Stability & Buoyancy

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# Stability & Buoyancy - PowerPoint PPT Presentation

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

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
• Floating object is acted on by forces of gravity and forces of buoyancy
• Static equilibrium SFi = 0
• Three conditions of static equilibrium:
• 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
• 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 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 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

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