Page 22: of Maritime Reporter Magazine (November 2004)

Naval Architecture & Marine Engineering

The Physics of Parametric Roll

When momentum is small, and the pendulum is shorter, it is easier than normal to pick up speed. / V

J ot2

Therefore, the distance travelled is farther. \

When momentum is large the pendulum is longer and it is easier to move against gravity. a2 > a.

Ny a2 > ot. the new generation of large, fast, fine formed, high deck capacity containerships has refocused attention on the problem.

Forces that induce roll are always present at sea.

They are resisted by a ship's intact stability, a balanc- ing force inherent to its shape that makes the vessel behave like a pendulum in its give-and-take with the sea. Should a force cause the ship to roll, stability pro- vides the counter-force that tries to return it to the neu- tral position. The momentum of the return movement pushes the ship a little beyond neutral, a process that continues in ever-smaller swings until momentum is exhausted and the rolling stops.

In parametric roll, something happens to upset that balance. Instead of consuming momentum, the ship accumulates it, rapidly and dangerously.

Ironically, part of the problem is a consequence of good design. Below the waterline, a typical container- ship is designed for speed, with a narrow bow and stern and a full midship section. Above the waterline, it is designed to maximize on-deck stowage capacity by extending a wide main deck as far forward as possible, inducing significant bow flare, and as far aft as possi- ble with a large stern overhang.

As the vessel passes through the waves, it encounters a series of wave peaks and troughs. The speed at which this happens is called the encounter frequency. If the

Containerships are Particularly Susceptible to Parametric U<>ll ship length is close to the wavelength, it will experi- ence a series of situations in which the midship is sit- ting either deep into a peak or shallow in a trough, while, at the same moment, the bow and stern are each either shallow in a trough or deep in a peak respective- ly. In terms of the hull's contact with the sea, the ship effectively changes its beam on a regular basis, from slim (when the midship is on a peak) to wide (when the bow and stern are on peaks).

Because stability varies with beam, as the vessel drives through the series of wave fronts, its stability - the source of its resistance to roll - changes dramati- cally as the midship moves from crest (maximum) to trough (minimum). This variation is the underlying condition that drives parametric roll. vjB«P»$t

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Circle 210 on Reader Service Card 22 Maritime Reporter & Engineering News