Deep math to find cargo ships

Cargo ships lost over 3,000 containers in 2020, and reportedly another 1,000 have already fallen overboard in 2021, according to the World Shipping Council. For comparison, the Council estimated an average annual loss of 779 containers between 2017 and 2019. The damage is inconvenient for you, but can also disrupt entire supply chains.

A team from the Norwegian University of Science and Technology (NTNU) might have a solution to these maritime woes. Using a few simple calculations, researchers can predict the height and direction of incoming waves without relying on expensive, and occasionally unreliable, wave radar equipment on the vessel itself. Currently the team is testing their method on stationary ship models. But one day, it could help captains avoid disaster.

“If we know the waves, then we know everything we want,” says Zhengru Ren, postdoctoral fellow at NTNU. Waves hold crucial information about ocean variables, like the swell height and depth, which provide valuable insight to sea captains. In March, Ren and company published a paper in the journal Marine Structures detailing their new wave-analysis approach.

“…MARINE TECHNOLOGY IS MOVING TOWARD DIGITALIZATION…ONE HUNDRED YEARS AGO, CAPTAINS HAD NO INFORMATION ABOUT THE SEA STATE.” It involves a concept called the “wave buoy analogy,” which relies on a ship’s size, shape, and motion responses to the water to understand the overall sea state (including wave direction, height, and frequency). This all hinges on the scientists’ ability to treat ships like buoys. The flotation markers sit on the ocean’s surface, moving in tandem with the sea itself—rising and falling with a wave’s peaks and troughs—so, the buoy’s movement (or the ship, in this case) is a proxy for the ocean’s movement.

Ren’s team has added in a new factor: the ship’s often asymmetrical geometry. The team can add that data into its pre-sail calculations, called “response amplitude operators” (RAOs). Ren says captains can easily plug those into a simple algebraic equation, along with a vessel’s motion, then use regression-based methods to solve for the wave spectrum. That’s a measurement detailing the sequence of waves in the sea, helping captains see into the ocean’s future behavior.