Determining an Appropriate Parabolic Model

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Determining an Appropriate Parabolic Model

In this procedure, I am trying to determine an appropriate parabolic

model that fits the data I collected of whirlybird wing length vs.

time, doing so by using first principles. Also to find out which wing

length would produce longest flight time.

Method:

Firstly, I made a whirlybird model and timed how long it took to reach

the floor from a certain height. This procedure was repeated several

times, each time lessening the wing length and keeping the same

height. For each wing length, the bird was dropped three times for

maximum accuracy. Once this data was collected it was transferred into

a graph, and strange points were excluded. After this an appropriate

parabolic function was introduced, being as close as possible to the

original points. The turning point was the place where the wing length

would produce longest flight time.

Results:

[IMAGE]

Length (m)

Time 1 (s)

Time 2 (s)

Time 3 (s)

Average (s)

16

1.38

1.12

1.25

1.25

14

1.19

1.17

1.5

1.29

12

1.75

1.49

1.85

1.70

10

2.18

2.21

2.41

[IMAGE]2.27

8

2.35

2.19

2.44

[IMAGE]2.33

6

2.12

2.1

2.09

2.10

4

1.62

1.68

1.66

1.65

2

1.03

0.91

1.02

0.99

0

0.79

0.87

0.7

0.79

Above is my original data. In the graph, it can be seen that there are

two significant points that do not fit in a parabolic shape well, and

these are the first point and the last point. I decided to remove

these from my final data. The result is shown below.

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