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Published byZayne Bachus Modified about 1 year ago

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Stability & Buoyancy

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Objectives Principles of Stability Principles of Stability Archimedes Principle Archimedes Principle Terminology of ship’s hydrostatics Terminology of ship’s hydrostatics Stability & moments -> staying upright Stability & moments -> staying upright Metacenter, Center of Gravity, Center of Buoyancy, etc. Metacenter, Center of Gravity, Center of Buoyancy, etc. Stability curves Stability curves

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Principles of Stability Floating object is acted on by forces of gravity and forces of buoyancy Floating object is acted on by forces of gravity and forces of buoyancy Static equilibrium F i = 0 Static equilibrium F i = 0 Three conditions of static equilibrium: Three conditions of static equilibrium: Stable: return to same position if tipped Stable: return to same position if tipped Neutral: when rotated, will come to rest in any position Neutral: when rotated, will come to rest in any position Unstable: will come to rest in new position if force acts on it Unstable: will come to rest in new position if force acts on it

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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 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 ( = 1 ton/35ft 3 seawater) Depth to which ship sinks depends on density of water ( = 1 ton/35ft 3 seawater)

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Archimedes Principle Ship sinks until weight of water displaced by the underwater volume is equal to the weight of the ship Ship sinks until weight of water displaced by the underwater volume is equal to the weight of the ship Forces of gravity: G = m ship g =W ship Forces of gravity: G = m ship g =W ship Forces of buoyancy: B = water V displaced Forces of buoyancy: B = water V displaced W ship = water V displaced

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Archimedes Principle Forces act everywhere on ship -> too tough to analyze Forces act everywhere on ship -> too tough to analyze Center of Gravity (G): all gravity forces as one force acting downward through ship’s geometric center Center of Gravity (G): all gravity forces as one force acting downward through ship’s geometric center Center of Buoyancy (B): all buoyancy forces as one force acting upward through underwater geometric center Center of Buoyancy (B): all buoyancy forces as one force acting upward through underwater geometric center

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Archimedes Principle Center of Gravity (G): Center of Gravity (G): Changes position only by change/shift in mass of ship Changes position only by change/shift in mass of ship Does not change position with movement of ship Does not change position with movement of ship Center of Buoyancy (B): Center of Buoyancy (B): Changes position with movement of ship -> underwater geometric center moves Changes position with movement of ship -> underwater geometric center moves Also affected by displacement Also affected by displacement G

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Hydrostatics Terminology Displacement: total weight of ship = total submerged volume of ship (measured in tons) Displacement: 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) 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 ship’s ability to survive flooding) Reserve Buoyancy: volume of watertight portion of ship above waterline (important factor in ship’s ability to survive flooding) Freeboard: vertical distance from waterline to main deck (rough indication of reserve buoyancy) Freeboard: vertical distance from waterline to main deck (rough indication of reserve buoyancy)

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Hydrostatics Terminology As draft & displacement increase, freeboard and reserve buoyancy decrease As draft & displacement increase, freeboard and reserve buoyancy decrease

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Moments Def’n: tendency of a force to produce rotation or to move an object about an axis Def’n: tendency of a force to produce rotation or to move an object about an axis Distance between the force and axis of rotation is the moment arm Distance between the force and axis of rotation is the moment arm Couple: two forces of equal magnitude in opposite and parallel directions, separated by a perpendicular distance Couple: two forces of equal magnitude in opposite and parallel directions, separated by a perpendicular distance G and B are a couple G and B are a couple

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Moments Depending on location of G and B, two types of moments: Depending on location of G and B, two types of moments: Righting moment: tends to return ship to upright position Righting moment: tends to return ship to upright position Upsetting moment: tends to overturn ship Upsetting moment: tends to overturn ship Magnitude of righting moment: Magnitude of righting moment: RM = W * GZ (ft-tons) RM = W * GZ (ft-tons) GZ: moment arm (ft) GZ: moment arm (ft)

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Metacenter Def’n: the intersection of two successive lines of action of the force of buoyancy as ship heels through small angles (M) Def’n: 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 If angle too large, M moves off centerline

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Metacenter Metacentric Height (GM) Metacentric Height (GM) Determines size of righting/upsetting arm (for angles < 7 o ) Determines size of righting/upsetting arm (for angles < 7 o ) GZ = GM*sin Large GM -> large righting arm (stiff) Large GM -> large righting arm (stiff) Small GM -> small righting arm (tender) Small GM -> small righting arm (tender)

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Metacenter Relationship between G and M Relationship between G and M G under M: ship is stable G under M: ship is stable G = M: ship neutral G = M: ship neutral G over M: ship unstable G over M: ship unstable STABLEUNSTABLE

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Metacenter v. Stability Curves At this point, we could use lots of trigonometry to determine exact values of forces, etc for all angles -> too much work At 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 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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Plot GZ (righting arm) vs. angle of heel Plot GZ (righting arm) vs. angle of heel Ship’s G does not change as angle changes Ship’s G does not change as angle changes Ship’s B always at center of underwater portion of hull Ship’s B always at center of underwater portion of hull Ship’s underwater portion of hull changes as heel angle changes Ship’s underwater portion of hull changes as heel angle changes GZ changes as angle changes GZ changes as angle changes

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