# MAT 10042_2014

## Scenario:

In a maritime environment it's often necessary to protect specific assets from potential collision, or simply from being approached too closely by unidentified vessels. In this project we will look at the mathematics underlying the user interface to this function.

In particular, we will suppose that there is a sensitive facility, say an oil platform, at a specific location given by a set of coordinates. We imagine that the user has requested a critical distance, designated D, and a critical time, designated T. We decide that if a vessel will approach to be less than distance D, and the time of the closest approach will be less than T from now, then an alarm should be raised.

This is called the Closest Point of Approach (CPA) calculation.

After implementation and demonstration the customer declares that this is, in fact, not what they wanted. What they wanted was an exclusion zone of radius D, and that if a vessel was going to enter that exclusion zone in less than time T then the alarm should be sounded.

This is called the Time To Incursion (TTI) calculation.

## Project - Phase 1:

Your task is to investigate the mathematics underlying these calculations. Within your group you should derive the calculations that need to be done in order to determine if an alarm should be raised for a given vessel on a given course, travelling at a given speed.

The outcome of this phase of the project will be equations that take a vessel's location and velocity, and the location of the protected asset, and determine whether or not an alarm condition exists.

## Project - Phase 2:

You now have a choice between three options.

• a) You may further investigate the CPA calculation, exploring the benefits
and drawbacks of the calculation, and experimenting with scenarios that
do and do not raise the alarm. The objective is to understand all the
implications of this calculation, and the parts played by the parameters D and T.
• b) As for part A, but for the TTI calculation instead.
• c) Compare and contrast the two calculations, discussing which is better,
which might be more appropriate, and the benefits and drawbacks of each.
Whichever of these options you choose, your results are to be presented in a poster whose intended audience is a Master Mariner or Harbour Master. They would be expected to understand the problem itself, but will most likely not immediately understand why one technique is more appropriate than the other, and will need clear examples to explain the difference, implications, and benefits.

## Techniques and Methods:

To help you understand the context you are encouraged to play with tools such as GeoGebra to make a dynamic model of the situation, and then to explore what happens as you change the settings of D, T, and the vessel's location, course, and speed. It is not necessary to do so, but it may help your understanding of the implications of the different possible values.

## Timing:

This project will last for three weeks, starting on March 10th, and the final date for handing in is March 28th. You are strongly encouraged to produce a simplistic mockup of the poster by March 21st, and to spend the last week producing and fine tuning details on the final version.