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Principles of Stability

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References INE: Ch 22 (389-400)INE: Ch 22 (389-400) INE: Ch 23 (401-402, 409)INE: Ch 23 (401-402, 409) PNE: Ch 3 (1-10)PNE: Ch 3 (1-10) HW: LG #24HW: LG #24

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Principles of Stability GravityGravity –Force exerted on a body drawing towards the center of the earth. Acts through center of gravity (G) BuoyancyBuoyancy –An object floating in liquid displaces a volume of liquid equal to the submerged volume of the object. This exerts a pressure on all surfaces of the object resulting in a force opposing gravity through the center of buoyancy (B)

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Principles of Stability Archimedes PrincipleArchimedes Principle –object submerged in fluid is buoyed up by a force equal to the weight it displaces DisplacementDisplacement –Weight of ship equal to weight of water displaced by volume of underwater body of ship –W = V x 1/35 –Displacement depends on density of water (salt vs fresh)

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Archimedes’ Principle –An object floating or submerged in a fluid is buoyed up by a force equal to the weight of the fluid displaced Displacement Curve: Plots draft vs displacement for a particular ship

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Vocabulary Draft: how far your boat is in the water, measured in ft or ydsDraft: how far your boat is in the water, measured in ft or yds Freeboard: what is left above water (rough measure of reserve buoyancy)Freeboard: what is left above water (rough measure of reserve buoyancy) Depth of hull: gunwale to keelDepth of hull: gunwale to keel Reserve buoyancy: volume of the watertight portion of ship above waterlineReserve buoyancy: volume of the watertight portion of ship above waterline

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WATERLINE DEPTH OF HULL DRAFT FREEBOARD RESERVE BUOYANCY

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Reference Points Keel (K): bottom line of ship, base lineKeel (K): bottom line of ship, base line Center of buoyancy (B): single force that acts vertically upward. Located at geometric center of underwater body. Moves as ship heelsCenter of buoyancy (B): single force that acts vertically upward. Located at geometric center of underwater body. Moves as ship heels Center of gravity (G): single force that acts vertically downward. Located at geometric center of ship. Does not move as ship heelsCenter of gravity (G): single force that acts vertically downward. Located at geometric center of ship. Does not move as ship heels

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Reference Points (con’t) When at rest, B and G lie on same vertical line.When at rest, B and G lie on same vertical line. Metacenter (M): intersection of two lines of action of B as ship heelsMetacenter (M): intersection of two lines of action of B as ship heels

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Terms Metacentric Height - GMMetacentric Height - GM –measure of stability Righting Arm (GZ)Righting Arm (GZ) –Perpendicular distance between the lines of action between the two forces –GZ = GM (sin (Φ)) G Z M Ф B

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Terms CoupleCouple –Two forces of equal magnitude acting in opposite and parallel directions produce a rotation motion –Created when ship heels and Buoyant force and Gravity are no longer in line with each other –When inclining a ship, this couple produces either a righting moment or an upsetting moment depending on the relative location of B and G –RM = W x GZ

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Linear Measurements KG: height of center of gravity above keelKG: height of center of gravity above keel GM: Metacentric height (measure of initial stability to 7 degrees, after that we use stability curve)GM: Metacentric height (measure of initial stability to 7 degrees, after that we use stability curve)

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States of Stability Positive: M above GPositive: M above G Neutral: M and G same positionNeutral: M and G same position Negative: M below GNegative: M below G GM used as a measure of stability up to 7º, after that values of GZ are plotted at successive angles to create the stability curveGM used as a measure of stability up to 7º, after that values of GZ are plotted at successive angles to create the stability curve

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Stability Curve (Cont) Effects of draft on righting arm:Effects of draft on righting arm: –Righting arms (GZ) decrease –Displacement (W) increases –Righting moment overall may increase or decrease. Function of hull shape, magnitude of displacement change

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Effect Of Draft On Righting Arm

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Definitions Roll: Back/forth motion transverselyRoll: Back/forth motion transversely Pitch: Back/forth motion longitudinallyPitch: Back/forth motion longitudinally Yaw: Side to SideYaw: Side to Side List: Difference between Port and Stbd draftList: Difference between Port and Stbd draft Trim: Difference between fwd/aft draftTrim: Difference between fwd/aft draft Center of Flotation: Point at which ship trims aboutCenter of Flotation: Point at which ship trims about

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Cross Curves of Stability Takes a probable range of drafts (displacements)Takes a probable range of drafts (displacements) For each draft, GZ value calculatedFor each draft, GZ value calculated Calculations made over various angles of heelCalculations made over various angles of heel Data all plotted on Cross Curves of StabilityData all plotted on Cross Curves of Stability

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Stability Curves l A plotted series of GZ values at successive angles l Factors: – G does not change position as heeling angle changes – B is always at the geometric center of the volume of the underwater hull – The shape of the underwater hull changes as heeling angle changes

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Effects of Weight Shifts Weight shifts effect Center of Gravity (G)Weight shifts effect Center of Gravity (G) Shift of G will be in same direction of weight shift (vertical, horizontal, fore/aft)Shift of G will be in same direction of weight shift (vertical, horizontal, fore/aft) GG 1 = (w) (s) / WGG 1 = (w) (s) / W –GG 1 : Distance of shift of Center of Gravity –w: Shifted component weight –s: Distance component is shifted –W: Weight of entire system

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Effects of Weight Shifts (con’t) Vertical Shifts:Vertical Shifts: –As G shifts up, for a given angle of heel, righting arm decreases (ship less stable) Horizontal Shifts:Horizontal Shifts: –G will shift in the direction of weight shift, causing the ship to heel to one side –Righting arm is decreased since G is moved from centerline toward B

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Free Surface Effect Occurs when a compartment or tank is only partially flooded / filledOccurs when a compartment or tank is only partially flooded / filled As the ship rocks, water wants to maintain a level condition causing “sloshing” of waterAs the ship rocks, water wants to maintain a level condition causing “sloshing” of water As water shifts in direction of heel, Center of Gravity shifts thus decreasing the righting armAs water shifts in direction of heel, Center of Gravity shifts thus decreasing the righting arm This effect reduced by pocketingThis effect reduced by pocketing

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Summary

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Lec 4: Fluid statics, buoyancy and stability, pressure

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