- 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
Fundamental of Buoyancy
DisplacementThis 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- ListingThe 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
Affects of listing to larger angles or low freeboard
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 MomentsWhen 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 StabilityThe 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.
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