Engineering Problem Solving

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Engineering Problem Solving
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What Is Engineering?

• Classical answers to this question have included
• Engineering is the application of science and
  mathematics to solve technical problems and
  create new systems, products, or devices to
  benefit civilization.
• The end result of science is new knowledge. The
  end result of engineering is design.
• ABET Engineering is the profession in which a
  knowledge of the mathematical and natural
  sciences gained by study, experience, and
  practice is applied with judgment to develop ways
  to utilize, economically, the materials and
  forces of nature for the benefit of mankind.

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What Is Engineering?

• Classical answers to this question have included
• Engineering is the application of science and
  mathematics to solve technical problems and
  create new systems, products, or devices to
  benefit civilization.

Does this make sense? If someone is working on a
nuclear weapon, and we decide that is not a
benefit to civilization, does that make that
person not an engineer?
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What Is Engineering?

• Classical Answers to this question have included
• Engineering is the application of science and
  mathematics to solve technical problems and
  create new systems, products, or devices to
  benefit civilization.

Does this make sense? If someone can solve a
technical problem without using science and
mathematics, does that mean that person is not an
engineer? Yes, typically we do use them, but
also the engineer will typically breathe while
doing so. We dont put that in the definition.
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What Is Engineering?

• Classical Answers to this question have included
• Engineering is the application of science and
  mathematics to solve technical problems and
  create new systems, products, or devices to
  benefit civilization.

Does this make sense? Dont technicians and
technologists solve technical problems? How do
we tell an engineer from a technician? Our
definition should tell us this.
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What Is Engineering?

• Dr. Daves answer to this question is
• Engineering is technical problem solving,
  specifically the solving of problems that have
  not been solved before.
• Technology is technical problem solving,
  specifically the solving of problems that have
  been solved before.
• Science is knowledge gaining.
• It is easy to confuse science with engineering,
  because
• Scientists have to solve problems to gain
  knowledge.
• Engineers typically gain knowledge to solve
  problems.

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The Technological Team

• Scientist Engineer Technologist
  Craftsperson
• Theory lt------------------------------------------
  ----gtPractice

This spectrum of theory versus practice is often
used to define the fields. It does not define
the fields, it is the result of the differences
in the goals of the individuals within the
fields. The goals define the fields, not the
characteristics that follow from the goals.
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Problem Solving

• ... is the foundation of all engineering
  activities.
• ... is the process of determining the best
  possible action to take in a given situation.

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Two Types of Problems Analysis and Design

• Analysis Problems - closed-ended problems which
  determine the properties of a given device or
  system, and generally have only a single correct
  solution.
• Design Problems - open-ended problems to create a
  system or device that has given properties, and
  generally have multiple correct solutions.
• A formal, systematic problem-solving methodology
  is useful for both types of problems.

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Analysis Problems
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The Analysis Process - 5 Steps

• 1. Define problem - diagram or sketch is good.
• 2. Collect information - data, theories,
  assumptions, approximations.
• 3. Generate a solution - maybe several possible
  ways.
• 4. Refine and implement - use a tool
  spreadsheet, MATLAB, or other computer
  program/language.
• 5. Verify and test - estimate, work another way,
  try other data input, compare with a plot, check
  dimensional consistency.

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The Analysis Process - 5 Steps This time in
English

• 1. Understand and analyze the problem
• diagram or sketch is good
• 2. Collect information
• data, theories, assumptions, approximations
• 3. Develop algorithm(s) for a solution
• might want to try several possible ways
• 4. Implement and refine the implementation
• use a tool pencil paper, calculator,
  spreadsheet, MATLAB, etc.
• 5. Verify and test
• estimate, work another way, try other data input,
  compare results with a plot, check units

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The Analysis Process - What is an algorithm?

• 1. Understand and analyze the problem
• diagram or sketch is good
• 2. Collect information
• data, theories, assumptions, approximations
• 3. Develop algorithm(s) for a solution
• might want to try several possible ways
• 4. Implement and refine the implementation
• use a tool pencil paper, calculator,
  spreadsheet, MATLAB, etc.
• 5. Verify and test
• estimate, work another way, try other data input,
  compare results with a plot, check units

An algorithm is an ordered set of steps for
solving a problem - Unambiguous - In
sequence - Solves the problem - Terminates
after a finite number of steps
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Problem-Solving Tools

• Calculator, pencil, and paper
• Electronic spreadsheet
• Math software
• Programming languages

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Example Typical math word problem

• 1. Understand and analyze the problem
• Bill is shopping for some carpet for his den,
  which is 12 x 18 feet. The carpet he likes is
  20 per square yard. He has 500 to spend.
  After purchasing the carpet, will he be able to
  purchase a 5 Happy Meal with the money left
  over?

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Word Problem (contd)

• 2. Collect information
• 500 available
• 20 per square yard
• 9 square feet per square yard

18 ft 6 yds
12 ft 4 yds
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Word Problem (contd)

• 3. Develop an algorithm
• Find dimensions of room in yards.
• Find area of room in square yards.
• Multiply by cost of the carpet per square yard to
  get total cost.
• Subtract total cost from money available.
• Is remainder enough for Happy Meal?

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Word Problem (contd)

• 4. Implement and refine the implementation
• Compute steps using a pencil and paper, or a
  calculator.
• 12ft 4 yd, 18ft 6yd
• Area 4yd 6yd 24 sq yd
• Total cost 20 per sq yd 24 sq yd 480
• Leftover 500 - 480 20
• Compare 20 gt 5 ?
• Yesbuy the meal!

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Word Problem (contd)

• 5. Verify and test
• Rework problem in feet, rather than yards.
• Estimate and compare
• 12 x 18 is close to 10 x 20 200 sq ft
• 200 sq ft is close to 20 sq yds
• 20 sq yds times 20 each is 400
• This is the same order of magnitude as our 480
  answer.
• Estimates are used simply to check whether your
  answer makes sense.

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Example Maximum Height of a Projectile

• 1. Understand and analyze
• A snowball is tossed straight up in the air with
  an initial velocity of 100 ft/sec. The moment it
  leaves the throwers hand it is 6 ft above the
  ground. What is the maximum height reached by
  the snowball?

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Example Maximum Height of a Projectile

• 2. Collect information
• no wind resistance or friction constant downward
  acceleration due to gravity
• h(t) h0 v0t - 0.5gt2

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Example Maximum Height of a Projectile

• 3. Develop an algorithm
• Take derivative of h(t)
• Solve h(t)0 for tmax
• Plug tmax into h(t) to determine height

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Example Maximum Height of a Projectile

• 4. Implement algorithm
• h(t) v0 gt
• h(t) 0 ? tmax v0/g 3.11 sec
• h(tmax) h0v0tmax-0.5gtmax2
• 165.3 ft

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Example Maximum Height of a Projectile

• 5. Verify test
• Is it reasonable? Are the units correct?
• Make a table of t and h values
• t in s h in feet
• 0 6
• 1 89.9
• 2 148.1
• 3 161.1
• 4 148.4

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Communicating Solutions

• All solutions should be clearly labeled,
  documented, and commented.
• Standards will be followed in this course for
• Spreadsheet solutions
• MATLAB solutions

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Spreadsheet Solutions

• Provide standard labeled sections.
• Use separate, labeled sheets to divide the work
  logically.
• Label columns, rows, important cells.
• Use (but dont overuse) color to delimit ranges
  in a consistent way.
• Use named ranges - carefully.

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MATLAB Solutions

• Provide standard labeled sections.
• Insert comments or subsection headings liberally.
• Choose meaningful, consistent variable names.
• Entire program should execute correctly from the
  top.

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Design Problems
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The Design Process - 5 Steps

• 1. Define the problem.
• 2. Collect information.
• 3. Generate multiple solutions.
• 4. Analyze and select a solution. (Use a tool.)
• 5. Test and implement the solution. (Use a
  tool.)
• This is a contingent, iterative process.

There is an alternative view on design. Lets
look at design again in a different way.
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Define the problem
Test implement a solution
Gather information
Engineering Design Process
Generate multiple solutions
Analyze select a solution
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Design is a Circle

• Invention is where poetry and engineering come
  together. It is a creative endeavor where the
  heart beats faster with each intuitive leap, yet
  success is measured by the stern, unforgiving
  ruler of the Scientific Method. Its not a
  predictable process you never march a straight
  path to your goal. Instead, you crisscross the
  same ground over and over again as you search for
  the answer that youre sure is there somewhere.
  Every successful invention is the result of false
  starts, dead ends, disappointments, self-doubt,
  perseverance, and the elation that comes when
  your faith in yourself is at last rewarded.
  Nowhere is this more evident than in the tale of
  the invention of the airplane. (From
  http//www.first-to-fly.com/History/inventin.htm)

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Design is a Circle Try and Try Again

• When you design something, you try something that
  you think will work.
• Usually, it doesnt.
• Then, you try again, using what you learned in
  your first try.

This is design!
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The Design Process

• The design process is an iterative process. You
  try again and again.

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Design Means Work

• Invention is 10 inspiration, and 90
  perspiration.

The conclusion? Engineers smell bad?
No, the conclusion is that there are many steps
and skills involved.
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The Design Process

• The design process includes analysis. These
  steps are analysis, and can be done physically,
  on paper, or on a computer.

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• Not everything that the Wrights did was a
  success. Of the seven aircraft that they built
  from 1899 to 1905, only two worked well enough to
  be flown any length of time -- the 1902 glider
  and the 1905 Flyer 3. Some, like the 1901 glider
  (above) were dismal failures. (From
  http//www.first-to-fly.com/History/inventin.htm)

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Wright Brothers Gain Knowledge to Solve Problems

• Wilbur and Orville decide to carry on. They test
  wing shapes to get more lift. This was an early
  test, using a bicycle.

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Wright Brothers Gain Knowledge to Solve Problems

• They test over 200 wing shapes in a wind tunnel
  to find which ones produce the most lift. The
  wind tunnel is shown here.

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Wright Brothers Gain Knowledge to Solve Problems

• Wilbur and Orville test over 200 wing shapes in a
  wind tunnel to find which ones produce the most
  lift. They even have to design the wind tunnel.
  The brothers build a new glider based on the
  results.

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Wright Brothers Gain Knowledge to Solve Problems

• Wilbur and Orville test over 200 wing shapes in a
  wind tunnel to find which ones produce the most
  lift. They even have to design gadgets to be able
  to test their wing shapes in the windtunnel.

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The Result A Flying Machine

• The result of their guess and test method was the
  first airplane. We try to teach this guess and
  test method in engineering.
• Guessing is often glorified, and does require
  experience and a little bit of inspiration.
• Testing, though, often takes longer. This is
  easier to teach, though by no means easy.

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Wilbur and Orville were a Design Team
The results are, as they would say, history.