lecture notes of naval architecture i
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7/15/2019 Lecture Notes of Naval Architecture I
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Course Contents
• Ship Types and Hull forms
• Transverse stability at small and large angles
• Longitudinal stability and trim• Stability when grounded
• Horsepower and hull resistance
• IMO regulations
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1 Ship Types
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Classification of Ship by UsageClassification of Ship by Usage
•Merchant Ship
• Naval & Coast Guard Vessel
• Recreational Vessel
• Utility Tugs
• Research & Environmental Ship
• Ferries
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Classification of Ship by Support Type
• Aerostatic Support
- ACV (Air Cushion Vehicles)- SES (Captured Air Bubble)
• Hydrodynamic Support
- Hydrofoil
- HYSWAS (HYdrodynamic Small Waterplane Area Ship)
- Planning Hull
• Hydrostatic Support
- Conventional Ship
- Catamaran
- SWATH (Small Waterplane Area Twin Hull)
- Deep Displacement
• Submarine
- Submarine
- AUV/ROV4
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- Supported by cushion of air generated by a fan.
- ACV (Air Cushion Vehicle)
hull material : rubber
propeller : placed on the deck
amphibious operation
- SES (Surface Effect Ship)side hull : rigid wall(steel or FRP)
bow : skirt
propulsion system : placed under the water
water jet propulsionsupercavitating propeller
not amphibious operation
Aerostatic Support
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Air Cushion VehicleAir Cushion Vehicle6
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SES Ferry
NYC SES
Fireboat
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250’ SES Ferry
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• Planning HullPlanning Hull
-- supported by the hydrodynamic pressure developed supported by the hydrodynamic pressure developed under the hull at high speed under the hull at high speed
-- V or flat type shapeV or flat type shape-- commonly used in pleasure boat, patrol boat,commonly used in pleasure boat, patrol boat,missile boat, racing boatmissile boat, racing boat
Hydrodynamic SupportHydrodynamic Support
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• Hydrofoil ShipHydrofoil Ship
-- supported by a hydrofoil, like wing on an aircraftsupported by a hydrofoil, like wing on an aircraft
-- fully submerged hydrofoil shipfully submerged hydrofoil ship
-- surface piercing hydrofoil shipsurface piercing hydrofoil ship
Hydrodynamic Support
Hydrofoil Ferry
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Hydrostatic Support
• Displacement ship
- conventional type of ship
- carries high payload
- low speed
• SWATH
- small water plane area twin hull (SWATH)- low wave-making resistance
- excellent roll stability
- large open deck
- disadvantage : deep draft and cost
• Catamaran/Trimaran- twin hull
- other characteristics are similar to the SWATH
• Submarine12
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SWATH vessel13
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Archimedes Principle
Law: a body floating or submerged in a fluid
is buoyed up by a force equal to the weight of
the water it displaces
Depth to which ship sinks depends on density
of water (r = 1 ton/35ft3
seawater)
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Ship sinks until weight of water displaced by
the underwater volume is equal to the weight
of the ship
Forces of gravity: G = mshipg =Wship
Forces of buoyancy: B =rwaterVdisplaced
Wship = rwater Vdisplaced
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• A FLOATING BODY DISPLACES A VOLUME
OF WATER EQUAL IN WEIGHT TO THE
WEIGHT OF THE BODY.
DISPLACEMENT
00
G
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DISPLACEMENT
00
G
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DISPLACEMENT
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G
B
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DISPLACEMENT
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G
B
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DISPLACEMENT
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G
B
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DISPLACEMENT
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G
B
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Center of Gravity (G):Center of Gravity (G): all gravity forces as
one force acting downward through ship’sgeometric center
Center of Buoyancy (B):Center of Buoyancy (B): all buoyancy forcesas one force acting upward through
underwater geometric center
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Definition
11-- PerpendicularsPerpendiculars Imaginary lines perpendicular to the base line or plane (and the
water line)
On the ship there is a :
-- Forward PerpendicularForward Perpendicular (F(Fpppp or For Fpp))
This is the line crosses the intersection of the water line and the
front of the stem
--Aft PerpendicularAft Perpendicular (A(Apppp or Aor App))
This line usually aligns the centre line of the rudder stock. This
is the imaginary line around which the rudder rotates.
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2. Waterlines2. Waterlines
The waterline of a ship lying in the water . There are different
waterlines (i.e load-lines) for different loading conditions, suchas:
-- Light waterlineLight waterline
The waterline of a ship carrying only her regular inventory.
-- Fully loaded waterlineFully loaded waterline
The waterline of maximum load draft in sea water.
-- Construction (Scantling) waterlineConstruction (Scantling) waterline (C(CWLWL))
The waterline used as the limit to which the various structuralcomponents are designed .
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33-- Plimsoll Mark (freeboard mark)Plimsoll Mark (freeboard mark)
The freeboard mark is a symbol indicating the maximal
immersion of the ship in the water, leaving a minimal freeboard for safety.
The mark consists of a circle
with a diameter of 300 mm,
through which a horizontallines is drawn with its upper
edge going through the centre
of the circle.
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This level indicates the minimal freeboard in salt water summer
conditions. Beside this circle the loadline mark consists of a number of
horizontal lines indicating the minimal freeboard required for other than
summer conditions.All freeboard lines are 25 mm wide and are connected by a vertical line.
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The freeboard mark is placed
midships on each side of the ship.
The minimal operating freeboard
depends on:
-Ship’s position at sea
-The time of year (summer, winter,etc,.._
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44-- Deck LineDeck Line
In general this is the extended line from the upper side of the
freeboard deck at the ship’s side.
The deck line is placed above the Plimsoll mark so that the
freeboard can be easily monitored by the ship’s crew or other
interested parties
55-- Permanent marks on the shipPermanent marks on the ship’’s hulls hullIt is very important the draft marks can be accurately read
as easily as possible.
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1. Draft to portside fore :
53.8 dm
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2. Draft to portside fore:
5.17 meters
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3. Draft on the stern is given in
meters and feet: 9.36 m = 30’ 7”
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4. Draft to starboard aft: 9.35
meters
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5- Draft midships: 7.00 meters
6- Deck line
7. Plimsoll mark
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Dimensions
FP Forward Perpendicular
AP After Perpendicular
WL Waterline
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36 WL WaterlineWL Waterline
CL CentrelineCL Centreline
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11- Length over all LOA
It is the overall length of the vessel, i.e the horizontal distance over the
extremities from stem to stern
22- Length between perpendicular LPP
It is the horizontal distance between the FP and AP
33-- Length waterline LLWLWL
Horizontal distance between the fore and aft when the ship is loaded atthe summer mark, less the shell.
44-- Breadth over allBreadth over all BBOAOA
The maximum breadth of the ship as measured from the
outer hull on the starboard to the outer hull on port side,including rubbing bars, permanent fenders.
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44-- Breadth or beamBreadth or beam BMLD
The greatest moulded breadth, measured from side to side at the
outside of the frames, but inside the shell
55- DepthDepth D
The vertical distance between the base line and the upper continuous
deck and is measured at the half L pp at the side of the ship
66- Draft ForwardDraft Forward (TFWD)
Vertical distance between the waterline and the underside of the
keel, as measured at the forward perpendicular
66- Draft at the sternDraft at the stern (TAF)
Vertical distance between the waterline and the underside of the
keel, as measured at the after perpendicular
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77- FreeboardFreeboard
The distance between the waterline and the top of the deck at the side ( at
the deck line). The term summer freeboard means the distance from the
top of the summer loadline and the upper edge of the deck line
88- Air draftAir draft
The vertical distance between the waterline and the highest point of the
ship. The air draft is measured from the summer mark.
SheerSheer
This is the upward rise of the ship’s deck from mid length towards the
bow and stern. The sheer gives the vessel extra buoyancy at the stem
and stern
CamberCamber
The transverse curvature of the weather deck. The curvature
helps to ensure sufficient drainage of any water on deck
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Base lineBase line
Top of the flat keelplace
Keel (K)Keel (K)Inter section of the base line and the center line plane
Beam: B Camber
Depth: D
Draft: T
Freeboard WL
K
CL
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FlareFlare
•• FlareFlare : outward curvature of ship’s hull surface above the waterline
• Tumble HomeTumble Home : opposite of flare
Tumble HomeTumble Home
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Positions of the shipPositions of the ship
ListList
Heeling to one side about the fore and aft axis
Heel to port side
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Trim (t)Trim (t)
The difference between the draft at the stern and the draft at the stem i.e
the trim fore (tF) + the trim aft (tA)
On an even keelOn an even keel, in proper trim
The draft of the stern equals the draft of the stem
Trim by head TF
more than TA
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Trim by stern TA more than TF
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Volumes and weightsVolumes and weights
Register ton (RT)To determine the size of a ship the RT is used. It is based on
volume where one register ton equals 100 cubic feet or 2.83
m3
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Gross Register TonnageGross Register Tonnage
The Gross Register Tonnage (GRT or GT) usually called Gross Tonnage,
is calculated using a formula that takes into account the ship’s volume in
cubic meters below the main deck and the enclosed spaces above themain deck
Net Register TonnageNet Register Tonnage
The Net Register Tonnage is also a non-dimensional number that
describes the volume of the cargo space. The NT is derived from the
GT by subtracting the volume of space occupied by:
- crew
- Navigation equipment
-The propulsion equipment- work stations
- Ballast
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Volume of DisplacementVolume of Displacement V mV m33
The displacement is the volume of the part of the ship below the
waterline including the shell plating, propeller and rudder
DisplacementDisplacement ΔΔ tonton
The displacement is the weight of the volume of water displaced by the
ship
Lightship weight (ton)Lightship weight (ton)
This is the weight of the ship including the regular inventory
but without any cargo, fuel or crew. The regular inventory
includes: anchors. Life-saving equipment, lubricating oil,
paint
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Deadweight (ton)Deadweight (ton)
This is the weight of the a ship can take on until the maximal allowable
immersion is reached. This is a fixed value, unique to each ship.
Cargo Capacity (t)Cargo Capacity (t)
This is the total weight of cargo a ship is designed to carry at a
given time.
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Hull Form CoefficientsHull Form Coefficients
Line coefficients define the characteristics of the vessel’s shape at and
below the waterline. This makes it possible to get an impression of the
shape of the underwater body of a ship without extensive use of anydata.
11-- Block Coefficient, Coefficient of finenessBlock Coefficient, Coefficient of fineness CCBB
The block coefficient gives the ratio of the volume of the underwater
body (V) and the rectangular block bounded by LPP
, BMLD
and draft (T).
The vessel with a small block coefficient is reoffered to as fine.
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2- Waterline coefficient CW
The waterline coefficient gives the ratio of the area of the waterline (Aw)
and the rectangular plane bounded by LPP, BMLD.
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Midship Section CoefficientMidship Section Coefficient CCMM
The midship (main frame) coefficient gives the ratio of the area of the
midship section (AM
) and the area bounded by BMLD
and T.
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Prismatic CoefficientPrismatic Coefficient CCPP
The prismatic Coefficient gives the ratio of the volume of the underwater
body and the block formed by the area of the Midship Section AM and LPP.
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When the principal dimensions, displacement and hull form coefficients
are known, one has an impressive amount of design information, but not
yet a clear image of the exact geometrical shape of the shape. The shape
is given by the lines plane.
The shape of a ship can vary in height, length and breadth. In order to
represent this complex shape on paper, transverse sections of the hull
are combined with two longitudinal sets of parallel planes, each one
perpendicular to the others
Since the ship is a 3-dimensional shape, data in x, y
and z directions is necessary to represent the ship hull.
(Table of Offsets)Table of Offsets)
Lines
- body plan (front View)- shear plan (side view)
- half breadth plan (top view)
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Half Half --Breadth PlanBreadth Plan
- Intersection of planes (waterlines) parallel to the baseline (keel).
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Shear PlanShear Plan
-Intersection of planes (buttock lines) parallel to the centerline
plane
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Body PlanBody Plan
- Intersection of planes to define section line
- Sectional lines show the true shape of the hull form
- Forward sections from amidships : R.H.S.- aft sections from amid ship : L.H.S.
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WaterlinesWaterlines
Horizontal sections of the hull are called waterlines. When
the waterlines are projected and drawn into one view fromabove, the result is called a waterline model.
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StationsStations
Evenly spaced vertical cross-section in transverse direction are
called sections (ordinates). Usually the ship is divided into 20ordinates, from the centre of the rudder stock (ordinate 0) to
the intersection of the waterline and the mould side of the stem
(ordinate 20)
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Verticals / Bow and ButtocksVerticals / Bow and Buttocks
Lengthwise section are called verticals or bow and buttocks
lines. These longitudinal sections are parallel to the plane of symmetry of the ship.
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General ArrangementGeneral Arrangement
There are a number of
stationary components
and spaces. These have
an indirect relationship to
Ship stability.
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There are a number of variables important to stability. The
location of these variables is dependent upon:
-The distribution of weight on the ship
-The distribution of upward force (buoyancy) on the
submerged part of the hull.
These variables are:
Geometrical centre of the water plane area or tipping centerCentre of flotationCOF or C.F
KeelKeelK
MetacenterMetacenterM
Volumetric centre of the submerged part of the hullCentre of buoyancyB or COB
Mean mass of spacesCentre of gravityg or COg
Mass or centre of gravity of ship, cargo and added cargoCentre of gravityG or COG
ExplanationExplanationTermTermAbbreviationAbbreviation
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E l 1E l 1
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Example 1Example 1
A ship has a length and breadth at the waterline of 40.1 m and 8.6
m respectively. If the water-plane area is 280 m2 calculate the
coefficient of fineness of the water-plane area (CW
).
SolutionSolution
Example 2Example 2
A ship floats at a draught of 3.20 m and has a waterline length and
breadth of 46.3 m and 15.5 m respectively. Calculate the block
coefficient (C B) if its volume of displacement is 1800 m3.
SolutionSolution
E l 3E l 3
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Example 3Example 3
A ship has length 200 m and breadth 18 m at the waterline. If the
ship floats at an even keel draught of 7.56 m in water RD 1.012 and
the block coefficient is 0.824 calculate the displacement.
SolutionSolution
Example 4Example 4
A ship floats at a draught of 4.40 m and has a waterline
breadth of 12.70 m. Calculate the underwater transverse area
of the midships section if C M is 0.922.
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Example 5Example 5
A ship has the following details: Draught 3.63 m; Waterline length
48.38 m; Waterline breadth 9.42 m;
Cm 0.946; Cp 0.778.
Calculate the volume of displacement.
SolutionSolution
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Tonnes per Centimetre immersion TPCTonnes per Centimetre immersion TPC
The TPC for any given draught is the weight that must be
loaded or discharged to change the ship’s mean draught by
one centimetre (1cm)
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Where:
TPC : tonnes per cm
WPA : water plane area m2
ρ : water density 1.025 t/m3
E l 6E ample 6
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Example 6Example 6
Calculate the TPC for a ship with a water-plane area of 1500 m2
when it is floating in:
(a) fresh water;
(b) dock water of RD 1.005;
(c) salt water
Solution:Solution:
LOAD/DISCHARGELOAD/DISCHARGE
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LOAD/DISCHARGELOAD/DISCHARGE
Example 7Example 7
M.V. Almar has a displacement of 13200 ton at an initial mean draught of 4.40 m in salt water and is required to complete loading with a
draught of 6.70 m (displacement will reach 20610 ton). Calculate the
amount of cargo that must be loaded.
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8
Load line dimensionLoad line dimension
Fresh Water Allowance (FWA)Fresh Water Allowance (FWA)
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9
Fresh Water Allowance (FWA) is the number of millimetres by which
the mean draught changes when a ship passes from salt water to
fresh water, or vice-versa, when the ship is loaded to the Summer
displacement.The FWA is found by the formula:
TPCSW is the salt-water TPC value for the summer load draught.
Example 8Example 8
A ship floats in SW at the Summer displacement of 1680
tonnes. If the TPC SW is 5.18, how much will the draught
change by if the ship is towed to a berth where the density
of the water is 1.000 t/m3?
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10
Example 9Example 9
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11
Example 9Example 9
A section of steel plate to be used in the construction of a ship’s deck has
dimensions as shown.
Calculate the area of the plate.
Example 10Example 10
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12
A ship’s water-plane area has half-ordinates from aft to forward as
follows:
0.6 m, 1.5 m, 1.6 m, 1.4 m and 0.0 m. If the half-ordinates are equally
spaced at 4.2 m apart, calculate:(a) the total water-plane area;
(b) the TPC if the ship is floating in salt water (RD 1.025).
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13
Example 11Example 11
A plate section has dimensions as shown. Calculate the area.
Example 12Example 12
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14
A small boat has a half water-plane area with equally spaced half-
ordinates as follows:
0.20 m, 1.20 m, 1.70 m, 1.82 m, 1.75 m, 1.65 m and 1.21 m.
The half-ordinates are equally spaced at 1.40 m apart.Calculate the water-plane area.
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Ship CentroidsShip Centroids
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Centre of buoyancy C.Bentre of buoyancy C.B
B (centre of buoyancy C.B) indicates the location of the
result ing buoyancy of the displaced seawater. The location of
B is dependent upon the hull’s form. B is the volumetric
centre of the hull. Buoyancy is equal to the weight
(displacement) of the ship.
Location of Metacenter M
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Location of Metacenter MWith a heeling angle up to about(5-10)º.It is assumed the point MM
lies at the intersection of the vectorof buoyancy and the centerline
With larger lists, point M isdefined as follows: The
intersection of 2 successive linesof buoyancy with a very smallincrease of angle of inclination. MM
is then found outside the verticaloutside the vertical
plane of symmetryplane of symmetry
F l l ti t k ith MM t id th
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For calculation purposes, we can not work with MM outside thevertical plane of symmetry. Thus, a false metacenter, NN is usedfor the calculation the intersection
Point NN is on the centreline at theintersection of the buoyancy loadline and the centreline.
The importance of M’s location totransverse (initial) stability is great.
The location of M depends on thelocation of B.
The location of G in relation to M ismainly for the stability as follows:
- Positive (G under M)- Neutral (G at M)
- Unstable (G above M)
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Centre of GravityCentre of Gravity
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Centre of GravityCentre of Gravity
The total weight of the ship is concentrated at point G(centre of gravity)
g = centre of gravity of component
G = centre of gravity of the entire ship
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Movement of centre of gravityMovement of centre of gravity
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g yg y
The movement of G can be quickly made clear if only one (large )weight is relocated on board or loaded, G then moves:
-In the movement direction of the weighty
- across a distance of GG1 = (w x h)/ Δ (for transferring load)
GG1 = (w x h) / ( Δ+w) (for adding weight)
Inclining Test ( Experiment)Inclining Test ( Experiment)
In order to calculate the correct GM of the empty ship, theship must undergo an inclining experiment ( stability test) todetermine KG
The weight of the empty ship mustbe as accurate as possible
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The weight of the empty ship must be as accurate as possible
During the test:
-The ship must be free to roll ( mooring wires slack, etc..)- it must be calm with no wind
- no disturbance waves
-The test must be conducted multiple times both starboard
and portside with consistent outcome to ensure an accurateresult.
A known weight (1) is moved transversely across distance (2)
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A known weight (1) is moved transversely across distance (2)as a result of which the
ship lists.
(1)The weight must be so large that:- The ship remains within an initial range of stability max list 9-10º
- Equal to about 2 % displacement(2) Approximately ½the breadth
The ship’s list due to relocating the weight is accuratelymeasured. This can be done by means of a plumb line. If theplumb line is used, it is usually suspended in a hold where theweight hangs in a tank of water to stabilize the plumb line.
The result is determined by measuring the distance the pendulummoves on a tape line (QR)
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STABILITY REFERENCE POINTS
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CL
M
G
B
K
etacenter
ravity
uoyancy
eel
STABILITY REFERENCE POINTS
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other
oose
eats
ids
CL
M
G
B
K
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B
WATERLINERESERVE BUOYANCY
B1
B
THE CENTER OFBUOYANCY
RESERVE BUOYANCY FREEBOARD DRAFT
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B
WATERLINERESERVE BUOYANCY
RESERVE BUOYANCY, FREEBOARD, DRAFTAND DEPTH OF HULL
CENTER OF BUOYANCY
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B
WLWL
B
WL
B
WL
B
WL
B
CENTER OF BUOYANCY
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BBBBBBBB
B
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G
G1
KGo
KG1
GG1
KGo
KG1
THE CENTER OFGRAVITY
CENTER OF GRAVITY
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CENTER OF GRAVITY
• POINT AT WHICH ALL WEIGHTS COULDBE CONCENTRATED.
• CENTER OF GRAVITY OF A SYSTEM OFWEIGHTS IS FOUND BY TAKINGMOMENTS ABOUT AN ASSUMED CENTEROF GRAVITY, MOMENTS ARE SUMMEDAND DIVIDED BY THE TOTAL WEIGHT OF THE SYSTEM.
MOVEMENTS IN THE
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MOVEMENTS IN THE
CENTER OF GRAVITY
• G MOVES TOWARDS A WEIGHT ADDITION
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G
KGo
G1
KG1
MOVEMENTS IN THE
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MOVEMENTS IN THE
CENTER OF GRAVITY
• G MOVES TOWARDS A WEIGHT ADDITION
• G MOVES AWAY FROM A WEIGHT REMOVAL
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GGGGGG
G1
KG1
KGo
G
MOVEMENTS IN THE
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MOVEMENTS IN THE
CENTER OF GRAVITY
• G MOVES TOWARDS A WEIGHT ADDITION
• G MOVES AWAY FROM A WEIGHT REMOVAL
• G MOVES IN THE DIRECTION OF A WEIGHT SHIFT
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G G2
METACENTER
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THE
METACENTER
C L
B
B20
B45
M
M20
M45
M70
B70
METACENTER
M
BB1 B2
METACENTER
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BBBBBBBBB
METACENTER
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B SHIFTS
M
0o-7/10o
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CL
B
M
0 7/10
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C L
BB20
M
M20
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C L
M
M20
M45
B
B20 B45
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C L
B
B20
B45
M
M20
M45
M70
B70
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C
L
M20M45
M70
M90
B
B20
B45B70
B90
M
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MOVEMENTS OF THE
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MOVEMENTS OF THE
METACENTER
THE METACENTER WILL CHANGEPOSITIONS IN THE VERTICAL PLANE WHENTHE SHIP'S DISPLACEMENT CHANGES
THE METACENTER MOVES IAW THESE
TWO RULES:
1. WHEN B MOVES UP M MOVES DOWN.2. WHEN B MOVES DOWN M MOVES UP.
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M
G
B
M
G
B
G
M
B
M1
B1
G
M
B
M1
B1
G
M
B
M1
B1
G
M
B
M1
B1
LINEAR MEASUREMENTS INSTABILITY
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CL
M
G
B
K
GM
KG
BM
KM
STABILITY
M
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G
B1
Z
G
B1
M
B
G
B1
M
B
THE THREE CONDITIONS
OF STABILITYPOSITIVE
NEUTRAL
NEGATIVE
Vertical Weight Shifts
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G
B
M
G1G1G1G1
G1
G1G1
KGo
KG1
GG1= KG1 - KGo
GG1
KG1 = (Wo KGo) (w x kg)
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Wf
WHERE;w = Weight Shifted
kg = Distance ShiftedWo = Original Displacement
KGo = Original Height of G
Wf = Final Displacement±= + if shift up/- if shift down
KG1 = (Wo x KGo) ±(w x kg)
W
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G
B
M
G1G1G1G1
G1
G1G1
12 FT
Wo = 2000 T
30 FT
25 T
KG1?
Wf
45T
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M
B
G
17T
8 FT
33 FT
Wo = 3400 T
15.5 FT
KG1 = (Wo x KGo)±(w1xkg1)±(w2xkg2)
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Wf
WHERE;w1&2 = Weights Shifted
kg1&2 = Distances Shifted
Wo = Original Displacement
KGo = Original Height of G
Wf = Final Displacement±= + if shift up/- if shift down
Vertical Weight Additions
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g
G1
M
B
G
Vertical Weight Additions
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g
M
B
G
G1
M
B
G
M1
B1
G1
M
B
GG1
M
B
G
M1
B1
G1
M
B
GG1
M
B
G
M1
B1
G1
M
B
G
G1
M
B
G
M1
B1
G1
KGoKG1
GG1
KG1 = (Wo x KGo) ±(w x kg)
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Wf
WHERE;KGo = Original Height of G
Wo = Original Displacement±= + if addition/- if removalw = Weight Added/Removed
kg = Distance Keel to "g" of wtWf = Final Displacement
16 TONS ADD
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42 FT
Wo = 2000 TONS
KGo = 12 FT
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Examples
A ship displaces 5000 t and has an initial KG of 4.5 m. Calculate thefi l KG if i ht f 20 t i d ti ll d f th l
Example 1Example 1
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final KG if a weight of 20 t is moved vertically upwards from the lowerhold (Kg 2.0 m) to the upper deck (Kg 6.5 m).
Example 2Example 2A ship displaces 12500 t and has an initial KG of 6.5 m. Calculate thefinal KG if 1000 t of cargo is loaded into the lower hold at Kg 3.0 m.
Example 3Example 3A ship has a displacement of 13400 t and an initial KG of 4.22 m. 320 tof deck cargo is discharged froma position Kg 7 14 m Calculate the
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of deck cargo is discharged from a position Kg 7.14 m. Calculate thefinal KG of the ship.
Example 4Example 4
A ship displaces 10000 t and has a KG of 4.5 m. The following cargo is worked:Load: 120 t at Kg 6.0 m;
730 t at Kg 3.2 m.Discharge: 68 t from Kg 2.0 m;
100 t from Kg 6.2 m.Shift: 86 t from Kg 2.2 m to Kg 6.0 m.Calculate the final KG.
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Example 5Example 5
Prove that the KM of a box-shaped vessel changes with draught asshown below for the range of draughts 1.00 m to 15.00 m given that
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s o beo o e a ge o d aug s 00 o 5 00 g e alength is 100 m and breadth is 20 m.
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From the values calculated it is seen that as draught increases, KM reduces to aminimum value and then starts to increase again.
Example 6A box-shaped vessel has length 20 m and breadth 6 m.Calculate:
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(a) the moment of inertia for all the axis’ of rotation shown;(b) the moment of inertia about the two axis’ passing through the centre
of flotation using the parallel axis’ theorem.
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Example 7Example 7
A ship of 6000 tonnes displacement has KM 7.3 m and KG 6.7 m, andis floating upright. A weight of 60 tonnes already on board is shifted 12m transversely. Find the resultant list.
Example 8Example 8
A ship of 8000 tonnes displacement has a GM 0.5 m. A quantity of grain in the hold, estimated at 80 tonnes, shifts and, as a result, the
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gcentre of gravity of this grain moves 6.1 m horizontally and 1.5 mvertically. Find the resultant list.
Example 9Example 9
A ship of 13 750 tonnes displacement, GM 0.75 m, is listed degrees tostarboard and has yet to load 250 tonnes of cargo. There is space
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available in each side of No. 3 between deck (centre of gravity, 6.1 mout from the centreline). Find how much cargo to load on each side if
the ship is to be upright on completion of loading.
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Example 10Example 10
A ship of 9900 tonnes displacement has KM 7.3 m and KG 6.4 m. Shehas yet to load two 50 tonne lifts with her own gear and the first lift is to
be placed on deck on the inshore side (KG 9 m and centre of gravity 6m out from the centreline). When the derrick plumbs the quay its head is15 m above the keel and 12 m out from the centreline. Calculate themaximum list during the operation
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