Chapter 6 Problem Solving. Chapter 5 Summary Types of Problems Analytical Problem Solving Estimations Creative Problem Solving Brainstorming

Chapter 6

Problem Solving

Chapter 5 Summary

Types of ProblemsAnalytical Problem Solving Estimations

Creative Problem Solving Brainstorming

Recall “Engineering” DefinitionFunctional Description: Short Answer = Technical PROBLEM

SOLVING The Output of ALL Engineering is

The Solution to a Practical Problem Fulfillment of a Practical Need

Long Answer = PRACTICAL-PROBLEM SOLVING Through the Application of the Quantitative (Number-Based) Disciplines Mathematics Sciences; e.g., Physics, Chemistry, Biology Empiricism (Experiments and Tests)

Class Exercise

What IS a Problem? i.e., DEFINE “Problem”

1. ?2. ?3. ?4. ?5. ?6. ?

What is a “Problem”

A Problem Short Definition: is Any Question or

Matter Involving Doubt, Uncertainty or Difficulty

Long Definition: is a situation, quantitative or qualitative, that confronts an individual or team, that requires resolution, and for which the individual/team sees NO APPARENT PATH TO THE SOLUTION

Types of Problems

ResearchKnowledge/UnderstandingTroubleshootingMathematicsResourceSocialDesign

Classes of Problems…detail

Scientific Research Prove/Disprove a hypothesis (explanation)

Example: A scientific hypothesis may be that Room Temperature Superconductivity is Produced by a Specific Molecular-Electronic Configuration of Rare-Earth Ceramic Materials

Understanding Example: an engineer notices That a CVD

Machine Behaves Differently In Denver Than in Kyushu

http://images.google.com/imgres?imgurl=http://www.zolo.com/DESIGN/hypothesis.gif&imgrefurl=http://www.zolo.com/hypothesis.html&h=292&w=297&sz=5&tbnid=iNynFunt_FQJ:&tbnh=108&tbnw=110&start=3&prev=/images%3Fq%3Dhypothesis%26hl%3Den%26lr%3D

Classes of Problems cont.Trouble Shooting The Video Output of an Inspection

MicroScope Works Fine With “composite” (single-cable) Video Signals, but “S” (Super VHS or 2-cable) Video Signals Produce a BLACK Screen

Math Problems Find Pv that Satisfies This

Equationt

P

Dr

Pr

rrv

v

v

11 2

2

Digression – Soln to Math Prob

Liquid Source Vapor Bubble Saturation Transient

0.0

0.2

0.4

0.6

0.8

1.0

0.0 0.3 0.5 0.8 1.0 1.3 1.5 1.8 2.0 2.3 2.5

Radial Position Inside Bubble, r (mm)

Va

po

r S

atu

rati

on

Fra

cti

on

, v

Pv(r,t) (t=0.01 s)Pv(r,t) (t=0.04 s)Pv(r,t) (t=0.10 s)Pv(r,t) (t=0.15 s)Pv(r,t) (t=0.25 s)Pv(r,t) (t=0.35 s)Pv(r,t) (t=0.50 s)

file = BubPv(t)1.xls

• Bubble Diameter = 5 mm

• D for TEOS in N2 = 0.05 cm2/s Increasing Time

P r t

n r rn r r

evn o

o

n Dt r

n

o,sin

1 2 1 1

1

2 2 2

Classes of Problems cont.$-Resource Problems e.g.; How Will We Get The Money to

Fund our Start-Up Company?

Social Problems Example: How to Reduce Crime

Rates?

Design Problems e.g.; Design a New, Inexpensive,

Easy-to-Use, Attractive, Lightweight, Wireless Headset for Cell Phones

11

Common Engineering ProblemsCommon Engineering Problems Engineering Problems Generally Fall

into Two Broad Categories• Analytic• Creative

Analytic Problems (bridge failure load)• There is one correct answer• Involves math, number crunching,etc• Your toolbox

Creative Problems (design a bridge)• No one right answer• How you use your tools

12

Design ProblemsDesign Problems

Require The Maximum Application of Engineering Capability• Creativity

• Quantitative & Graphical Skill

• Teamwork

• Technical Knowledge

See also: http://www.asa3.org/ASA/education/think/intro.htm

13

Creative Problem Solving Creative Problem Solving 1. Identify problem2. Define goals3. Research similar attempts4. Brainstorm (team or individual)5. Analyze analytic problem solving here6. Develop models and test7. Make decision8. Communicate with team, specify9. Implement, commercialize10. Prepare post-implementation review and

assessment

Analytic Problem Solving

1. Drawing2. List Known Parameters3. Label Unknowns4. Equations5. Answer with Units

Example Problem

1. Drawing2. List Known Parameters3. Label Unknowns4. Equations V = Vo - gt ( g = 9.8

m/sec2 )5. Answer with Units

How long will a 0.058kg tennis ball be in the air if it is thrown upward at 45.7m/s?

Some Helpful Equations

Radius of a Circle or Sphere: rDiameter of a Circle or Sphere: d=2r Circumference of a Circle: S = 2r = dArea of a Circle: A= r2

Volume of a Sphere: V = (4/3) r3

Surface Area of a Sphere: A = 4r2

Volume of a Cylinder: V = hr2

Surface Area of a Cylinder: A= 2r2 + 2hrPythagorean Theorem: c2 = a2 + b2

Engineering Exercise

You are asked to build a storage tank for 22 cubic meters of gasoline.You want to use the least amount of metal to keep your construction costs low. Suppose that you use 1-centimeter thick steel sheets to create storage tanks.

Engineering Exercise (con’t)

If you had a tank in the shape of a cube, then how long would each side be?What would be the inner surface area of the tank?How much metal would you need (volume)?

Engineering Exercise (con’t)

If you had a tank in the shape of a sphere, then what would its radius be?What would be the inner surface area of the tank?How much metal would you need (volume)?

Engineering Exercise

If you had a tank in the shape of a cylinder, then what would its radius be?What would be the inner surface area of the tank?How much metal would you need (volume)?

Aha! We will need to make some assumptions.

TEAMWORK

Each team will now make a different assumption and record their results on the table on the chalkboard.

Who uses the least metal for the cylindrical tanks?

Team h r A Vmetal

1 h=0.5r2 h=1r

3 h=1.5r

4 h=2r

5 h=2.5r

6 h=3r

7 h=3.5r

8 h=4r

Recorders: To the chalk board…

Write down your team name.Write down your assumption about the connection between h and r.Write down the equation for the volume of a cylinder.Substitute.Solve for r.Find A.Find the volume of the metal. Vmetal

Optimization?Height=2 Radius

0

0.1

0.2

0.3

0.4

0.5

0.6

Vo

lum

e (

Cu

bic

Me

ters

)

0.5 1 2 3 4 5 6 7

Height to Radius Ratio

Cylindrical Tanks

How do we know that h=2r is the best?

1. We can use trial-and-error.2. We can prove it using calculus.

Estimation – a subset of analytical problems

Quick answers, when quick decisions needed (out in the field)Verify complicated analysisGain insight into issues involvedHow to “break in” young engineers!Ben Franklin estimated size of a molecule In the 18th century!

Estimation #1

Team Exercise Estimate How many Ping Pong balls can fill

this room (3 minutes)1. Drawing2. List Known Parameters3. Assumptions important!4. Label Unknowns5. Equations6. Answer with Units

Estimation #2

Team Exercise Estimate the speed of hair growth in

miles per hour. (3 minutes) What would be a more appropriate

unit for the speed of hair growth? Design an experiment that could

better estimate the speed of hair growth. (1 minute)

Back of the Envelope Calculations

A crude but educated guessWe estimate not only the values of numbers we need, but which numbers are appropriate, and how to perform the calculation the emphasis here is on “order of

magnitude” estimates – to the nearest factor of 10

it is also important to remember that these are rough estimates and to place only appropriate reliance on the results

Accuracy of calculationsA well-known curve of a calculation’s accuracy versus mental effort goes like:

% error

effort

errors in various assumptions cancel out so rapid apparent improvement is made

better understanding may actually make things worse

hard work means that the model yields improved results

R. HornseyBOTE 31

How many piano tuners live in NYC? Approximately how many people are in New York City?

10,000,000 Does every individual own a piano?

No Would it be reasonable to assert that "individuals don't tend to

own pianos; families do? Yes.

About how many families are there in a city of 10 million people?

Perhaps there are 2,000,000 families in NYC. Does every family own a piano?

No. Perhaps one out of every five does.

That would mean there are about 400,000 pianos in NYC.

R. HornseyBOTE 32

How many piano tuners are needed for 400,000 pianos? Some people never get around to tuning their piano; some people tune

their piano every month. If we assume that "on the average" every piano gets tuned once a year, then there are 400,000 "piano tunings" every year.

How many piano tunings can one piano tuner do? Let's assume that the average piano tuner can tune four pianos a day.

Also assume that there are 200 working days per year. That means that every tuner can tune about 800 pianos per year.

How many piano tuners are needed in NYC? The number of tuners is approximately 400,000/800 or 500 piano

tuners.

[email protected] • ENGR-10_Lec-16_Problem_Solving.ppt33

Bruce Mayer, PE Engineering-10: Intro to Engineering

BrainstormingBrainstorming – for creative – for creative problem solvingproblem solving

Definition of Brainstorming Different types of Brain Storming Ways to create effective Brainstorming How Brainstorming can be used



Importance of BrainstormingImportance of Brainstorming

Increases ability to figure out different ways in which to cure or solve a problem• Can Yield Unexpected and Elegant

Solutions

Allows opportunity for synergism within a company or organization• Whenever Possible, Make the Session

Cross-Disciplinary



BrainStorm(ing) DefinedBrainStorm(ing) Defined

BrainStorm• A sudden clever Plan or idea,

violent disturbance of the mind

BrainStorming• A CONFERENCE technique of Solving

Specific Problems, Amassing information, Stimulating Creative Thinking, Developing New Ideas by Unrestrained and Spontaneous Participation In Discussion



Types of BrainstormingTypes of Brainstorming Individual

• Completely Private & Open– Don’t have to worry about

any one else's opinion

Group• Builds team unity • Use Other Peoples Ideas as “Jumping Off”

Points – a “NonLinear” Process• Helps To Create “Outside The Box”

Thinking



¿¿¿¿Question??Question?? Has Anyone in the Class been Involved

in a Formal “BrainStorming” Session?

If So, can you briefly describe what happened?

Thanks so Much



Effective BrainstormingEffective Brainstorming

Brainstorming is “Free Form”• But Without Proper Structure It can Lose

Focus and Wander off Track

At Session-Start Present the ISSUE and outline GROUND RULES• Yields more effective use of time

• Allows Everyone in the group to start thinking about the REAL ISSUE



Rules of BrainstormingRules of Brainstorming

1. Stress quantity over quality• Want the Maximum Number of Ideas

2. Freewheeling should be encouraged• Want Violent Mind Disturbances

3. Suspend judgment • Negative Comments Inhibit The

Freewheeling Atmosphere

4. Ignore seniority• Everyone’s Ideas Have Equal Value



BrainStorming CheckListBrainStorming CheckList

Proposed change Description

Substitute

Combine

Adapt

Modify, magnify, minify

Other uses

Eliminate

Rearrange, reverse

What is used: material, process, person place or approach ?

Could units/systems be combined

What else is like this, what can I copy, Does it suggest other ideas

Could I change meaning, color, form or shape? Can something be subtracted?

Are there new ways to use this ?

Can a part, function, person be removed ?

Can components be interchanged, can it be transposed, turned upside down ?



BrainStorming Session BrainStorming Session Start with a specific statement of problem Allow all members time to assimilate problem Ask each member in turn Build on ideas, allow wild and wacky ones Write ideas down, do not interrupt flow

• WhiteBoard or FlipChart

When group is exhausted of ideas, go back and clarify• Prioritize Ideas Only

– Avoid Negative Comments if Possible



Brainstorm an idea for a Final ProjectBrainstorm an idea for a Final Project

Should take no more than 20 hours to complete

Should cost no more than $15 in materials

Open ended -- a variety of solutions Fun to do Competitive in terms of performance Examples from past classes…



Motivate the BrainStromersMotivate the BrainStromers

Reward the group for coming up with solution or new idea• Money talks

• Time off

Make it an “experience”• Provide Refreshments

• No Time Limits

• Professionally Uninhibited Environment



Create an Effective AtmosphereCreate an Effective Atmosphere

The Normal Work Environment can be• Unconsciously Inhibiting

• Certainly Distracting (phones, eMail, etc.)

Leave work premises – Be Creative• Manager’s Home

• Roaring Camp Small-Gage RailWay

• A Different Company Facility

Take ROUTINE away from the situation



BrainStorming SummaryBrainStorming Summary

Brain Storming Is Effective When Done Right• Can be A WASTE OF TIME if Done Wrong

Can help to create Team/Org Unity Helps to Take Routine Away From The

Office – Encourages New Thinking New Ideas Get Generated For Possible

Solutions

Documents

Chapter 6 Problem Solving. Chapter 5 Summary Types of Problems Analytical Problem Solving Estimations Creative Problem Solving Brainstorming