Navigating is necessary, with mathematics – 10/17/2023 – Marcelo Viana

According to a report by the World Shipping Council, almost 1,400 containers fall from cargo ships into the sea every year (in 2020 there were more than 3,000 losses!). It is a significant damage to world trade.

This problem can be mitigated if we know how to better predict the height, depth and direction of the waves. Meteorology is an important factor, but there are others: even in good weather, waves can behave in very different ways. Specific radar equipment can help, but it is expensive and not every ship has it, and it is not always reliable.

In an article published in the journal Marine Structures, researchers from the Norwegian University of Science and Technology proposed an interesting approach. The initial idea is called “wave buoy analogy”: thinking that the ship is a buoy, rising and falling together with the ocean itself, and using this floating movement to calculate information about the present and, above all, future behavior of the sea. waves.

In theory, the calculation is very simple: just solve a linear equation, which is the easiest type there is. Of course, difficulties arise in practice. The team is currently testing the method on stationary ship models, with promising results. A challenge will be required to apply it to moving ships, the analogy of which to buoys is less obvious.

One issue that needed to be resolved is that ships do not have a buoy shape (doughnut or ball): the geometry of the ship’s hull needs to be taken into account in the calculation. In fact, the wave-buoy analogy has been known since the 1980s, but the Norwegian team found that by itself it does not give very precise results.

To make it work, they needed to smooth the data using a technique called the Bézier curve, named after the French engineer Pierre Bézier (1910–1999), who developed and popularized it. I’ll talk about him next week.

The most curious thing is that Bézier was working for Renault, and his objective was to enable the use of computers to design beautiful and functional bodies for the cars produced by his employer. That these same ideas are equally useful in navigation and, in fact, are the basis of virtually any CAD (computer-aided design) project today, is yet another manifestation of the universality of mathematics that makes it such a powerful tool for understanding and changing the world. world.

LINK PRESENT: Did you like this text? Subscribers can access five free accesses from any link per day. Just click the blue F below.