Altitude dependence of thermal wake width

Research Group: Jonas Hildebrand, Carl Peterson, and Hever J. Zelaya Solano

Launch: Whitworth Spring 2019

''Our goal was to find a correlation between the altitude and the width of the thermal wake that is caused by a weather balloon rising through the atmosphere. We used a series of small DS1820 temperature sensors along two 2.5 meter carbon fiber arms to detect difference in temperature as we got outside of the thermal wake to try to find how the width changes as we ascended into the atmosphere. We concluded that are arms weren't long enough because we didn't see a significant temperature difference from the DS1820's closer to the pod to the ones further from the pod.

Atmospheric Layers
There are many layers to the atmosphere around Earth. Starting from the surface of earth the layers are troposphere, stratosphere, mesosphere, thermosphere and exosphere. The helium balloon will be reaching about 30 km from the earth's surface and pop in the Stratosphere. As the distance increases from earth through the layers of the atmosphere, the temperature decreases. Earth's average temperature is about 20°C which decreases to about -60°C as you enter the tropopause, the space between the troposphere and the stratosphere, which is 10 km to 11 km. The temperature remains constant until about 20 km and then gradually increases to about -45°C at 30 km. The temperature sensors must be calibrated to deal with temperatures as low as -60°C to retrieve data for testing thermal wake.



Thermal Wake
As the balloon rises and absorbs the heat from the sun it's temperature will increase. If thermal wake executes what is expected, the temperature behind the helium balloon will form a wave similar to a speed boat in water.

There are many factors that affect thermal wake. One is the viscosity of the substance in which the object is moving in. In this case, the air will make the wake be longer than that of water. The shape and size of the weather balloon will also affect the thermal wake. The tear drop shape of the balloon will cause the wake to be thinner than different shapes. When the balloon rises to an environment of lower pressure the volume will increase, also increasing the thermal wake.

Temperature Sensor and Wire Connection
The way the temperature sensors are set up to the wire is through soldering and heat shrink. Each one of the three legs of the temperature sensors are connected to their respective wire of the three wires that make up the entire strand, power leg (right) to power (red) wire, data leg (middle) to data (yellow) wire, and ground leg (left) to ground (green) wire. If any of the wires touch a problem arises, giving purpose to the heat shrink. Each of the two arms and the tail are their own separate circuit but within each circuit there are the three wires: ground, power, and data, twisted together. With the new connectors we used to secure the temperature sensors, the connections with the sensors and the strand becomes more efficient because even if a sensor falls out or gets disconnected, we can still read the rest of the strand.

Theory
Since the thermal wake is very similar to the wake behind a speedboat, we predict that the temperature behind the helium balloon will be hotter in the middle and colder on the outside of the wake. Thermal waves are not visible to the naked eye unlike water waves and therefore we need temperature sensors attached to long arms to measure whether our hypothesis is correct. With data from the temperature sensors we will be able to analyze the temperature at different distances from the pod to see how thermal wake affects temperature.

Pod Design
We constructed a new pod due to wear and tear on the last group's pod. 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. Across the box were 2 wooden sticks which were used to hold the mbed, and on site another two wooden sticks were used to sandwich the flight computer. We decided against placing the flight computer on the lid due to the disadvantages it brought to setting up on site. The battery was connected to the bottom of the computer. 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. 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. The pod is the furthest away from the balloon so that the tail can flow freely below the balloon. The box we used for the pod was a new box due to many holes from previous launches. Though the box changed, the design corresponding to how the arms were attached to the pod remained the same.

Inside the Pod
To measure the change of air temperature caused by the thermal wake, we assembled two probe arms and a tail. Each of the arms are cylindrical carbon fiber rods that are sent through holes in the pod and secured using clamps. The tail goes through a hole on the bottom of the pod and zip tied to secure it. The design to secure the arms was the same as the group from last year but the design to secure the flight computer was altered. The mbed was held in place using four wooden rods, two on top and two on the bottom.

Temperature Sensor Design
Attached to each rod, there are 22 temperature sensors on each arm, respectively. They were connected to three pin plastic headers that make sure the ends of the temperature sensors have no chance of touching, and we added heat shrink around the exposed parts of the DS1820 legs to make sure that the legs wouldn't touch if pinched or twisted. These header pins are then soldered to 3 leads of a braid of three wires, a red one for power, a green one for ground, and a yellow one in the middle for data. Then these new soldered connections are wrapped with heat shrink so that the exposed leads couldn't touch. This improves on the connection design and adds protection to the wire and temperature sensor connections to protect against any physical contact where there shouldn't be. These wires are wrapped tightly around the carbon fiber rods to keep the temperature sensors in a perpendicular orientation to the box. Also a string was tied from the ends of both rods to the pod to give the rods more stability. In addition to the arms, we have a 10 meter long tail hanging from the bottom of the pod with a temperature sensor every meter.

Reconstructing the Arms/Tail Wires
The wires for the arms/ tails from the previous year were left in bad conditions with broken wires and weak connections to the temperature sensors. We un-soldering all the temperature sensors from the wires and used a new approach for re-soldering them. Then we used connectors and soldered those directly the wire to allow for easy attachment and removal of the temperature sensors. This way we can take out the temperature sensors without having to de-soldering them which saves time and resources. We used this system for all the wires for both the arms and tails.

Electrical Design
We used a custom made pcb made by a student here at Whitworth. It uses a breakout for the mbed microcontroller which allows for easy access to plug in a micro SD card reader and a simpler way to create circuit. We had 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.

Inputs
We used a total 54 D1820 temperature sensors soldered together in parallel. The sensors were split between three wires, two for the arms of the pod and one for the tail. Each set of sensors was connected to the main bread board with three connections; positive, ground, and signal. Each signal wire has a 4.7 kiloohm resistor used as a pull up resistor. This resistor changes the voltage in the sensors allowing use to effectively read the DS1820s.

Code
The code for the Mbed is pretty straightforward. It relied on a few external libraries, like the DS1820 library, extended library, and the SD file system library. The code started by mounting the SD card, and if that failed the Mbed would start flashing its LED lights and the entire program would exit. Once the card mounted, three dynamic arrays were created, one for each arm and one for the tail of the DS1820 sensors to send data to. 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 every 10 seconds and written onto the SD card in the correct file.

|Source Source Code

Validation and Calibration
Most of the time used before the launch was spent for calibration of the the temperature sensors.

We calibrated the temperature sensors by comparing the temperature readings of the DS1820 sensors compared to the temperature reading of Fluke Thermocouple thermometers. Then the real data would be modified post-launch.

Before collecting any temperature data, we gathered every temperature sensor's ID and related it to a number we gave every sensor from 0 to 59. This number was also written on the outside of the temperature sensor. The sensor IDs were all recorded in an excel spreadsheet.

Calibration Techniques
When calibrating the sensors, we first had to figure out if the correlation between the sensors and the actual temperature were linear or exponential. In order to determine this we used a freezer box and one temperature sensor. We waited until the freezer box reached –10°C and placed the sensor and the thermocouple probe in the freezer box.Then we turned off the freezer box and as the temperature rose we recorded the temperature every .5°C as read by the thermocouple. Once this data was collected we plotted the data on an excel graph to see the relationship of the DS1820 to the actual temperature. The results were that the correlation was linear, and this let us know that we could make a graph to describe the general behavior of the temperature sensors compared to the Fluke's readings.

For calibration of the rest of the sensors, since we didn't have time to use the freezer box to test all of them, so we used a different approach. We used 3 small containers and filled them with ice, cool water, and warm water respectively. Once this was done, we placed a thermocouple probe into each container and one by one we recorded data of the temperature read from each sensor as we tested them with a range of temperatures. Everything was recorded on excel and this allowed for our next step which was modification of the Data.

Modification of the Data
Once the true temperatures from the fluke and each sensor's temperature were collected, they had to be formatted to provide helpful calibration. On Excel, we took the sets of data from validation and produced graphs out of them with the true temperature on the y-axis and each sensor's temperature on the x-axis, and we noticed that the temperature differences didn't deviate very much from each other. Next we made a best fit graph that described the behavior of the temperature sensors compared to the fluke generally, then created a best fit line with a linear equation y=mx+b for every sensor. After receiving data from the flight, we uploaded the data to an excel file. Once uploaded we used the best fit line equation to modify the readings from the flight to get the most accurate temperatures from the launch.

Data and Analysis
The weather balloon that was launched on April 18, 2019 reached an altitude of approximately 31,000 meters. Arm 1 read all 22 sensors but more than half of them were fluked, however 10 sensors were able to collect data the entire flight. Arm 2 read all of the sensors and collected data the entire time, and the tail only read 2 sensors and collected data for those two the entire flight. The raw data collected by the SD card can be found here:    The following texts and figures are based off of the data that was collected during the launch and flight of the weather balloon.

Arm 2
We created an altitude versus temperature graph (degrees Celsius, figure 7) on the ascend. We also made an average for each quarter of the arm and plotted the altitude versus those temperature averages on the ascend(figure 8).

Arm 1
Although all the sensors received data, not all of it was applicable data. As shown in the Arm 1 data file, there were some sensors that were reading unusable data. Due to this, we only kept 10 out of the 20 sensors read which limited our data analysis. Because of this our group decided that we weren't going to rely on this data, but still in an attempt to see the fluctuation of temperature we created a temperature versus time graph (figure 9).

Tail
Unfortunately the tail only read two temperature sensors. Also, during the launch the tail looped around itself and didn't flow freely down as planned. For this reason out group decided not to rely on the tail for optimal data analysis. We still created a temperature versus time graph (figure 10) to look for a pattern.

Analysis
We used Arm 2 primarily for our data analysis since it was the only reliable data source for the flight where all the sensors read temperatures that made sense. First we wanted to see if there was a significant change across the arms, maybe that could tell us something. We created a Temperature versus Position graph at the time 3884 seconds into the flight. We were expecting that the sensors would read colder sensors on the outside but that wasn't the case. We also thought that because of the wake of a boat, that there would be a fluid change in temperatures almost like a sine wave across the arms, but that wasn't the case either. What we found was that the readings were sporadic and weren't really correlated except they were within 5 degrees of each other. This led us to believe this could be due to calibration or something else unrelated that we didn't account for.

Using the Temperature versus Time graphs of the tail, arm 1, and arm 2, we can see that they shared a common patterned of a steady descent then a gradual increase until about the 7900 second mark when the temperature suddenly dropped until there was no more data. With the use of the altitude versus average temperature graph, we can see that generally the temperatures weren't that far off from each other, and although we were expecting the temperatures to decrease at the ends of the arm, they weren't. That could be because either the calibration of the sensors weren't as accurate as we thought, or that the thermal wake was larger than the arms could go. We noticed that the temperatures across the arm didn't decrease gradually but were sporadic, yet within 10 degrees of each other. When calibrating we didn't use really low temperatures which could explain why this occurred. A significant observation we made was that after the balloon popped (which occurred at around 7900 seconds) the temperatures got significantly colder in all the sensors in arm 1, arm 2, and the tail. We believe this occurred because on the ascend, the weather balloon had created such a massive thermal wake that all the sensors were within it, but once the balloon started dropping the thermal wake vanished causing the sensors to be exposed to the true temperature at their altitudes. This would support the notion that the thermal wakes radius extended farther then the arms could reach. This would mean that we weren't able to determine the size of the thermal wake, but were able to provide evidence that there is one.

Conclusion
The launch was successful in that the arms were able to receive significant data during the ascend of the weather balloon. As the balloon rose through the Troposphere the temperature slowly decreased until it reached the Tropopause where the temperature began slowly increasing as the balloon traveled through the Stratosphere where it then dropped at 31,000 meters before the mbed died at around 21,000 meters. Going back to our original question of how the width of the thermal wake is affected during ascension towards near space, we have to say that our data is inconclusive. We believe that the arms were within the thermal wake during the duration of the flight and because of this aren't able to determine a change in the thermal wake width if any. We were able to find data that fit with what we already knew about the temperature fluctuations the higher in altitude the balloon went. Although we didn't get any conclusive data, we believe that the data we gathered can be used by future groups as a basis for what patterns and phenomena to expect. We have made modifications to last years project in hopes that future groups may not only collect data, but collect meaningful data that will answer the initial question.

Future Suggestions
A suggestion for future thermal wake groups would be to secure the temperature sensors to the headers, because on the descent we lost 19 temperature sensors, which costs a lot of money to replace. For future teams, we would suggest to use electrical tape to where the temperature sensors connect with the headers to make sure that the sensors can't escape during the flight. Next, when it comes to calibration and validation, we would suggest to use a wider range of temperatures to test all of the sensors so that the best fit lines for each temperature sensors can be the most accurate for finding the real temperature. Another thing we concluded is that the arms that we used weren't long enough to observe the change in temperature due to the thermal wake, so for future groups we would suggest to extend the measuring length to assure that they can observe where the thermal wake extends to due to the altitude and volume of the balloon. Also, we would make sure that the sensors on each arm were equal distance away from the pod, to be able to compare temperatures radially for more concrete data. Another alternative is, if the tail isn't necessary, the pod can be moved up to try to find the edge of the wake before it gets too wide. We also didn't get much data on one of the arms and the tail, and as we tested the connections we noticed that it would connect all the way through only at certain angles, so assuming that our soldering was perfect, some parts of the wires might have faulty connections, so we would suggest to either be more efficient when soldering to make sure all of the connections were 100% secure, or to affirm this conclusion about the wires and acquire new wires.

References/Works Cited
Cannon Coats, Chris Roberts, Matthew Christianson, William Engelhardt, "Characterization of a thermal wake of a weather balloon", 2018. http://www.whitworthnearspace.org/wiki/Characterization_of_the_thermal_wake_of_a_weather_balloon

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

St. Catherine University Thermal Wake research project https://studylib.new/doc/10179881/high-altitude-thermal-wake-investigation