# The Perfect Storm

## The Movie

The Perfect Storm is a 2000 semi-factual movie based on the real-life story of the fishing trawler the Andrea Gail, which sunk during an incredible storm in the Atlantic during 1991. The movie is filled with mathematical scenarios including deciding whether to risk their lives to return their fishing catch to shore through a storm.

## Math Scenario 1: Finding the Fish

When the fishing boat first heads out, they are initially unsuccessful in finding any fish, which causes tension amongst the crew and also sets up the bad decisions made later in the movie.

Let’s say it takes 2 hours to fully investigate a potential fishing location, which will give the crew an idea of whether there are any fish in a circle of radius 5 km.

If they work 16 hours a day for a week, what area of ocean can they investigate for fish in a full 7 day week? Ignore any transit time between search locations.

*Area = hours worked per day × days per week / hours per location × circle area*

*Area = 16 × 7 / 2 × PI × r ^{2}*

*Area = 16 × 7 / 2 × PI × 5 ^{2}*

*Area = 4398 km ^{2}*

## Math Scenario 2: Risking the Storm

The fishermen finally get a big catch of fish, but the ice machine on the boat breaks down, giving them a very limited time to return to shore before their catch spoils.

Knowing there is a storm in the area, the crew make the fateful decision to head back through the building storm.

*Dikobrazik / 123rf.com.*

Let’s say the crew had decided to try an alternative port, as shown in the diagram above. One option would be the Azores, approximately 2200 km east and 600 km south of their position.

The other option would be a route back to Bermuda, avoiding the worst of the storm and travelling one quarter of a circle to Bermuda, located approximately 600 km south and 600 km west of their current position. Due to wave conditions, they estimate their speed going to Bermuda will be about 40% of the speed they’d achieve going to the Azores.

We can work out which option will result in the ship reaching the safety of port quickest.

**Option 1: Azores**

We can use Pythagoras’ Theorem:

*Distance = sqrt(horizontal distance ^{2} + vertical distance^{2})*

*Distance = sqrt(2200 ^{2} + 600^{2})*

*Distance = 2280 km*

**Option 2: Bermuda**

*Distance = 0.25 × circle perimeter*

*Distance = 0.25 × 2 × PI × r*

*Distance = 942.5 km*

For Bermuda to be the faster option, the distance must be less than 40% of the distance to the Azores.

*Bermuda to Azores distance ratio = 942.5 / 2280*

*Bermuda to Azores distance ratio = 0.4134*

It isn’t, so the ship would reach the safety of the Azores slightly before reaching Bermuda.

## Real Life Example: Wave Height

Wave height is a highly studied area for many reasons: boat designers and insurance companies need to know how common giant “ship sinking” waves are, while scientists are interested in how large waves can get.

The “significant wave height” is a commonly used term that describes the average of the highest one third of waves during a certain time period. However the very largest individual waves can be significantly bigger again, up to twice as large as the significant wave height.

If you are monitoring an ocean buoy and get the following wave height readings, we could calculate the average and significant wave height:

*5, 5.5, 5.3, 4.7, 5.8, 5.6, 5.8, 5.4, 5.7*

The average wave height can be calculated by adding up all the wave heights and dividing by the number of readings:

*Wave height average = 48.8 / 9*

*Wave height average = 5.42 m*

The largest three numbers are:

*5.8, 5.8, 5.7*

So the significant wave height is:

*Significant wave height = (5.8 + 5.8 + 5.7 ) / 3*

*Significant wave height = 5.77 m*

Let’s say you kept doing this for a while during a storm (thousands of readings) and got an overall significant wave height of 5.6 metres.

The largest wave that occurred during that storm is likely to have been approximately double that – around 11 metres!