Rogue Wave Math

In the September edition of the Fishermen’s Voice Tom Seymour’s article on Rogue Waves touched on the source of the rogue wave phenomenon. Reading the article, retired marine and ocean engineer Henry Cygan of South Thomaston offered an explanation of the science of rogue waves. Cygan studied ocean engineering in Hawaii and marine engineering in Southern California. He spent his career working in the oil industry in offshore oil exploration, ship design, repair and construction.

Cygan said he enjoyed reading Seymour’s article, but he wanted to make a single comment. That comment was regarding the math used to calculate the scale and power of large waves combining. He also offered a graphic description of the development of a giant rogue wave. That image was based on his experiencing a 70ft rogue wave aboard a 212ft research vessel at the Flemish Cap in 1974.

Cygan said his explanation was one he had offered to others, including scientists, who had described the cumulative height effect of colliding waves. But those explanations, he said, excluded the math and therefore what is actually happening when large waves collide.

Calculating the energy potential in two combining waves is done by squaring the height of one wave, squaring the height of the other wave, then totaling the two squared heights. The square root of that total is the height of the resultant wave. For example, “It takes two 70 foot waves colliding to get a 100 foot rogue wave,” Cygan said.

The square of 70' (70 X 70) equals 4,900'. 4900'+4,900'=9,800.' The square root of 9,800' is 98.99' (98.99 X 98.99 equals 9,799).

It is not the height of waves that are accumulating, said Cygan, but the energy in those waves. Also, the number of waves that can combine in this way is generally limited to two or three waves. The famous Perfect Storm was three storms driving large waves that collided at the Flemish Cap in November of 1991. The Flemish Cap, 350 miles east of St. John, Newfoundland, is a plateau below shallow water surrounded by deeper water. Large waves in what became known as the Perfect Storm struck the Flemish Cap at different angles, swept around it and collided on the other side of the Cap. The collision of the energy in these waves created the 100 foot high rogue wave that sank the FV Andrea Gail.