a height of about 97,000 feet which is close to the middle of the stratosphere. Below (Figure 1) is a visual representation of the various atmospheric layers above the earth's surface.

Characteristics of thermal wake
Next, we researched the characteristics of wake and the thermal wake of our weather balloon. The wake behind a body is a reverse flow region where the air flow moves toward the body, and the air behind the thermal wake has a lower density. Wake is usually a semi-triangular region of moving fluid, radiating out from behind a moving body. Wake appears vaguely the same through most fluids, with different spreads depending on the viscosity of the fluid. The water behind a speedboat is most likely the best visual representation of the radiating, triangular nature of wake (Figure 2).

As air is a less viscous fluid than water, the wake will be more elongated behind the object. We also found that the thermal wake decreases in size as the air density decreases, so the wake should be larger at lower altitudes, assuming that all other factors remain the same. It also seems that thermal irregularities can occur from sources other than the wake which could distort our data.

The shape and size of the weather balloon plays a significant role in how the thermal wake behaves. The teardrop shape of our balloon minimizes the size of the thermal wake in comparison to other possible shapes, as the wake can be tapered inwards by the lower point. As the balloon ascends, its volume increases due to the lower air pressure, and this increase in volume can also increase the size of the thermal wake.

The thermal wake itself is theoretically shaped like an isosceles triangle. One obstacle that we could have encountered is how far away our sensors are from the balloon. Our research pod was the last in the series of pods connected to the weather balloon. Therefore, it is possible that our sensors were located beyond the scope of a measurable portion of the thermal wake. The length of the thermal wake depends upon numerous factors such as the velocity of object, density of the fluid, thermal conductivity of the fluid, and the size and shape of the object moving through the fluid.

Temperature sensors
An additional factor to consider is the effect of the paint on our temperature sensors. It seems that different colors and types of paint can significantly alter exterior temperatures and somewhat alter interior temperatures. darker colors absorb more heat into the sensor while lighter colors reflect the majority of the heat/sunlight. Due to this, white or silver colored paint would likely be the best option for covering our sensors.

Mechanical Design
To measure the fluctuations of air temperature in the wake of the balloon, we assembled two probe arms and a tail. Each of the arms are cylindrical carbon fiber rods, approximately 2.5 meters long and 3 millimeters wide. Because of their relative thickness, they are prone to bowing and bending in the atmospheric winds, which might distort the collection of our data. The rods have been pushed into the body of the pod, with about 2 meters extending out on two of the opposite sides.

Attached to the rods themselves, the actual data collection points are 21 and 22 DS1820 temperature sensors on each arm, respectively. They were soldered into a two meter segment of wire. The wire is a braid of three different colored smaller wires. We chose red, yellow, and green wires to compile the larger braid. The DS1820s have three legs, one for power, one for ground, and one for data. We used the red wire as ground, the yellow wire as signal, and the green wire as power. This was not the best idea as most electronics use the red wire as the power wire. After they were soldered into the wire, the sensors were heat-shrunk onto the solder joints to prevent short-circuits. This braid is wrapped around the carbon fiber rods which provide the structural support for our strings of temperature sensors. Additionally, because we assumed that the arms would be moving about during flight, we tied a string from the ends of both rods to the command module to give them more stability.

In addition to the two arms, we attached a long string of temperature sensors to the bottom of our pod. These sensors are not stabilized by a rod, but rather we just let them hang freely below the pod and let gravity pull them in a generally downward direction. The tail is approximately 10 meters long, with a sensor soldered in every meter.

Because the arms are 2.5 meters long, the pod had to be assembled on site. However, we made the pod as easy to assemble as possible to minimize set up time at the launch. The pod itself is a reflective-foil covered styrofoam box, with a removable lid (Figure 3). To maximize space inside the pod, we zip tied the flight computer to the lid (Figure 4). The battery was secured with the computer, also with zip ties. Screwed and zip-tied into the base of the pod are two metal clamps. The arms were inserted through holes in the sides of the box and were secured down with the clamps (Figure 5). The tail was inserted into a hole in the bottom of the pod. We then made several small loops in the wire, and zip-tied those loops into the pod for stability. Our pod was furthest away from the balloon so our tail could hang down unobstructed. The final mass of the pod was 0.980 kg.

Electrical Design
We used a custom made pcb made by a student here at Whitworth. It uses a breakout for the Mbed micro controller with easy access to plug in a micro SD card reader and a simple way to create a circuit. We used two arms and a tail in an attempt to get our sensors far enough away from the balloon to detect both the normal temperature and the temperature change caused by the thermal wake (Figure 6).

Inputs

We used a total of 54 DS1820 temperature sensors soldered together in parallel. They were split up between three wires, two for the arms of the pod and one for the tail. Each set of sensors was connected to the main board with three connections; positive, ground, and signal. On each signal wire there is a 4.7 kiloohm resistor used as a pull-up resistor. This resistor changes the voltage in the sensors, allowing us to effectively read the DS1820s.

Code
The code for controlling the Mbed was fairly straightforward. It relied on a few external libraries ,like the DS1820 library, the extended timer library, and the SD file system library. The flow of the code started by mounting the SD card. If that failed, the entire program would exit. Once the card was mounted, three vectors of temperature sensor objects were created, one for each arm and one for the tail of DS1820 sensors. After that, the extended timer was started, which was needed to keep track of time passed longer than the built-in timer could manage. Finally, the data is gathered from each sensor and written onto the SD card in the correct file.

|Source Source Code

Validation and Calibration
Much of the time used before launch was spent calibrating the temperature sensors. The sensors would be calibrated through finding their temperature readings compared to a true temperature reading; the real data would then be modified post-launch.

Before we collected any temperature data, we collected every temperature sensor's ID and related it to a number we gave every sensor, 1-90. The sensor IDs were all recorded in a separate file:

Calibration Techniques

Our first proposed method of calibrating the sensors was to create a temperature control box. This was made out of a large styrofoam box with Peltzier modules attached to make the box cold. The box was completely insulated save a hole at the top with a heat sink. The heat from the heat sink was displaced using a fan outside of the box. The heat sink went through the box and was attached to the two Peltzier modules with the hot side on the outside and the cold side on the inside. Once this setup was complete, a breadboard with multiple temperature sensors was placed in the box. There was also a fluke temperature sensor that had its wire going through the box to measure the true temperature. The box's temperature was lowered to mimic the cold temperature of space.

The box design proved too difficult to build and troubleshoot with the time we had, so our group used a cooler with dry ice instead. Before every trial we waited until the box was approximately -10 degrees C. When it had reached the appropriate temperature, we put a fluke temperature probe, as well as breadboard with several temperature sensors plugged into it, into the box. We then started recording the data from each individual sensor, then removed the sensors from the cooler and took the reading from the fluke sensor outside of the box synchronously with the DS1820s in order to receive multiple different temperature values. The fluke temperature sensor was taped to the breadboard to get the most accurate reading near the sensors.

Before we calibrated the sensors, we had to ensure they were recording data, and recording in the manner that was expected. Therefore, before we started analyzing the data, we looked to see if the readings we got from the sensors started out relatively cold, then got warmer as time went on. If the sensors read how they were supposed to, despite having accurate readings or not, then we considered them to be preemptively valid

Modification of the Data

Once the true temperatures from the fluke and each sensor's temperatures were collected, they had to be formatted to provide a helpful calibration.

On Mathematica, we took all the sets of data from the validation and made graphs out of them with the true temperature on the y-axis and each sensor's temperature on the x-axis. The data points were mostly linear, so we could calculate the properties of the best-fit line and use that line to find the true temperature readings. The slope and y-intercept were calculated for each data set and put into a table (identified by their numbers). The table can be found here:. Every linear equation was different for each temperature sensor. Below are a few samples of the many equations we derived.



The above graph is not used quantitatively. However, it displays the differences that can exist between each sensor. One can imagine that if the x-axis was stretched backwards to -40 degrees C (the expected lowest temperature of the atmosphere where the balloon was flying), there would be a large discrepancy between the results. The temperatures would be greatly adjusted upon analysis, which would potentially distort our results.

Because of an undetected short, we were unable to collect data during flight. However, if we had gathered data, we had a process to analyze it. Once the real data was gathered, we would have taken the temperatures for each sensor and put it into the best fit line equation. Since $$y = mx + b$$, for every $$x$$ value we put in (the real data) we get a $$y$$ value, which is the true temperature.

Data and Analysis
Unfortunately, we were unable to collect any data during the flight. During transportation to the launch site, one of the tanks of helium that was used to fill the balloon came loose and rolled over both arms of the pod. Due to the lack of time until the launch, we were unable to determine if there was any damage to the sensors. Thus, we did not catch the short the tanks caused before launch. Once we got back after launch, we checked each arm for any electrical shorts. One short was discovered right where the tank had rolled over the arm. The short broke the circuit for both the sensors and the computer; this was the most likely cause for our lack of data.

However, from our preliminary research and background information, we made some hypotheses about what would affect our thermal wake and how it would affect it. The table below contains a categorization of what we predicted would likely enlarge the thermal wake or diminish it. From our experiment, we would have hoped to grasp a better understanding of what the overarching affects are on the thermal wake of the balloon. Since there are so many factors that could potentially alter the thermal wake, we would not have been able to discern to what extent each factor influenced the thermal wake. Based on the two categories, we could have discovered which of the two had a greater impact, and therefore we could make generalizations about which factors are the most influential.

Conclusion
Unfortunately, we are not able to conclude anything about the thermal wake of the weather balloon as we had hoped to.

However, even though we were unable to gather any data, more progress has been made so that the next group will be able to succeed where past groups have not. We have fixed things and made some components more efficient as well as found other methods that future groups can use to improve the calibration process and other aspects of the project.

Further Improvements
We assumed that painting the sensors white would reduce the amount of thermal energy that they would absorb from the sun, thus causing them to warm up less. We never actually tested this. This would be a good thing to test on a sunny day to see if a black sensor actually reads a warmer temperature than a white one.

Measuring the width of the balloon will also help with the data that is collected after the flight because the diameter of the balloon should affect the size of the thermal wake. Also, measuring how vertically far away the arms are from the balloon will be useful to measure the wake.

A more effective method of calibrating the sensors than using a cooler with dry ice is needed. We were not able to get the temperature low enough to get a good calibration. We attempted to build a freezer box but were unable to make it function. As the cooler and dry ice method only produced temperatures around -6 degrees Celsius, we do not know how the sensors would behave at the low temperatures our balloon would be reaching (around -40 C).

It might be a good idea to look into other ways of getting the sensors away from the main pod. Our current design should work but was a large hassle to deal with, especially without a lot of experience soldering smaller electronics. There were many times that a short would be found and we would have to tear apart the work we had already completed and find where the mistake was. Finding a way to connect the sensors in such a way that, if a short does happen, it will be easy to locate, is something that should be looked in to.

References/Works Cited
Julia Abbott, Matthew Harlan, Mateo Reynoso, and Hannah Tompkins, Continued Exploration of the Characterization of the Thermal Wake of a Weather Balloon During Ascent, 2017

http://howthingsfly.si.edu/aerodynamics/pressure-drag

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https://en.wikipedia.org/wiki/Wake

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https://www.researchgate.net/publication/298193466_Theoretical_and_trial_study_of_thermal_wake_in_the_infrared_detection_of_submarines

https://www.cambridge.org/core/journals/journal-of-fluid-mechanics/article/analysis-and-characterisation-of-momentum-and-thermal-wakes-of-elliptic-cylinders/5F88BAA3DE267AE7C0F9AA43E484FB35

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