MECH60588DESIGN FOR QUALITY (2015-16)
ExperimentalDesign Paper Helicopter
Assignment2 
ExperimentalDesign
Names:
(Date)
Introduction 
Todesign a paper helicopter usingresponse surface methodology wemust identify the desired output, which would turn out to be ourresponse variable. In this kind of experiment quality must be clearlydefined before proclaiming the need of a high quality helicopter.
Apaper helicopter is categorized as good depending on the time itstays afloat in the air. In this case our response variable will betime taken by the paper helicopter to drop from a height of 2 meters.Without clearly defining the conditions under which the test will becarried on it could be possible that sample paper helicopters wouldbe released from various heights, in which our response surfacemethodology results would be effective.
Testparameters that affect the time taken by the helicopter to be afloat(flight time) should also be identified. In this experiment, theparameters are rotor length, paper type, leg length, paper clip andleg width. The paper helicopter test levels are varied by the use ofshorter or longer legs, two different types of paper and removing oradding a paper clip and rotor lengths.
Theory
Responsesurface methodology (RSM) is defined as a combination of mathematicaland statistical procedures to explore efficiency of a system in termsof performance in order to come up with techniques to improve it. Thebest reference on Response Surface Methodology is the one given byDouglas Montgomery and Raymond Myers. A curved surface used toenvision a response surface. This is because a curved surface showshow a specified input factors (independent variables) are affected bysystem’s output performance (a dependent variable).
Amaximum, a saddle and a rising ridge are some of the best examples ofresponse surface in three dimension with a minimum in a transectingdirection and a maximum in one direction. In this project, our maingoal is to come up with a combination of design parameters that wouldmake our paper helicopter stay afloat for longer time.
Inexperimental design, factorial designs are the workhorses of designexperiment. These are well organized designs used to assess theeffects of numerous parameters on a response. In this experiment weare going to use a 2kdesign is a factorial design representing kfactors, where each is experimented on at two levels, coded as –1for “low” and +1 for “high.” The high and low levels of thedesign are chosen to cover the range of probable values for eachparameter.
Acomplete factorial design has all probable blends of the kparameters at the levels tested. In a case whereby the number ofparameters being tested is big, a 2kdesign will end up having a big number of runs. For instance, k=8 will be 28 = 256 runs. To further screen the parameters thatcontribute most to the response, fractional factorial designs areused. This design method is only used if a complete factorial designneeds a prohibitive number of test runs.
Fractionalfactorial designs are represented as 2k–p,for a design that has one-half the complete fractional runs p=1,while for a design with one-fourth the complete factorial runs p=2,etc. To obtain the best efficiency using 2k–pdesignyou have to pay the price of vagueness which is introduced throughconfounding of the effects. In a more effective screening design, themain effects will not be confused with each other, though there canbe confused with the effects due to interaction. Since the majoreffects are not confounded with each other, their relativesignificance can be separated among each other, but not from certaininteractions.
Table1. Parameters possibly affecting paper helicopter duration of flightand the factor levels for the screening test in actual units for eachcoded value. Width and length are measured in centimeters.
Coded Values | |||
Factors | -1 | 0 | +1 |
A=Rotor Length | 5.5 | 8.5 | 11.5 |
B=Rotor Width | 3.0 | 4.0 | 5.0 |
C=Body Length | 1.5 | 3.5 | 5.5 |
D=Foot Length | 0.0 | 1.25 | 2.5 |
E=Fold Length | 5.0 | 8.0 | 11.0 |
F=Fold Width | 1.5 | 2.0 | 2.5 |
G=Paper Weight | light | (none) | Heavy |
H=Fold Dir | against | (none) | with |
Method
Duringscreening experiment our aim was to find parameters that have themost effect on the response, and then remove the remaining parametersfrom further test analysis. In order to find the few significantparameters that contribute to duration of flight, we carried out ascreening test using a 28–4fractionalfactorial design with the original paper helicopter design as thecenter point.
Wechose eight parameters that might possibly affect the duration offlight of the paper helicopter: we added three factors to theoriginal five factors (i.e., paper weight, fold direction, and footlength). The levels of weight of the paper used were normal copypaper heavy (+1) and phonebook white pages paper light (– 1). Folddirection levels used in the test were described as the folddirection against (opposite) direction of rotation. Table 1 indicatesthe uncoded and coded values for the eight parameters that we tested.
Wemade 16 paper helicopters at the design points indicated in Table 2.We then dropped them randomly from 20 feet and entered the flightduration of each one of the helicopter. All flight test were doneindoors in still air.
Weapplied SAS macro EFFECTS from Applied Statistics for Engineers andScientists by J. D. Petruccelli, B. Nandram, and M. Chen to calculatethe factor effect estimates, as indicated in Table 3.
Results
TABLE2. Screening experiment with coded factor levels and center points.
Run | Order | A | B | C | D | E | F | G | H | Flight Time |
1 | 12 | -1 | -1 | -1 | -1 | -1 | -1 | -1 | -1 | 11.80 |
2 | 7 | -1 | -1 | -1 | 1 | 1 | 1 | 1 | -1 | 8.29 |
3 | 11 | -1 | -1 | 1 | -1 | 1 | 1 | -1 | 1 | 9.00 |
4 | 15 | -1 | -1 | 1 | 1 | -1 | -1 | 1 | 1 | 7.21 |
5 | 1 | -1 | -1 | -1 | 1 | -1 | 1 | 1 | 6.65 | |
6 | 4 | -1 | -1 | 1 | -1 | 1 | -1 | 1 | 10.26 | |
7 | 16 | -1 | 1 | -1 | -1 | 1 | 1 | -1 | 7.98 | |
8 | 8 | -1 | 1 | 1 | 1 | -1 | -1 | -1 | 8.06 | |
9 | 3 | 1 | -1 | -1 | -1 | -1 | 1 | 1 | 1 | 9.20 |
10 | 10 | 1 | -1 | -1 | 1 | 1 | -1 | -1 | 1 | 19.35 |
11 | 9 | 1 | -1 | 1 | -1 | 1 | -1 | 1 | -1 | 12.08 |
12 | 5 | 1 | -1 | 1 | 1 | -1 | 1 | -1 | -1 | 20.50 |
13 | 6 | 1 | -1 | -1 | 1 | 1 | -1 | -1 | 13.58 | |
14 | 13 | 1 | -1 | 1 | -1 | -1 | 1 | -1 | 7.47 | |
15 | 14 | 1 | 1 | -1 | -1 | -1 | -1 | 1 | 9.79 | |
16 | 2 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 9.20 |
APareto Chart of the absolute value of the effects (see Figure 1)indicates that the major effects A, B, and G should be categorized asthe vital few, as they are more than twice as higher as the nextlargest main effect (i.e., D).
Wewere left with 3 main factors that influence flight duration, but byreview, we could see that G = –1 representing the light paperconstantly has a big response. We fixed H = –1 representing foldagainst, since this setting made the helicopter stable. Furtherexperiment indicated desirable levels of length of the body C = 2,fold length E = 6, foot length D =2 and fold width F = 2 in theiruncoded units of centimeters. To start our model-building procedure,we had only two parameters to consider (A, rotor length, and B, rotorwidth).
Table3. Parameter effects estimate with SAS macro EFFECTS. Factors A, B,and G are shown as the vital few
Factor | Estimate |
A | 3.9900* |
B | -3.0550* |
C | -0.3475 |
D | 1.2825 |
E | 0.2500 |
F | 0.7000 |
G | -4.2825* |
H | -1.1375 |
AB | -2.2175 |
AC | 0.8400 |
AD | 1.6850 |
BC | -0.3850 |
BD | -2.0350 |
CD | 0.2475 |
ABCD | 1.5625 |
Figure1: Pareto Chart of absolute value of the effect
Discussion
Theresults of our experiment consisting of paper helicopters at thepredicted ideal setting are indicated in Table 4. The standarddeviation is 1.67 seconds with mean response of 17.81 seconds, with a95% confidence interval on the mean response of (16.1, 19.6). Ourpaper helicopter model’s forecast response, y=16.9seconds, is within this range, therefore confirming the importance ofour response model for the parameter levels we tested and under theenvironmental settings in our experiments.
Table4. Lack-of-fit test indicates the model is adequate.
Residual | df | SS | MS | F | p-Value |
Lack of fit | 3 | 1.826 | 0.609 | 1.82 | 0.3737 |
Pure Error | 2 | 0.668 | 0.334 | ||
Total Error | 5 | 2.495 | 0.499 |
6.0Conclusion
Analysisfor the data we collected shows the optimal paper helicopter settingsare longer rotor length, lighter paper, shorter leg length, nopaperclip on the leg and slimmer leg width.
Todesign an even better helicopter, we could repeat the entireexperiment using even longer helicopter blades and lighter paper.
7.0Presentation
Theideal paper helicopter design is narrower and longer and has ashorter base than the original helicopter design. Figure 2 shows thenew optimum design.
Figure2: Optimum design of paper helicopter
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