Volume of Displacement (∇)
The volume of displacement is the total
volume of the fluid displaced by the ship.
Volume
of displacement is given by,
∇
= ∆ /ρ
For
seawater, ρ = 1.025 ton/m3
Displacement (∆)
Displacement
is defined as the total mass of the ship when afloat including everything on
board, which is equal to the weight of water displaced.
Displacement
is given by,
∆
= Dead wt. + Light ship wt.
Longitudinal centre of
buoyancy from midship (LCB)
The
centre of volume of fluid displaced by a ship is known as the centre of
buoyancy; its projection in the plan is known as longitudinal centre of
buoyancy. It is given as distance forward or aft of midship and is represented
by the longitudinal centroid of the curve of immersed cross-sectional areas.
Vertical centre of
buoyancy above base line (VCB)
The
centre of volume of fluid displaced by a ship is known as the centre of
buoyancy; its projection in the section is known as vertical centre of
buoyancy. It is given as the distance above the keel denoted by KB and is
represented by the vertical centroid of the Water plane area curve.
By
Morrishes approximate formula;
VCB
below the waterline = 1/3(d/2+∇/AW)
Where,
d = draught in m
∇ = volume of
displacement in m3
AW = Water plane area
in m2
Water plane area (AW)
Water plane area is the area of the
horizontal plane which passes through a floating ship on a level with the
waterline. The water plane area at any draught is calculated by sympsonising the
half breadths at ordinate stations.
Longitudinal centre of
floatation from midship (LCF)
Longitudinal
centre of floatation is the centroid of the water plane and is the axis about
which a ship changes trim when a mass is added, removed or moved
longitudinally.
Tonne per centimeter
immersion (TPC)
The
tonne per centimeter immersion of a ship at any given draught is the mass
required to increase the mean draught by 1 centimeter.
TPC = (AW*ρ)/100
For
seawater ρ = 1.025 ton/m3
∴TPC in sea water
= 0.01025×AW
Moment of inertia (I)
The
second moment of area of a water plane, commonly known as moment of inertia, is
a measure of the resistance of a water plane to a change in its state of rest.
The moment of inertia is found by putting the cube of the half breadths through
Simpson’s multipliers. The sum of these products is multiplied by h/3, by two
for both sides and by 1/3 which is a factor in water plane inertia.
Moment
of inertia is the mass property of a rigid body
that defines the torque needed for a desired angular acceleration about an axis
of rotation. Moment of inertia depends on the shape of the body and may be
different around different axes of rotation. A larger moment of inertia around
a given axis requires more torque to increase the rotation, or to stop the
rotation, of a body about that axis. Moment of inertia depends on the amount
and distribution of its mass, and can be found through the sum of moments of
inertia of the masses making up the whole object, under the same conditions.
Moment to change trim
by 1 cm (MCTI)
Moment
to change trim by 1 cm is the change of trim in inches, caused by the
application of a moment.
MCT1 cm = (∆*GML )/12L
Metacentre (M)
The
metacentre is the point of intersection of the normal to a slightly inclined
water plane of a body, rotated without change of displacement, through the
centre of buoyancy pertaining to that water plane through the center of
buoyancy pertaining to the upright condition.
Its
projection in plan and section are known as longitudinal and transverse metacentre respectively.
Meta-centric height
(GM)
The
meta-centric 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 meta-centric height implies greater initial stability
against overturning. Meta-centric height also has implication on the natural
period of rolling of a hull, with very large meta-centric heights being
associated with shorter periods of roll.
Transverse
meta-centric radius (BMT) = IT/∇
Longitudinal
meta-centric radius (BML) = ILCF/∇
Transverse
meta-centre above base line (KMT)
= KB + BMT
Longitudinal
meta-centre above base line (KML)
= KB + BML
Wetted surface area of the
hull (S)
The
wetted surface area of a ship is the area of the ship’s hull which is in
contact with water. This area may be found by putting the transverse girths of
the ship, from water line to water line, through Simpson’s rule and adding
about ½ percent to allow for the longitudinal curvature of the shell.
Formulae
for wetted surface area are;
Denny’s formula:
S= (1.7*L*T) +
∇/T
S= c (∇*L)1/2
Taylor’s formula:
Where,
S= wetted surface area in m2, L= length of barge in m, T=draught in m,
∇=volume
of displacement in m3, C=coefficient which depends on shape of the
ship.
and coefficient of forms which we have discussed in Topic - 2
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