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

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Stability buoyancy l.jpg

Stability & Buoyancy


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Objectives

  • Principles of Stability

  • Archimedes Principle

  • Terminology of ship’s hydrostatics

  • Stability & moments -> staying upright

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

  • Stability curves


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Principles of Stability

  • Floating object is acted on by forces of gravity and forces of buoyancy

    • Static equilibrium SFi = 0

  • Three conditions of static equilibrium:

    • Stable: return to same position if tipped

    • Neutral: when rotated, will come to rest in any position

    • 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

  • Depth to which ship sinks depends on density of water (r = 1 ton/35ft3 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

    • Forces of gravity: G = mshipg =Wship

    • Forces of buoyancy: B = rwaterVdisplaced

      Wship = rwaterVdisplaced


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Archimedes Principle

  • 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 Buoyancy (B): all buoyancy forces as one force acting upward through underwater geometric center


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G

Archimedes Principle

  • Center of Gravity (G):

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

    • Does not change position with movement of ship

  • Center of Buoyancy (B):

    • Changes position with movement of ship -> underwater geometric center moves

    • Also affected by displacement


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Hydrostatics Terminology

  • 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)

  • 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)


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Hydrostatics Terminology

  • 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

    • 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

    • G and B are a couple


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Moments

  • Depending on location of G and B, two types of moments:

    • Righting moment: tends to return ship to upright position

    • Upsetting moment: tends to overturn ship

  • Magnitude of righting moment:

    • RM = W * GZ (ft-tons)

    • 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)

    • If angle too large, M moves off centerline


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Metacenter

  • Metacentric Height (GM)

    • Determines size of righting/upsetting arm (for angles < 7o)

      GZ = GM*sinf

    • Large GM -> large righting arm (stiff)

    • Small GM -> small righting arm (tender)


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Metacenter

  • Relationship between G and M

    • G under M: ship is stable

    • G = M: ship neutral

    • G over M: ship unstable

STABLE

UNSTABLE


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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

  • 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

  • Plot GZ (righting arm) vs. angle of heel

    • Ship’s G does not change as angle changes

    • Ship’s B always at center of underwater portion of hull

    • Ship’s underwater portion of hull changes as heel angle changes

    • GZ changes as angle changes



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