Engineering Quarterly Summer 2023

Engineering Quarterly VOL.V. . . No.4

SUMMER 2023

W ELCOME !

The Engineering Quarterly is published four times each year by the Hamm School of Engineering at the University of Mary. In each issue, we include articles from each of the seven majors we offer: Electrical Engineering, Mechanical Engineering, Civil Engineering, Environmental Engineering, Computer Science, Construction Engineering, and Construction Management. The intended audience of the Engineering Quarterly includes engineers, engineering students, engineering alumni, future engineering students, and people working in related fields such as science, computing, and mathematics.

In this summer issue we describe our student design projects from the spring semester, research our faculty are undertaking, new laboratory modules that we design and construct over the summer to improve the educational experience of our students, fun summer activities in which we participate as faculty, and some of our editorial thoughts on things like Artificial Intelligence and other current and past advancements that have been influenced by clever engineers. As usual, we also include some fun games and problems that you might like to try. Enjoy!

Dr. Terry Pilling

2023 S ENIOR D ESIGN P ROJECTS

On Friday, April 22, the Seniors presented their design projects from Professor Tom Volkman’s Senior Design course.

The projects this year consisted of: Lincoln Highway Project: Dalton Bruce, Aidan Kelly, Taylor Morrison, and John Nauertz Missouri River Bridge: Gabriel Brooks, Mara Dalton, Paige Lang, and Jonas Mitzel I-94/Bismarck Expressway Interchange: Joseph Fesenmaier, Thomas Freas, Marcus Morehead, Parker Wahl Rocket Launched Unmanned Aerial Vehicle: Cole Kitzenberg, Abraham Luedtke, Pierre Miller, John Sammons, John Soupir Snow Bike: Derek Faul, Benjamin Niemuth, David Ruiz, and Brett Thompson All-Terrain Track Vehicle: Nathan DesMarais, Jackson Gallagher, Margaret Kuhar, and Ben Pihl

M ICHAEL G ORDER , PE

Michael Gorder, who graduated from the University of Mary in 2019, has earned his license as a Professional Engineer. Michael joined Moore Engineering after graduation and is a Project Engineer with their Bismarck Office.

We all enjoy visiting with Michael when he returns to campus for our alumni events and to represent his company at the fall and spring career fairs each year. Michael is the first graduate from our engineering school to get his PE license. Congratulations Michael!

We have our senior design presentations at the same time each year as the meeting of our Industry Advisory Board so industry engineers can attended the presentations and help the faculty judge them. At the Hamm School of Engineering, our senior design projects are multidisciplinary projects involving engineering students from different departments.

Many projects that are designed in industry are multidisciplinary ones and it is therefore important for our students to experience this aspect of the process. It involves learning how to delegate the best engineer for a given part of the design and also how to communicate effectively across disciplines. It also allows our students to choose more interesting projects for their capstone senior design course.

University of Mary

FREE

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Engineering Quarterly SUMMER 2023

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with the track and obstacles spread throughout the entire floor plan including classrooms, hallways, lobby, and design center.

ENR 281: S OPHOMORE D ESIGN

By ANTHONY GARCIA

The Hamm School of Engineering prides itself on student design. We incorporate design projects as part of many of our courses including ones which, traditionally, do not contain design projects at most universities. In addition to those courses, we also have courses, from sophomore through to senior level, that are entirely design-based. This past semester our sophomore ENR 281 students completed the engineering group designs that they began in ENR 280 last semester.

Project Reports were required to be professional and detailed including: • title page • executive summary • table of contents • design problem and objectives • literature review/background theory • design conceptualization The goals of this project were as follows: - design a remote control car that satisfies the client’s requirements.

- design a dynamic structure that satisfies the client’s requirements.

- design a static structure that will assist in completing the race track.

Each group tasked with designing remote con- - make the designs as engineering (i.e. metrol cars and parts of the race track, including chanical, electrical, energy) efficient and ecodesigning both a static and a dynamic struc- nomic as possible. ture.

- remain within a budget of $450 to cover manufacturing costs for prototypes and final designs.

- ensure that all materials are designed and fabricated, for example, students can not simply purchase an already functioning remote control car and modify it.

• initial ideas, process, and decisions • detailed design documentation including assumptions made, function of the system, ability to meet Engineering Specifications, prototypes developed, testing and results relative to Engineering Specifications • cost analysis • manufacturing processes used • human factors considered • all technical drawings, diagrams, figures and tables • laboratory test plans and results • work breakdown structure • scheduling (Gantt chart) • bill of materials • safety • conclusions • acknowledgments, references, and appendices

Each team was assigned a client/sponsor who provided specifications on the car and dynamic structure. The race course was constructed in the Senior Design Center, the Engineering Fundamentals classroom, and the Engineering building hallway and lobby. Course deliverables included a detailed project report, detailed designs, and a presen- The race took place on Monday, April 24 at tation.

5:30pm in the Hamm School of Engineering

The race was exciting, with clients (i.e. professors) required to complete one of the race laps all on their own without the help of the students. In the end a team emerged victorious. After two semesters of designing, building, testing, and redesigning, victory is sweet for the team that wins the competition each year.

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E LECTRONIC H OURGLASS

By FINNLEY SOMDAHL

Sophomore engineering student Finnley Somdahl designed an electronic hourglass for fun this semester. Professor Waldenmaier had asked him if there was some way he could create an electronic hourglass for board games. Waldenmaier likes to play board games but finds it annoying that the hourglass that comes with the game and is used for timing the turns is a traditional one with sand in it. The problem is that you can’t adjust the time that it takes to empty and, after one player’s turn is completed, you have to wait until the hourglass empties before the next player can go. He figured an engineering student should be able to design an electronic version that solves these problems and also looks cool at the same time.

Finnley took up the challenge and solved the problems admirably. Here is a YouTube video of Finnley’s hourglass in action: https: //youtu.be/f6xpr-_pMvQ

Engineering Quarterly SUMMER 2023 to become increasingly important to today’s world. Looking forward, its importance will continue to increase as it is predicted to add 4.7 trillion dollars to the nation’s GDP by the year 2030.

We would like our engineering students to be on top of these developments to ensure that they can pursue any careers they choose – even those that require expertise in neural networks and artificial intelligence. The fact that our graduates not only understand how to use A.I., but are even able to write their own neural network, from scratch, in the C programming language, will place them at the top of the pile when they apply for engineering positions in this emerging industry.

M ECHANICAL L AB D ESIGN

By ANTHONY GARCIA, JAMES CARRICO, AND DAYAKAR LAVADIYA

3

large industrial power plants. It operates by boiling a working fluid (most often water) using a heat source, expanding the high-pressure steam through a turbine to produce mechanical work, condensing of the steam back into the liquid phase, and pumping it back into the boiler to complete the cycle.

The heat input to the boiler unit is controlled using the voltage regulator attached to a heating element. The pressure and temperature at the inlet and outlet of the boiler and the steam turbine are recorded simultaneously. The heat released to the environment is determined by measuring the temperature difference between the inlet and outlet of the heat exchange unit. The thermal efficiency is then evaluated as nth = 1 −

qout qin

The second laboratory is a heat transfer laboratory in which the experimental tasks are designed to be performed by senior-level unThis summer the Mechanical Engineering dergraduate students alongside the theory part faculty designed and constructed two new lab- of their EME474: Heat and Mass Transfer oratories for our Mechanical Engineering pro- course. gram. These were a thermal laboratory and a heat transfer laboratory.

A RTIFICIAL I NTELLIGENCE L AB

By TERRY PILLING

This summer I designed a new laboratory module for my ENR 338: Advanced Engineering Mathematics course which will be incorporated into the course this fall. In the module, the students learn to design and build their own artificial intelligence.

The thermal laboratory facilitates a handful of bench top experimental set-ups that will aid in validating the application of laws of thermodynamics. The laboratory tasks are designed to be performed by senior-level undergraduate students alongside the theory part of their EME441: Thermodynamics-II course. The The specific aims of the laboratory include specific aims of the laboratory include • providing hands-on experience to the students to observe, understand and validate the thermodynamic cycles learned in the classroom.

• providing hands-on experience to the students to observe, understand and validate the heat transfer principles learned in the classroom

• performing a case study resulting in deThe module begins with our Mechanical En• performing a case study for enhancing sign recommendations gineering, Electrical Engineering, and Comcycle efficiency. puter Science students learning the complex mathematics involved in neural networks and backpropagation. The mathematical material is a natural continuation of their Calculus I, II, III, and Differential Equations courses, all of which are prerequisites to ENR 338.

The students then write the neural network in the C programming language using knowledge acquired in their ENR 210 and ENR 304 courses. After the network has been written, they “train” the network using training data that is freely available on the internet. Finally, they test the A.I. on new data and see how well it does.

One experiment is designed to demonstrate Artificial Intelligence has come into the Newton’s law of cooling and incorporates two public eye this year as a result of the retasks: lease, and astonishing success, of OpenAI’s One experiment is to determine the thermal language model, ChatGPT. However, A.I. has efficiency of the Rankine Cycle. The Rankine 1. Determination of the heat transfer (free convection) from rectangular fins been around for many years and continues cycle is the vapor power cycle used in most

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Engineering Quarterly SUMMER 2023

4 A

2. Determination of the effect of forced convection on heat transfer from the heated rectangular fins at varying air velocities Convection is the mode of energy transfer between a solid surface and the adjacent liquid or gas that is in motion. It involves the combined effects of conduction and advection. While natural or free convection involves fluid motion occurring through natural means such as the buoyancy effect, which manifests itself as the rise of warmer fluid and the fall of the cooler fluid, the forced convection involves the forced flow of fluid over a surface by external means such as a pump or a fan. The physics of convection heat transfer over a hot surface is captured using Newton’s law of cooling expressed as

The faculty and staff of the Hamm School of Engineering had a beach volleyball team this summer! We played every Thursday night, starting in June, at Sertoma Park in Bismarck.

Team members included professors James Carrico, Dayakar Lavadiya, Terry Pilling, Jerika Cleveland, and Patricia Smith as well as friends and professors from other departments. We didn’t win many games but we had a lot of fun, exercise, and a great opportunity to enjoy the beauty of the parks along the bank of the Missouri River.

12 m

B 5m

How long does the block take to move from A to B in Yolanda’s design?

(Z) Zoe builds a two-stage track. The first stage drops 9 meters over a horizontal run of 2 meters. The second stage drops the final three meters over a horizontal run of three meters.

Q = hc A (Th − T∞ ) where hc is the convective heat transfer coefficient, A is the surface area of the solid surface and T∞ is the ambient temperature of the fluid The Bismarck-Mandan area is a beautiful, reflowing over the material surface. laxing, and family-friendly place to spend the summer, rife with activities for individuals and families of all age groups. It really is a great place to live and work.

A

9m 12 m

2m

B B RACHISTOCHRONE P ROBLEM

5m

How long does the block take to move from A to B in Zoe’s design?

By PATRICK KELLY

Three engineers, Xavier, Yolanda, and Zoe, are commissioned to design a track which will guide a 1 kilogram block from A to B, as shown in the figures below, in the least amount of time. The block starts from rest at A and may not be propelled in any way other than by the force of gravity. The track is made of frictionless material. The velocity of the block as it reaches B is irrelevant. Take ⃗g = 10 meters per second-squared, directed straight down.

The professors at the Hamm School of Engineering continuously evaluate, modify, and improve our courses and laboratories as we gather input from industry, our alumni, and our current student outcomes. These new mechanical engineering laboratories are part of that continuous improvement process and will help us to remain at the top in undergraduate (X) Xavier builds a straight track from A to engineering education.

B, because this is the shortest distance.

S YNCHRONIZED BALLS P ROJECT

By TERRY PILLING

There is a YouTube video that made its way around social media last year in which a guy wrote a computer program showing a number of balls bouncing back and forth between two walls in a synchronized fashion. The walls were in the shape of a V as shown in the picture below:

A

FACULTY S UMMER VOLLEYBALL

By JAMES CARRICO

12 m

B 5m

How long does the block take to move from A to B in Xavier’s design?

(Y) Yolanda builds a track which drops 12 meters vertically, has a very small curved section, and then runs 5 meters horizontally to B, because the average speed is greatest in this case.

While watching this video a person naturally assumes that the balls are moving according to the laws of physics, i.e. that they follow projectile motion. You may even imagine that you could actually set up this situation with real balls and they would move in the fashion shown in the video. In fact, it turns out that these balls are not moving in the obvious assumed way and, if you set up an actual experiment, you would find they do not synchronize as they do in the video. This makes the video much less impressive – since much of the viewers’ surprise and awe when watching comes from their belief that the motion shown is modeling reality. Instead, YouTube videos like this should be thought of as art projects

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Engineering Quarterly SUMMER 2023

rather than experimental simulations of realI S A RTIFICIAL I NTELLIGENCE REALLY ity.

SMARTER THAN US ?

By ASSAL HADDAD One of the projects assigned to the sophomore students in my ENR 304 course, in groups of two, was to write a program in the There is this scene in Tom & Jerry where C programming language and using OpenGL graphics to try to recreate the result from Tom is chasing Jerry into a circular tube, and he ends up catching his own tail thinking he YouTube. Can you do it? got Jerry. He pulls his tail with all his might and he starts to spin endlessly inside that tube.

What’s annoying about this specific scene is EEL 314: S IGNALS & S YSTEMS P ROBLEM that my brain easily surrenders into believing

By NANCY KELLY that: yes, this is what happens when a cat pulls its own tail. I am totally tempted to believe, on a subconscious level, that Tom should be A continuous-time periodic signal x(t) is hilariously spinning in circles, while accordreal valued and has a fundamental period T = ing to physics he should be static and, maybe, 6. The nonzero Fourier series coefficients for pull off a handful of hair from his tail; a simx(t) are ple free body diagram on Tom shows no external force which means no rotation or any a0 = 1, actual displacement should occur. This scene ∗ a2 = a−2 = j/2, reveals how human minds enjoy and get enter∗ tained being fooled into believing a more draa5 = a−5 = −2. matic scenario than the actual boring one. We chose fiction over reality because it is more Express x(t) in the form fun. ∞ X It is tempting to believe that AI is going x(t) = Ak cos(ωk t + ϕk ). to evolve beyond us; recreating the creation k=0 story. But actually no matter how smart it gets, we will always be smarter. Now it could be stronger, faster, more accurate, even more K EN K EN P UZZLE suitable to survive; but that’s not smarter. It

By NANCY KELLY could actually completely annihilate our race, but still it won’t be smarter than us. It can only rip a handful of hair from the big uniKenKen (similar but slightly different verse soul, but it won’t move an inch in any from ‘KenDoku’) is a style of arithmetic logic direction, because it is based in us and only puzzle invented in 2004 by Japanese math us. We move, it moves. We stop, it stops, teacher Tetsuya Miyamoto. KenKen derives and if we die, it dies. I can imagine in 200 from the Japanese word for cleverness. As years AI will be so accurate in simulating my in Sudoku, the goal of each puzzle is to fill current-2023 humanity that I won’t be able to a grid with digits –– 1 through 4 for a 4 × 4 tell the difference. But children born in 200 grid, 1 through 5 for a 5 × 5, 1 through 6 for a years won’t be fooled because they will be 6 × 6, etc. –– so that no digit appears more smarter than me right now and they will easily than once in any row or any column. The detect digital facsimiles of human behavior. grids are divided into heavily outlined groups I realize that we humans are also guilty of of cells called cages and the numbers in the the imitation sin all the time. When a toddler cells of each cage must produce a certain ‘tar- is talking, he is basically trying to imitate his get’ number when combined using the spec- parents and siblings. The toddler has no idea ified mathematical operation. Digits may be what he wants to say. I see this in creative repeated within a cage, as long as they are not artistic work all the time. We are all trying in the same row or column. Single-cell cage to channel a hero of ours whether consciously is a free space. or subconsciously. But it is imitating, or at Here is your KenKen challenge for this is- its best, it is a deep understanding of the cresue of Engineering Quarterly. I hope you en- ative algorithm of our favorite artist. We see joy solving it. The solution can be found at movies trying to be a Pulp Fiction look alike, the end of the issue. or some musician trying to act or sound like Miles Davis ... we see this all the time. But that’s not all that we do.

8+ 1− 3× 10+ In every iteration, in every cycle of imitation, something happens. A spark, a vision, a voice, a fuzzy feeling, that all of a sudden 5 elevates us to a new level of existence. AI can only move in closed circles. We move in upward spirals. During that spiral rise we 24× 5 5+ capture something else from the universe that isn’t ours. Something “external”. We accumulate and incorporate some mass that is not 7+ 15× human into our human minds. We accumulate all kinds of stuff; smell, sounds, chemicals, breeze of air, color, etc. It is very random and 1− you can never expect what you’re going to get.

But most important, it is not of a human origin “yet”. It will soon be after digesting that moment.

5

We do this every minute. We are really good in doing this, or we are very lucky to be able to “do” this, or even for “this” to be done to us. We have been accumulating those little droplets of creativity since the dawn of time. It happens so often that we don’t even realize that it is happening until later. It is so common in our species that we can’t find two humans that think or feel exactly the same way. All through the history of learning, there was always a moment of vision just before that learning moment; there was a small explosion that lead to learning new stuff. AI can definitely learn faster than us, but it lacks that motivation to learn.

Colin Wilson’s entire work was basically a one big investigation into those historical moments where one human accidentally connected to the external energy of the universe.

In that context he goes on saying that a spider is the greatest engineer of our time, but it only builds its home based on a pre-programmed code. It is unable to visualize its web before going out and building it. It is something that the dumbest carpenter on earth can do; visualize something that doesn’t exist...yet.

AUDITORY P ROCESSING

By NANCY KELLY

One of the simplest musical instruments is a small open-topped box with rubber bands stretched across the opening. When plucked or struck, a rubber band will vibrate at a specific frequency that depends on its composition, length, width, thickness, and degree of tension. Taking advantage of this dependence, which is evident in certain flexible materials, a typical stringed musical instrument includes several such strings, chosen and tuned to vibrate at selected frequencies.

A natural structure that can vibrate in this manner is the basilar membrane, which is found deep inside the mammalian ear. The basilar membrane is composed of fibrous tissue whose mass and stiffness both change gradually over its length. This membrane lies within the cochlea, a snail-shaped bony spiral canal located in the inner ear. To produce the sensation of hearing, sound vibrations are transmitted to the cochlea and transduced into electrical activity along the basilar membrane.

This membrane is a tonotopic organ, which means that its response to sound vibrations is both frequency and locationdependent. For example, for high frequencies, the basilar membrane vibrates close to the entrance of the cochlea, while for low frequencies, it vibrates at the other end, towards the

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opening at the top of the cochlea. The frequency mapping is shown in the above Figure. Consequently, the basilar membrane’s vibrations decompose a sound into sinusoids of varying amplitudes and frequencies as different regions of the membrane respond to different frequency ranges. These sound components are mapped to corresponding locations in the primary auditory cortex of the brain, where they are further processed and interpreted.

The resonance behavior of the basilar membrane can be modeled as an array of overlapping bandpass filters, called auditory filters. An example of such a filter bank is shown in the Figure below, although considerably more filters would be needed to accurately model the membrane’s behavior. However, filter bandwidths do increase as center frequency increases, which indicates that the decomposition is more specific at lower frequencies.

The resonance range of the basilar membrane in the human ear is approximately 2020,000 Hz, and, as can be seen from the Figure, filtering is more precise below 5000 Hz. Almost all energy in human speech sounds can be found at frequencies below this threshold, which indicates that speech production and human auditory processing are highly coordinated.

This leads to the question: did human speech develop in such a way as to be more readily processed by listeners, or was it the other way around? Given that the articulators used to produce human speech are so flexible and so readily controlled by their users, while the auditory function of the inner ear is generally inaccessible, the answer is likely that human beings adjusted their way of speaking to accommodate the characteristics of the auditory processing system.

E NGINEERING P UBLIC H EALTH

By TERRY PILLING

The COVID-19 viral pandemic has been declared officially over in a statement made by the Centers for Disease Control and Prevention on May 05, 2023: May 11, 2023, marks the end of the federal COVID-19 PHE declaration. After this date, CDC’s authorizations to collect certain types of public health data will expire. The United States has mobilized and sustained a historic response to the COVID-19 pandemic. As a nation, we now find ourselves at a different point in the pandemic – with more tools and resources than ever before to better protect ourselves and our communities.

Engineering Quarterly SUMMER 2023 While reflecting on the pandemic and on the huge global response from the medical and engineering community: to build temporary medical facilities, manufacturing facilities for masks and medical devices, to care for the ill, and to develop a vaccine, I thought about many other times in the past when the nation’s engineers, medical professionals, and politicians, have worked together, on a vast scale, for the sake of the nation’s public health.

In this article I decided to choose one example that has improved the lives of almost all of us but is, perhaps, not well known to many – the fluoridation of the nation’s public water supply. Water fluoridation has been in the news lately after it was discovered that the City of Buffalo, New York, stopped adding fluoride to its water in 2015 causing residents, in 2023, to instigate a class action lawsuit against the city.

Fluoridation of public water supplies began in the mid-20th century as a public health measure to prevent tooth decay. The history of this practice is complex, and involves both scientific and political elements.

The first hint that fluoride might be beneficial for dental health came from observational studies in the early 20th century. Dentists noticed that people who lived in areas with naturally high levels of fluoride in their water had fewer cavities than people in areas with low levels of fluoride. This led to a series of studies that showed a clear correlation between fluoride concentration in water and dental health.

Dr. Frederick McKay (1874-1959) was one of the first to observe the correlation between fluoride and fewer cavities. McKay was born on March 12, 1874, in Ontario, Canada, and he moved to the United States to study dentistry at the University of Pennsylvania.

After graduating in 1898, he moved to Colorado Springs, Colorado, to open a dental practice.

Shortly after starting his practice, McKay noticed a high prevalence of brown stains (now known as dental fluorosis) on the teeth of his patients. However, he also observed that despite the discoloration, the affected teeth were surprisingly resistant to decay. Curious about this phenomenon, McKay began investigating the cause.

Over the next three decades, McKay and his colleagues studied this condition, which they called “Colorado Brown Stain.”

They initially suspected that the staining was caused by factors such as poor nutrition, overconsumption of pork or milk, or even overuse of locally mined lead and copper.

In 1909, McKay shared his findings at a meeting of dental professionals in Colorado.

His presentation was heard by Dr. Green Vardiman Black, who was a leading dental researcher at the time and is often referred to as the father of modern dentistry. Black was intrigued by McKay’s observations and agreed to work with him to investigate the cause of the Colorado Brown Stain.

McKay and Black, by the 1920s, had begun to suspect that something in the local water supply was responsible for the stains. In 1923, they found evidence to support this hypothesis when McKay learned of a similar condition affecting residents of Oakley, Idaho,

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where a water pipeline from a warm springs had been introduced recently. Further studies in other communities, including Bauxite, Arkansas, confirmed that the water was the source of the problem.

Finally, in 1931, the specific cause of the staining was identified as fluoride by Dr. H. Trendley Dean and his team at the National Institute of Health, who used newly developed methods to measure the fluoride content of water samples.

Dean then initiated studies across the U.S. and found a correlation between fluoride levels in water and dental caries (cavities). Based on these findings, Dean hypothesized that a certain level of fluoride would provide the benefits of cavity prevention without causing fluorosis.

The first trials of water fluoridation were conducted in the mid-1940s in Grand Rapids, Michigan. Before initiating the trials, researchers spent several years collecting baseline data on the dental health of the city’s residents. The results of the Grand Rapids trial were overwhelmingly positive: tooth decay rates dropped significantly in the city, especially among children.

Following these successful trials, other cities began to fluoridate their water, and the practice soon spread across the United States.

The U.S. Public Health Service officially endorsed water fluoridation in 1950.

Throughout its history, water fluoridation has sparked controversies in a similar fashion to the ones we observed surrounding testing, masks, vaccines, etc. during the COVID19 pandemic. With fluoridation, critics raised concerns about the ethics of mass medication, the potential for adverse health effects, and the reliability of the early studies that supported fluoridation. Some people were also simply uncomfortable with the idea of adding chemicals to the public water supply.

The history of water fluoridation provides a clear example of how scientific research can be translated into public health policy. It also highlights the challenges that can arise when implementing such policies. Despite its controversial nature, the fluoridation of public water supplies has led to significant improvements in dental health, particularly in communities with poor access to dental care.

Engineers and engineering companies have played, and continue to play, an important role in the process of water fluoridation.

Water fluoridation requires careful planning, design, and execution to ensure that the right amount of fluoride is added to the water supply consistently and safely. Several different systems can be used to add fluoride to a water supply, including dry additive feed systems, liquid additive feed systems, and systems that use fluorosilicic acid. Each of these systems must be carefully designed, built, and maintained to ensure it operates properly and engineering companies often work closely with municipal water authorities to design and implement these systems.

Fluoride additives used for water fluoridation are derived from phosphate rock. This rock is mined and then processed to make many different products, including fertilizers, animal feeds, and various chemicals used in industrial processes. During the process

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of making phosphate fertilizers, phosphate rock is treated with sulfuric acid to produce phosphoric acid. This process also creates a byproduct gas called silicon tetrafluoride.

This gas is captured and treated with water to produce a liquid product called fluorosilicic acid which is one of the most commonly used additives for water fluoridation. It is shipped in liquid form to water treatment plants, where it is added to the water supply in small amounts.

All of these fluoride compounds are very carefully purified and processed to remove impurities. They have to meet strict quality standards set by the American Water Works Association and the National Sanitation Foundation, which require that fluoride additives do not contain contaminants at levels that could pose a risk to health. These standards are enforced by the U.S. Environmental Protection Agency.

In addition to the practical aspects of water fluoridation, engineers and engineering companies are also involved in researching and developing new technologies and methods for fluoridation. This involves testing different types of additives, developing new types of feed systems, and studying the impacts of fluoridation on various aspects of the water supply system.

Massive public health projects that improve the lives of everyone have occurred since the founding of the country and will continue to occur as advances are made in science, engineering, and medical technology.

Sometimes, as was the case during the pandemic, the engineering, medical, and political response is rapid and highly publicized. Other times the response is slow, measured, and not as well known to the general public. The longterm result, ideally, is the same in both cases – a healthier environment for the nation and its future generations.

B RACHISTOCHRONE S OLUTION

The following are the three times: (Xavier) 1.678s (Yolanda) 1.872s (Zoe) 1.668s Note that the optimal shape for such a track was determined by J. Bernoulli in 1696!

S IGNALS & S YSTEMS S OLUTION

x(t) = 1 − cos

2π π t− 3 2

− 4 cos

5π t 3

S YNCHRONIZED BALLS S OLUTION The following is the code from one of the student solutions.

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synch.c // Compile: // gcc synch.c -lGL -lGLU -lglut -lm #include <GL/gl.h> #include <GL/glu.h> #include <GL/glut.h> #include <stdio.h> #include <math.h> #include <unistd.h> #define Lx 800 #define Ly 800 #define NUM 16 #define SIDES 40 #define RADIUS 30 #define PI 3.1415927 #define dt 0.01 int count = 0; double t=0,R[NUM],T[NUM],X[NUM],Y[NUM], V[NUM],V0[NUM], red[10]= {0.0,0.0,0.0,0.0,0.0,0.0,0.5,1.0,1.0,1.0}, green[10]= {0.0,0.0,0.5,1.0,1.0,1.0,1.0,1.0,0.5,0.0}, blue[10]= {0.5,1.0,1.0,1.0,0.5,0.0,0.0,0.0,0.0,0.0};

void Initialize(void); void display(void); void draw_walls(void); void connect_balls(void); void draw_ball(int, double, double); void move_ball(void); void keys(unsigned char, int, int); int main(int argc, char *argv[]){ glutInit(&argc, argv); glutInitDisplayMode(GLUT_DOUBLE | GLUT_RGB); glutInitWindowPosition(200, 10); glutInitWindowSize(1000, 600); glutCreateWindow("Synchronized"); glutDisplayFunc(display); glutKeyboardFunc(keys); Initialize(); glutMainLoop(); return 0; } void Initialize(void){ glClearColor(0.0, 0.0, 0.0, 0.0); gluOrtho2D(-Lx, Lx, 0, Ly); for (int k=0; k<NUM; k++){ R[k] = 300.0+20.0*k; V0[k] = R[k]/10000.0; V[k] = V0[k]; T[k] = 3.0*PI/4.0; X[k] = R[k]*cos(T[k]); Y[k] = R[k]*sin(T[k]); } } void move_ball(void){ // the time loop tells how many time // steps between each new display for (float t=0; t<60*dt; t+=dt){ for (int k=0; k<NUM; k++){ T[k] += V[k]*dt; // reflect on right boundary if( T[k] < PI/4.0 ) { // reset to original V to synch V[k] = V0[k]; // reset to same theta on opposite // side of wall to keep the timing T[k] = PI/2.0 - T[k]; } // reflect on left boundary if( T[k] > 3*PI/4.0 ) { count++; if (count == 23*NUM ) sleep(5); // reset to original V to synch V[k] = -V0[k]; // reset to same theta on opposite // side of wall to keep the timing T[k] = 3.0*PI/2.0 - T[k]; } X[k] = R[k]*cos(T[k]); Y[k] = R[k]*sin(T[k]); } } } void display(void){ glClear(GL_COLOR_BUFFER_BIT); draw_walls(); connect_balls(); for (int k=0; k<NUM; k++) draw_ball(k, X[k], Y[k]); move_ball(); glutSwapBuffers(); glutPostRedisplay(); } void draw_walls(void){ glColor3f(1.0,0.0,0.0); glBegin(GL_LINES); glVertex2f(-0.75*Lx,0.75*Lx); glVertex2f(0,0); glVertex2f(0,0); glVertex2f(0.75*Lx,0.75*Lx); glEnd();

} void draw_ball(int k, double x, double y){ glColor3f(red[k%10],green[k%10],blue[k %10]); glLineWidth(5.0); glEnable(GL_LINE_SMOOTH); glBegin(GL_LINES); for(int i=0;i<=SIDES;i++){ glVertex2f(x,y); glVertex2f( x+RADIUS*cos(2*PI*i/SIDES), y+RADIUS*sin(2*PI*i/SIDES) ); } glEnd(); } void connect_balls(void){ glColor3f(1.0, 1.0, 1.0); glEnable(GL_LINE_SMOOTH); glLineWidth(2.0); glBegin(GL_LINES); for(int k = 0; k<(NUM-1); k++) { glVertex2f(X[k],Y[k]); glVertex2f(X[k+1],Y[k+1]); } glEnd(); } void keys(unsigned char key, int x, int y){ switch(key) { case ’q’: exit(0); default: break; } }

The code works to reproduce the motion just like the YouTube video but, as you can see, it is not modeling reality. Instead it is designed to produce the synchronized effect.

The students also wrote similar simulations using the laws of projectile motion and found that the synchronized effect does not occur except in very contrived situations. Perhaps you can find a collection of initial heights, initial velocities, and a particular boundary shape which will produce synchronized motion while remaining within the constraints of reality (i.e. without violating the laws of physics)?

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Contact Information To comment on the articles, or to inquire for more information about our engineering program, we welcome you to email: Engineering@umary.edu Next issue: November 2023

VOL.V. . . No.4

Engineering Quarterly SUMMER 2023

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