Stability Flashcards
Buoyancy
An upward force Exerted by a fluid that opposes the weight of a partially or fully immersed object
Centre of Buoyancy
Point where the total buoyancy force is considered to move upwards. This is the centroid of the ships underwater volume
Gravity
A downwards force that attracts a body to the centre of the Earth
Centre of Gravity
Point where the total weight force of the ship is considered to act vertically downwards
Metacentric height
Vertical distance from the ships centre of gravity to the transverse metacentre
Transverse metacentre
Point of intersection between force line through B, and centre line at a small angle
KM
Vertical distance from the Keel to the Metacentre
KG
Vertical distance from the Keel to the Centre of Gravity
How is the Density of a substance defined
The density of a substance is defined as its mass per unit volume
Define Relative Density
A ratio of the density of a substance compared to that of Fresh water.
FW 1.000
SW 1.025
Dock water lies in between
Law of Flotation
Every floating body displaces its own mass of the fluid in which it floats
Archimedes Principle
When a body is wholly or partially submersed in a liquid, it experiences an upthrust (apparent loss of weight) equal to the mass of liquid that is displaced. This is called Buoyancy Force
Displacement
Mass of the vessel at any given moment floating at any draught between light displacement & Summer draught marks.
Displacement Formula
Δ = Underwater Volume x RD of the water.
Underwater volume is calculated by the formula:
V = (L x B x D) m3
Light displacement
Mass of the vessel when complete and ready for sea but with no passengers, stores,
fuel, or cargo on board. An Empty Ship.
Load displacement
Mass of the vessel fully loaded with cargo, etc. floating at her assigned freeboard.
Deadweight
Difference between lightship displacement and displacement at any given draught.
Tonnes per Centimetre Immersion
The mass required to load/discharge in order to change the mean draught by 1cm. It is
used to derive ‘change in draught’ over small increments.
TPC = (Waterplane Area/100) x Density
Reserve Buoyancy
Volume of enclosed watertight spaces between the Load Line and the freeboard deck.
The Reserve of Buoyancy must prevent the deck line submerging when the largest watertight compartment is bilged.
Righting Lever
Horizontal Distance (in metres) between the vertical line of buoyancy, acting through B, and the ships centre of gravity when the ship is heeled.
Z is the point on the vertical line of buoyancy force when it is perpendicular to the centre of gravity
Righting Moment
The result of the ships displacement (buoyancy force) acting against the end of the righting Lever (GZ)
Righting Moment (t-m) = Δ (t) x GZ (m)
Characteristics of a Stiff Vessel
Large GM, small KG
Hard to incline initially
Large righting lever
Undue stress on cargo
Racking stress
Uncomfortable
Define Stable Equilibrium
For a vessel to be in a state of stable equilibrium, the opposing forces of gravity and buoyancy must be equal and opposite each other
When these two forces act in opposition, and when not in line (due to an external heeling force such as swell) they create a righting moment
This righting moment is calculated by multiplying the distance between the points at which two forces act by the force of one of them
If the moment tends upwards, she is in stable equilibrium
Stable Equilibrium
G is below M. The vessel has a positive GM and therefore a positive righting moment. A stable
vessel will return to the initial position when the external heeling force is removed.
Neutral Equilibrium
G is at M. The vessel has zero GM and therefore no righting lever. This vessel when heeled by an
external force will not return to the upright when the heeling force is removed but will remain at the angle of heel achieved.
Unstable Equilibrium
G is above M
An unstable vessel when heeled by an external force may reach a point of neutral equilibrium by bringing G to M, to create an angle of Loll
Characteristics of a Stiff Vessel
- Difficult to incline initially.
- Reserve of Stability, large GM.
- Large righting lever, GZ, easy to keep relatively upright.
- Short roll period, violent/jerky uncomfortable nature, racking stresses.
Tender Vessel
- Easy to incline initially.
- Small reserve of Stability, GM.
- Small GZ, less able to return to upright once inclined.
- Long slow lazy roll period, comfortable, less movement of weights & less stress on the
ship’s structure.
Effects of loading a ship
Changing weight distribution on a vessel will change the draught, thereby changing the underwater volume of the ship.
This will move the centre of Buoyancy and also the centre of gravity.
Change in direction of G will be directly proportional to the position of the weight added or removed, and the distance from the keel
Consumption of fuel and water on passage
Centre of gravity will rise
GM will decrease as weight is removed
Decrease in draught as weight is removed
Can create a list if consumption is uneven
Potential large risk of FSE if tanks are widely spaced and un baffled, further reducing GM
