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?