 # How do you calculate GZ?

## How do you calculate GZ?

GZ=GM sin φ and is called the righting lever. GM is known as the metacentric height. For a given position of G, as M can be taken as fixed for small inclinations, GM will be constant for any particular waterline.

What is a GZ curve in ship stability?

GZ is known as the righting arm. The plot of the righting arm GZ calculated as the function of the heel angle, at constant displacement and vertical centre of gravity KG values, is used to measure the ship stability at large angles of heels. It is called the curve of statical stability.

How is ship stability calculated?

GM – Metacentric Height: This measurement is calculated by subtracting KG from KM (GM = KM – KG). GM is a measure of the ship’s initial stability. BM – Metacentric Radius: The distance between the Center of Buoyancy and the Metacenter.

### What is the formula for dynamical stability?

Ship Stability When the ship is upright the force ‘W’ acts upwards through B and downwards through G. These forces act throughout the inclination; b = w. This is known as Moseley’s formula for dynamical stability.

What is G in stability?

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.

What is maximum GZ on GZ curve?

The maximum righting lever (GZMAX), represented by point ‘B’ in the graph is proportional to the largest static heeling moment that is required to bring the ship back to its upright position. The value of maximum GZ and the angle at which it occurs, are important values.

## What is stability curve?

In algebraic geometry, a stable curve is an algebraic curve that is asymptotically stable in the sense of geometric invariant theory. This is equivalent to the condition that it is a complete connected curve whose only singularities are ordinary double points and whose automorphism group is finite.

What is the initial stability of a ship?

Initial stability or primary stability is the resistance of a boat to small changes in the difference between the vertical forces applied on its two sides.

What is angle of Contraflexure?

Angle of contraflexure – the angle of heel up to which the rate of increase of GZ with heel is increasing. Though the GZ may increase further, the rate of increase of GZ begins to decrease at this angle. The range of stability – where all GZ values are positive. The maximum GZ lever & the angle at which it occurs.

### What is angle of heel?

Angle of loll is the state of a ship that is unstable when upright (i.e. has a negative metacentric height) and therefore takes on an angle of heel to either port or starboard. When this occurs, the vessel goes to neutral equilibrium, and the angle of heel at which it happens is called angle of loll.

How does the GZ curve affect ship stability?

In case of Ship A, even when the initial metacentric height becomes slightly negative (notice the initial slope for Loadcase 2), the ship will heel upto a certain angle, but as the ship keeps heeling, due to the convex upward curvature of the GZ curve the righting lever becomes positive again.

Which is the true stability of a ship?

The stability of a ship thus is GZ T rather than GM T. The GZ at various angles of heel i.e. GZ curve represents the true stability status or picture of the ship.

## What is the stability curve in figure 4-2?

Figure 4-2 is a typical curve of stability in which a series of righting arms is plotted vertically against corresponding angles of heel which are plotted horizontally. This curve indicates that initial stability increases with angle of heel at almost a constant rate, but at larger angles the increase in GZ begins to level off.

How is the GZ curve used in Denmark?

In order to assess whether a vessel has sufficient stability, the Danish Maritime Authority has a number of requirements, all of which have to be met. The GZ curve is used for this purpose. The requirements ensure that the vessel has: 1. Sufficient beginning stability (stability at small heeling) 2.