Whirlybird


Yr 11 MATHS B
ASSIGNMENT
Task one
The aim of this assignment was to determine and create the most suitable
and efficient Whirlybird which could sustain flight times the longest. The
method followed to achieve this was a series of flight test. Different
sizes of Whirly birds were created in 2cm intervals in the length and the
width. Then each model will be dropped from the same height keeping all
variables the same, six times and recording the flight time to the ground.

The recorded flight times will be analysed and used to determine the best
Whirlybird. It will be analysed using different mathematical methods and
graphs to provide suggestions. The process taken to complete the experiment
followed the method explicitly. The recording of the whirlybird drops were
unaffected by natural elements such as the weather because it was kept
indoor in a controlled environment (wind resistance and hight control were
not a problem). The timing using a stop watch was kept by the same person
so reaction time would not defer while recording. When transferring the
data to a computer for analysis, the means and standard deviation were
calculated for each of the six drops of each whirlybird and put into datal
plots. The data plots were used to break down the information and put into
TI Interactive. It would then use it aid in the analysis process by
plotting graphs and calculating a regression.

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Task 2
Lengths cm |1ts |2nd |3rd |4th |5th |6th |mean |SD | |2 |1.42 |1.78 |2.03
|2.08 |1.6 |1.42 |1.7217 |0.291 | |4 |2.82 |1.87 |3.07 |3.16 |2.55 |2.86
|2.7217 |0.4684 | |6 |3.72 |3.6 |3.51 |4.37 |4.05 |3.69 |3.8234 |0.3246 |
|8 |4.3 |4.96 |6.01 |4.64 |4.93 |4.95 |4.756 |0.2876 | |10 |5.56 |5.38
|4.66 |4.89 |4.82 |4.77 |5.0134 |0.36604 | |12 |3.76 |3.87 |3.57 |4.03
|3.02 |3.74 |3.655 |0.3506 | |14 |1.92 |1.89 |2.3 |2.48 |3.42 |3.25 |2.8625
|0.5548 | |16 |2.01 |2.32 |2.35 |1.81 |1.98 |2.12 |2.0984 |0.2088 | |
The data above is all the information gathered during the wing length
flight tests, it was used during the experiment for the analysis process.

It consists of the six drops for each whirly bird and the mean and standard
deviation of each set. The Mean and standard deviation were calculated to
easily identify the best length for a whirlybird. The data marked in RED
were selected as the out riders they were taken out of the calculation to
ensure the results were ordinary and not unique for the information.


Task 3
The data below is the graphical representation of the results recorded
during the flight test for the best length of a whirly bird. TI Interactive
was used because of it ability to produced the most accurate and reliable
results for finding the quadratic regression and line of best fit for the
graph. The graph bellow was chosen because it depicts the movements of the
data accurately along the graph.


picpic
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(9.16379, 4.55496) Maximum
Task 4
A separate investigation was set up to the determine the best width for the
whirlybirds wings. It followed the same process and method as the first
experiment. Except for the fact that the width length would only be between
one and three cm. It had the same six drops for each of the three
whirlybirds and was recorded under the same conditions as the first
experiment, it was then recorded and the same calculations were made before
transferring the data onto a computer. It was then analysed and the
following were created using TI Interactive quadratic regression, a
graphical display and data table.


Task 5
Width cm |1st |2nd |3rd |4th |5th |6th |mean |SD | |1 |2.01 |2.32 |2.35
|1.81 |1.98 |2.12 |2.0983 |0.2088 | |2 |1.8 |2.19 |2.08 |2.28 |1.89 |2.11
|2.048 |0.2009 | |3 |2.7 |5.22 |5.76 |4.68 |2.7 |7.09 |4.6917 |1.7381 | |
The data above is all the information gathered during the wing Width flight
tests; it was used during the experiment for the analysis process. It
consists of the six drops for each whirly bird and the mean and standard
deviation of each set. The Mean and standard deviation were calculated to
easily identify the best Width for a whirlybird. The data marked in RED
were selected as the out riders they were taken out of the calculation to
ensure the results were ordinary and not unique for the information.


Task 6
The data below is the graphical representation of the results recorded
during the flight test for the best width of a whirly bird. TI Interactive
was

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