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Aim: In this task you will develop model functions representing the tolerance of human beings

to G-forces over time.

Introduction and Background

The resulting acceleration on an object as a result of several different forces acting on it

is referred to as “G-force”. The force is in relation to gravity, in that it is the force of gravity

acting on a celestial body. A G-force is equal to twice the force of gravity 2g(“2gees”).

According to Astronauts there are different forms of G-forces. “Eye balls-in” refers to

forward acceleration, where the body is pushed backwards and backwards acceleration is

referred to as “eyeballs-out”.

It’s been proven human’s are able to withstand forward acceleration rather than

backwards acceleration. Studies showed that humans are able to withstand 17g eyeballs in

compared to 12 g eyeballs out, and were able to do so for a long period time still maintaining

consciousness. Some examples are roller coaster rides which expose humans to these G-forces

but to small samples and in very short time periods.

+Gx(g)

The task

The following table illustrates the tolerance beings to horizontal G-force. The notation “+Gx”

represents a positive acceleration in the horizontal direction i.e. eyeballs-in, so that a force of

+Gx of 20 means a forward accelerating of 20 (which humans can tolerate for 0.1 minutes).

Horizontal G-Force

Time (minutes)

Time (mins)

+Gx (g)

0.01

35

0.03

28

0.1

20

0.3

15

1

11

3

9

10

6

30

4.5

The graphing program I used was Geogebra. The program allowed me to create the

graph and also manipulate the x and y numbers to match that of the chart above. I was also

able to manipulate the image so I could capture an appropriate shot. In the graph, my x values

are represented by the time values. The time is represented by the domain of

where x because the value of time can not equal 0. The value of “y” is represented by the

horizontal G-force . The graph appears to be decreasing in relation to the

horizontal G-force in relation to an increase in time. This suggests that human beings can

tolerate a significantly less horizontal G-force for an extended period of time. This will only lead

to assume this trend will continue so long as the graph continues

To plot the ln (x) I used the program graphmatica, it was able to effectively plot the graph

y= ln (x) and y= -ln (x). The reason I chose the function y= -ln (x) was because it would be

reflected through the x-axis and this more accurately reflect the graph of the “tolerance of

human beings to horizontal G-force.” As well the asymptote of would still be reflected in

this graph. The graph in red represents the function y= ln(x) and the graph in white represents

the function y= -ln(x).