SHIP STABILITY

Center of Flotation

• It is the point at which the ship would pivot when the trim is changed.
• It is the geometric centre of the water-plane area of the ship (at that draft).
• It depends on the HS draft of the ship.

• The hydrostatic draft of a ship is the draft measured at the COF.
• When COF is amidship, the mean draft & HS draft are the same.

Center of gravity (COG) is a point through which the force of gravity is considered to act vertically downward with a force equal to the weight of the ship.

GG1 = wd/w

Center of buoyancy (COB) is a point through which the force of buoyancy is considered to act vertically upward with a force equal to the weight of water displaced by the ship.

KB of a box-shaped or ship-shaped = d/2

KB of a triangular-shaped vessel = 2/3d

It is the vertical distance between the center of gravity (G) and the metacenter (M)

GM is termed positive when KG is less than KM.

GM is termed negative when KG is greater than KM.

What is virtual loss of GM? How will you control it?

The virtual loss of GM is a loss in stability due to the free-surface effect.

• When a vessel with a partially filled tank rolls at sea, the liquid in the slack tank moves towards the lower side, causing the period of roll to increase.
• Vessel behaves as if her GM has been reduced, which is said to be an imaginary loss of GM.
• To control it, keep the tank either empty or completely full.

When a vessel is heeled, the force of gravity and buoyancy are separated by a horizontal distance called the righting lever (GZ)

For a small angle of heel (up to 15°) ⇒ GZ = GM Sinθ

For a large angle of heel, the wall-sided formula ⇒ GZ=Sinθ (GM + 1/2 BM Tan²θ)

A moment which tends to return the vessel to upright is known as the righting moment (RM)

Formula:  RM=W.GZ

Stable equilibrium: When a vessel is heeled, if she tends to come back to her original condition, she is said to be in stable equilibrium.

GM is positive; KG must be less than KM.

Unstable equilibrium: When a vessel is heeled, if she tends to continue heeling further, she is said to be in unstable equilibrium.

GM is negative; KG must be greater than KM.

Neutral equilibrium: When a vessel is heeled, if she has no tendency to return to her original condition or to continue heeling further, she is said to be in neutral equilibrium.

GM is zero; KG equals to KM.

• In an unstable equilibrium, GZ will be negative & the moment is known as the upsetting moment.
• As when in unstable equilibrium, the vessel will continue to heel due to the capsizing or an upsetting lever.
• But at a large angle of heel, as B moved from B1 to B2, the M moved upwards till coincides with G.
• KM increases sufficiently equal to KG.

At Angle of Loll, GM is negative (GM is not zero)

                               GZ is zero

• At this point, the GZ is zero & there is no tendency of the vessel to either heel more or become upright.
• Since the GM is negative and BM is positive, the vessel will never capsize but shall tend to remain in a state of oscillation, that is, to and fro.
• The angle of inclination at which the above condition occurs is known as Angle of Loll.

This is a very dangerous situation, as it occurs suddenly & violently, causing the following:
(i) Human injury or loss of lives.
(ii) Shift of cargo as the lashing may part.
(iii) Shift of stores and spares.
(iv) Deck cargo might go overboard.
(v) Oil pollution may occur.
(vi) Grounding (in case of shallow water)

Corrective action
→ lower the ‘G’

This can be done as follows (lower the G):

(i) Reduce FSC by emptying or pressing up the slack tank.
(ii) Take ballast in the DB tank on the heeled side.
(iii) Never take ballast on the other side because the listing moment created makes the vessel flop over to the other side & may even capsize.
(iv) Transfer liquid from the upper to the lower position.
(v) Deballast the topside tank from the opposite side of the heel.
(vi) If a shore crane is available, G can be lowered by loading cargo at a lower position, discharging cargo from the upper position, or shifting cargo from the upper to the lower position.

When a vessel with a slack tank rolls at sea, it causes an imaginary loss of GM. It is called Free Surface Effect (FSE)

 The loss of GM can be calculated, i.e., the free surface correction.

FSC = i.di/W

where i = moment of inertia

          di = density of liquid

          W = displacement

Moment of inertia can be calculated by lb³/12

Shearing forces: When two external forces act in opposite directions on any part of a structure to shear it, the forces are known as shearing forces. It is measured in tons.

Bending moment: It is the amount of bending caused to the ship’s hull by external forces and is known as the bending moment. The bending moment can be hogging as well as sagging. It is measured in ton-meters.

Load displacement is the maximum displacement of a ship when loaded or floating at her summer draft in SW.

Deadweight of a ship is the total mass of cargo, fuel, FW, etc., that a ship can carry when floating at her summer draft in SW.

Waterplane coefficient is the ratio of the area of the waterplane to the area of a rectangle having the same length & maximum breadth.

Block coefficient is the ratio of underwater volume to the volume of rectangle having same extreme dimensions.

Cb = Underwater volume/LXBXD

Reserve buoyancy is the volume of enclosed space above the waterline.

 RB = Total volume – underwater volume

Intact buoyancy is the undamaged compartment within the damaged length of the ship.

Example: If No. 3 DB is damaged & No. 3 Hold is still intact, then No. 3 Hold buoyancy is referred to as intact buoyancy.

It is the number of tons that causes the ship to rise or sink by 1 cm.

TPC = A/100 x density; unit = t/cm

It is the number of inches by which the mean draft of the ship changes when she passes from SW to FW.

FWA = W/40 TPC

• The ship sinks more.
• Seawater has more density & has higher buoyancy; Freshwater has less density & has less buoyancy.

• So, the ship enters from SW to FW and sinks more.
• The following will change: Draft, u/w volume, COF

• General particulars
• General arrangement and capacity plan showing capacity, COG, etc.
• Hydrostatic particulars
• Hydrostatic curves
• Free surface correction table
• Cross curve of stability particular
• Plimsoll mark detail
• Trim Tables
• Arrival/departure conditions

It is intended to provide information on the ship’s watertight subdivisions and equipment related to maintaining the boundaries and effectiveness of the subdivision so that, in the event of damage, proper precaution can be taken to prevent progressive flooding.

It is divided into three parts

• Damage control booklet
• Damage stability calculation
• Damage control plan

It is the term mainly used in maritime law. It specifies whether the ship has passed the required tests and safety checks to be able to sail without any mishaps.

• A vessel is seaworthy when all its parts & equipment are fit for their intended purpose.
• It is operated by an adequate and competent crew.
• The aspect of seaworthiness is not limited to the physical fitness of the vessel; it also includes the vessel’s equipment, competency of crew, and documentation.

The plan needs to show the

• Layout of all compartments, such as cargo tank, ballast tank, fuel tank, etc.
• Means of closure, such as valves, watertight bulkheads, hatches, or cargo tank domes, and their positions.
• Arrangement for the correction of the list during flooding.

It is a graph wherein the righting levers (GZ) are plotted against the angle of heel for the displacement & KG for that voyage.

It is drawn by the chief officer for every voyage.

We get the following information from it:

• GZ value for any angle of heel.

                    → which is used to calculate the righting moment by formula: RM = W × GZ

• The maximum value of GZ.
• The angle of heel at which maximum GZ occurs.
• The angle of heel at which GZ becomes zero again.
• The approximate angle at which the deck edge submerges.

• The information required to construct a GZ curve is found by the KN curve.
• It is a graph wherein the righting levers (KN) are plotted against displacement.
• Separate curves are drawn for different values of θ: 10°, 20°, 30°, 45°, 60°, and 75°.
• The graph is constructed for an assumed value of KG (i.e., 0).

Since GZ is a function of KN, KG, and θ.

Then, we calculate GZ as GZ = KN − (KG × sin θ)

Angle of heel at which the righting lever returns to zero.

Angle of heel upto which the rate of increase of GZ with heel is increasing.