buoyancy & stability in naval architecture
Post on 31-Oct-2015
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Stability & Buoyancy
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ObjectivesPrinciples of StabilityArchimedes PrincipleTerminology of ships hydrostaticsStability & moments -> staying uprightMetacenter, Center of Gravity, Center of Buoyancy, etc.Stability curves
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Principles of StabilityFloating object is acted on by forces of gravity and forces of buoyancyStatic equilibrium SFi = 0Three conditions of static equilibrium:Stable: return to same position if tippedNeutral: when rotated, will come to rest in any positionUnstable: will come to rest in new position if force acts on it
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Archimedes PrincipleLaw: a body floating or submerged in a fluid is buoyed up by a force equal to the weight of the water it displacesDepth to which ship sinks depends on density of water (r = 1 ton/35ft3 seawater)
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Archimedes PrincipleShip sinks until weight of water displaced by the underwater volume is equal to the weight of the shipForces of gravity: G = mshipg =WshipForces of buoyancy: B = rwaterVdisplaced
Wship = rwaterVdisplaced
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Archimedes PrincipleForces act everywhere on ship -> too tough to analyzeCenter of Gravity (G): all gravity forces as one force acting downward through ships geometric centerCenter of Buoyancy (B): all buoyancy forces as one force acting upward through underwater geometric center
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Archimedes PrincipleCenter of Gravity (G):Changes position only by change/shift in mass of shipDoes not change position with movement of shipCenter of Buoyancy (B):Changes position with movement of ship -> underwater geometric center movesAlso affected by displacement
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Hydrostatics TerminologyDisplacement: total weight of ship = total submerged volume of ship (measured in tons)Draft: vertical distance from waterline to keel at deepest point (measured in feet)Reserve Buoyancy: volume of watertight portion of ship above waterline (important factor in ships ability to survive flooding)Freeboard: vertical distance from waterline to main deck (rough indication of reserve buoyancy)
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Hydrostatics TerminologyAs draft & displacement increase, freeboard and reserve buoyancy decrease
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MomentsDefn: tendency of a force to produce rotation or to move an object about an axisDistance between the force and axis of rotation is the moment armCouple: two forces of equal magnitude in opposite and parallel directions, separated by a perpendicular distanceG and B are a couple
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MomentsDepending on location of G and B, two types of moments:Righting moment: tends to return ship to upright positionUpsetting moment: tends to overturn shipMagnitude of righting moment:RM = W * GZ (ft-tons)GZ: moment arm (ft)
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MetacenterDefn: the intersection of two successive lines of action of the force of buoyancy as ship heels through small angles (M)If angle too large, M moves off centerline
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MetacenterMetacentric Height (GM)Determines size of righting/upsetting arm (for angles < 7o)GZ = GM*sinfLarge GM -> large righting arm (stiff)Small GM -> small righting arm (tender)
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MetacenterRelationship between G and MG under M: ship is stableG = M: ship neutralG over M: ship unstableSTABLEUNSTABLE
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Metacenter v. Stability CurvesAt this point, we could use lots of trigonometry to determine exact values of forces, etc for all angles -> too much work GM used as a measure of stability up to 7, after that values of GZ are plotted at successive angles to create the stability curve
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Stability Curve
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Stability CurvePlot GZ (righting arm) vs. angle of heelShips G does not change as angle changesShips B always at center of underwater portion of hullShips underwater portion of hull changes as heel angle changesGZ changes as angle changes
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