Stability

Stability

Fundamental of Buoyancy

• A Floating body displaces a volume of water equal to the weight of the body
  
• A Floating body will be buoyed up by a force equal to the weight of the water displaced

Displacement

This is the equivalent mass of sea water (sg = 1.025) displaced by the hull. It is therefore equal to the Total weight of the vessel. The units are tons (long)

Small angle stability- Listing

The center of Buoyancy B is a theoretical point though which the buoyant forces acting on the wetted surface of the hull act through.
The center of Gravity is the theoretical point through which the summation of all the weights act through

Affects of listing

The position of the center of buoyancy changes depending on the attitude of the vessel in the water. As the vessel increases or reduces its draft so the center of buoyancy moves up or down respectively caused by increase in water displaced. As the vessel lists the center of buoyancy moves in a direction governed by the changing shape of the submerged part of the hull. For small angles the tendency is for the center of buoyancy to move towards the side of the ships which is becoming more submerged

Affects of listing to larger angles or low freeboard

Note this is true for consideration of small angle stability and for vessels with sufficient freeboard. In the example shown above when the water line reaches and moves above the main deck level a relatively smaller volume of the hull is submerged on the lower side for every centimeter movement as the water moves up the deck. The center buoyancy will now begin to move back towards centreline

The Metacenter M is a theoretical point through which the buoyant forces act and small angles of list. At these small angles the center of buoyancy tends to follow an arc subtended by the metacentric radius BM which is the distance between the Metacenter and the center of buoyancy.
A the vessels draft changes so does the metacenter moving up with the center of buoyancy when the draft increases and vice versa when the draft decreases. For small angle stability it is assumed that the Metacenter does not move

Righting Moments

When a vessel lists there center of buoyancy moves off centreline. The center of gravity , however, remains on centerline

For small angles up to 10 degrees depending on hull form the righting Arm GZ can be found by
GZ = GM (Metacentric Height) x SinØ It can be seen that the greater the metacentric height the greater the righting arm is and therefore the greater the force recovering the vessel ( Righting Moment RM )to the upright position.

Negative Stability

The above examples all show the metacentre above the centre of gravity. This creates a righting arm at small angles always returning the vessel to the upright position. Where the metacentre is at or very near the centre of gravity then it is possible for the vessel to have a permanent list due to the lack of an adequate righting arm. Note that this may occur during loading operations and it is often the case that once the small angle restrictions are passed the metacentric height increases and a righting arm prevents further listing. In a worst case the metacentre may be substantially below the center of Gravity.

Stability Curve

Draft Diagram

The Draft diagram is a simple and quick method of determining the following
• Moment to Trim per cm (MTC)
• Tonnes per Centimetre Immersion (TPC)
• Height of Metacenter (KM)
• Longitudinal Center of Flotation (LCF)
• Longitudinal Center of Buoyancy (LCB)

Worked example.

A line is drawn joining the ford and aft draft marks. (Blue Line). The Displacement can be read directly off
A horizontal line is drawn passing through the intersection of the blue line onto the displacement curve (Red Line). MTC, TPC, KM & LCB are read where the redline intersects their respective scales.
A vertical line (green) is dropped from the intersection of the blue line with the displacement curve from which can be read the LCF off the respective scale

Cross Curves of Stability

This may be used to determine the righting arms at different displacements and different angles of inclination