static stability of ships

8/11/2019 Static Stability of Ships

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Static Stability

2014-09-24Hyun ChungDivision of Ocean Systems Engineering

OSE503 Intro. to NA & OE


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Book ContentsLets get under wayGeneral arrangementsWorking areas and accommodationsDesign proceduresHull forms

Statics stabilityDynamic stabilityResistance and poweringPropulsion devicesChoosing propulsion machineryWind powerHull strength requirementsMaterials of constructionStructural arrangements

Miscellaneous design matters 2


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Contents

Buoyancy & HydrostaticsBasics of fluid mechanics

Pressure in a fluidBuoyancy

Hydrostatic StabilityMetacenterMetacentric height

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Fluid

A fluid is a substance that continuallydeforms in response to external forces.

Fluids are a subset of the phases ofmatter and include liquids, gases ,plasmas and, to some extent, plastic

solids .Hence , fluid liquid

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DensityDensity of a fluid, Definition: mass per unit volume

= mass/volumeUnits: kg/m 3

Affected by changes in temperature andpressure .

Typical values:Air: 1.23 kg/m 3

Fresh water: 1000 kg/m 3, Sea water: 1025 kg/m 3

Summer/Winter draft5


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Viscosity

Definition: A measure of the resistance of afluid which is being deformed by either

shear stress or tensile stress.Fluid thickness ineveryday terms. That is,water is "thin ", havinga lower viscosity, whilehoney is "thick",having a higherviscosity.

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PressureDefinition: force per unit area

p = F/AUnits: Pascal, Pa(=N/m 2)1 bar = 10 5 Pa,1 psi = 6,895 Pa

The standard atmospheric pressure

101,325 Pa ~ 1 barPressure in a fluid

p= *g*h

= fluid density g = gravity constant h = height of the fluid

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Hydrodynamics vs. Aerodynamics

Similar but not quite the sameDensity

Compressible / incompressiblePresence of free surface

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Buoyancy

An upward actingforce exerted by a

fluid that opposes anobjects weight.Weight of thedisplaced water .

Eureka

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Pressure in a Static Fluid

Force Equilibrium

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Pressure in a Static Fluid

In a static fluid pressureis the same at alllocations with the samedepth .Pressure increases withdepth.Pressure acts on a pointin all directions equally .Pressure actsperpendicular to thesurface.

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Buoyancy on a Submerged Body

Fully submerged Partially submerged(floating)

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Example) Iceberg

The tip of the iceberg

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Example) Submarine

How to dive and surface

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Buoyancy in the Air

e.g.) Hot air balloons, airships, blimps

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Stability of a SystemThree states of equilibrium: Disturbe

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Stable Neutral Unstable


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Ship Stability

Ships must besufficiently stable

Otherwise

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What is stability?

http://www.youtube.com/watch?v=oNIyvRq5U8U

http://www.youtube.com/watch?v=S rp5MN1QYiQ

http://www.youtube.com/watch?v=xMbk6_nkH70

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http://www.youtube.com/watch?v=oNIyvRq5U8Uhttp://www.youtube.com/watch?v=oNIyvRq5U8Uhttp://www.youtube.com/watch?v=Srp5MN1QYiQhttp://www.youtube.com/watch?v=Srp5MN1QYiQhttp://www.youtube.com/watch?v=Srp5MN1QYiQhttp://www.youtube.com/watch?v=xMbk6_nkH70http://www.youtube.com/watch?v=xMbk6_nkH70http://www.youtube.com/watch?v=xMbk6_nkH70http://www.youtube.com/watch?v=Srp5MN1QYiQhttp://www.youtube.com/watch?v=oNIyvRq5U8U


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Metacenter

When a stable vessel isheeled , the buoyant lineof force will intersect theships centerlinesomewhere above thecenter of gravity.

This intersection point iscalled the metacenter , M.

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Predicting GM

How to compute?

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Metacentric Height

The distance between the center of gravity, G andthe metacenter M, is called the metacentricheight , GM.

Positive stability is found whenever the positionof the metacenter is above the vertical center ofgravity.

In general, GM remains essentially constant forsmall heel angles.GZ (=GM*sin) is called the righting arm .

GM>0 Stable GM


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Predicting GM

KB: Height of the center of buoyancy above

the baseline ( keel ).For ordinary ship forms, KB~0.52T

BM = I / VI : Moment of inertia of the waterplane areaV : Volume of displacement

KG: Height of the center of gravity abovethe baseline (keel )

GM = KB + BM - KG

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Inclining Experiment

In an existing vessel, GM can be found bythe inclining experiment .

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Ideal value of Stability

A reasonable value of GM is about 3~5 %of the beam .

Smaller values leave too little margin in caseof accident, careless loading, topside icing,etc.Greater values lead to excessive stability. Itwill lead to short, uncomfortable rolling thatmay dangerous to sailors and passengerson the ship.

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Free Surface Effect

If the ship heels to one side the internalliquids will flow in the same direction.

This has the effect of reducing themetacentric height.There will be no freesurface effect if thetank is completelyfilled with the internalliquid.

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Lifting a Weight

If a heavy object is suspended from the endof a boom off from the deck, the center ofgravity jumps at the top of the boom.

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Range of StabilityRighting Moment vs. Angle of Heel

Range ofStability

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Longitudinal Static Stability

Longitudinal Metacentric Height

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Flooding and Subdivision

Effect of flooding due to hull damage

31Titanic


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Bulkheads and SubdivisionBulkheads : Transverse wallsto increase the structuralrigidity and create

watertight compartmentsOne CompartmentStandard : Any onewatertight compartmentmay be open to the seawithout immersing theuppermost deck or allowingthe ship to capsize.

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Effect of Flooding

If a compartment is flooded, the buoyancyprovided by that compartment will be lost .

Then the ship will sink deeper and itslongitudinal center of buoyancy will usuallymove and cause trim .Once the deck goes into the water,transverse stability decreases rapidly.

Note that GM=KB+BM-KG

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Permeability

The volume of water that can enter adamaged compartment is less than thevolume of compartment by the volume ofcargo or machinery inside the compartment.

Typical values85% for machinery spaces, 63% for ordinarycargo holds, 70% for container holds, 85% foraverage RO/RO holds

Permeability =Empty Volume

Molded Volume

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Stability of Submarines

Stability of a fully submerged body

G

B

GM = KB + BM KG= GB

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Extra slides

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Solids vs. Fluids

A solid can be deformed byan external force, however

its shape does not changeindefinitely.A fluid cannot resistdeformation force. Its shapewill change continuously aslong as the force is applied.

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Liquids and Gases

The response to an applied pressure(force/area) is quite different.

The physical property that describes thechange of volume with applied pressure iscalled the compressibility.

Compressible coefficient, (V/p)

Practically, water can be assumed to beincompressible. (0.1% volume change under20 bars pressure)

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Hydrostatics

Buoyancy applied to an object

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Ship Stability

When we say a ship is (statically)stable, we mean the boat will

Float upright when at rest in still waterReturn to its initial upright position ifgiven a slight, temporary deflection toeither side by some external force.

Unstable shipsNeutrally stable ships

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Rocking chair analogyThe center of weight is

higher than the center ofsupport which is on thefloor.When the chair leans back,the center of support alsomoves and so keeps thechair from tipping over.

Metacenter

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Example

An object with a circular section

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Range of Stability

What happened to stability characteristicsat larger angles of heel ?

Usually the righting moment will start toincrease. It increases approximately linearly atsmall angles.It will reach a maximum at about the angle ofheel at which the deck edge starts to immerse.Beyond that it will tend to decrease andeventually drop to zero.At any greater angle the vessel will capsize.

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Longitudinal Static Stability

A ship rarely capsizes in the fore-and-aftdirection.

However, the trim change by adding orremoving or shifting weights on the ship inthe longitudinal direction is an importantconcern.

The measure for this trim changeMTI: Moment to trim one inchMCT: Moment to change trim one centimeter

static stability of ships

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