# The Effect of Paper Airplane Length on Flight Distance

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### Literature Review

The Wright Brothers' invention is still relevant today, even when discussing paper airplanes. Even small changes in the design of a paper airplane can have large effects of on its flight pattern. For example, changes in wing shape and weight distribution could impact whether or not the plane flies in a straight line or in a curving pattern. One important aspect of the flight pattern is flight distance. Several design factors play a role in affecting flight distance, but one factor in particular could have a vital effect: the paper airplane’s length. However, it is not immediately clear if increasing the length, while maintaining the same overall design, would increase or decrease the flying distance. One could argue that increasing the length of the paper airplane will increase the surface area, which would increase the flight distance. In a recent book on aircraft control, Stevens and Lewis (2003) explain that an increase in surface area allows for more aerodynamic lift, and lift is a key property for aerodynamic force. Something that the Concorde Aircraft was able to achieve. Further, this aerodynamic force is key for keeping a flying object moving through the air. Alternatively, it could be argued that increasing the length will increase the weight, which would decrease the flight distance. In their book on flight physics, Torenbeek and Wittenberg (2009) explain that the more weight that an object has, the more aerodynamic force is needed to keep that object in motion. Therefore, if holding the other factors of force equal (such as with propeller strength in an airplane, or throwing strength with a paper airplane), an object with more weight will travel less distance. Given that long flight distance is generally a desirable attribute of paper airplanes, it is useful to examine how exactly length affects it.

### Experimental Design Steps

To test this hypothesis, I conducted an experiment using paper airplanes of three different lengths: short, medium, and long. The steps for constructing the paper airplanes are as follows:

1) I obtained three unused pieces of paper and altered the length using a pair of scissors.

2) One piece of paper was not altered; this was considered the long paper airplane (11 inches).

3) The length of the second piece of paper was reduced by cutting two inches off from the end; this was considered the medium paper airplane (9 inches).

4) The length of the final piece of paper was reduced by cutting four inches off from the end; this was considered the short paper airplane (7 inches).

5) All three pieces of paper were then folded into the basic “dart” paper airplane (see figure 1). For visual step-by-step instructions on how the “dart” paper airplane is folded, see figure 2.

### Sequence of Events

Once the paper airplanes were cut and folded, they were taken to a long indoor hallway for flight distance testing as follows:

1) First a piece of tape was placed on the floor at one end of the hallway. This tape marked the standing location for throwing the paper airplanes.

2) Next, each paper airplane was thrown with the same force five times each. The total distance travelled for each throw was measured from the tape mark to the furthest tip of the paper airplane, in inches using a tape measure.

### Tools

1) Three pieces of paper standard letter (8.5 x 11 inches) copy paper

2) One piece of duct tape

3) Measuring tape

4) Pencil and paper

5) Calculator

Variables

Independent variable: the length of the paper airplane constitutes the independent variable.

Dependent variable: the flight distance was the dependent variable.

### Internal Validity

Importantly, the same paper airplane type, or design, was used for each paper airplane, and only the original length of the piece of paper varied. This was crucial for strengthening the internal validity of the experiment by making sure that no differences in flight distance resulted from differences in paper airplane type.

### Hypothesis

Because paper is such a light material, it is likely that the difference in surface area will have a larger effect than the difference in weight. Therefore, I hypothesize that as the length of a paper airplane is increased, the flight duration will also increase.

### Results

In order to determine which paper airplane had the largest flight distance, the average inches flown over all five throws, for each paper airplane was calculated. It was found that the short paper airplane travelled an average of 204 inches; the medium paper airplane flew an average of 264 inches; and the long paper airplane flew an average of 288 inches. See figure 2 for a graphical representation.

## Conclusion

### Hypothesis Confirmation

The results from this experiment provide evidence in confirmation of the hypothesis that longer length results in longer flight distance in paper airplanes. The medium paper airplane flew a greater distance than the short, and the long paper airplane flew a greater distance than both the short and medium paper airplanes.

### Experimental Design as Key Factor

By controlling for extraneous variables such as differences in paper airplane type, flight location, and force, these results can be interpreted with some degree of confidence.

### Replication and Validity

However, it is important to replicate these findings to make sure there that the results weren’t due to chance, or to experimenter error. By repeating the experiment multiple times, the possible effects of chance and error are greatly reduced. Further, there are some limitations to this study in that only one type of paper airplane was used and that only a small range of lengths was used. It is possible that the effect of length on flight distance varies depending on the paper airplane type or at extreme lengths. It is thus not only important to replicate these results, but to add further research before definitively concluding that increases in paper airplane length results in increased flight distance.

References

Paper Airplanes. (2014). Retrieved April 6, 2014, from http://www.multiplyleadership.com/rose-petal-press/paper-airplanes/

Stevens, B. L., & Lewis, F. L. (2003). Aircraft control and simulation (2nd ed.). Hoboken, N.J.: John Wiley.

Torenbeek, E., & Wittenberg, H. (2009). Flight physics essentials of aeronautical disciplines and technology, with historical notes (pp. 1 online resource (xii, 535 p.)). Retrieved from https://libproxy.usc.edu/login?url=http://dx.doi.org/10.1007/978-1-4020-8664-9