SHIP Buoyancy Stability Presentation

8/19/2019 SHIP Buoyancy Stability Presentation

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Stability &Stability &BuoyancyBuoyancy



ObjectivesObjectives

• Principles of StabilityPrinciples of Stability• Archimedes PrincipleArchimedes Principle

• Terminology of ship’sTerminology of ship’s

hydrostaticshydrostatics• Stability & moments -> stayingStability & moments -> staying

uprightupright

• etacenter! "enter of #ravity!etacenter! "enter of #ravity!"enter of $uoyancy! etc%"enter of $uoyancy! etc%

• Stability curvesStability curves



Principles of StabilityPrinciples of Stability• loating object is acted on by forces of gravity and forces of buoyancyloating object is acted on by forces of gravity and forces of buoyancy

• Static e'uilibriumStatic e'uilibrium ΣΣFFii = 0= 0

• Three conditions of static e'uilibrium(Three conditions of static e'uilibrium(• Stable(Stable( return to same position if tippedreturn to same position if tipped

• )eutral()eutral( *hen rotated! *ill come to rest in any position*hen rotated! *ill come to rest in any position

• +nstable(+nstable( *ill come to rest in ne* position if force acts on it*ill come to rest in ne* position if force acts on it



Archimedes PrincipleArchimedes Principle•

,a*( a body oating or,a*( a body oating orsubmerged in a uid is buoyedsubmerged in a uid is buoyed

up by a force e'ual to theup by a force e'ual to the

*eight of the *ater it*eight of the *ater it

displacesdisplaces

• .epth to *hich ship sin/s.epth to *hich ship sin/s

depends on density of *ater 0depends on density of *ater 0

1 2 ton345ft1 2 ton345ft44 sea*ater6sea*ater6




Ship sin/s until *eight ofShip sin/s until *eight of*ater displaced by the*ater displaced by the

under*ater volume is e'ual tounder*ater volume is e'ual to

the *eight of the shipthe *eight of the ship• orces of gravity(orces of gravity( # 1 m# 1 mshipshipgg

1717shipship

• orces of buoyancy(orces of buoyancy( $ 1$ 1

*ater*ater88displaceddisplaced

WWshipship == ρρwaterwaterVVdisplaceddisplaced



Archimedes PrincipleArchimedes Principle

• orces act every*here on shiporces act every*here on ship-> too tough to analy9e-> too tough to analy9e

• "enter of #ravity 0#6("enter of #ravity 0#6( allall

gravity forces as one forcegravity forces as one forceacting do*n*ard throughacting do*n*ard through

ship’s geometric centership’s geometric center

•

"enter of $uoyancy 0$6("enter of $uoyancy 0$6( allallbuoyancy forces as one forcebuoyancy forces as one force

acting up*ard throughacting up*ard through

under*ater geometric centerunder*ater geometric center




"enter of #ravity 0#6("enter of #ravity 0#6(• "hanges position only by"hanges position only bychange3shift in mass of shipchange3shift in mass of ship

• .oes not change position.oes not change position *ith*ithmovement of shipmovement of ship

• "enter of $uoyancy 0$6("enter of $uoyancy 0$6(• "hanges position"hanges position *ith movement of*ith movement of

ship -> under*ater geometric centership -> under*ater geometric center

movesmoves

• Also a:ected by displacementAlso a:ected by displacement

#



;ydrostatics;ydrostatics

TerminologyTerminology• .isplacement(.isplacement( total *eight of ship 1total *eight of ship 1

total submerged volume of shiptotal submerged volume of ship

0measured in tons60measured in tons6

• .raft(.raft( vertical distance from *aterline tovertical distance from *aterline to

/eel at deepest point 0measured in feet6/eel at deepest point 0measured in feet6• <eserve $uoyancy(<eserve $uoyancy( volume of *atertightvolume of *atertight

portion of ship above *aterlineportion of ship above *aterline

0important factor in ship’s ability to0important factor in ship’s ability to

survive ooding6survive ooding6• reeboard(reeboard( vertical distance fromvertical distance from

*aterline to main dec/ 0rough indication*aterline to main dec/ 0rough indication

of reserve buoyancy6of reserve buoyancy6



;ydrostatics;ydrostatics

TerminologyTerminology

• As draft & displacement increase!As draft & displacement increase!

freeboard and reserve buoyancy decreasefreeboard and reserve buoyancy decrease



omentsoments

• .ef’n( tendency of a force to.ef’n( tendency of a force toproduce rotation or to move anproduce rotation or to move an

object about an a=isobject about an a=is• .istance bet*een the force and.istance bet*een the force and

a=is of rotation is the moment arma=is of rotation is the moment arm

• "ouple( t*o forces of e'ual"ouple( t*o forces of e'ual

magnitude in opposite andmagnitude in opposite and

parallel directions! separatedparallel directions! separatedby a perpendicular distanceby a perpendicular distance• # and $ are a couple# and $ are a couple



omentsoments• .epending on location.epending on location

of # and $! t*o typesof # and $! t*o typesof moments(of moments(• <ighting moment(<ighting moment(

tends to return ship totends to return ship to

upright positionupright position• +psetting moment(+psetting moment(

tends to overturn shiptends to overturn ship

• agnitude of rightingagnitude of righting

moment(moment(• < 1 7 #?< 1 7 #? 0ft-tons60ft-tons6

• #?( moment arm#?( moment arm 0ft60ft6



etacenteretacenter

• .ef’n( the.ef’n( the

intersection of t*ointersection of t*o

successive lines ofsuccessive lines of

action of the forceaction of the forceof buoyancy asof buoyancy as

ship heels throughship heels through

small angles 06small angles 06• @f angle too large! @f angle too large!

moves o: centerlinemoves o: centerline



etacenteretacenter•

etacentricetacentric;eight 0#6;eight 0#6• .etermines si9e of.etermines si9e of

righting3upsettingrighting3upsetting

arm 0for angles arm 0for angles BBoo66

#? 1 #sin#? 1 #sin

• ,arge # -> large,arge # -> large

righting arm 0sti:6righting arm 0sti:6• Small # -> smallSmall # -> small

righting armrighting arm

0tender60tender6



etacenteretacenter

• <elationship bet*een # and <elationship bet*een # and • # under ( ship is stable# under ( ship is stable

• # 1 ( ship neutral# 1 ( ship neutral

•

# over ( ship unstable# over ( ship unstable

STABLESTABLE UNSTABLEUNSTABLE

bili S bili



etacenter v% Stabilityetacenter v% Stability

"urves"urves• At this point! *e could useAt this point! *e could use

lots of trigonometry tolots of trigonometry to

determine e=act values ofdetermine e=act values of

forces! etc for all angles ->forces! etc for all angles ->

too much *or/too much *or/

• # used as a measure of# used as a measure of

stability up to BC! after thatstability up to BC! after that

values of #? are plotted atvalues of #? are plotted at

successive angles to createsuccessive angles to create

the stability curvethe stability curve



Stability "urveStability "urve



Stability "urveStability "urve• Plot #? 0righting arm6 vs% angle of heelPlot #? 0righting arm6 vs% angle of heel

• Ship’s # does not change as angle changesShip’s # does not change as angle changes• Ship’s $ al*ays at center of under*aterShip’s $ al*ays at center of under*ater

portion of hullportion of hull

• Ship’s under*ater portion of hull changesShip’s under*ater portion of hull changes

as heel angle changesas heel angle changes• #? changes as angle changes#? changes as angle changes



DuestionsDuestions

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SHIP Buoyancy Stability Presentation