CALCULUS 3 PROJECT 1

In this project our team of engineer-pirates was to evaluate the pros and cons of an escape path, which was to be utilized after stealing a flux capacitor from Buzz Lightyear and his fellow Space Rangers, and provide our captain with answers to his queries about various aspects of his chosen escape path.

I was the leader of my group, and used Mathematica to write the code for the project. Some of the answers we had to provide our captain involved computing TNB Frames, trajectories of objects in 3D space, the speed and acceleration of those objects, and the curvature of their paths. The graphs shown below are a sample of those in the technical report, on which my group scored a 96%.

Calculus 3 Project 1: About

Escape Path Trajectory

In this figure, the trajectory of the escape path over a time interval of 10 minutes is mapped using 601 points, from time 't=0' at the green dot to time 't=601' at the red dot.

Escape Path & Missile Path

The black line follows the same trajectory as in the previous figure. The red line follows the trajectory of a missle that Star Command will shoot at us once they have realized we have stolen the flux capacitor.

Distance Between the Escape Pod & Missle

Our captain had obtained information about Star Command's missle, and realized that as long as we stayed farther than half a mile away from the missle, it wouldn't detonate. This graph shows the distance between the escape pod and the missile, illustrating that if everything goes to plan there shouldn't be any need to worry about the missile.

TNB Frame and Acceleration Vector at 9.05 Minutes

Our captain was interested in seeing the TNB Reference Frame at this particular instant in time. In this graph the unit tangent vector can be seen in red, the unit normal vector can be seen in green, and the unit binormal vector can be seen in blue. The acceleration vector of the escape pod at this instant in time can also be seen in black.

TNB Frames at 5 Second Intervals

Our captain also asked us to graph the TNB Reference Frame at several instances in time in order to see how it changes as time progresses. This graph shows the same vectors in the same colors as the previous figure.

Speed Graph & Max Speed

Our captain was interested in knowing just how fast we would be travelling in our escape. This graph shows the speed as a function of time, with the maximum speed our escape pod obtained graphed as a horizontal line.

Normal Componend of Acceleration and The Spacesickness Line

As our captain informed us, one of our crew members was susceptible to spacesicnkess whenever the normal component of acceleration exceeded three times the gravity of the planet we were on. This graph shows the normal component of acceleration with respect to time and the line above which our crew member would get spacesick, illustrating that our fellow crew member might get sick toward the last few seconds of our escape.

Curvature of the Escape Path

Our captain pointed out some structural integrity issues with our escape pod if the curvature of our escape path ever exceeded two units. This graph shows the curvature of our path as a function of time and a horizontal line at two units, illustrating that there is a strong possibility of structural integrity issues around 8.5 minutes into our escape.

Calculus 3 Project 1: Work