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# Lesson 23a - Buoyanc.. - 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

• Principles of Stability

• Archimedes Principle

• Terminology of ship’s hydrostatics

• Stability & moments -> staying upright

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

• Stability curves

• 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

• 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)

• 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

• 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 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

• 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)

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

• 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

• 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)

• 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

• 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)

• Relationship between G and M

• G under M: ship is stable

• G = M: ship neutral

• G over M: ship unstable

STABLE

UNSTABLE

• 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

• 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