Metacentric height

The metacentre of the floating body, for example, a vessel is important for the stability of the floating position of the ship. If the float position disturbed by an external force, so there is the old swimming position after the end of the fault again when the metacentre is above the center of gravity. The vessel is located in such as a cradle, which rolls on the circumference of a circle. The center of the circle corresponds to the metacentre.

Definition

The metacentre of a vessel or generally a floating body, the intersection of the lift vectors that belong to two neighboring angular orientations. So there are at any rotation axis and each angular position a metacentre. Of importance and therefore also provided with a special name for the Breitenmetazentrum M or MB ( for rotations around the longitudinal axis ) and the Längenmetazentrum ( for rotations about the transverse axis ) ML, where the ship is generally accepted floating upright.

Calculation

The metacentric height above the keel K is obtained by adding the route Kiel - form focus B and the smallest moment of inertia of the waterplane area divided by the displaced volume:

2 examples:

1 ) A pontoon with the length L and the width B of the depth T.

The volume,

The area moment of inertia about the longitudinal axis,

The geometric center of gravity is on.

Thus, the distance

2 ) A circular cylinder of diameter D and length L floats on draft T. An account is not required here because the lift vector always passes through the center of the circle. This applies to every angle of heel and every draft. Thus is.

Metacentric height

The distance from the center of gravity G to metacentre M is called metacentric height GM. The center of gravity G of the floating body is located vertically below the metacentre of the assumption that no external forces or moments acting on the body. That is, the body moves until this condition is met. The metacentric height is significant for assessing the stability at low heel angles. They can be determined by an inclining experiment, so that you can determine the position of the center of mass. An estimate of the metacentric height can also be obtained from the rolling period.

Righting lever

To assess the stability of a ship, the knowledge of the metacentric height is generally not sufficient. Rather, the entire course of the righting moment versus the angle of heel is important. To obtain a vendor independent of the vessel size value divided you the righting moment by the ship's weight and so receives the righting lever. It is equal to the distance of the center of gravity from the lift vector. The metacentric height GM is equal to the slope of the tangent to the curve at the origin.