Ship Stability

Ship StabilityShip Stability prepared by: prepared by: Guided by:Guided by:

WHAT IS SHIP WHAT IS SHIP STABILITY ?STABILITY ?

The ability of the object or vessel The ability of the object or vessel to float free on the water surface to float free on the water surface without sinking and gravitational without sinking and gravitational force acting on it is grater than force acting on it is grater than that of buoyancy force acting on that of buoyancy force acting on it is called stability of the shipit is called stability of the ship..

ObjectivesObjectives

Archimedes PrincipleArchimedes Principle

Terminology of ship’s hydrostaticsTerminology of ship’s hydrostatics

Metacenter, Center of Gravity, Center of Metacenter, Center of Gravity, Center of Buoyancy, couple etc.Buoyancy, couple etc.

Stability curvesStability curves

Archimedes PrincipleArchimedes Principle Law: ALaw: A body floating or body floating or

submerged in a fluid is buoyed submerged in a fluid is buoyed up by a force equal to the up by a force equal to the weight of the water it displacesweight of the water it displaces

Archimedes PrincipleArchimedes Principle Ship sinks until weight of water Ship sinks until weight of water

displaced by the underwater volume displaced by the underwater volume is less to the weight of the ship.is less to the weight of the ship. Forces of gravity: Forces of gravity: G = mG = mshipshipg g

=W=Wshipship

Forces of buoyancy: Forces of buoyancy: B = B = waterwaterVVdisplaceddisplaced

WWship ship = = waterwaterVVdisplaceddisplaced

Archimedes PrincipleArchimedes Principle

Forces act everywhere on ship -> Forces act everywhere on ship -> too tough to analyzetoo tough to analyze

Center of Gravity (G):Center of Gravity (G): all gravity all gravity forces as one force acting downward forces as one force acting downward through ship’s geometric centerthrough ship’s geometric center

Center of Buoyancy (B):Center of Buoyancy (B): all buoyancy all buoyancy forces as one force acting upward forces as one force acting upward through underwater geometric through underwater geometric centercenter

Archimedes PrincipleArchimedes Principle Center of Gravity (G):Center of Gravity (G):

Changes position only by change/shift Changes position only by change/shift in mass of shipin mass of ship

Does not change positionDoes not change position with with movement of shipmovement of ship

Center of Buoyancy (B):Center of Buoyancy (B): Changes positionChanges position with movement of with movement of

ship -> underwater geometric center ship -> underwater geometric center movesmoves

Also affected by displacementAlso affected by displacement

G

Hydrostatics Hydrostatics TerminologyTerminology

Displacement:Displacement: total weight of ship = total weight of ship = total submerged volume of ship total submerged volume of ship (measured in tons)(measured in tons)

Draft:Draft: vertical distance from waterline to vertical distance from waterline to keel at deepest point (measured in feet)keel at deepest point (measured in feet)

Reserve Buoyancy:Reserve Buoyancy: volume of watertight volume of watertight portion of ship above waterline portion of ship above waterline (important factor in ship’s ability to (important factor in ship’s ability to survive flooding)survive flooding)

Freeboard:Freeboard: vertical distance from vertical distance from waterline to main deck (rough indication waterline to main deck (rough indication of reserve buoyancy)of reserve buoyancy)

Hydrostatics TerminologyHydrostatics Terminology

As draft & displacement increase, As draft & displacement increase, freeboard and reserve buoyancy decreasefreeboard and reserve buoyancy decrease

MomentsMoments

Def’n: tendency of a force to produce Def’n: tendency of a force to produce rotation or to move an object about an rotation or to move an object about an axisaxis Distance between the force and axis of Distance between the force and axis of

rotation is the moment armrotation is the moment arm Couple: two forces of equal magnitude Couple: two forces of equal magnitude

in opposite and parallel directions, in opposite and parallel directions, separated by a perpendicular distanceseparated by a perpendicular distance G and B are a coupleG and B are a couple

MomentsMoments Depending on location Depending on location

of G and B, two types of of G and B, two types of moments:moments: Righting moment:Righting moment: tends tends

to return ship to upright to return ship to upright positionposition

Upsetting moment:Upsetting moment: tends tends to overturn shipto overturn ship

Magnitude of righting Magnitude of righting moment:moment: RM = W * GZRM = W * GZ (ft-tons) (ft-tons) GZ: moment armGZ: moment arm (ft) (ft)

MetacenterMetacenter

Define as the Define as the intersection of two intersection of two successive lines of successive lines of action of the force of action of the force of buoyancy as ship buoyancy as ship heels through small heels through small angles (M)angles (M) If angle too large, M If angle too large, M

moves off centerlinemoves off centerline

Metacentric heightMetacentric height Ship’s Metacentric Ship’s Metacentric

height is define as height is define as distance from distance from center of gravity center of gravity (G) to the (G) to the metacenter is metacenter is known as the known as the ship’s ship’s METACENTRIC METACENTRIC HEIGHT(GM)HEIGHT(GM)

MetacenterMetacenter Relationship between G and MRelationship between G and M

G under M: ship is stableG under M: ship is stable G = M: ship neutralG = M: ship neutral G over M: ship unstableG over M: ship unstable

STABLESTABLE UNSTABLEUNSTABLE

Metacenter v. Stability Metacenter v. Stability CurvesCurves

At this point, we could use lots of At this point, we could use lots of trigonometry to determine exact trigonometry to determine exact values of forces, etc for all angles -values of forces, etc for all angles -> too much work > too much work

GM used as a measure of stability GM used as a measure of stability up to 7°, after that values of GZ are up to 7°, after that values of GZ are plotted at successive angles to plotted at successive angles to create the stability curvecreate the stability curve

Stability CurveStability Curve Plot GZ (righting arm) vs. angle of heelPlot GZ (righting arm) vs. angle of heel

When a series of values for GZ at When a series of values for GZ at successive angles of heel are plotted successive angles of heel are plotted on a graph which result in STABILITY on a graph which result in STABILITY CURVECURVE

Ship’s G does not change as angle changesShip’s G does not change as angle changes Ship’s B always at center of underwater Ship’s B always at center of underwater

portion of hullportion of hull Ship’s underwater portion of hull changes as Ship’s underwater portion of hull changes as

heel angle changesheel angle changes GZ changes as angle changesGZ changes as angle changes

Stability CurveStability Curve

ConclusiConclusionon

Ship stability normally refers to the Ship stability normally refers to the ability of a floating vessel to resists the ability of a floating vessel to resists the overturning forces encountered in the overturning forces encountered in the course of its operations. Which is arise course of its operations. Which is arise from weather, wind, waves etc.from weather, wind, waves etc.

Stability calculations solves this forces Stability calculations solves this forces and apply them in a practical way to a and apply them in a practical way to a mathematical model of the ship so that mathematical model of the ship so that the response of the vessel can be the response of the vessel can be examined for various magnitudes of examined for various magnitudes of overturning.overturning.

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