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SL Type II Mathematics Portfolio

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Introduction

G-Force Tolerance

SL Type II Mathematics Portfolio

         G-force, measured in (g), is a force that acts on a body as a result of acceleration or gravity. Human tolerances of the g-force are depending on the magnitude of the g-force, and the length of time it is being applied, the direction it acts, and the location of application. The human body has a better chance at surviving horizontal g-force. Horizontal g-force is referred as “eyeballs-in”. Vertical acceleration upwards is referred to as “blood towards feet”. Research shows that humans have a much high tolerance for “eyeballs-in” than any other g-forces. The standard 1g on the Earth’s surface is caused by gravity, and to prevent humans from free-falling. As the G-forces increases, the time that a human can tolerate it significantly decreases.

Human Tolerance vs. Horizontal G-force

+Gx (g)

Time (min.)

 35

0.01

28

0.03

20

0.1

15

0.3

11

1

9

3

6

10

4.5

30

From the examination of human tolerance to horizontal G-force, a model function will be developed to represent the relationship between them. This portfolio will be focused on creating a function that best suits the table of value above.

        It is clear that +Gx, measured in gravity (g), is the independent variable in this case as it is affecting the time humans can tolerate. Thus, we can let image00.pngimage00.png horizontal G-force.

...read more.

Middle

image14.pngimage14.png

image15.pngimage15.pngimage16.pngimage16.pngimage17.pngimage17.png

image16.pngimage16.png                0.1image19.pngimage19.pngimage20.pngimage20.png

image21.pngimage21.pngimage22.pngimage22.pngimage23.pngimage23.png

image24.pngimage24.pngimage25.pngimage25.pngimage26.pngimage26.png

image27.pngimage27.pngimage28.pngimage28.pngimage30.pngimage30.png

image31.pngimage31.pngimage32.pngimage32.pngimage33.pngimage33.png

image34.pngimage34.pngimage35.pngimage36.pngimage36.png

image37.pngimage37.pngimage38.pngimage38.pngimage39.pngimage39.png

image41.pngimage41.pngimage42.pngimage42.pngimage43.pngimage43.png

image20.pngimage20.png

image44.pngimage44.png

image45.pngimage45.png

image46.pngimage46.png

image47.pngimage47.png

image48.pngimage48.png

image49.pngimage49.png

image51.pngimage51.png

image52.pngimage52.png

Right now, there are seven image53.pngimage53.png as well as sevenimage54.pngimage54.png. They are listed below.

image05.pngimage05.pngimage06.pngimage06.pngimage07.pngimage07.png

image34.pngimage35.pngimage35.pngimage36.pngimage36.png

image49.pngimage49.png

In order to find the image57.pngimage57.png which is most appropriate for the model function, we must take the average of all of image53.pngimage53.png and divide it by the number ofimage58.pngimage58.png. However, the values image59.png and image49.pngimage49.png do not fit into the average range of -3 to -4. Thus, we will eliminate those 2 values for this calculation.

image60.pngimage60.png

image61.pngimage61.png

image62.pngimage62.png

After finding the average of image63.pngimage63.png, we can use the same method to find the average of image65.pngimage65.pngby substituting image66.pngimage66.png . Again, image14.pngimage14.png and image52.pngimage52.png  does not fit in the range of the calculation, thus, we can omit those 2 values.

image12.pngimage12.pngimage13.pngimage13.pngimage14.pngimage14.png

image41.pngimage41.pngimage42.pngimage42.pngimage43.pngimage43.png

image52.pngimage52.png

image68.pngimage68.png

image69.pngimage69.png

image70.pngimage70.png

The equation which I came up with is image71.png

image72.png

        When this function is graphed with the original data points, it is apparent that the model functions, appeared in dark black, differs from the original data.

...read more.

Conclusion

image40.pngimage40.png value below 0. This is another limitation as we cannot properly predict the image50.pngimage50.png values when the image40.pngimage40.png value is below 0.

        In conclusion, I see that my model can be implied to all other relations between Human Tolerance time and G-Force. This is because all of those relationships would undergo decay, and it is certain that as G-Force is increasing, the tolerance time is decreasing. Thus, with the alternation of the image75.pngimage75.png value, I can find the functions of other relations between Tolerance Time and G-Force.

...read more.

This student written piece of work is one of many that can be found in our International Baccalaureate Maths section.

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