Different Centres
The centre of buoyancy is the centre of the volume of water which the hull displaces. This point is referred to as B in naval architecture. The centre of gravity of the ship is commonly denoted as point G or VCG. When a ship is stable, the centre of buoyancy is vertically in line with the centre of gravity of the ship.
The metacentre is the point where the lines intersect (at angle φ) of the upward force of buoyancy of φ ± dφ. When the ship is vertical the metacentre lies above the centre of gravity and so moves in the opposite direction of heel as the ship rolls. The metacentre is commonly designated as point MT in naval architecture.
The distance between the centre of gravity and the metacentre is called the metacentric height. This distance is also abbreviated as GM. As the ship heels over, the centre of gravity generally remains fixed with respect to the ship because it just depends upon position of the ship's weight and cargo, but the surface area increases, increasing BMφ. The metacentre, Mφ, moves up and sideways in the opposite direction in which the ship has rolled and is no longer directly over the centre of gravity.
The righting force on the ship is then caused by gravity pulling down on the hull (effectively acting on its centre of gravity) and the buoyancy pushing the hull upwards (effectively acting along the vertical line passing through the centre of buoyancy and the metacentre above it). This creates a righting moment (a kind of torque) which rotates the hull upright again and is proportional to the horizontal distance between the centre of gravity and the metacentre. The metacentric height is important because the righting force is proportional to the metacentric height times the sine of the angle of heel.
When setting a common reference for the centres, the molded (within the plate or planking) line of the keel (K) is generally chosen; thus, the reference heights are:
KB - to Centre of Buoyancy
KG - to Centre of Gravity
KMT - to Transverse Metacentre
Read more about this topic: Metacentric Height
Famous quotes containing the word centres:
“I perceive that in these woods the earliest settlements are, for various reasons, clustering about the lakes, but partly, I think, for the sake of the neighborhood as the oldest clearings. They are forest schools already established,—great centres of light.”
—Henry David Thoreau (1817–1862)
“We all have—to put it as nicely as I can—our lower centres and our higher centres. Our lower centres act: they act with terrible power that sometimes destroys us; but they don’t talk.... Since the war the lower centres have become vocal. And the effect is that of an earthquake. For they speak truths that have never been spoken before—truths that the makers of our domestic institutions have tried to ignore.”
—George Bernard Shaw (1856–1950)