Mathematics Portfolio. In this portfolio project, the task at hand is to investigate the relationship between G-force and time by developing models that represent the tolerance of human beings to G-forces over time.

Authors Avatar

Math Portfolio Project

In this portfolio project, the task at hand is to investigate the relationship between G-force and time by developing models that represent the tolerance of human beings to G-forces over time. G-force is used to describe the acceleration that results when different forces are applied to an object. For example the g-force acting on a stationary object resting on the earth’s surface is 1 g as it results from the Earth surface’s resistance to gravity. Because there are no other forces acting on the object besides gravity, the g-force acting on a stationary object is equal and opposite to gravity.

However, when the object is under acceleration, the two different types of g-force are vertical g-force and horizontal g-force. Horizontal g-force is the measure of acceleration perpendicular to the spine which can either be forward or backward acceleration. In this portfolio I will be looking at the human tolerance for forward acceleration where the g-force pushes the body backwards.  Experiments have shown that untrained humans can tolerate up to 17 g of forward acceleration for several minutes without losing consciousness. Upwards vertical g-force, which drives the blood downwards to the feet, away from the head is typically a lot less tolerable for humans because it poses problems for the brain and eyes. On average humans can handle approximately 5 g before losing consciousness.

With the data given, I will develop individual functions that model the relationship between the time tolerable for humans versus the various measurements of forward horizontal g-force on a subject, as well as the relationship between time and upward vertical g-force. I will compare hand generated and computer generated functions to see how well the models fit the data, and discuss any limitations to the models.   

The models will be based on the data:

In both these sets of data I will define the independent variable as the G-force represented along the y-axis, and the dependent variable as the time represented on the x-axis:

  • where +Gx represents the positive acceleration in the horizontal direction in grams.
  • where +Gz represents the positive acceleration in the vertical direction in grams.
  • where t represents the time in minutes that the humans are exposed to the g-force given

There are two parameters for which the data holds true:

  1. That there is a scaling factor that moves the value of time up as it increases. There is already a trend when looking at how t increases. Each consecutive value seems to rise by .02 and .07, for which the values then seem to move a decimal place to the right to .2 and .7, and then to 2 and 7, and lastly and increase of 20.
  2. That there is an exponent or a power that must determine the functions rate of growth or decay. From the clear decrease in +Gx the exponent is likely to be negative, and whether it is an integer or a rational or irrational number, will also determine the function’s overall shape and behavior.
Join now!

The constraint to this data is that the value along the x-axis, time is always to be positive. Because time is not tangible but a representation of the duration of the day, it has come to the conclusion that time cannot be negative. Therefore whether or not this function holds true for a negative t value is irrelevant because of the real life situation at hand. Another constraint is that the data does not hold in account that there is a moment when g-force is zero in a weightless situation or a vacuum.  

Initial Data Plot:

...

This is a preview of the whole essay