Mercer University



ISE 482L – Lab VII

Design of Experiments Lab

Paper Planes Experiment

Purpose:

The purpose of the lab is to design an “optimal” paper airplane using a 2-factor factorial experiment (2k) approach. In week one, students will perform a 1/8 fractional factorial experiment on a paper airplane design that contains 6 design parameters, each design parameter containing two possible factors. In week two, using the interaction effects from the fractional factorial experiment, students will select the best combination of design parameters to create the “optimal” paper airplane. Experiments will be performed to assess the performance of this “optimal” design.

Time Frame:

Week 1- Assembling and testing initial airplane designs; results will be concluded out of class using Minitab, Excel, etc.

Week 2- Develop and test the new airplane design using results of DOE from week 1.

Materials and Equipment:

• Paper of varying thickness

• Scissors

• Flat working surface

• Ruler

Student Setup:

The students will work in groups of two.

Design parameters / factors:

• Paper Type

• Length of Wing

• Width of Body

• Length of Body

• Wing Type (Angled or Non-Angled)

• Paper Clip

Procedure:

Week 1: Creation of Initial Airplane

In this lab, 8 paper airplane designs will be created as defined below. The designs will vary based on the 6 design parameters. Trials will then be performed to assess the performance of each design. The performance measure of interest is the average distance traveled by the airplane in four trials.

Determine the Number of Trials Required:

Knowing that the experiment is a 2k fractional factorial design; and that 1/8 of the number of trials is acceptable; and that there are 6 factors and 2 responses; what is the number of required airplanes which need to be created?

(Answer):

2(6-3) =8;

Plane Design:

As stated before, this experiment is a 2-factor factorial experiment. The only factors for this experiment are high and low level values/characteristics. Therefore, the first two designs will be a completely high level and completely low level airplane.

Partner 1 will make their paper airplane the low level factor airplane, meaning they will be required to use the following materials:

Low Level Paper Airplane Design

|Materials |Low Level |

|Paper Type |Standard Copy Paper |

|Length of Wing |User Defined |

|Width of Body |User Defined |

|Length of Body |User Defined |

|Wing Type (Angled or Non-Angled) |Non-Angled |

|Paper Clip |User Defined |

The rows that state, “User Defined”, simply means that the airplane creator can determine these lengths or number of paper clips, there are no predetermined values.

Partner 2 will make their paper airplane the high level factor airplane meaning they will be required to use the following materials:

High Level Paper Airplane Design

|Parameter |High Level |

|Paper Type |Bonded |

|Length of Wing |User Defined, greater than Partner 1 |

|Width of Body |User Defined, greater than Partner 1 |

|Length of Body |User Defined, greater than Partner 1 |

|Wing Type (Angled or Non-Angled) |Angled |

|Paper Clip |User Defined, greater than Partner 1 |

The columns that state, “User Defined, greater than Partner 1”, simply means that the airplane creator can determine these lengths or number of paper clips on their own, but needs to make sure that their values are greater than Partner 1’s values.

In addition to the High and Low level designs, 6 “Intermediate” designs must be completed in order to carry out the fractional factorial experiment. Design parameters for each intermediate design are listed in the tables below. Make sure you mark your designs so airplanes designs can readily be identified.

Intermediate Design 1

|Parameter |Level | Parameter Specs. |

|Paper Type |1 | |

|Length of Wing |-1 | |

|Width of Body |-1 | |

|Length of Body |-1 | |

|Wing Type (Angled or Non-Angled) |-1 | |

|Paper Clip |1 | |

Intermediate Design 2

|Parameter |Level |Parameter Specs |

|Paper Type |-1 | |

|Length of Wing |1 | |

|Width of Body |-1 | |

|Length of Body |-1 | |

|Wing Type (Angled or Non-Angled) |1 | |

|Paper Clip |-1 | |

Intermediate Design 3

|Parameter |Level |Parameter Specs |

|Paper Type |1 | |

|Length of Wing |1 | |

|Width of Body |-1 | |

|Length of Body |1 | |

|Wing Type (Angled or Non-Angled) |-1 | |

|Paper Clip |-1 | |

Intermediate Design 4

|Parameter |Level |Parameter Specs |

|Paper Type |-1 | |

|Length of Wing |1- | |

|Width of Body |1 | |

|Length of Body |1 | |

|Wing Type (Angled or Non-Angled) |-1 | |

|Paper Clip |-1 | |

Intermediate Design 5

|Parameter |Level |Parameter Specs |

|Paper Type |1 | |

|Length of Wing |-1 | |

|Width of Body |1 | |

|Length of Body |-1 | |

|Wing Type (Angled or Non-Angled) |1 | |

|Paper Clip |-1 | |

Intermediate Design 6

|Parameter |Level |Parameter Specs |

|Paper Type |-1 | |

|Length of Wing |1 | |

|Width of Body |1 | |

|Length of Body |-1 | |

|Wing Type (Angled or Non-Angled) |-1 | |

|Paper Clip |1 | |

Recording Distances:

Knowing that 4 trials is acceptable, complete 4 runs with the each airplane, then find the average distance covered by the airplane.

Low Level Airplane Distance:

|Runs |Distance (inches) |

|1 | |

|2 | |

|3 | |

|4 | |

|Average | |

High Level Airplane Distance:

|Runs |Distance (inches) |

|1 | |

|2 | |

|3 | |

|4 | |

|Average | |

Intermediate Design 1 Distance:

|Runs |Distance (inches) |

|1 | |

|2 | |

|3 | |

|4 | |

|Average | |

Intermediate Design 2 Distance:

|Runs |Distance (inches) |

|1 | |

|2 | |

|3 | |

|4 | |

|Average | |

Intermediate Design 3 Distance:

|Runs |Distance (inches) |

|1 | |

|2 | |

|3 | |

|4 | |

|Average | |

Intermediate Design 4 Distance:

|Runs |Distance (inches) |

|1 | |

|2 | |

|3 | |

|4 | |

|Average | |

Intermediate Design 5 Distance:

|Runs |Distance (inches) |

|1 | |

|2 | |

|3 | |

|4 | |

|Average | |

Intermediate Design 6 Distance:

|Runs |Distance (inches) |

|1 | |

|2 | |

|3 | |

|4 | |

|Average | |

Determining Effects of Control Parameters:

Input the main effects into Minitab, also include the interaction effects. This is done by performing a Factorial Design, graphs like the figures below are typical output from Minitab.

[pic]

[pic]

Interaction Examples:

[pic]

No Interaction Present between Wing Type and Paper Type

[pic]

Interaction occurs between Body Length and Paper Clip

After evaluating the Minitab output results, the interactions with the intersecting lines indicates that there is an interaction with the two parameters, likewise if there is no intersection, then the two parameters do not have an interaction.

Which control parameter or parameters had the greatest effect? And why? (Hint: Pareto Chart, but say why you chose it if used)

Lab Design Problem

There is a known problem with this lab. When you find the problem, suggest changes to this lab by modifying this document.

Week 1 Deliverables:

1. Modified lab

2. Minitab Analysis including Main Effect Plot and Interaction Plot

3. Lab report, including how and why lab was modified, and identification of parameters that have the greatest effect and how these were chosen.

Week 2: Creation of Improved Airplane Design

Based on the most influential variables and the interaction effects, create the “ultimate” paper airplane. Re-run the experiment 4 times and note the distances. Conclude in the lab write-up the change you made to the airplane, and whether your resultant design effected the distance of your airplane.

Fill out the following table of the changes you made.

|Materials |New Design |

|Paper Type | |

|Length of Wing | |

|Width of Body | |

|Length of Body | |

|Wing Type (Angled or Non-Angled) | |

|Paper Clip | |

Airplane Distance for New Design:

|Runs |Distance (inches) |

|1 | |

|2 | |

|3 | |

|4 | |

|Average | |

Were the distances longer? Were the results what you expected?

Conclude the experiment by completing the written report, the format can be seen on the following page.

Report: The written report should include the following:

1. Purpose

2. Procedure:

a. A summary of your experimental design, describe who was involved and how you made your initial airplane, materials used, testing protocol used.

b. Describe what computer or book aides were used

3. Results:

a. Provide all required and any supplemental tables and graphs in the body of the report. At the minimum there should be a graph for all significant interaction effects, and a Minitab factorial design test determining the interaction effects.

b. Clearly state the expected relationship between the initial designs of high and low performance planes, to the final design.

c. Explain how you determined what factors were significant.

d. Conclude how you interpreted the results from Minitab.

4. Conclusions:

a. Discuss how well the results matched the expectations.

b. Explain the discrepancies between expected and actual results.

c. Explain whether Minitab helped or hindered your understanding of the experiment

d. Make suggestions to make this experiment better.

e. Conclude where human error may have played a role in this experiment. If so how can the human error be eliminated.

5. Appendix- Include all data and calculations in an appendix.

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