3.1 Dangerous ship responses in following and quartering seas
The period with which a ship travelling in following and quartering waves encounters the waves
becomes longer than in head or bow waves, and principal dangers caused in such situations are as
follows:
.1 Surf-riding and broaching-to
When a ship is situated on a steep forefront of high wave in following and quartering sea
condition, the ship can be accelerated to ride on the wave; this is known as surf-riding.
When a ship is surf-ridden, the so-called broaching-to phenomenon may occur, which
endangers the ship to capsize as the result of sudden change of ship's heading and
unexpected large heeling.
.2 Reduction of intact stability caused by riding on the wave crest at midship
When a ship is riding on the wave crest, the intact stability will be decreased substantially
according to the ship form. The amount of stability reduction is nearly proportional to the
wave height and the ship may lose the stability when the wave length is one to two times
of ship length and wave height is large. This situation is especially dangerous in
following and quartering seas, because the duration of riding on wave crest, i.e. the time
of inferior stability, becomes longer.
.3 Synchronous rolling motion
Large rolling motions may be excited when the natural rolling period of a ship coincides
with the encounter wave period. In case of navigation in following and quartering seas
this may happen when the transverse stability of the ship is marginal and therefore the
natural roll period becomes longer.
.4 Parametric rolling motion
Unstable and large amplitude roll motion will take place if the encounter wave period is
approximately equal to half of the natural roll period of the ship. This type of rolling can
occur in head and bow seas where the encounter wave period becomes short. In
following and quartering seas, this can occur particularly when the initial metacentric
height is small and the natural roll period is very long.
.5 Combination of various dangerous phenomena
The dynamic behaviour of a ship in following and quartering seas is very complex. Ship
motion is three-dimensional and various detrimental factors or dangerous phenomena
such as additional heeling moment due to deck in water, water shipping and trapped on
deck or cargo shift due to large roll motions, may occur in combination with the
above-mentioned phenomena simultaneously or in a sequence. This could create
extremely dangerous combination which may cause ship capsize.
3.2 Dangerous navigation conditions in following and quartering seas
There exist two kinds of critical conditions of encounter waves under which the dangerous
phenomena as above-mentioned are excited:
.1 When the ship speed approaches to the phase velocity of wave
When the ship speed is so high that its component in the wave direction approaches to the
phase velocity of wave, the ship will be accelerated to reach surf-riding and broaching-to
(paragraph 3.1.1). The critical speed for the occurrence of surf-riding is considered to be
1.8√L (knots), where L is ship length. It should be noted that there is a marginal zone
(1.4√L ~ 1.8√L) below the critical speed, where a large surging motion may occur, which
is almost equivalent to surf-riding in danger. In these situations, a significant reduction of
intact stability (paragraph 3.1.2) may also be induced with longer duration; and
.2 When the ship speed is nearly equal to the group velocity of wave
When the ship speed component in the wave direction is nearly equal to the wave group
velocity, that is a half of the phase velocity of the dominant wave components, the ship
will be attacked successively by high waves. The expectable maximum wave height of
the successive waves can reach almost twice of the observed wave height of the sea state
concerned.
In this situation, the reduction of intact stability (paragraph 3.1.2), synchronous rolling
motions (paragraph 3.1.3), parametric rolling motions (paragraph 3.1.4) or combination
of various dangerous phenomena (paragraph 3.1.5) may occur and create the danger of
capsize .