Conclusions
Our projected aimed to determine how altering weight and drag of a paper airplane affected the total distance and speed. The null hypothesis predicted changing the weight and drag would not have a significant impact on the distance and speed. Our project changed course when we realized the velocity would not vary dramatically during the first 50 cm of flight. Our new destination included analyzing how rear elevator flap angle and mass impacted distance and drag. Return to your seats and fasten your seat belts as we begin our decent.
We wanted to find out how mass affected both the distance traveled and the drag of the paper airplane. As you can see in our Statistical Analysis section though, the mass did not significantly affect neither the distance nor drag. Our Regression and Correlation Analysis did show that there was an overall negative trend in Distance vs. Mass and a positive trend in Drag vs. Mass. We believe that the planes traveled a shorter distance as mass increased because the lift force was smaller in comparison to the weight, causing it to fall faster. The drag increased as mass increased because the planes had a higher momentum, thus having a higher speed for a longer time. This was confirmed at the end of our Regression and Correlation section.
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We did however come to an interesting conclusion regarding the mass of the plane. We found that as the mass of the plane increased, the distance became much more predictable and consistent. This can be seen in the graph below (Figure 30).
The above figure shows that as the paper mass increases, the high and low distance values from our 10 trials draw closer to the average. This is also show with the standard deviations of each paper distance: 0.111 m for Normal Paper, 0.075 m for Construction Paper, and 0.043 m for Card Stock Paper. We believe this happens since a heavier object will be less affected by air. The almost "random" forces that air puts on a projectile become less influential with a higher mass since the momentum and gravitational force are bigger in comparison. Although this was not an initial goal of our project, it was a very interesting and concrete conclusion.
Figure 30: This graph shows how the high, average, and low values of distance change with paper types.
Conclusion #1
By: Vaughn Chambers
Conclusion #2
By: Conner Reyer
Although an objective of our project was to figure out how the flap angle affected velocity, we quickly realized that because of our method of measuring velocity there would only be minor fluctuations in velocity, not drastic changes. This was because we measured initial velocity through the first 50 cm using the same weight to pull the air track cart and starting the cart in the same position for each trial (see Figure 31).
Figure 31: This graph shows how the velocity did not significantly vary between planes with different flap angles.
With the small fluctuations seen in our data samples, we did verify that the larger velocity created a greater drag force. This can be seen in Figure 29 on the Analysis page, showing how the lower the number of frames the higher the velocity which, in turn, results in a higher drag force. However, we were ultimately unable to measure how the flap angle affected the velocity of each plane.
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For further study to get a better understanding of how the velocity was affected due to flap angle, it would be wise to measure the time the plane was in flight. The distance the plane flew divided by the time it was in the air would give us the average velocity of the plane. This would then give a more accurate representation of the drag force.
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Overall, a more accurate experiment would have been to test the lift force. As the plane leaves the air track cart gravity pulls the plane towards the floor. The lift of the plane, generated mostly by the difference in air pressures above and below the plane, allows the plane to level out before hitting the floor and glide horizontally before landing. Elevator flaps on paper airplanes allow for more lift to achieve a more gradual decent with a longer glide time. This was seen in our data, looking at the average distances between a 0° elevator flap, and the 30°, 60°, and 90° flaps in Figure 25.
Conclusion #3
By: Lake Bender
At the beginning of our experiment, we set out to discover how the change in drag would affect the distance traveled by the paper airplane. However, during the course of this study, we realized that we would have to see how flap angle altered distance and drag, instead. We found that distance was being affected in extraordinary ways by a change in elevator flap angle, while drag did not change very much at all. The drag is what we had anticipated would have been affected by a change in flap angle, which was not the case. This made us curious to take a closer look at our data to see how flap angle affected distance, and what flap angle would provide the best results in a plane being designed for flying long distances.
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As can be seen by the results during our analysis, all flap angles provided significantly different distance readings, aside from 30Ëš and 60Ëš, which did not have enough statistical evidence to claim that they were different. Although there is statistical difference between the steeper angles, a 0Ëš flap angle differed tremendously from the remaining angles. Please reference Figure 25 on the Analysis page. As can be seen, a 0Ëš elevator flap angle showed consistent short travel distances when compared relatively to the 30Ëš, 60Ëš, and 90Ëš flap angles. Given this statistical evidence, we are lead to believe that a flap angle greater than 0Ëš will provide much farther traveling distance when compared to having no elevator flap (or a flap angle of 0Ëš), assuming a completely horizontal release velocity . This is an interesting finding that we could draw important conclusions from that will aid in more effective paper plane designs in the future. As can be seen below in figure 32, the paths traveled by the planes at 0Ëš elevator flaps versus those with 30Ëš, 60Ëš, and 90Ëš flap angles traveled much shorter.
Figure 32: This graph is an exaggerated depiction of the different paths the planes took.
The Final Destination
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At the beginning of our experiment we thought that increasing the mass of the plane would increase its distance and velocity. We were also under the impression that we could alter the drag of the plane directly with the elevator flaps. When we found out we could not do this and that the velocity did not change significantly, we pursued finding how flap angle and mass would affect drag and distance.
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The mass of the plane did not have a statistically significant impact on the distance or drag of the plane. However, there was an overall positive relation between mass and drag, and an overall negative relation between mass and distance. We believe that the plane fell faster on a more downward path as mass increased since it had more momentum and a smaller relative lift force.
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The rear elevator flaps did have a statistically significant impact on distance, but did not on drag. The distance of the plane peaked at 30°, and was followed closed by 60° and 90°. The 0° distances were much lower than every other flap angle and was statically different from them as well. We were very surprised that flap angle changed the distance without changing the drag significantly. We originally believed that flap angle would affect drag, and therefore affect distance, but this was not the case. Distance must have been affected by the lift which was influenced by the flap angle. A major shortcoming of this project was not incorporating the lift into the experiment. We also should have varied the velocities of the planes to observe how that affected its flight. With these two additional components we could have better mastered the art of the paper airplane.
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As we touch down, we are glad that this journey has transformed you from the novice paper pilot you were before, into the expert you now are. Good luck and stay safe on your future high-velocity adventures. Please join us again soon.
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Figure 33: This picture represents the three most handsome flight attendants you will ever fly with.