Maths Standard Level

SL TYPE II

Candidate Number: 002379- 015

School Number: 002379

School Name: ESCAAN International School

Jan Bogaarts Ramirez

13/01/2012

Introduction:

When various forces being applied on one body or object that results in a certain acceleration, on that body, a force will act and we call it G-force. An interesting aspect of G-Force is the way human beings tolerate it, in fact the terminology that we use for G-Force on human bodies was developed by astronauts and is based on their sensations. When the acceleration is forward we refer to the G-Force as “eyeballs-in”, when backwards as “eyeballs-out”, when upwards as “blood towards feet”. G-force is measured in (g) “gees” so if there is a G-force equivalent to four times the force of gravity it is 4g. In this project I’m going to analyse, define and comment any apparent trends, models or statistics I will obtain from observing the data I was given about horizontal and vertical G-force tolerance of human beings, measured in time, and try to obtain the function modelsthe data and so the graph that we can make.

The first thing we have to observe is that human are more tolerant to horizontal G-force and of the two horizontal types we are stronger against “eyeballs-in”. This just means that we can withstand more G-force power in thatway without fainting or long term harming ourselves. +Gx (g) represents a positive acceleration in the horizontal direction i.e. eyeballs-in, so that a force of +Gx of 20 means a forward acceleration of 20. This was observes in previous experiments:

Horizontal “eyeballs-in” G-force & time humans tolerate it |Time (min) |+Gx (g) |

|0,01 |35,0 |

|0,03 |28,0 |

| 0,10 |20,0 |

|0,30 |15,0 |

|1,00 |11,0 |

|3,00 |9,0 |

|10,00 |6,0 |

|30,00 |4,5 |

To examine and analyse the data as well as possible, I developed a graph. Using the graph I will develop a function that best suites the collected data and represents the relationship between it.

First, to clear up the notation I state that f (+Gx) = time. This means the independent variable is +Gx, in gravity (g), since it affects how much time the human body will resist the power of the force. The dependent variable is Time, in minutes, since, depending on the intensity of the G-force, it will increase or decrease. Also, we can say that y>0 because we have to be able to measure the tolerance and this wouldn’t be possible with a value of 0 or less and x > 0 because in this case G-Force will always be positive since it is “eyeballs-in”/ positive acceleration.

By simply observing the graph we can already see that as the G-force increases the Time of tolerance decreases and when it decreases the time increases. But it is not that easy, there is a lot of more information we can take from the graph. We can also say that as x approaches positive infinity, y comes closer to zero but it never reaches it and this is called an assymptope. This also happens as X is approaching 0; then Y approaches positive infinity. I can also observe that the graph is similar to an exponential X -1, X >0

[pic]

And fits well with the actual graph so I decided to use this function as the modelling function: f(x) = a(x-d) b+c. Since there is also no horizontal or vertical translation the c and d values are equal to 0 so that leaves us with a & b values. Using my trigonometric function knowledge I knew that a serves for the stretch or compression of the graph whereas the b value determines...