This document defines key terms and concepts related to ship stability, including Archimedes' principle, center of gravity, center of buoyancy, metacenter, righting arm, and free surface effect. It explains that a ship is stable when its center of buoyancy is below and to the side of the center of gravity, and that the metacenter indicates the ship's stability based on its position relative to the center of gravity. Additionally, it discusses how stability curves illustrate a ship's righting arm at different angles of heel and how the free surface effect can negatively impact stability when compartments are only partially filled with water.

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GENERAL PRINCIPLES
OF STABILITY
A Brief By Lance Grindley

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Objectives
 Understand Archimedes’ principle
 Understand the following terms and how they relate to ship
stability
– Center of Gravity
– Center of Buoyancy
– Reserve Buoyancy
– Couple
– Righting Arm
– Righting Moment
 Be able to define the terms related to how the ship moves
 Be able to explain the free surface effect and how it is
related to ship stability

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Archimedes Principle
 It’s why ships float

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WATERLINE
DEPTHOFHULL
DRAFTFREEBOARD
RESERVE BUOYANCY

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Terms
 Center of Gravity – “G”
– An imaginary point within the ship through which all
gravity can be seen to act
– A spatially weighted average of smaller, individual
weights around the ship
– Is this fixed or can it move?
 Center of Buoyancy – “B”
– An imaginary point within the ship through which the
buoyant force can be seen to act
– Is this fixed or can it move?
– How would you want your “B” to be positioned relative
to “G”?

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Terms (cont)
 Metacenter – “M”
– Intersection of two successive lines of action of the
buoyant force as the ship heels through a very small
angle
– What does this tell us?
• It’s position with respect to “G” (“GM” or metacentric height)
gives us an indication of stability
 “Z”
– A point along the line forming the metacenter that
creates a right triangle with “M” & “G”

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More Terms
 Couple
– Two forces of equal magnitude acting in opposite and
parallel directions
– When inclining a ship, this couple produces either a
righting moment or an upsetting moment depending on
the relative location of B and G
 Righting Arm
– GZ = GM (sin (angle)) (in feet)
 Righting Moment
– RM = Weight x GZ (W) (ft-tons)

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STABILITY CURVES
 A plotted series of GZ values at
successive angles
 Factors involved
– 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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EFFECT OF DRAFT ON
RIGHTING ARM

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How the ship moves
 Roll
– Back/forth motion transversely
 Pitch
– Back/forth motion longitudinally
 Yaw
– Side to Side
 List
– Diff. between Port and Stbd draft
 Trim
– Diff. between fwd/aft draft

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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
– Causes “sloshing” of water
– Momentum of water will bang against the
tank’s sides, further causing instability of the
vessel in that direction

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Review/Summary
 Define the following:
– Trim
– List
– Pitch
 What is the center of gravity?
 What is the metacenter and what does it tell us
about ship stability?
 State Archimedes’ principle. Why is it important?
 What is a righting arm?

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QUESTIONS ????