Ship Stability and Equilibrium

• Equilibrium describes an object at rest in its natural environment, where all acting forces are equal, maintaining its center of gravity (G).
• Ships experience three equilibrium states: stable, neutral, and unstable.
• A floating ship remains stationary and upright only when launched or in dry dock.
• Otherwise, it is considered in its natural state, floating in still or moving water.
• Archimedes' principle and the Law of Flotation apply for a ship to be in equilibrium.
• Stable equilibrium occurs when buoyancy forces act vertically upwards through the center of buoyancy (B).
• These buoyancy forces must equate and oppose the ship's weight, which acts downwards through the center of gravity (G).
• Vessels that meet these conditions float upright or roll around the vertical axis in a seaway, unless list or heel forces are present.
• Initial stable equilibrium relates to the vertical metacentric height (GM), and KM is determined via calculations and tests during construction, and is then tabled for use for varied load conditions.
• GM is positive when the metacentre (M) is above G along the centerline.
• Equilibrium is assessed with the ship heeled to small angles (10-15°) by external forces, as larger angles require detailed calculations guided by regulatory requirements.
• Stable equilibrium describes a ship's ability to return to its original upright position after being heeled at a small angle, once the heeling force is removed.
• In a heeled vessel, the center of gravity (G) remains constant, with the ship's weight acting downwards through G.
• The center of buoyancy (B) shifts in the direction of the heeling force, becoming B1.
• Buoyancy/upthrust acts vertically upwards through B1, intersecting the centerline at the transverse metacentre (M).
• Lever GZ, or the righting lever, acts with G as the fulcrum.
• The combined action attempts to correct the heel, returning the ship upright and is known as the Righting Moment or Transverse Moment of Statical Stability.
• The Righting Moment = W x GZ.
• GZ is linked to GM and the heel angle (Θ); G lying below M denotes a positive GM and vessel stability.
• A reasonably small metacentric height (GM) indicates a tender ship with a small righting lever at small angles, resulting in a slow roll.
• This condition may affect machinery due to unnecessary friction from pistons rubbing against liners during rolling.
• A large metacentric height (GM) results in a stiff ship that resists rolling, causing short rolling periods that can be uncomfortable and dangerous for personnel and cargo.
• In unstable equilibrium, the initial metacentric height GM is negative, or the transverse metacentre is below G.
• The lever (GZ) helps the heeling force, forcing the ship to an even larger heel angle, meaning the ship is unable to return to its original upright position.
• The lever GZ becomes a capsizing lever, contributing to a capsizing moment.
• When the transverse metacentre (M) and center of gravity (G) align, no lever is introduced, and no righting moment occurs, so the ship remains at the angle it adopts.
• This condition of neutral equilibrium means the ship is unstable if the center of gravity (G) rises, and more stable if it lowers.
• This is hazardous when fuel, water or other stores are used, or moving weights when initial GM is small, reducing the value to zero.
• A ship may become unstable when underway, even if initial equilibrium was stable, and may take up a list angle called the Angle of Loll, oscillating around this angle.
• Actions taken with a ship in this state starts with identifying whether the angle is due to list or loll.
• An angle of LIST occurs due to shifting weights across the centerline, whereas an angle of LOLL occurs when G moves vertically to coincide with M.
• The procedure to correct the loll angle prevents the ship from becoming unstable.
• To correct loll angle:
  • Ballast or fuel may be transferred from the lowest point of the ship to the port centre.
  • Fuel can be transferred from starboard wing tanks to the port centre if of the same grade.
  • The GM may be gradually increased through ballasting once the loll angle is corrected.

Free Surface and Slack Tanks

• Free surface is the unrestricted movement of liquid on a ship's deck or in a partially filled tank.
• This increases ships rolling action due to liquid moving freely with the tanks.
• It introduces sloshing, increasing forces on structural members and moments above the center of gravity, causing violent rolling.
• Decks should allow water to flow away freely, and tanks are typically fitted with baffle plates to reduce this effect.