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STAT 375

Dr. Heidi Lindsey

Group 3

Group Project: Paper Helicopter Flight Times

Making paper helicopters is an American pastime that every good Truman student indulges in at least one point in their college career. Nothing quite compares to watching a paper helicopter float its way down from the top of the SUB stairwell or in Pickler’s lobby area. In order to maximize the happiness of Truman students everywhere, we decided to conduct an experiment to find the best paper helicopter design that allows for the longest flight time.

Our group was interested in the different variables that could affect helicopter leaf flight times. To do this, we conducted a 3x3x2 Paper Helicopter Factorial Design experiment. Our goal was to see the various flight times based on different types of helicopter paper planes. Eighteen helicopters were dropped with five trials per varied helicopter characteristics. The factors that we considered were wing lengths (short, medium, and long), body lengths (short, medium, and long), and whether or not the the wing was folded. Each helicopter was dropped from the second floor of Pickler Memorial Library, and the time it took to hit the ground of the first floor was recorded, in seconds, using a timer on stopwatch. All of the paper helicopters were dropped five times in orders 1-18. The bodies of the helicopters were held as they were released and dropped.

We chose to look at three difference variables, including: wing length, body length, and whether there was a fold or not. Our hypothesis was such that folding the wings might affect the flight the helicopter, we ended up folding half of the helicopter’s wings and leaving the other helicopter’s wings unfolded. We predicted that the flight times would be longer when the wings were folded, due to increased air resistance. We also predicted that increasing the length of the wing would be positively correlated to length of flight time. Lastly, we predicted that the longer the body of the helicopter, the slower the speed it would take to reach the ground floor of Pickler Library, due to increased area of air resistance against the helicopter. Each of the eighteen helicopters had paper clips on the bottom to help pull the helicopter remain stabilized during the fall. Without using the paper clips, the helicopter could have had a difficult time falling to the ground in the proper way, and would more than likely taken two to three times longer to conduct.

The paper helicopters were made out of regular 8”x11” printer paper and created various wing and body length, and folded or unfolded wings. For wing and body length, we had three lengths: short (3in), medium (4in), and long (5in). Then each helicopter was labeled with their wing length, body length and fold type and numbered from 1-18. One being the helicopter with 3-inch wings, 3-inch body, and no fold. We dropped the paper plane helicopters in a “fixed” order, from 1-18.

The helicopters were dropped from the second floor northwest corner of Pickler Library. xx stood at the second floor and dropped the paper planes while xxx stood at the bottom to time and record the data with pencil and paper. After that, xxxx imported the data into an excel file.

In this data set, the variables we have are three independent variables which is wing length, body length and fold type. Also, we have one response variable which is the time we recalled. We have checked all of the assumptions for independence, normality, and equal variance. Independence was, technically, not met because we used the same helicopters for multiple drops. However, had we not done this, the amount of time put into making the helicopters would have been much more. Because the helicopters did not sustain any alterations after each drop, we will assume that independence was met. Second, we checked the normality assumption. The four in one plot (Figure 1) gives us a very good indication that this experiment demonstrates normality. To be more confident, we ran a probability plot versus the residuals (Figure 2). This shows that some of the data falls outside of the bounds for normality. Finally, we checked the assumption for equal variance. Figure 3 shows that the Levene’s p-value is 0.866, which is larger than the alpha of 0.05. We can assume that variances are equal.

We coded our information into minitab as such. For wing length, 1 = short length wings, 2 = medium length wings, and 3 = long length wings. For body length, 1 = short length body, 2 = medium length body, and 3 = long length body. For fold, 1= no fold and 2 = fold. When we looked at the ANOVA output (Table 2), we found that the three-way interaction term was significant, so we included all main effects and interactions in our model statement.

After we determined that the interaction variable was significant, we decided to run post hoc tests. We chose Tukey’s HSD because it is one of the more reliable tests. With Tukey’s we found that many of the different combinations of wing length, body length, and fold were indistinguishable from each other (Table 3). We couldn’t determine a best or worst combination of these variables. However, the top two combinations that were indistinguishable from each other were a long wing length, with a short body, and no fold and a long wing length, with a long body, and no fold.

In conclusion, we found that a combination of these three factors had a significant effect on the flight time of the paper helicopters. The top two combinations, as found by running Tukey’s HSD, were long wings, a short body, and no fold or long wings, a long body, and no fold. One thing that could have improved our experiment would be to have actually made seventy-two paper helicopters so that none of the flight times could have been affected by damage sustained after each test. Another variable that would have been interesting to experiment with would have been the type of paper because students carry many different types and it would have been beneficial for them to know which one to use for the longest flight times.

Our group members consisted of .... Our group met to conduct the making of the helicopters and to conduct the experiment itself. Specifically, dropped the airplanes from the 2nd floor, recorded the flight times, used our collected data to enter into Excel and Minitab, and helped wrap up our experiment and data collection by analyzing and interpreting our conclusion. Overall, this experiment was educationally intriguing, and helped add useful, “real-life” application to the concepts we have been learning this semester.

Appendix

Table 1: 3x2x2 Factorial Experiment: Paper Helicopters

			Length
Factors		1	2	3
	Wing Length	3”	4”	5”
	Body Length	3”	4”	5”
	Fold Type	No fold	Fold

Table 2:

Analysis of Variance

Source	DF	Adj SS	Adj MS	F-Value	P-Value
Wing Length	2	14.6097	7.3049	52.78	0.000
Body length	2	4.7377	2.3688	17.12	0.000
Fold	1	5.0980	5.0980	36.84	0.000
Wing Length*Body length	4	1.7899	0.4475	3.23	0.017
Wing Length*Fold	2	0.2759	0.1380	1.00	0.374
Body length*Fold	2	0.4854	0.2427	1.75	0.180
Wing Length*Body length*Fold	4	3.5019	0.8755	6.33	0.000
Error	72	9.9645	0.1384
Total	89	40.4630

Table 3:

Grouping Information Using the Tukey Method and 95% Confidence

Wing Length*Body length*Fold	N	Mean	Grouping
3 1 1	5	4.988	A
3 3 1	5	4.402	A	B
3 1 2	5	3.862		B	C
3 3 2	5	3.566		B	C	D
1 1 1	5	3.550			C	D
3 2 2	5	3.492			C	D
2 1 1	5	3.434			C	D
2 3 1	5	3.380			C	D
1 2 1	5	3.366			C	D
3 2 1	5	3.284			C	D
2 1 2	5	3.206			C	D	E
2 2 1	5	3.144			C	D	E
1 3 2	5	3.000				D	E
2 3 2	5	2.954				D	E
1 3 1	5	2.910				D	E
1 1 2	5	2.856				D	E
2 2 2	5	2.826				D	E
1 2 2	5	2.412					E

Means that do not share a letter are significantly different.

Figure 1:

Figure 2:

Figure 3: