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MARCH 2014

Equations in Engineering Practice Colin SelleCk

Knovel Know More. Search Less. Equations in Engineering Practice Colin Selleck

knovel introduction

The Knovel White Papers are a series of thought provoking presentations that address important issues facing the world of engineering. Each white paper is authored by a leading contributor seeking to advance the discussion by offering new insights and practical knowledge.

This white paper provides a brief history of equations and the practical applications of equations in engineer-ing practice. We hope that the perspective of this white paper will help to deepen your understanding of why equations are critical to engineering practice and, hence, why today’s engineers need the tools to effectively develop and use equations across the multitude of disciplines they serve.

Meet The Author

Colin Selleck received his B.S. in Mechanical Engineering from Louisiana State University in 1978 and his M.S. from the same institution in 1980. He then began his career at Sandia National Laboratories in Albuquerque, NM where he developed some of the first computer graphics user interfaces that gave engineers and scientists the ability to graphically visualize the results of complex finite element analyses.

In 1987, Selleck joined a newly-formed robotics department at Sandia and was a member of a team that developed the first robotics-based radiation inspection systems for nuclear waste transportation containers. The system was one of the first to program a robot to touch an object by using a force sensor to detect contact. Selleck’s contribution was the development and programming of computer vision algorithms that lo-cated the container as it arrived on trucks at the waste storage facilities.

In 1990, Selleck began designing and coding geometry sensors based on a structured lighting technique that used lasers and cameras to scan objects and build 3D maps. These maps were used to plan safe and efficient ro-bot motions while operating in unknown environments. This was especially critical in tasks such as remediating nuclear waste and deploying robots into hazardous situations.

Selleck left Sandia in 1997 and began consulting with the University of New Mexico’s Manufacturing Engineering robotic laboratory that performs research in coordinated robot motion, simulation-based system realization, optimal grasp planning, trajectory generation, and mobile navigation.

Since 2006, Selleck has been a lecturer in Mechanical Engineering at Binghamton University where he teaches robotics, measurements and instrumentation, and senior capstone design. He is a member of two engineering honorary societies: Tau Beta Pi and Pi Tau Sigma.


equations in engineering Practice

It is undeniable that equations have greatly influenced the course of humanity, beginning 2300 years ago when Pythagoras developed his infamous theorem that led to surveying, map making, geometry, and eventually to the non-Euclidian dimensions that Einstein used for his ground-breaking theorems. In the West, the cultural awakening of the Renaissance saw an increased interest in observing and modeling the natural world, driven by the insatiable curiosity of our species and the realization that these models eventually foster the inventions that have so rapidly changed the landscape. These include telescopes to reach the stars, machinery to produce foods and fabrics, sailing ships to promote trade and exploration of the Earth, and power generation to fuel it all. The crucial introduction of the Gutenberg printing press enhanced the dissemination of this newly-acquired knowledge with a rapidity never before seen, allowing truths and ideas to flow across the continents. Eventually came the farms, buildings, roads, and bridges that provided food, shelter and the means of swift mobility, all for a fraction of the time and energy humanity was accustomed to expending just to stay fed and warm.

In this crucible of idle time and protection from the elements, humanity began unravelling the intricacies of our world and, most importantly, modeling nature using equations that predicted future outcomes. Great advances in knowledge were enabled by the perfection of the scientific method and its tenets of observation, hypoth-esis, prediction, experimentation, and analysis that are structured in such a way that it has become the only process of discovery that has yielded powerful and world-changing results in the fields of physics, chemistry, astronomy, and the life sciences. For this scientific method has woven into its very fabric the ability to self-correct its course over generations as new and more accurate experiments and theories are developed. The hallmark of this method is the realization that no theory is so complete that it cannot be falsified and genuine scientists are continually trying to expose flaws in existing theorems, including their own, occasionally to the point of breaking into vast new intellectual domains. To the uninitiated, it may seem as if the method itself is flawed as there is no unequivocal final answer, but the truth of the matter is that complete knowledge is not only impossible, but in fact undesirable, as unknowns continually drive the search for new ideas and theories.

An examination of an equation (e.g., E = mc2) will reveal the presence of symbols (usually denoted by Greek or Latin letters), numbers, and operators that define relationships between these entities. In pure mathematics, the symbols represent abstract concepts far removed from the natural world, and only the operational rules between symbols and the techniques for constructing and solving equations are defined. Out of pure mathematics arise the sophis-ticated tools and techniques that allow engineers and scientists to construct intricate models with some inkling of how to actually solve the equations contained therein. For engineers and scientists, these symbols represent any-thing from a physical phenomenon to an abstract concept, and each has not only a numerical value, but also a unit constructed from the fundamental units. Each of the latter is based on a single perceived physical phenomenon and is well-defined to a high degree of precision. The fundamental units include length, mass, time, temperature, current, and luminosity, with units of meter, kilogram, second, kelvin, ampere, and candela respectively.1

one must divide one’s time between politics and equations. But our equations are much more important to me, because politics is for the present, while our equations are for eternity. – Albert einstein

“ “The International System of Units (SI) also defines the mole or quantity of substance as a fundamental unit, but this was created to ease the calculations of chemistry and can easily be eliminated by using Avogadro’s constant. Regardless, it is not based on a perceived physical phenomenon as the other fundamental units are.

1


The other important component of an equation is revealed by the very word equation: the equals sign. In use since the mid 16th century, it represents “is equal to” and reveals the heart of building physical models with equations: de-veloping new concepts or re-visualizing old ones, isolating variables while ignoring others, mixing in universal con-stants such as the speed of light or the gravitational constant, and arranging them mathematically so that each side of the equals sign is the same in value and units. This is followed, of course, by verifying the new equation through reproducible experimentation and only then is the equation accepted into the canon of knowledge for all to use.

It comes as no surprise that equations are widely used in engineering practice across many different fields. Engineers use equations not only to predict but also to parameterize their designs, such as calculating the size of a structural member or choosing capacitance values on a circuit board. As shown in Figure 1, studies performed by Chestnut Hill Advisors in 2010 and 2013 reveal that a majority of engineers need an equation at least once a week and one third need an equation at least once a day.

Figure 1. Frequency of equation use by engineers

One area that has many thousands of equations is calculating stress and strain in components, structures, and bridges. These calculations allow designers to properly size their designs so that the costs of production are minimized while still building a safe and useful product. Many of these equations have been empirically derived from laboratory testing over generations and are meticulously catalogued.

Finite element analysis (FEA) use is prevalent and at its root are the equations of state that define thermodynamic properties. It should be noted that while FEA is available in all computer aided design software, it can lead to incorrect analyses as FEA can become unstable, especially near areas of high stress concentration. One would be well-advised to also search for the appropriate equations and perform hand calculations to verify the results of any FEA analysis.

HOW OFTEN DO YOU NEED AN EQUATION?

Source: Chestnut Hill Advisors, 2013

2010 2013

5

10

15

20

25

30

35

40%

onCe A montH onCe A WeeK >onCe A WeeK >onCe A DAY

18 1713

25

323135

30


The oil and gas industry uses equations in the sizing of pumps and pipes and in the design of refineries and storage facilities. Equations are also used in the field to predict well bore pressures and temperatures, allowing engineers to optimize the production system. Much effort has also been put into creating equations of state of fluids that allow engineers to predict the behavior of oil and gas as it makes it way from the well to the consumer. Equations are also used in the exploratory phase to estimate how much oil is available in a newly-discovered reservoir.

The production of chemicals, which are the raw materials of the technology engine, also requires equations in many different areas. Mass and energy balance of chemical processes are essential to designing optimal production facilities. Equations are also used in calculating reaction rates, phase equilibrium, chemical reactor design, and minimizing air and water pollution.

The electronics industry uses equations in circuit design, packaging, and in designing techniques to remove heat from high-speed processors. The design of new instruments, gaming consoles, home entertainment compo-nents, power electronics, computers, sensors, and data acquisition systems all depend heavily on equations.

Where do engineers find the many equations they need to do their job efficiently and correctly? Not surpris-ingly, 78% use a website, and this is on the rise, having increased 19 percentage points since 2010 (see Figure 2). This reveals the double-edged sword of the worldwide web – while it is quick, easy to use, and accesses an astounding amount of data, the vast majority of the information available is not peer-reviewed. This problem is not unique to engineers: everyone from students to professionals across many fields are accessing data that may be incorrect. Before the creation of the worldwide web, peer-reviewed books, periodicals, and journals were the only source of equations, and while that may be inconvenient for many reasons, the information they contained could be used with a high level of confidence.

Figure 2. Source of equations for engineers

HOW DO YOU FIND THE EQUATION?2010 2013

20

40

60

80

100%

LooK UP FInD It on FInD It on PReVIoUS ASK PReVIoUS SAVeD on PRInteD teXt WeBSIte ComPAnY eLeCtRonIC CoLLeAGUe PRInteD eLeCtRonIC

IntRAnet DoCUment LISt DeVICe

79

59

79 78

62

42 46 45

29

6357

2816



This can be a problem, as engineers must validate their work as what they do will likely affect people and prop-erty in one way or another, even causing injury or death. Engineers and their employers are typically aware of this danger. Figure 3 shows that even though the web was the source of the equation, only 4% use a website to validate their work. The three most common ways of validation are committees of peers, codes or best practices, and other calculation programs.

Figure 3. How engineers get their work validated

What tools are engineers using to archive their results? Figure 4 shows that 87% save their calculations on their hard drive, though it should be noted that cloud storage is on the rise, probably because data can be accessed from almost anywhere as long as there is an Internet connection.

Since Excel is so universally used, it is not surprising that 84% use it to share their calculations with colleagues, as shown in Figure 5. Creating and debugging Excel worksheets is time-consuming and prone to errors, be-cause the equations are not presented legibly as one would see in a text book, but are encoded in an arcane language that is unreadable.

HOW DO YOU GET YOUR WORK VALIDATED? (2013)SometImeS moSt oFten

50 45 40 35 30 25 20 15 10 5

%

CommIttee CoDeS/BeSt AnotHeR SPeCIALIzeD CA oR ComPARe teSt In otHeR oF PeeRS PRACtICeS CALCULAtIon SoFtWARe ComPLIAnCe on WeB A LAB

PRoGRAm (e.G. FeA)

46 46

34

24 22 22

1215

2620

128

18

4 48



Figure 4. How engineers save their calculations

Figure 5. How engineering results are communicated to others

HOW DO YOU SAVE YOUR CALCULATIONS FOR FUTURE USE? 100 90 80 70 60 50 40 30 20 10

%

mY HARD DRIVe oUR Km PoRtABLe PRInt & FILe emAIL CLoUD-BASeD Do not SAVe

83

24 23 23 20

6 2

87

2718 18

2113 1

2010 2013

SYStem meDIA ARCHIVe

HOW DO YOU DELIVER YOUR CALCULATION WORK TO OTHERS?2010 2013

90 80 70 60 50 40 30 20 10

%

USe eXCeL USe WoRD USe PoWeR USe CALCULAtIon USe emAIL USe otHeR Don’t neeD PoInt PACKAGe to DeLIVeR

73

34

84

3833

27 2518

6

35

196 5 2




Finding the right equation is important, but subsequent tasks such as validating and archiving are equally so. It would seem that demand exists for engineering content/service providers to create new leading-edge products that allow engineers to easily find equations, then calculate, validate, share, and store their work. From these data it would seem the most useful tools for an engineer would include the following:

•Peer-reviewedandcomprehensiveequationswithexplanatorytext. •Searchtoolstoquicklyfindtheappropriateequationandrelevanttext. •Downloadableworksheetthathastheequationalreadyenteredandasampleproblemworkedout. •Web-basedsymbolicequationsolverthatpresentsequationsinatextdocument. •ExportofPDFsoftheworksheettoshareworkwithcolleagues. •Archiveofresultslocallyorinthecloud(ifsecurityconcernsallow)forlaterretrievaltosolvenew problems or to review and validate work.

The development and use of equations by engineers and scientists has a rich history built on many hours of research and experimentation performed by colleagues from across the globe in a multitude of disciplines. This has resulted in vast stores of knowledge that can be drawn upon to assist in the design and production of all the modern conveniences that humanity has come to depend upon. As it stands, today’s engineers do not have all the tools to efficiently mine this knowledge to accomplish their required tasks of search, calculate, document, validate, and archive. But with ever-expanding technological advances and increasing demand for peer-reviewed and accurate information, it can only be a matter of time before this is realized, and, if wisely used, engineers – and thus the world – can only benefit.


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About knovel

Knovel is a cloud-based application integrating technical information with analytical and search tools to drive innovation and deliver answers engineers can trust. Knovel users include hundreds of thousands of engineers and applied scientists worldwide. Knovel has more than 700 customers worldwide including 74 of the Fortune 500 companies and more than 400 leading universities. Knovel was acquired by Elsevier in January 2013. For more information, visit www.knovel.com or call (866) 240-8174.

About elsevierElsevier is a world-leading provider of scientific, technical and medical information products and services. The company works in partnership with the global science and health communities to publish more than 2,000 journals, including The Lancet and Cell, and close to 20,000 book titles, including major reference works from Mosby and Saunders. Elsevier’s online solutions for engineers include ScienceDirect, Scopus, Reaxys, Geofacets, Engineering Village and now, Knovel.

A global business headquartered in Amsterdam, Elsevier employs 7,000 people worldwide. The company is part of Reed Elsevier Group PLC, a world-leading provider of professional information solutions in the Science, Medical, Legal and Risk and Business sectors, which is jointly owned by Reed Elsevier PLC and Reed Elsevier NV. The ticker symbols are REN (Euronext Amsterdam), REL (London Stock Exchange), RUK and ENL (New York Stock Exchange).

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