Download - Lesson 23a - Buoyancy & Stability
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8/11/2019 Lesson 23a - Buoyancy & Stability
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Stability &Buoyancy
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Objectives
Principles of Stability Archimedes Principle
Terminology of ships 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 anyposition
Unstable:will come to rest in new position if forceacts on it
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Archimedes Principle
Law: a body floating or submerged in afluid is buoyed up by a force equal to theweight of the water it displaces
Depth to which ship sinks depends ondensity of water (r= 1 ton/35ft3seawater)
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Archimedes Principle
Ship sinks until weight of waterdisplaced by the underwater volume isequal to the weight of the ship
Forces of gravity: G = mship
g =Wship
Forces of buoyancy: B = rwaterVdisplaced
Wship = rwaterVdisplaced
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Archimedes Principle
Forces act everywhere on ship -> tootough to analyze
Center of Gravity (G):all gravity forces
as one force acting downward throughships geometric center
Center of Buoyancy (B):all buoyancy
forces as one force acting upwardthrough underwater geometric center
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Archimedes Principle
Center of Gravity (G): Changes position only by change/shift in
mass of ship
Does not change positionwith movement of
ship Center of Buoyancy (B):
Changes positionwith movement of ship ->underwater geometric center moves
Also affected by displacement
G
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Hydrostatics Terminology
Displacement:total weight of ship = totalsubmerged volume of ship (measured in tons)
Draft:vertical distance from waterline to keel atdeepest point (measured in feet)
Reserve Buoyancy:volume of watertight portionof ship above waterline (important factor inships ability to survive flooding)
Freeboard:vertical distance from waterline tomain deck (rough indication of reservebuoyancy)
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Hydrostatics Terminology
As draft & displacement increase,
freeboard and reserve buoyancy decrease
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Moments
Defn: tendency of a force to producerotation or to move an object about anaxis
Distance between the force and axis ofrotation is the moment arm
Couple: two forces of equal magnitude inopposite 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 ofmoments:
Righting moment:tends toreturn ship to upright position
Upsetting moment:tends tooverturn ship
Magnitude of righting
moment: RM = W * GZ(ft-tons)
GZ: moment arm(ft)
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Metacenter
Defn: the intersectionof two successive
lines of action of theforce of buoyancy asship heels throughsmall angles (M)
If angle too large, Mmoves off centerline
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Metacenter
Metacentric Height(GM)
Determines size ofrighting/upsetting arm
(for angles < 7o)
GZ = GM*sin
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 oftrigonometry to determine exact valuesof forces, etc for all angles -> too muchwork
GM used as a measure of stability up to7, after that values of GZ are plotted atsuccessive angles to create the stabilitycurve
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Stability Curve
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Stability Curve Plot GZ (righting arm) vs. angle of heel
Ships G does not change as angle changes
Ships B always at center of underwater portion ofhull
Ships underwater portion of hull changes as heelangle changes
GZ changes as angle changes
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Questions?