Stat 496 Experiments with a Paper Helicopter

Stat 496 Project

Experiments with a Paper Helicopter

This semester the Stat 496 project will be divided into a series of experiments. Each experiment will involve paper helicopters as the experimental units. The experiments will correspond to different types of experiments that we will discuss during the course of the semester. You can complete an experiment once we have covered the associated material in class. For all experiments you will start with the standard helicopter and will modify (manipulate) aspects of the helicopter to investigate what effect those aspects have on the response: flight time in seconds. All experiments should incorporate the basic principles of a well designed experiment. Each part should be written up in the form of a report that includes an executive summary (although this will appear first it is usually written last), a description of the experiment including discussion of how the basic principles of experimentation were used, the experimental data clearly showing that randomization was used, an analysis of the experimental data (you can include appropriate JMP output), appropriate conclusions based on your data and analysis.

Experiment 1: Comparative Experiment. (10 points)

For the first experiment you will investigate the effect of folding the standard helicopter’s tail in half has on the flight time for the standard paper helicopter. You will have two groups: standard and tail folded in half. You should first decide how many helicopters you will have in each group. You must justify your choice of number of helicopters statistically. You should design an experiment that incorporates control, randomization and replication. Your report should discuss how each of these principles is used in the experiment. You should actually perform the experiment and collect the data. Your report should include the data and it should be clear from the data that randomization was used. Analyze the data. You can use JMP to analyze the data. Report your findings and what conclusion you come to regarding the effect of folding the tail in half.

Experiment 2: One Factor Experiment. (10 points)

For the second experiment you will investigate the effect of the drop height on the flight time for a standard paper helicopter. The five levels of drop height are 1, 1.25, 1.50, 1.75 and 2 meters. Again, you should decide how many helicopters you will drop from each height and justify this choice statistically. You should also decide whether to run this as a completely randomized or a randomized complete block experiment. You should design an experiment that incorporates control, randomization and replication. Your report should discuss how each of these principles is used in the experiment. You should actually perform the experiment and collect the data. Your report should include the data and it should be clear from the data that randomization was used. Analyze the data. You can use JMP to analyze the data. Report your findings and what conclusion you come to regarding the effect of drop height.

Experiment 3: Two Factor Experiment (15 points)

For the third experiment you will investigate the effects of wing length and wing width on the flight time for a helicopter. Wing length will have 3 levels; 10 cm, 8 cm and 6 cm. The standard helicopter has a wing length of 8 cm with a body length of 3 cm. When wing length is changed so is body length so that the body and wing are always 11 cm. Wing width will have 3 levels; 4.5, 4 and 3.5 cm. In order to change the wing width you will have to cut off some of the wing. You always want the outside edges of the wing and body to be continuous so any cutting should be on the inside edge of the wings. Again, you should decide how many helicopters you will have for each configuration of wing length and wing width. You should also decide whether to run this as a completely randomized or a randomized complete block experiment. You should design an experiment that incorporates control, randomization and replication. Your report should discuss how each of these principles is used in the experiment. You should actually perform the experiment and collect the data. Your report should include the data and it should be clear from the data that randomization was used. Analyze the data. You can use JMP to analyze the data. Report your findings and what conclusion you come to regarding the effects of wing length, wing width and interaction between these two aspects of the wing.

Experiment 4: Fractional Factorial Experiment (40 points)

For the final experiment you will investigate six (6) factors simultaneously. The factors are:

A: Tail length: 5 cm to 10 cm (tail folded over)

B: Height of drop: 1 m to 3 m

C: Wing length: 5 cm to 10 cm

D: Wing width: 2.5 cm to 4.5 cm

E: # of paper clips: 1 to 3

F: Wing fold: standard or with fold

Because this experiment will be done towards the end of the semester, you will be limited in the amount of time you have to do the experiment. This puts a premium on being efficient in collecting your data. You want to be able to determine the effects of the various factors and interactions but with the smallest number of experimental runs. You should design an experiment that incorporates control and randomization. Your report should discuss how each of these principles is used in the experiment. You should actually perform the experiment and collect the data. Your report should include the data and it should be clear from the data that randomization was used. Analyze the data. You can use JMP to analyze the data. Report your findings and what conclusion you come to regarding which effects; main and interaction, are statistically significant. Come up with a prediction equation based on your analysis. Using the prediction equation, come up with a prototype design of the paper helicopter that will take 2 seconds to reach the ground. Make several helicopters based on your prototype design and fly them. Report, analyze and comment on the results of these confirmatory runs.

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