Question

Describe the effect on GM of rolling and how bilge keels, anti rolling tanks and stabilizer fins reduce the amplitude of rolling.

The natural rolling period of a ship maybe estimated by the formula:

2πk/√gGM seconds

Rolling period P=

where GM is the metacentric height

k is the radius of gyration of the loaded ship about a longitudinal polar axis.

Thus a large metacentric height will produce a small period of roll, although the movement of the ship may be decidedly uncomfortable and possibly dangerous. A small metacentric height will produce a long period of roll and smooth movement of the ship.

The simplest form of stabilization, bilge keels, are often fitted even when other more sophisticated methods of roll reduction are used. Cheap and easy to maintain, they can provide up to 30% roll amplitude reduction and are effective when a ship is at rest or making headway.

These stabilizes use the movement of slack liquid in a tank to produce a moment in opposition to the rolling, moment.  Since the liquid, in the tank, is a separate mass from the vessel it will possess different inertia.  When the vessel rolls, there will be a time lag before the water begins to-move in the same direction.   If the water movement in the tank can be controlled so that it is continuously out of phase with the movement of the vessel, then there will be an anti-roll moment

The tank system to control the water movement may be one of three types, namely;

Pure Passive in which the movement of water is controlled by vertical or horizontal restrictions such as baffle plates or manually operated valves.

Controlled Passive in which the water movement is controlled by air or water valves
acting in response to a roll sensing device such as a gyro.

Active Controlled in which the water movement is aided by the addition of an impeller  or pump.   Large masses of water need to be moved continually which requires high power.   Initial high cost together with higher maintenance make this an expensive  system.   Control is again  related to a roll sensing device such as a gyro.

Anti-heeling tanks

Container ships and RO-RO (roll on—roll off) vessels are usually fitted with anti-heel tanks which enable the ship to be kept upright during uneven loading of cargo. Transfer of liquid from one tank to the other is by pump or compressed air.

Controlled passive system stabilizing tanks are used in the anti-heeling arrangements of some ships. The simplest method in this scheme, for transferring the liquid, makes use of compressed air admitted to the top of either tank, to force the liquid from one to the other.

FIN STABILISERS

This system consists of fixed or retractable fins fitted port and starboard, ideally at the point of maximum beam and with the fin axes intersecting the round of bilge in line with the ships rolling centre.

The fins are aerofoil in shape, similar to a rudder, and produce a hydrodynamic force when turned to an angle to the flow of water. As the water flows around each fin, pressure differences are created, generating a force with an vertical component (lift) and a longitudinal component (drag). The fins are fitted port and starboard at about bilge keel level in the midship region of the ship so that forces generated give a maximum couple to oppose rolling