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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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objectives
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
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
archimedes principle
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)
archimedes principle5
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

archimedes principle6
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
archimedes principle7

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
hydrostatics terminology
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)
hydrostatics terminology9
Hydrostatics Terminology
  • As draft & displacement increase, freeboard and reserve buoyancy decrease
moments
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
moments11
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)
metacenter
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
metacenter13
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)
metacenter14
Metacenter
  • Relationship between G and M
    • G under M: ship is stable
    • G = M: ship neutral
    • G over M: ship unstable

STABLE

UNSTABLE

metacenter v stability curves
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
stability curve17
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