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Assignment 2: Robust paper planes
- a robust design study in MF2024, 2010
Ulf Olofsson
KTH Machine Design
School of Industrial Engineering and Management
MF2024 Robust and probabilistic design
School of Industrial Engineering and Management
November 2010
ASSIGNMENT 2 – ROBUST DESIGN OF PAPER PLANES
In this assignment you will plan and conduct a robust design experiment to determine the
most robust design of paper planes. The control parameters and the noise parameters are
given in Table 1. The objective function to be optimized is the distance the plane flies and
glides to stop on the floor.
Table 1 Factors and levels for the robust design experiment.
Level 1
Level 2
Controllable Factors
A=Weight of paper
One sheet
Two sheets
B=Configuration
Configuration 1
Configuration 2
C=Width of paper
100 mm
150 mm
D= Length of paper
150 mm
200 mm
Level 1
Level 2
Uncontrollable factors
F=Launch height
Standing on ground
Standing on chair
G=Launch angle
Horizontal to ground 45º above horizontal
H=Ground surface
Concrete
Polished tile
Figure 1 Example of different plane configurations
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Assigment tasks
This is an individual assignment, but you are allowed to work together in groups of 2-4
students when you plan and conduct the experiments. During this initial phase of the
assignment the following tasks should be performed:
1. Decide on two plane configurations to investigate. The planes are to be made from
ordinary copy paper and the configurations will not be varied throughout the
experiment.
2. Set up a test plan with controllable and uncontrollable factors according to Table 1.
Use 24-1-innerarray for the controllable factors and a 23-1-outerarray for the
uncontrollable factors. This means that you will evaluate 8 different plane designs and
perform 4 tests with each design.
3. Conduct the experiments according to your test plan. All planes are launched by the
same person in a closed room or hallway with no air currents. When launching a
plane, the elbow must be touching the body and only the forearm, wrist and hand are
used to send the plane into flight. Evaluate the distance the plane flies and glides to
stop on the floor, measured to the nose of the plane.
Once the experimental data has been collected the evaluation of the result is done by each
student individually. This part of the assignment includes following tasks:
4. Compute the mean and standard deviation of the response parameter for each instance
of the inner array.
5. Compute the main effects of the controllable factors on both the mean value and the
standard deviation of the response parameter.
6. Decide if any of the factors have a statistically significant effect on either the mean
value or the standard deviation of the response parameter. You can use a normal
distribution chart and/or compute the standard deviation of the effects.
7. Present your work and result in a written technical report. The report should include a
description of the two configurations evaluated (use photos), your test plan with the
factors and the levels for the robust design experiment, and of course your result and
conclusions. Interesting questions to discuss are: Which of the 16 designs has the
longest flight distance? Which of the 16 designs is to be considered most robust?
Which plane design would you suggest if looking for a robust design that fly as far as
possible?
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The assignment
• It is an individual task (1 report per person), but you are allowed to work
together in groups of 2-4 student in planning and conducting the tests.
• Matlab and Microsoft Excel are suitable tools for the evaluation of the
experiments.
• If you choose to use Matlab your code should be added in Appendix to the report.
This assignment is graded and it should be solved individually. Present the result in a written
technical report. Send the report to mf2024@md.kth.se not later than Friday December
3, 2010. The e-mail must also include:
1 The subject Assignment 2
2. Your name
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