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
Characteristics of a Tender Vessel
Easier to incline initially
Small GM, Large KG
Smaller righting lever
More comfortable than a stiff vessel for crew and passengers
Danger of synchronous rolling
Chance of dangerous Gv through fuel consumption
Free surface effect
The phenomenon caused by the free movement of liquids on board ship, be it in tanks or on deck
Free Surface Correction
The vertical rise in the ships centre of gravity when making stability calculations for fluids on board.
Difference between GM and GvM is the Free surface Correction
How to Use a Hydrometer
Measures the Relative density of a fluid (In this case, Dock water)
Use a clean bucket of water
Fill with dock water
Allow water to stand
Ensure Hydrometer is clean and dry
Place in water and spin gently to remove air bubbles
Allow water to settle
Read Density at bottom of the Meniscus
Dry and pack away Hydrometer
Formula for Fresh Water Allowance (FWA)
1/48 of Summer Draught
or
Displacement / 4 x TPC (SW)
Formula for Dock water allowance
DWA = FWA x (1025 - Dock water density) / 25
Details found on the Hydrostatic particulars card of a vessel
- Draught, in salt water (RD 1.025).
- Displacement.
- TPC – Tonnes per Centimetre Immersion.
- KMT – Transverse Metacentric Height.
- KML – Longitudinal Metacentric Height.
- VCB – Vertical Centre of Buoyancy.
- LCB – Longitudinal Centre of Buoyancy.
- LCF – Longitudinal Centre of Floatation.
- MCTC – Moment to Change Trim by 1cm.
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
Returning from Angle of Loll
Caused by use of stores, fuel etc. Or by poor and improper loading
Must be done with extreme caution
Add weight to the low side to bring G down towards K, to turn the angle of Loll into an angle of List, and become stable.
Once the vessel has returned to a stable equilibrium, weight can now be added low down on the high side to correct the list
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
Formula for Water plane Area
Length x Breadth (waterline)
Sinkage/Rise formula for TPC
Change of Draft = Weight / TPC
Weight is either added OR discharged
Weight = CoD x TPC
How to find GM using a hydrostatic table
GM = KMT - KG
Effects of fuel consumption on passage
KG will increase
GM will decrease
Decrease in draft
Could create a list if burned unevenly
FSE could potentially arise
Define Free Surface effect
Phenomenon caused by the free movement of liquids and substances on board ship
Has an adverse effect on a vessels stability
Define Free Surface Moment
Energy created by the free movement of liquid in a tank/hold
Calculated by the mass of liquid x Length of tank
Free Surface Correction
A correction made to a ships solid GM for stability calculations
A reduction in a ships solid GM through the free surface movement (Virtual G)
G-Gv is the FSC
GM corrected formula
GM solid - FSC
TPC Formula
(Aw x p) / 100
p is shorthand for Density
Sinkage/Rise formula
W / TPC
Formula for Finding the weight needed to get a desired Sinkage and rise
W = CoD x TPC
Displacement Formula
(Length x Breadth x draft) x Density of water
Finding a different measurement other than displacement using displacement formula
Change formula and symbology
I.e.
Length = Displacement / (breadth x draft x density of water)
etc etc
Righting Moment Formula
Displacement x GZ
GZ formula
GZ x Sin theta
GM corrected Formula
GM solid - FSC
RD formula
Density (p) substance / density (p) Fresh water
Minimum legal allowance for GM for a yacht on arrival in port
0.15m
