Topic - 9 STABILITY CALCULATIONS

Introduction

Ship stability is an area of naval architecture and ship design that deals with how a ship behaves at sea, both in still water and in waves. Stability calculations focus on the center of gravity and center of buoyancy of vessels and on how these interact.

Ship stability, as it pertains to naval architecture, has existed for hundreds of years. Historically, ship stability calculations for ships relied on rule of thumb calculations, often tied to a specific system of measurement.

Definitions of related terms 

Centre of gravity (G)

Center of gravity is an imaginary point in the exact middle of a weight where the entire weight may be considered to act. The weight always acts vertically downwards.

Centre of buoyancy (B)

Centre of buoyancy is an imaginary point in the exact middle of the volume of displaced water where the entire buoyancy may be considered to act. (The force of) buoyancy always acts vertically upwards.

Metacentre (M)

Metacentre is a point in space where the vertical line upwards through the centre of buoyancy of the ‘inclined’ vessel cuts through the vertical line upwards through the centre of buoyancy of the ‘upright’ vessel.

Meta-centric height (GM)

Meta-centric height is the vertical distance between the Centre of Gravity (G) and the Metacentre (M). If M is above G the vessel will stay upright and if G is above M the vessel will capsize. i.e., GM positive is Stable, GM negative is Unstable.

Righting lever (+GZ) or Overturning lever (-GZ)

Righting lever is the (horizontal) distance between the two (vertical) ‘lines of action’ of the buoyancy force (upwards), and the gravity force (downwards). The size of GZ is the measure of how stable or unstable the vessel is at any particular angle of heel. For small angles of heel (less than 15°), the ‘righting’ or ‘overturning lever’ GZ = GM x sinθ (where is the angle of heel, in degrees).

Initial Stability

To be adequately stable, the meta-centric height (GM) of the loaded vessel, floating upright in still water, is required to be above a minimum value.

GM_min = 0.35 meters is a recommended minimum guidance value.

Meta-centric height can be calculated using the formula:

GM = KB + BM – KG

(Where the distances between K, B, G, and M are all in meters, KB is the vertical distance from the keel to the centre of buoyancy, BM is the vertical distance from the centre of buoyancy to the metacentre, and KG is the vertical distance from the keel to the centre of gravity).

The vertical distance between the centre of buoyancy (B) and the metacentre (M), that is

BM =I / V (where I is the inertia of the water plane area, and V is the volume of displacement.)

For a rectangular water plane area, such as that displaced by a pontoon barge, the ‘roll inertia’

I = (l x b3)/12, and for a box shaped barge the ‘displaced volume’ is V = (L x B x T) (where

L is the length, B is the beam, and T is the draught).

In order to more exactly determine the position of the centre of gravity (G) and the meta-centric height (GM) for a particular barge, an inclining experiment needs to be conducted and the results used for a stability analysis. In an inclining experiment weights are moved to the outer edge of the deck of the barge and the heel that results is measured with a pendulum.