Principles of StabilityPrinciples of Stability

ReferencesReferences

• INE: Ch 22 (389-400)INE: Ch 22 (389-400)

• INE: Ch 23 (401-402, 409)INE: Ch 23 (401-402, 409)

• PNE: Ch 3 (1-10)PNE: Ch 3 (1-10)

• HW:HW: LG #24 LG #24

Principles of StabilityPrinciples of Stability• GravityGravity

– Force exerted on a body drawing towards the center Force exerted on a body drawing towards the center of the earth. Acts through center of gravity (G)of the earth. Acts through center of gravity (G)

• BuoyancyBuoyancy– An object floating in liquid displaces a volume of An object floating in liquid displaces a volume of

liquid equal to the submerged volume of the object. liquid equal to the submerged volume of the object. This exerts a pressure on all surfaces of the object This exerts a pressure on all surfaces of the object resulting in a force opposing gravity through the resulting in a force opposing gravity through the center of buoyancy (B)center of buoyancy (B)

Principles of StabilityPrinciples of Stability• Archimedes PrincipleArchimedes Principle

– object submerged in fluid is buoyed up by a force object submerged in fluid is buoyed up by a force equal to the weight it displacesequal to the weight it displaces

• DisplacementDisplacement– Weight of ship equal to weight of water displaced by Weight of ship equal to weight of water displaced by

volume of underwater body of shipvolume of underwater body of ship– W = V x 1/35W = V x 1/35– Displacement depends on density of water (salt vs Displacement depends on density of water (salt vs

fresh)fresh)

Archimedes’ Principle– An object floating

or submerged in a fluid is buoyed up by a force equal to the weight of the fluid displaced

Displacement Curve:Plots draft vs displacementfor a particular ship

VocabularyVocabulary

• Draft: how far your boat is in the water, Draft: how far your boat is in the water, measured in ft or ydsmeasured in ft or yds

• Freeboard: what is left above water (rough Freeboard: what is left above water (rough measure of reserve buoyancy)measure of reserve buoyancy)

• Depth of hull: gunwale to keelDepth of hull: gunwale to keel

• Reserve buoyancy: volume of the Reserve buoyancy: volume of the watertight portion of ship above waterlinewatertight portion of ship above waterline

WATERLINE

DEPTH

OF

HU

LL

DR

AFT

FREEB

OA

RD

RESERVE BUOYANCY

Reference PointsReference Points

• Keel (K): bottom line of ship, base lineKeel (K): bottom line of ship, base line

• Center of buoyancy (B): single force that Center of buoyancy (B): single force that acts vertically upward. Located at geometric acts vertically upward. Located at geometric center of underwater body. center of underwater body. Moves as ship Moves as ship heelsheels

• Center of gravity (G): single force that acts Center of gravity (G): single force that acts vertically downward. Located at geometric vertically downward. Located at geometric center of ship. center of ship. Does not move as ship heelsDoes not move as ship heels

Reference Points Reference Points (con’t)(con’t)

• When at rest, B and G lie on same vertical When at rest, B and G lie on same vertical line.line.

• Metacenter (M): intersection of two lines Metacenter (M): intersection of two lines of action of B as ship heelsof action of B as ship heels

TermsTerms

• Metacentric Height - GMMetacentric Height - GM– measure of stabilitymeasure of stability

• Righting Arm (GZ)Righting Arm (GZ)– Perpendicular distance between the lines of Perpendicular distance between the lines of

action between the two forces action between the two forces

– GZ = GM (sin (Φ))GZ = GM (sin (Φ))G Z

M

Ф

B

TermsTerms• CoupleCouple

– Two forces of equal magnitude acting in opposite Two forces of equal magnitude acting in opposite and parallel directions produce a rotation motionand parallel directions produce a rotation motion

– Created when ship heels and Buoyant force and Created when ship heels and Buoyant force and Gravity are no longer in line with each otherGravity are no longer in line with each other

– When inclining a ship, this couple produces either When inclining a ship, this couple produces either a a righting momentrighting moment or an upsetting moment or an upsetting moment depending on the relative location of B and Gdepending on the relative location of B and G

– RM = W x GZRM = W x GZ

Linear MeasurementsLinear Measurements

• KG: height of center of gravity above keelKG: height of center of gravity above keel

• GM: Metacentric height (measure of initial GM: Metacentric height (measure of initial stability to 7 degrees, after that we use stability to 7 degrees, after that we use stability curve)stability curve)

States of StabilityStates of Stability

• Positive: M above GPositive: M above G• Neutral: M and G same positionNeutral: M and G same position• Negative: M below GNegative: M below G

• GM used as a measure of stability up to 7º, GM used as a measure of stability up to 7º, after that values of GZ are plotted at after that values of GZ are plotted at successive angles to create the stability curve successive angles to create the stability curve

Stability Curve (Cont)Stability Curve (Cont)

• Effects of draft on righting arm:Effects of draft on righting arm:– Righting arms (GZ) decreaseRighting arms (GZ) decrease– Displacement (W) increasesDisplacement (W) increases– Righting moment overall may increase or Righting moment overall may increase or

decrease. Function of hull shape, magnitude of decrease. Function of hull shape, magnitude of displacement changedisplacement change

Effect Of Draft On Righting Effect Of Draft On Righting ArmArm

DefinitionsDefinitions

• Roll: Back/forth motion transverselyRoll: Back/forth motion transversely

• Pitch: Back/forth motion longitudinallyPitch: Back/forth motion longitudinally

• Yaw: Side to SideYaw: Side to Side

• List: Difference between Port and Stbd draftList: Difference between Port and Stbd draft

• Trim: Difference between fwd/aft draftTrim: Difference between fwd/aft draft

• Center of Flotation: Point at which ship trims Center of Flotation: Point at which ship trims aboutabout

Effects of Weight ShiftsEffects of Weight Shifts

• Weight shifts effect Center of Gravity (G)Weight shifts effect Center of Gravity (G)• Shift of G will be in same direction of weight Shift of G will be in same direction of weight

shift (vertical, horizontal, fore/aft)shift (vertical, horizontal, fore/aft)

• GGGG11 = (w) (s) / W = (w) (s) / W

– GGGG11: Distance of shift of Center of Gravity: Distance of shift of Center of Gravity

– w: Shifted component weightw: Shifted component weight– s: Distance component is shifteds: Distance component is shifted– W: Weight of entire systemW: Weight of entire system

Effects of Weight Shifts Effects of Weight Shifts (con’t)(con’t)

• Vertical Shifts:Vertical Shifts:– As G shifts up, for a given angle of heel, As G shifts up, for a given angle of heel,

righting arm decreases (ship less stable)righting arm decreases (ship less stable)

• Horizontal Shifts:Horizontal Shifts:– G will shift in the direction of weight shift, G will shift in the direction of weight shift,

causing the ship to heel to one sidecausing the ship to heel to one side– Righting arm is decreased since G is moved Righting arm is decreased since G is moved

from centerline toward Bfrom centerline toward B

Free Surface EffectFree Surface Effect

• Occurs when a compartment or tank is only Occurs when a compartment or tank is only partially flooded / filledpartially flooded / filled

• As the ship rocks, water wants to maintain a As the ship rocks, water wants to maintain a level condition causing “sloshing” of waterlevel condition causing “sloshing” of water

• As water shifts in direction of heel, Center of As water shifts in direction of heel, Center of Gravity shifts thus decreasing the righting Gravity shifts thus decreasing the righting armarm

• This effect reduced by pocketingThis effect reduced by pocketing

SummarySummary