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**Stability**

*Buoyancy*

The Laws Of Buoyancy

Floating objects possess the property of buoyancy.

A floating body displaces a volume of water equal in
weight to the weight of the body.

A body immersed (or floating) in water is buoyed up by
a force equal to the weight of the water displaced.

Centre of buoyancy

C of B can be defined as the geometrical centre of the
underwater volume and the point through which the total force of buoyancy may
be considered to act vertically upwards with a force equal to the weight of the
water displaced by the body.

For the purposes of freeboard computation, ships are
divided into type “A” and type “B”.

Type “A” ships

A type “A” ship is one which:

Is designed to carry only liquid cargoes in bulk;

Has a high integrity of the exposed deck with only
small access openings to cargo compartments, closed by watertight gasketed
covers of steel or equivalent material; and

Has low permeability of loaded cargo compartments.

*Type “B”
ships *

All ships, which do not come within the provisions
regarding type “A” ships in above paragraphs, are considered as type “B” ships.

Type “B” ships, which have hatchways fitted with hatch
covers, are assigned freeboards based upon the values given in the rules.

Conditions of equilibrium

The condition of equilibrium after flooding shall be
regarded as satisfactory provided:

The final waterline after flooding, taking into
account sinkage, heel and trim, is below the lower edge of any opening through
which progressive down flooding may take place.

Such openings shall include air pipes, ventilators and
openings which are closed by means of weather tight doors or hatch covers, and
may exclude those openings closed by means of manhole covers and flush
scuttles, cargo hatch covers, remotely operated sliding watertight doors, and
sidescuttles of the non-opening type.

However, in the case of doors separating a main
machinery space from a steering gear compartment, watertight doors may be of a
hinged, quick-acting type kept closed at sea, whilst not in use, provided also
that the lower sill of such doors is above the summer load waterline.

If pipes, ducts or tunnels are situated within the
assumed extent of damage penetration, arrangements shall be made so that
progressive flooding cannot thereby extend to compartments other than those
assumed to be floodable in the calculation for each case of damage.

The angle of heel due to unsymmetrical flooding does
not exceed 15deg. If no part of the deck is immersed, an angle of heel of up to
17deg. may be accepted.

The metacentric height in the flooded condition is
positive.

When any part of the deck outside the compartment
assumed flooded in a particular case of damage is immersed, or in any case
where the margin of stability in the flooded condition may be considered
doubtful, the residual stability is to be investigated.

It may be regarded as sufficient if the righting lever
curve has a minimum range of 20deg. beyond the position of equilibrium with a
maximum righting lever of at least 0.1 m within this range. The area under the
righting lever curve within this range shall be not less than 0.0175 m. rad.

The Administration shall give consideration to the
potential hazard presented by protected or unprotected openings, which may
become temporarily immersed within the range of residual stability.

The Administration is satisfied that the stability is
sufficient during intermediate stages of flooding.

EXAMPLE OF GRAVITY -VS- BUOYANCY

1 ton of steel 1
ton of steel

If the cube of steel is placed in water it sinks.
There is not enough displaced volume for the forces of buoyancy to act upon. If
the ship’s hull is placed in the water it will float. The larger volume of the
ship’s hull allows the forces of buoyancy to support the hull’s weight.

The ship’s hull will sink to a draft where the forces
of buoyancy and the forces of gravity are equal.

Displacement

The weight of the volume of water that is displaced by
the underwater portion of the hull is equal to the weight of the ship. This is
known as a ship’s displacement.

The unit of measurement for displacement is the Metric
Tonne.

Gravity

The force of gravity acts vertically downward through
the ship’s center of gravity. The magnitude of the force depends on the ship’s
total weight.

Units Of Measure

Force: A push or pull that tends to produce motion or
a change in motion. Units:

Parallel forces may be mathematically summed to
produce one “Net Force” considered to act through one point.

Weight: The force of gravity acting on a body. This
force acts towards the center of the earth. Units: kilograms, etc.

Moment: The tendency of a force to produce a rotation
about a pivot point. This works like a torque wrench acting on a bolt. Units:

Moment = Weight x Lever Arm

Volume = Length x Breadth x Height

Volume: The number of cubic units in an object.

Units: cubic metres (cbm), etc. The volume of any
compartment onboard a ship can be found using the equation:

Salt Water = 1.025 gms/cc

Fresh Water = 1.00 gms/cc

Diesel Fuel = 0.92 gms/cc

Calculating The Weight Of Flooding Water

A compartment has the following dimensions:

Length = 20 M

Breadth = 20 M

Height = 8 M

The compartment is now flooded with salt water to a
depth of 6 M

1. First,
calculate the volume of water that has been added to the compartment.

Volume = Length x Breadth x Depth of Flooding Water

= 20 M x 20 M x 6 M

= 2400 cbm^{}

2. Second,
multiply the volume of water by its specific gravity.

Stability Reference Points

M - Metacentre

G -

B -

K - Keel

K - Keel: The base line reference point from which all
other reference point measurements are compared.

B -

The

When the ship’s hull is made heavier, the drafts
increase as the ship sits deeper in the water. “B” will move up.

When the ship’s hull is lightened, the drafts decrease
as the ship sits shallower in the water. “B” will move down.

The

G -

1. “G”
moves towards a weight addition

2. “G”
moves away from a weight removal

3. “G”
moves in the same direction as a weight shift

M - Metacenter: As the ship
is inclined through small angles of heel, the lines of buoyant force intersect
at a point called the metacenter.

As the ship is inclined, the center of buoyancy moves in an arc as it continues to seek the geometric center of the underwater hull body. This arc describes the metacentric radius.

As the ship continues to heel in excess of 7-10
degrees, the metacenter will move as shown.

The position of the metacenter
is a function of the position of the center of buoyancy, thus a function of the
displacement of the ship.

The position of “M” moves as follows:

As the

As the