Solar water disinfection (SODIS) is a process by which microbially contaminated water is disinfected by transmitting solar ultraviolet radiation to the water, rendering the bacteria inactive. The purpose of this project was to determine a residence time for disinfection in specific applications using a 3-log reduction in colony-forming units per milliliter (CFU/mL). The water was contained in quartz tubes and tested over both flat and parabolic reflectors. While UVA and UVB radiation are diffuse and independent of reflector style, water temperature is affected by solar concentration. The two reflector styles were studied to identify how insolation level and temperature affects the bacteria inactivation process. Escherichia coli, DH5α, was inoculated into sterile water and treated for 2, 4, and 8 h. The study had several conclusions, first that a 5-log reduction was achieved after 2 h, for all water temperature and insolation levels. The reflector style did not have a measurable effect on inactivation due to the short disinfection time, but the water temperature increased significantly with the parabolic reflectors. A thermal model of the two systems confirmed that the parabolic configuration resulted in higher energy input, making it the preferred configuration for disinfection with lower residence times.

According to a 2017 report from the World Health Organization (WHO) and UNICEF, 3 in 10 people globally do not have access to safe drinking water (World Health Organization 2017). As the Earth's climate continues to change and droughts become more common and sustained, the number has failed to improve. Unfortunately, access to clean water is not only restricted by physical barriers but also political ones. This problem disproportionally affects people in rural areas – the vast majority of people drinking untreated surface water (such as from lakes and rivers) live in rural areas while two-thirds of people with access to well-managed drinking water live in urban areas (World Health Organization 2017).

An in-home device or portable device capable of supplying safe drinking water has broad application in these rural areas. A popular option is Solar Water Disinfection (SODIS). It is inexpensive, user friendly, and sustainable. SODIS relies solely on solar energy and uses materials that are readily available in developing regions, which would rely most heavily on this technology. The SODIS process involves filling transparent containers (usually PET or glass) with untreated water and putting them outside in the sun; after several hours' residence time, the water should be safe to drink. The basic underlying theory is that UVA and UVB solar radiation is transmitted to the water, damaging the DNA of harmful microbes and rendering them inactive and unable to infect or cause disease (McGuigan et al. 2012).

Since the SODIS method was officially recognized by WHO as a viable water purification method, extensive research has been done to verify its disinfecting qualities on various microbes and viruses. Typically, disinfection is measured using log reduction, which compares the number of bacteria prior to treatment to the amount after treatment. So, a 3-log reduction means that there were 1,000 times more bacteria prior to treatment. Currently, there is no standard amount of reduction that defines safe drinking water. Many use a 3-log reduction; others use the detection limit of 25 CFU/mL (Mani et al. 2006). There is less consensus about how radiation dosage is measured. Berney et al. (2006) use T90, T99 and F90 which is the time and fluence (radiation dosage) to reach 90% or 99% inactivated under simulated UV conditions. Other teams use the time to define dosage over varying levels of radiation. For this reason, it is difficult to compare dosage amounts across studies. Another distinction is between researchers that use simulated UV radiation versus real sunlight. Berney et al. (2006) tried to separate the temperature effect from the radiation by heating the samples in a water bath to a certain temperature in a dark room as one form of treatment and treating the samples under natural sunlight but using water circulation to keep the reactors at a stable, low temperature as another treatment. Table 1 summarizes past research on SODIS treatment and categorizes the studies based on the microbe or bacteria studied, container material, how they measured success and dosage, and other notes such as what kind of UV light was used.

Table 1

Summary of existing SODIS research

AuthorYearBacteria studiedContainer materialVariables studiedOther notes
Mani et al. (2006)  2006 E. coli PET plastic Time (h), log count Real sunlight, reflective surfaces 
Boyle et al. (2008)  2008 B. subtilis endospores, Y. enterocolitica, E. coli, S. epidermidis, C. jejuni PET plastic Time (h), log reduction Real sunlight 
Ubomba-Jaswa et al. (2018)  2008 E. coli (K-12 and EPEC) Polystyrene plastic Time, log reduction Simulated sunlight 
Heaselgrave & Kilvington (2012)  2012 CV-B5, PV-2, Hepatitis A Polystyrene Time, log reduction Simulated sunlight 
Fontán-Sainz et al. (2012)  2012 C. parvum Methacrylate Fluence, turbidity Real sunlight, parabolic reflector 
Berney et al. (2006)  2006 S. typhimurium, E. coli, S. flexneri, V. cholerae Quartz T90, T99, F99, log reduction Temperature effect and sunlight variables were separated 
Present work 2018 E. coli Quartz Time, fluence, log reduction Real sunlight, parabolic and flat plate reflectors 
AuthorYearBacteria studiedContainer materialVariables studiedOther notes
Mani et al. (2006)  2006 E. coli PET plastic Time (h), log count Real sunlight, reflective surfaces 
Boyle et al. (2008)  2008 B. subtilis endospores, Y. enterocolitica, E. coli, S. epidermidis, C. jejuni PET plastic Time (h), log reduction Real sunlight 
Ubomba-Jaswa et al. (2018)  2008 E. coli (K-12 and EPEC) Polystyrene plastic Time, log reduction Simulated sunlight 
Heaselgrave & Kilvington (2012)  2012 CV-B5, PV-2, Hepatitis A Polystyrene Time, log reduction Simulated sunlight 
Fontán-Sainz et al. (2012)  2012 C. parvum Methacrylate Fluence, turbidity Real sunlight, parabolic reflector 
Berney et al. (2006)  2006 S. typhimurium, E. coli, S. flexneri, V. cholerae Quartz T90, T99, F99, log reduction Temperature effect and sunlight variables were separated 
Present work 2018 E. coli Quartz Time, fluence, log reduction Real sunlight, parabolic and flat plate reflectors 

The SODIS method has been in use for decades (Mani et al. 2006; McGuigan et al. 2012), but there has not yet been enough research to define a minimum safe residence time or radiation dosage (fluence) due to the complexity of the process. The challenge of this is due to variation in water quality, location, weather, UV sunlight conditions, water flow rate, and other variables. Many of these variables may now be measured using inexpensive sensors and controlled using low-cost microcontrollers, creating the possibility of an automated low-cost, high-volume, SODIS device in the future. While the question of minimum safe residence time is complex, this is a critical element to understanding and increasing automation in SODIS systems. A prototype SODIS reactor has been constructed with capability for low-cost automation; however, the controls sequence requires the design team to confidently predict the safe residence time under a variety of weather and flow conditions.

Flat plates reflect sunlight onto the backside of the reactor, while a parabolic trough concentrates the energy through the length of the reactor. Visible light is an example of beam radiation, which means it can be refracted and focused on a point. UVA and UVB radiation are approximately 70% diffuse, which means they cannot be reflected (Parisi & Turnbull 2005). Thus, the parabolic troughs do not dramatically increase the amount of radiation being transmitted to the water but do increase the amount of thermal energy and resulting temperature change.

The purpose of this particular project was to define the minimum safe fluence required to inactivate Escherichia coli in water and test how parabolic and flat reflectors affect residence time for the inactivation of E. coli in quartz reactors. Prior work with SODIS has shown that once the water temperature surpasses 45 °C, the thermal energy works with the radiation to inactivate bacteria (McGuigan et al. 2012). Other low-temperature studies (less than 40 °C) have focused only on the UV deactivation (Polo-López et al. 2019). In laboratory-controlled biology testing of E. coli, prior authors have observed temperatures of 60–70 °C for thermal deactivation without UV (Collis O'Neill & Middelberg 1995). Other research groups have studied the cleaning of water in solar cookers, typically without UV at temperatures near 65 °C (Ciochetti & Metcalf 1984). Innovative work focused on using nanoparticles for thermal deactivation was successful by maintaining water temperatures of 60 °C (Kulkarni et al. 2019).

We investigated the thermal deactivation opportunity combined with UV by building a heat transfer model of two SODIS configurations. Parabolic reflectors were compared with flat plates for their ability to concentrate the thermal (infrared) radiation, providing a higher temperature in the water. This project measured time and fluence and used a 3-log reduction to measure successful inactivation of bacteria. The research is the first to study parabolic reflectors using E. coli in real sunlight with a direct comparison to a flat plate collector.

To test the efficacy of the SODIS on contaminated water, a SODIS system was constructed that contains four quartz reactors held in frames. Two of the reactors were held over reflective flat plates, and two are held over reflective parabolic dishes. A thermocouple was inserted in the outer end of each reactor to measure the temperature change of the water within the reactor, and a pyranometer was installed on the system to measure insolation. Diagrams of the system and test setup are shown in Figures 1 and 2. The methodology for this project is best described in two parts: the water contamination process followed by data collection.

Figure 1

Schematic of the SODIS prototype used for the experimental work. The placement of thermocouples has been shown with stars, and the location of the pyranometer is shown in the center of the test area.

Figure 1

Schematic of the SODIS prototype used for the experimental work. The placement of thermocouples has been shown with stars, and the location of the pyranometer is shown in the center of the test area.

Close modal
Figure 2

Test schematic showing the collection of data and transfer to computer.

Figure 2

Test schematic showing the collection of data and transfer to computer.

Close modal

Water contamination process

Controlled contamination of the water with E. coli occurred over a 3-day microbiological process. Frozen E. coli (DH5α strain) was harvested and streaked on a Luria Broth (LB) Agar plate. After overnight incubation, the plate holds enough living E. coli colonies for future testing. Prior to any trial, a single E. coli colony was inoculated into 10 mL of liquid LB culture overnight. The third day, the optical density (OD600) of the culture was measured, and a small amount was inoculated into 1,200 mL of sterile water to achieve an optical density of OD600 = 0.130 which is about 108 CFU/mL.

Following the E. coli-water introduction process, the contaminated water was carefully transferred to the quartz reactors, which consist of a quartz cylinder that is open on each end and plugged with large rubber stoppers. Each quartz cylinder held about 250 mL. One end was plugged, and the infected water was slowly poured into the reactor, followed by plugging the other end. After the four reactors were filled with contaminated water, the reactors were carefully inserted into the SODIS frame. The remaining contaminated water (around 200 mL) was kept in a glass beaker indoors at room temperature as a control sample.

SODIS operation and data collection

Data collection for this project was largely dependent on an Arduino Uno Mega coded to output data to a laptop computer. The Arduino code began running as soon as possible after the reactors were exposed to the sunlight. The Arduino code read temperature and insolation data over the course of the trial, outputting the data to a text file for future analysis. Temperature data were taken by thermocouples that were inserted at the end of each reactor. Insolation data was taken by a pyranometer that was situated on the same plane of array as the SODIS, oriented facing north. A summary of the two sensor types and their accuracies are shown in Table 2. The data collection process is summarized in Figure 2.

Table 2

Sensors and their respective accuracies

SensorMeasurementAccuracy
Vernier pyranometer Insolation (W/m2±5% 
K-type thermocouples Temperature (°C) ±0.75% 
SensorMeasurementAccuracy
Vernier pyranometer Insolation (W/m2±5% 
K-type thermocouples Temperature (°C) ±0.75% 

At the end of each trial time, the data collection was paused, the reactors were taken out of the SODIS frame, uncapped, and a pipet was used to extract 7 mL from each reactor. Before and after taking the sample, the reactors were turned over to mix the water and ensure a well-mixed composite sample. After taking the sample, the reactors were reinserted into the SODIS and the trial was resumed. Samples were also taken from the control beaker after each trial. The sample water was then taken to the lab and plated following the standards outlined in Section 9215 of Standard Methods (Rice et al. 2012). We used 20 g/L of LB Broth (Lennox) from Sigma-Aldrich with 15 g/L of Bacto Agar from VWR for our LB agar plates.

The water was plated at full concentration and also at dilutions of 0.1 and 0.01 concentrations. The plated samples were then incubated for 48 h at 37 °C. After incubation, the colonies were large enough to be counted by hand visually. An example of the plated samples is shown in Figure 3. After all trials for a given day were completed, and all samples had been plated, the reactors, thermocouples, pipets, stoppers, and beakers were either disinfected with bleach or autoclaved.

Figure 3

Example of E. coli plates used for visual counts. (a) Sample treated by the SODIS for 4 h. (b) Sample left untreated for 4 h.

Figure 3

Example of E. coli plates used for visual counts. (a) Sample treated by the SODIS for 4 h. (b) Sample left untreated for 4 h.

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Heat transfer modeling methods

To understand the contribution of the heat to the disinfection process, a heat transfer model was developed to compare the parabolic concentration system to a traditional flat plate. The system was assumed to be quasi-steady state to make the relative heat transfer contributions more uniform.

The parabolic tubes were modeled using a concentration ratio (CR) commonly calculated for solar thermal application. The area of the collector was calculated as the surface area of the reflective parabolic trough. The surface area of the tube was calculated based on the length and diameter of the quartz tube. The CR was then used with the surface area to determine the heat transfer into the surface of the tube based on the insolation (I):
(1)
(2)
Once the total insolation was calculated, the relative radiation reflected was calculated by assuming an average reflectivity for quartz of 15% (qreflected). The heat transfer lost from the outside of the quartz tube due to convection was calculated using Newton's law of cooling. The surface temperature of the quartz tube was calculated, and the ambient air temperature was assumed to be 20 °C. The heat transfer coefficient of the air was calculated using the Rayleigh number (Ra) and Nusselt (Nu) correlations as recommended by Churchill & Chu (1975) for natural convection from a cylinder. Typical values for natural convection in a gas are typically between 2 and 25 W/m2 K. Properties of the air were calculated using 137 iterations to determine the correct film temperature using engineering equation solver (Klein 2007). The engineering equation solver iterations include adjusting the appropriate fluid properties for each change in temperature using the appropriate thermodynamic equation of state. These fluid properties included the thermal conductivity (k), the thermal diffusivity , viscosity , density , coefficient of volumetric thermal expansion , and the Prandtl number (Pr):
(3)
(4)
(5)
To determine the heat transfer into the water, Fourier's law was used to represent the conduction through the quartz tube (qquartz). The equation depends on the conductivity of the quartz (kq) and the radius of the inner and outer dimension of the tube (r1 and r2):
(6)
Newton's law of cooling was again used to determine the heat transfer due to convection in the water (qwater). The Nusselt correlation was approximated using natural convection inside an enclosure for the water (Bergman et al. 2011):
(7)
(8)
Once the heat transfer due to convection of the water, convection loss of the air, and the conduction of the quartz were known, conservation of energy was used to determine the relative heat transfer of each system. Iteration was used to determine all the temperatures in the system that were unknown at each surface:
(9)

SODIS experimental results

A 5-log reduction was achieved in each test regardless of residence time, water temperature, or weather conditions. Figure 4 shows the log reduction of E. coli over time, for two different tests. On August 2nd, samples were taken after 4 and 8 h, and on August 3rd samples were taken after 2, 4, and 8 h. The figure shows that 5-log reduction was achieved after approximately 2 h.

Figure 4

Log reduction of E. coli over time with treated and untreated samples. The solid and dashed lines differentiate data taken over separate trials. Untreated control samples are shown in purple with triangular markers. The treated samples are shown for parabolic (blue and round symbols) with the flat plate noted in green with square symbols. Please refer to the online version of this paper to see this figure in colour: http://dx.doi.org/10.2166/wh.2019.174.

Figure 4

Log reduction of E. coli over time with treated and untreated samples. The solid and dashed lines differentiate data taken over separate trials. Untreated control samples are shown in purple with triangular markers. The treated samples are shown for parabolic (blue and round symbols) with the flat plate noted in green with square symbols. Please refer to the online version of this paper to see this figure in colour: http://dx.doi.org/10.2166/wh.2019.174.

Close modal

Fluence, the full radiative dose, was also accounted for, as shown in Figure 5. Since Berney et al. (2006) used a quartz reactor material and tested E. coli, their results were included for comparison. They showed that 5-log reduction was achieved after 2,400 kJ/m2.

Figure 5

Log reduction of E. coli measured over fluence with treated and untreated samples. Solid and dashed lines differentiate between trials and the dashed-dotted line is approximate results from Berney et al. (2006). The blue and purple lines differentiate between treated and untreated (triangular) samples, the green-blue denotes flat plates and blue (circles) denotes parabolic trough. Please refer to the online version of this paper to see this figure in colour: http://dx.doi.org/10.2166/wh.2019.174.

Figure 5

Log reduction of E. coli measured over fluence with treated and untreated samples. Solid and dashed lines differentiate between trials and the dashed-dotted line is approximate results from Berney et al. (2006). The blue and purple lines differentiate between treated and untreated (triangular) samples, the green-blue denotes flat plates and blue (circles) denotes parabolic trough. Please refer to the online version of this paper to see this figure in colour: http://dx.doi.org/10.2166/wh.2019.174.

Close modal

Figure 5 shows data for two trials, differentiated between by dashed and solid lines. The dashed-dotted line in Figure 4 is the approximate results published by Berney et al. (2006). The dashed data in Figure 4 shows that 5-log reduction occurred after 4 h, where the same reduction occurred over 2 h in the solid-line data. This is because data were not taken at 2 h for the dashed data since the previously assumed standard residence time was 6 h. The 5-log reduction could have happened earlier than 4 h, but this cannot be known as there is no data before that time. The dashed data in Figure 4 is cut short compared with the others in that figure. This was because weather conditions created a lower insolation level during this test day despite the data collection time of 8 h.

The difference in water temperature between the flat and parabolic plates was studied to determine the difference in thermal efficiency. Results confirmed that the parabolic plate contributes to a much higher rate of temperature change than the flat plate, allowing the water temperature to breach the 45 °C threshold faster than the flat plate would. Figure 6 shows the incoming solar radiation and the water temperature behavior for the flat and parabolic reflectors.

Figure 6

Water temperature behavior for flat and parabolic reflectors. Incoming radiation is transmitted to the water by reflective plates, evidenced by the water temperature change.

Figure 6

Water temperature behavior for flat and parabolic reflectors. Incoming radiation is transmitted to the water by reflective plates, evidenced by the water temperature change.

Close modal

From the results of several water temperature tests, it was found that the parabolic reflector is, on average, two times more efficient. The parabolic reflectors transmit the incoming energy to the water, expressed as temperature change, much better than the flat plate configuration. In this case, the water in the parabolic system crossed the 45 °C threshold for improving performance after 1 h. This conclusion strongly supports the parabolic configuration as a design choice for automated and shorter residence time SODIS designs.

Heat transfer modeling results

The heat transfer modeling results and assumptions are shown in Table 3. The insolation values used were conservative at 1,000 W/m2, consistent with the experimentally measured values. The water temperature values were estimated based on the experimental range for each system. The Raleigh number and Nusselt correlation were calculated based on iteration with the relevant property values and temperatures in the system.

Table 3

Summary of parameters used for heat transfer calculations and results for each system

Variable nameUnitsParabolic system valueFlat plate system value
I W/m2 1,000 1,000 
 °C 23 23 
Tw °C 45 45 
 m2 0.040 0.00635 
CR – 5.013 
Raa – 98,367 57,415 
Nua – 7.761 6.754 
ha W/m26.56 5.528 
Raw – 379,343 1,508 
Nuw – 5.527 0.8756 
hw W/m2116.9 18.52 
qin 240 11.2 
qlost 21.22 8.79 
qreflected 36 1.68 
qquartz 182.8 0.7295 
Variable nameUnitsParabolic system valueFlat plate system value
I W/m2 1,000 1,000 
 °C 23 23 
Tw °C 45 45 
 m2 0.040 0.00635 
CR – 5.013 
Raa – 98,367 57,415 
Nua – 7.761 6.754 
ha W/m26.56 5.528 
Raw – 379,343 1,508 
Nuw – 5.527 0.8756 
hw W/m2116.9 18.52 
qin 240 11.2 
qlost 21.22 8.79 
qreflected 36 1.68 
qquartz 182.8 0.7295 

The model confirms that the parabolic trough configuration results in significantly higher energy input to the tubes, roughly 240 W versus the flat plate that inputs around 11.2 W. The higher temperatures that result in the parabolic system increase the losses due to reflection and convection in air, but the higher energy input to the quartz tube is significantly higher due primarily to the concentration of the energy. Since the flat plate configuration never reached the 45 °C threshold during the experimental work, the parabolic configuration is strongly recommended as a method to decrease residence time for the SODIS system, with much higher energy input and insolation capture.

A challenging aspect of SODIS research is that the field is unstandardized; every team uses different forms of solar radiation and metrics for success. Some use artificial sunlight over a specific range of wavelengths, while others use real broad-spectrum sunlight. Some report their results in terms of time, while others work in terms of fluence, which is total solar radiation dosage over time. This inconsistency makes comparing results to other studies difficult. This project was modeled closely after that of Berney et al. (2006), which cited the required residence time to be between 6 and 7 h of direct sunlight in Switzerland, which correlates to a fluence of 2,400 kJ/m2. Upon further investigation, however, this correlation depends on the assumption that average incoming solar radiation is approximately 100 W/m2, which is not accurate in most climates. True incoming solar radiation in full sun is approximately 950 W/m2, which was measured directly for this project by a pyranometer. Thus, a fluence of 2,400 kJ/m2 is reached after just 2 h. With this correction, the results of this project are similar to those of Berney et al. (2006), as shown in Figure 5.

A 5-log reduction was achieved in each test regardless of residence time, water temperature, or weather conditions. There was no measurable difference between the disinfection effectiveness of flat and parabolic reflectors. This is due to the overestimation in residence time; the timescales that were tested were not short enough to observe differences in reflector types. There was, however, a clear difference in temperature rate of change between the flat and parabolic reflectors, with the parabolic reflector having a thermal efficiency approximately double that of the flat plate. Since the water temperature of the parabolic reflector reached the 45 °C threshold much faster than the flat plate, it is assumed that the parabolic would have a shorter required residence time. This was confirmed by the results of the heat transfer model, indicating that the energy input to the flat plate is 20 times lower than the energy input to the parabolic system.

One limitation of this work is the relative difficulty in killing different types of bacteria. E. coli is one of the easier bacteria to kill, and we were not able to test more challenging bacteria like B. subtilis. Our research did not consider protozoa, another leading cause of water-borne illness. This limitation was due to the type of testing facility we used.

Future work is needed to evaluate and optimize the shorter residence times for parabolic collectors based on our work. This should include more testing at times less than 3 h, with a wider variety of bacteria like B. subtilis endospores, Y. enterocolitica, S. epidermidis, C. jejuni, C. parvum, and E. coli. This type of experimental work would allow more direct comparison with Boyle et al. (2008), Berney et al. (2006) and Fontán-Sainz et al. (2012). Testing with other bacteria is important to confirm the benefits of the thermal deactivation since E. coli was the only bacteria tested and deactivation temperatures or times for other harmful bacteria may be higher. For traditional SODIS systems, operating with the same irradiance, Pichel et al. (2019) reported that 20 min to 8 h were required depending on the type of bacteria.

Future research should also examine the impact of the quartz tubes and compare them with less expensive plastic tubes. If the thermal contributions in the parabolic configurations are significant, it may be possible to maintain a shorter residence time while using lower cost tubes.

Although the commonly cited residence time for successful solar water disinfection is 8 h, the literature shows a broad range of residence times between 2 and 8 h using various different reactor materials, as cited by Berney et al. (2006), Ubomba-Jaswa et al. (2018), and Boyle et al. (2008). The results of this project offer an additional data point for the SODIS technique using quartz reactors, with residence times of 2 h or less required for disinfection of E. coli.

The project also quantifies the potential impact of using concentrating parabolic reflectors, a previously unexplored opportunity. More work is required to find a safe minimum residence time using this SODIS model; however, the observed residence times of 2 h support the opportunity to develop small, automated SODIS systems.

A heat transfer model for parabolic and flat plate SODIS configurations has been developed that could be used by other researchers to help understand the relative contribution of temperature to the disinfection. The model confirms that the parabolic trough configuration results in significantly higher energy input to the tubes, roughly 240 W versus the flat plate that inputs around 11.2 W. The model confirms that the parabolic configuration is strongly recommended as a method to decrease residence time for the SODIS system, with much higher energy input and insolation capture. It is known that once the water temperature surpasses 45 °C, the thermal energy works with the radiation to inactivate bacteria (McGuigan et al. 2012). Both experimental and heat transfer modeling work confirms that the parabolic SODIS increases the temperature of the water much faster, making it the preferred configuration for reducing residence time.

Ultimately, the most important impact of this work relates back to the initial purpose of the SODIS technique: providing access to safe drinking water. If solar water disinfection can be optimized and safe residence time decreased, the net amount of available clean water increases. This is a simple method of disinfection that can be used in rural areas that lack access to safe drinking water. The long-term goal is the development of an automated SODIS system that can be easily implemented anywhere clean drinking water is scarce.

This work was funded in part by the Keck Foundation as part of the Shiley School of Engineering Undergraduate Research program at the University of Portland. Many thanks to the shop technicians at the Shiley School of Engineering, particularly Jacob Amos and Jared Rees. Thanks to the student team that designed the system: Jocelle Tade, Eric Domek, Delaney Ralph, Austin Pato, Parker Liebe, and DJ Werner. We are grateful to preliminary work on this idea conducted by Morgan Haines.

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