Team Exercise

If you have enough money to buy a car, what kind of car do you like to buy?

If you are a car design engineer, identify design goal and design parameters from your team’s preference

Taken from - http://homepages.stmartin.edu/

ETP 2005 – Dan HoustonThis material is based upon work supported by the National Science Foundation under Grant No. 0402616. Any opinions, findings and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the view of the National Science Foundation (NSF).

Team Exercise Well Posed Design Problem: Design a

new car that can: 1. Go from 0 - 60 mph in 6 seconds 2. Gets 50 miles/gal 3. Costs less than $10,000 to the

consumer 4. Does not exceed government

pollution standards 5. Appeals to aesthetic tastes

Team Exercise 1. Identify Problem e.g. we need

to build a new car since we are losing market share

2. Synthesis (integrating parts to for a whole) e.g. we can combine an aerodynamic body with a fuel efficient engine to make a new car with very high fuel efficiency

Team Exercise3. Analysis

identify relationships, distinguish fact from opinion, detect logic information, make conclusions from evidence, select relevant information, TRANSLATE REAL-WORLD PROBLEM

INTO MATHEMATICAL MODEL e.g. compare the drag of different body

types and determine if engine can fit under the hood

Team Exercise

4. Application (identify the pertinent information) e.g. What force is required to allow the car to go 60 mph knowing the car has a 30ft2 projected area and a 0.35 drag coefficient based on wind tunnel data?

Team Exercise

5. Comprehension (use the data and explicit theory to solve the problem) F = 1/2 Cd A V2

F=force Cd=drag coef. =air density

A=protected frontal area V=speed

Difficulties in Problem Solving

Most common difficulty: failure to use known information.

To avoid this problem: Write the problem in primitive form and

sketch an accurate picture of the setup (where applicable).

Transform the primitive statements to simpler language.

Translate verbal problems to more abstract mathematical statement(s) and figures, diagrams, charts, etc.

General Problem Solving Method

Define and understand problem1. Sketch the problem2. Gather information3. Generate and evaluate potential

solutions Use applicable theories and

assumptions

4. Refine and implement solution5. Verify and test solution

Define and Understand

Understand what is being asked Describe input/output (I/O)

what are you given knowns

what are you trying to find unknowns

Sketch the problem

Gather Information

Collect necessary data List relevant equations/theories State all assumptions

Generate Solution Methods Apply theories and assumptions. Typically, there is more than one approach

to solving a problem Work problem by hand using the potential

solution methods Break problem into parts; scale it down; etc.

e.g., if the problem was to calculate the average of 1000 numbers, work the problem by hand using, say, 10 numbers, in order to establish a method

Refine and Implement

Evaluate solution methods. accuracy ease of implementation etc.

Implement “best” solution.

Verify and Test

Compare solution to the problem statement Is this what you were looking for? Does your answer make sense?

Clearly identify the solution Sketch if appropriate

CHECK YOUR WORK!!

Don’t stop at getting an answer!! Think about whether the answer makes

physical sense. you are the instructor and you have to turn in

final grades. In your haste, you calculate the average of Susie’s grades (100, 70, 90) to be 78 and give Susie a C...

Getting It Right

The problem solving process may be an iterative process. If at first you don’t succeed (i.e., the

algorithm test fails), try again… The more thorough you are at

each step of the problem solving process, the more likely you are to get it right the first time!!

Team Exercise

Given: A student is in a stationary hot-air balloon that is momentarily fixed at 1325 ft above a piece of land. This pilot looks down 60o (from horizontal) and turns laterally 360o.

Note: 1 acre = 43,560 ft2

Team Exercise; cont’

Required: a) Sketch the problem b) How many acres of land are

contained by the cone created by her line of site?

c) How high would the balloon be if, using the same procedure, an area four times greater is encompassed?

Creative Problem Solving

The nine dots shown are arranged in equally spaced rows and columns. Connect all nine points with four straight lines without lifting the pencil from the paper and without retracing any line.

Individual Exercise (3 minutes)

Creative Problem Solving

Creative Problem Solving If you enjoy solving puzzles, you will enjoy

engineering Crick and Watson figured DNA when they

were young Engineers create from nature what did not

exist before In this creative process, the engineer

marshals skills in mathematics, materials, and other engineering discipline and from these resources create a new solution for a human need

Creative Problem Solving Engineering is not dull or stifling;

send people to moon, communication from battlefield, etc

Creative artists spent many years perfecting their skills

Engineers need patience, practice, and gaining problem-solving techniques by training

Self-Questions for Problem Solving

How important is the answer to a given problem?

Would a rough, preliminary estimate be satisfactory or high degree accuracy demanded?

How much time do you have and what resources are at your disposal? Data available or should be collected,

equipments and personnel, etc

Self-Questions for Problem Solving

What about the theory you intend to use? Can you use it now or must learn to use it? Is it state of the art?

Can you make assumptions that simplify without sacrificing needed accuracy?

Are other assumptions valid and applicable?

Optimize time and resources vs reliability

Engineering Method1. Recognize and understand the

problem (most difficult part)2. Accumulate data and verify

accuracy3. Select the appropriate theory or

principles4. Make necessary assumptions5. Solve the problem6. Verify and check results

Engineering Method Perfect solutions to real problems

do not exist. Simplify the problem to solve it; steady state, rigid body, adiabatic, isentropic, static etc

To solve a problem, use mathematical model; direct methods, trial-and-error, graphic methods, etc.

Problem Presentation Problem statement Diagram Theory Assumptions Solution steps Identify results and verify accuracy

Standards of Problem Presentation

Engineers should have ability to present information with great clarity in a neat, careful manner

Poor engineering documents can be legal problems in courts

Follow standard forms such as shown in the textbooks

Team Assignment Page 141 Problem 3.20

Algorithms Algorithm: “a step-by-step

procedure for solving a problem or accomplishing an end” (Webster)

Algorithms can be described by Pseudocode Flowcharts

Pseudocode English-like description of each step

of algorithm Not computer code Example - take out trash barrels

while there are more barrels

take barrel to street

return to garage

end

Flowcharts Graphical description of algorithm Standard symbols used for specific

operations

Input/Output

Start/Stop

Branch Test

Process Step

Process Flow

Flowchart ExampleDefine theproblem

Readinput

Solve theproblem

Can Isolve this?

Outputresults

What do I needto know?

Ask formore input

Begin

Can Isolve this?

End

yes

no

yes

no

Top Down Design State problem clearly Sketch problem Describe input/output (I/O) Work problem by hand Algorithm: pseudocode or flowchart

Decomposition - break problem into steps

Stepwise refinement - solve each step Test the algorithm/check your work!!

Example (Team exercise, 15 min) State problem clearly:

Given ax2 + bx + c = 0, find x. Describe I/O:

Input: a, b, c Output: x

Example (cont.) Hand example:

a=1, b=4, c=4 equation? (See Chapter 6,

Mathematics Supplement) x=?

Example (cont.) Algorithm development

write an algorithm in pseudocode to take any set of coefficients (i.e., a, b, c) and give the value of x for each set

Test your algorithm a,b,c = 1,4,4 a,b,c = 1,1,-6 a,b,c = 1,0,1 other good test cases?