What is transverse metacentric height?

What is transverse metacentric height?

The distance between G and M is known as the metacentric height (GM). A stable vessel when upright is said to have a positive metacentric height (GM), i.e. when the metacentre (M) is found to be above the centre of gravity (G). This is usually referred to as having a positive GM or a positive initial stability.

How do you find the Metacenter?

The position of the metacentre is found by considering small inclinations of a ship about its centreline, Figure 3.8. For small angles, say 2 or 3 degrees, the upright and inclined waterlines will intersect at O on the centreline. The volumes of the emerged and immersed wedges must be equal for constant displacement.

What is transverse metacentre of a ship?

Initial Transverse Metacentre Is defined as the point of intersection of successive lines of action of buoyancy force (Bf) when the ship is in the initial upright condition and subsequently heeled conditions. It is assumed to be at a fixed position when the ship is heeled within small angles only.

What is the minimum initial transverse metacentric height?

0.15 meter
Minimum metacentric height should be 0.15 meter.

When a weight is moved in transverse direction it may cause?

1. Movement of Weight Athwartship: Movement of any weight athwartship (in a transverse direction) will alter the position of the centre of gravity of the ship (from G to G1), as shown in the figure below.

What is transverse metacentric radius?

The metacentric radius BM depends entirely on the geometry of the underwater hull and can be calculated from the formula, BM = I/V where I is the transverse moment of inertia of the waterline plane about the centreline axis, and V is the immersed volume of the hull.

What is formula of metacentric height?

The metacentric height (GM) is a measurement of the initial static stability of a floating body. It is calculated as the distance between the centre of gravity of a ship and its metacentre. A larger metacentric height implies greater initial stability against overturning.

How can I increase my metacentric height?

A greater range of metacentric stability can be built into a ship by raising the uppermost watertight deck to a higher position above the calm-water plane of flotation. The ship can then heel to a greater angle before water comes over the lower deck edge.

What is height above keel?

The height of the metacentre above the keel, or other selected point, depends upon the shape and size of the underwater body and of the at-rest waterline. The total height KM is the sum of the height KB of the centre of buoyancy above the keel and the height BM of the metacentre above the centre of buoyancy.

What is the metacentric height of a ship?

The metacentric height ‘GM’ is the measure of initial stability of a ship at small angles of heel for all ships. In any condition of loading the GM should be positive. IMO criteria require that at all stages of loading, discharging or sailing the minimum GM should be 0.15 m.

What is the metacentric height of the transverse metacentre?

Metacentric Height. As stated above the distance between the Transverse metacentre M and the centre of gravity G is the GM, the metacentric height. If M is above G the metacentric height is Considered as positive and if below G, it is Considered as negative.

How to calculate the initial metacentric height ( GM )?

Moment of statical stability = W × GZ But in triangle GZM:GZ = GM sin θ ° ∴ Moment of statical stability = W × GM × sin θ ° From this formula it can be seen that for any particular displacement at small angles of heel, the righting moments will vary directly as the initial metacentric height (GM).

When to use GZ instead of metacentric height?

Metacentric height is no longer a suitable measure of stability and the value of the righting arm, GZ, is used instead. Adrian Biran, Rubén López-Pulido, in Ship Hydrostatics and Stability (Second Edition), 2014