Ship’s motions at sea

A vessel under sea has two types of movements:

• Desired, to move the ship from one point to another and get she achieves the objectives for which  was built
•  Unwanted, occurring mainly as a result of the waves and wind on the ship and causing trouble, inconvenience and danger to the vessel, persons and cargo, so they try to minimize them.

In this post I will only refer to the second type of movements, motions, relating to ships sailing on the surface.

The ship motion in a 3D space is made up, like any other solid, of the motion of its center of gravity and the movement or rotation around that point. The six possible motions, summarised in the following table, consist of three translations and three rotations, which refer respectively to the trajectory of the center of gravity and the rotations  around the main axes through it. Names are given in Spanish and English languages​​.

Reference axis	Translations	Turns r/ ref. axis
Longitudinal x	surge (avance)	roll (balance ó rolido)
Transversal y	sway (deriva)	pitch (cabeceo)
Vertical z	heave (arfada)	yaw (guiñada)

In the following drawing the three axes are shown, for which the movements of translation and rotation relate.

The most known ship motions are the roll around the longitudinal axis and the pitch about the transverse one. Then comes as most important the yaw motion, which has great significance in the ship maneuverability controlled by the rudder(s) and thruster(s). Other motions (translations) are less known and hardly considered as parameters that constrain the ship design.

I here mention some characteristics of the three most important motions and about their control at the  ship design stage. At this site some simple animations are displayed to show them (clicking with the mouse).

Roll: This motion is largely influenced by the ship  transverse stability and has a great importance on the comfort of persons on board and the safety of cargoes that for large rollings can move and threaten the vessel  stability. In this motion the two important factors are the amplitude, measured in degrees of heel, and its period, the time for one complete cycle port to starboard. There are formulas that relate the approximate value of the rolling period with some ship dimensions and features like transverse stability, measured by her metacentric height, which can serve as a guide in the initial ship design. One simple formula is this

T = k B / Sqroot (GM)

T: rolling period in seconds

K: constant that varies between 0.7 and 0.8 depending on type and size of vessel

B: Ship breadth in meters

GM: metacentric height in meters

The decrease in the rolling amplitude is achieved by bilge keels, which are placed in almost all vessels of a certain size and with stabilizers, active (retractable fins) or passive (tanks with liquid moving synchronously).

If the rolling period in a given vessel condition coincides with the period of the driving force, produced by the passage of the waves, the so-called resonance phenomenon occurs, in which the rolling amplitude is gradually increasing up to produce the ship capsizing, if not prevented by a change of course or speed to break the sync.

Pitching: This motion is closely related to the ship length and her longitudinal moment of inertia, conditioned by their weights distribution, lightship and cargo. It is an important factor in ship behavior at rough seas but it is difficult to consider in the initial design stage. A large pitching motion with insufficient forward draft can cause pounding in the hull bottom and produce structural damage, so Classification Societies require a minimum fore draft in ballast condition.

Yaw : This motion involves turning the ship around its vertical axis and can be produced by the action of wind and waves and in turn is mainly controlled by rudder(s). It is very important in the vessel design within the consideration of maneuverability issues. In the GetxoNaval program there is a module dedicated to maneuverability in the initial desing stage and, in particular, yaw motions are related to the so-called first and second overshoot angle.

References:

1. Basic design of the merchant ship (El proyecto básico del buque mercante). Ricardo Alvariño, Juan José Azpiroz , Manuel Meizoso. Naval Engineering Editorial Fund COIN
2. Theory and behavior of waves at sea. Josep R. Vidal Bosch
3. GetxoNaval program