Principles of Stability

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Principles of Stability
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References

• INE Ch 22 (389-400)
• INE Ch 23 (401-402, 409)
• PNE Ch 3 (1-10)
• HW LG 24

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Principles of Stability

• Gravity
• Force exerted on a body drawing towards the
  center of the earth. Acts through center of
  gravity (G)
• Buoyancy
• An object floating in liquid displaces a volume
  of liquid equal to the submerged volume of the
  object. This exerts a pressure on all surfaces of
  the object resulting in a force opposing gravity
  through the center of buoyancy (B)

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Principles of Stability

• Archimedes Principle
• object submerged in fluid is buoyed up by a force
  equal to the weight it displaces
• Displacement
• Weight of ship equal to weight of water displaced
  by volume of underwater body of ship
• W V x 1/35
• Displacement depends on density of water (salt vs
  fresh)

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Displacement Curve Plots draft vs
displacement for a particular ship
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Vocabulary

• Draft how far your boat is in the water,
  measured in ft or yds
• Freeboard what is left above water (rough
  measure of reserve buoyancy)
• Depth of hull gunwale to keel
• Reserve buoyancy volume of the watertight
  portion of ship above waterline

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FREEBOARD
WATERLINE
RESERVE BUOYANCY
DEPTH OF HULL
DRAFT
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Reference Points

• Keel (K) bottom line of ship, base line
• Center of buoyancy (B) single force that acts
  vertically upward. Located at geometric center
  of underwater body. Moves as ship heels
• Center of gravity (G) single force that acts
  vertically downward. Located at geometric center
  of ship. Does not move as ship heels

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Reference Points (cont)

• When at rest, B and G lie on same vertical line.
• Metacenter (M) intersection of two lines of
  action of B as ship heels

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Terms

• Metacentric Height - GM
• measure of stability
• Righting Arm (GZ)
• Perpendicular distance between the lines of
  action between the two forces
• GZ GM (sin (F))

B
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Terms

• Couple
• Two forces of equal magnitude acting in opposite
  and parallel directions produce a rotation motion
• Created when ship heels and Buoyant force and
  Gravity are no longer in line with each other
• When inclining a ship, this couple produces
  either a righting moment or an upsetting moment
  depending on the relative location of B and G
• RM W x GZ

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Linear Measurements

• KG height of center of gravity above keel
• GM Metacentric height (measure of initial
  stability to 7 degrees, after that we use
  stability curve)

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States of Stability

• Positive M above G
• Neutral M and G same position
• Negative M below G
• GM used as a measure of stability up to 7º, after
  that values of GZ are plotted at successive
  angles to create the stability curve

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Stability Curve (Cont)

• Effects of draft on righting arm
• Righting arms (GZ) decrease
• Displacement (W) increases
• Righting moment overall may increase or decrease.
  Function of hull shape, magnitude of
  displacement change

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Effect Of Draft On Righting Arm
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Definitions

• Roll Back/forth motion transversely
• Pitch Back/forth motion longitudinally
• Yaw Side to Side
• List Difference between Port and Stbd draft
• Trim Difference between fwd/aft draft
• Center of Flotation Point at which ship trims
  about

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Cross Curves of Stability

• Takes a probable range of drafts (displacements)
• For each draft, GZ value calculated
• Calculations made over various angles of heel
• Data all plotted on Cross Curves of Stability

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Stability Curves

• A plotted series of GZ values at successive
  angles
• Factors
• G does not change position as heeling angle
  changes
• B is always at the geometric center of the volume
  of the underwater hull
• The shape of the underwater hull changes as
  heeling angle changes

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Effects of Weight Shifts

• Weight shifts effect Center of Gravity (G)
• Shift of G will be in same direction of weight
  shift (vertical, horizontal, fore/aft)
• GG1 (w) (s) / W
• GG1 Distance of shift of Center of Gravity
• w Shifted component weight
• s Distance component is shifted
• W Weight of entire system

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Effects of Weight Shifts (cont)

• Vertical Shifts
• As G shifts up, for a given angle of heel,
  righting arm decreases (ship less stable)
• Horizontal Shifts
• G will shift in the direction of weight shift,
  causing the ship to heel to one side
• Righting arm is decreased since G is moved from
  centerline toward B

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Free Surface Effect

• Occurs when a compartment or tank is only
  partially flooded / filled
• As the ship rocks, water wants to maintain a
  level condition causing sloshing of water
• As water shifts in direction of heel, Center of
  Gravity shifts thus decreasing the righting arm
• This effect reduced by pocketing

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Summary