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Metacentre has a direct relationship with a ship's rolling period.
KM is the distance from the keel to the metacentre.
The metacentre is commonly designated as point M in naval architecture.
The distance between the centre of gravity and the metacentre is called the metacentric height.
There is also a similar consideration in the movement of the metacentre forward and aft as a ship pitches.
It is calculated as the distance between the centre of gravity of a ship and its metacentre.
The metacentre can be calculated using the formulae:
Metacentre is determined by the ratio between the inertia resistance of the boat and the volume of the boat.
The metacentre remains directly above the centre of buoyancy regardless of the tilt of a floating body, such as a ship.
This passenger, physicist Professor William Bragg, concluded that the ship's metacentre was just below her centre of gravity.
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 the point where the lines intersect (at angle φ) of the upward force of buoyancy of φ dφ.
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 point at which a vertical line through the heeled centre of buoyancy crosses the line through the original, vertical centre of buoyancy is the metacentre.
In the diagram to the right the two Bs show the centres of buoyancy of a ship in the upright and heeled condition, and M is the metacentre.
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.
In a boat, the swing arm is a distance called "GM" or "metacentric height", being the distance between two points: "G" the center of gravity of the boat and "M", which is a point called the metacentre.
"The Achilles has a distance of about 3 feet between the centre of gravity and the metacentre, and is a remarkable steady ship; whereas the Prince Consort, with a distance of 6 feet, rolls much more than the Achilles."
The metacentre is considered to be fixed for small angles of heel; however, at larger angles of heel the metacentre can no longer be considered fixed, and other means must be found to calculate the ship's stability.
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).
