Ship stability is a field of naval architecture that deals with how a ship behaves at sea, both in still water and waves. Stability calculations include concepts of center of gravity, the principle of floatation and Archimedes principle, concepts of buoyancy, metacenters of vessels, etc. It is a vast field of understanding and also very important in ship construction. The concept of hydrostatics and stability can be considered the most important factors to be paid attention to, ensuring the safety of the vessel and the people and cargo in it.

Let’s first understand the concept of hydrostatics.

The term hydrostatics in the maritime jargon is used very often. It refers to the floating of the ship and builds an understanding of this concept. Hydrostatics helps in many ways like :

• Can find the floating draft and other similar parameters of the ship by understanding the concepts of hydrostatics
• A pilot evaluation of the stability of the ship can be made with this understanding.

When a vessel is loaded with cargo, its draft and trim changes with respect to the weight of the load and storage location. The load can be anything from grains to ballast to people. For an architect to be able to build a hull form and for a master to understand the parameters of stability it is important for them to be familiar with the hydrostatic terms and significance of each. Here is the list of some important hydrostatic terms :

1. Centre of gravity
2. Centre of buoyancy
3. Mass displacement
4. Volume displacement
5. Longitudinal and transverse center of floatation
6. Metacenter
8. Metacentric height
9. Tones per cm Immersion (TPC)

Before proceeding any further, let me introduce you to certain ship terminologies that you might need to understand further concepts.

• Forward Perpendicular : The perpendicular drawn at the point where the bow of the ship meets the waterline while it floats at design draft.
• Aft Perpendicular : The perpendicular drawn to the load line through the after side of the rudder post.
• Length of Waterline : The length of the ship’s hull where it intersects the surface of water.
• Length Overall : The maximum length from the forward most point of the ship’s hull to the after most point.
• Keel : It is the lowermost part of the vessel at any point of the length. The baseline of the ship is the longitudinal line that runs along the keel.

SHIP STATIONS: A ship’s hull is longitudinally divided into various stations which are basically specified positions along the length of the ship. They are numbered zero from the aft perpendicular. The distance between each station is constant around midship where a parallel mid-body shape prevails, but as we move forward or after the hull shape attains some complex geometry because of which at these ends the distance between the stations is to be reduced.

Let’s now understand the important hydrostatic terms :

• CENTRE OF GRAVITY : The center of gravity of a body is the point where all the mass of the body is assumed to be concentrated and the point through which the force of gravity acts vertically downwards, with a force equal to the weight of the body. The longitudinal position of the center of gravity with respect to any reference point on the ship is called the longitudinal center of gravity.
• CENTRE OF BUOYANCY : It is the geometric center of the underwater volume. The longitudinal position of the center of buoyancy with respect to any reference point on the ship is called the longitudinal center of buoyancy.
• METACENTER : It is a point at which an imaginary vertical line passing through the center of buoyancy and center of gravity intersects the imaginary vertical line through a new center of buoyancy created when the body is displaced.
• CENTER OF FLOATATION : When a vessel floats at a particular draft, any trimming moment would act about a particular point on the water plane. The point is basically the centroid of the water plane and is called the center of floatation.
• METACENTRIC RADIUS : It is the vertical between the center of buoyancy of the ship and its metacenter. We can understand this simply by saying that a ship is like a pendulum swinging about its metacenter.
• METACENTRIC HEIGHT : This is the vertical distance from the center of gravity to the metacenter. This is a widely concerned term in the field of ship building. The value of the metacentric height is evaluated at various stages starting from the initial design stage to the hull design stage, after the construction and during operation.
• TONES PER CENTIMETER IMMERSION : The tones per centimeter immersion for any draft is the mass that must be loaded or discharged to change a ship’s mean draft to 1 cm. it varies with the water density and draught.

TPC = (A/100) x density of water displaced

• Fresh Water Allowance is the increase in draft when a vessel goes from salt water to fresh water.

FWA (cm)= (W/40) TPC

• Dock Water Allowance is the increase in the draft of a ship when it goes from salt water to dock water, and vice versa. The relative density of DW is between 1 to 1.025.

DWA= FWA x (change of RD/ 0.025)

### THE CONCEPT OF INTACT STABILITY

In 1993, IMO developed the intact stability criteria for various types of ships. The code includes various fundamentals of general precautions against, capsizing, weather conditions, the effect of free surface and icing and watertight integrity. The code also addresses other operational aspects like information for the master, including stability and operating booklets and operational procedures in unfortunate weather conditions. The intact stability is determined when the intactness of the hull or no watertight compartment is damaged. The postulate behind intact stability is the equilibrium of ships.

1. STABLE EQUILIBRIUM: A vessel is said to be in stable equilibrium when if she’s inclined, it returns to the initial position. For this, the vessel’s center of gravity must be below its metacenter i.e., the initial metacentric height must be positive.

At a small angle of the heel (less than 15°): GZ= GM sin θ

The lever GZ is referred to as the righting lever and is the perpendicular distance between the center of gravity and vertical through the center of buoyancy.

2. NEUTRAL EQUILIBRIUM: It’s the most dangerous situation possible and hence necessary precautions must be taken to avoid it. It’s the condition when the vertical position of the centre of gravity coincides with the transverse metacenter.

As in the figures, there is no room for righting lever at any angle of the heel. Hence any heeling moment would not generate a righting moment and the vessel shall remain in the heeled position. The risk is that at a larger heel, an unwanted shift due to cargo shifting may give rise to unstable equilibrium.

3. UNSTABLE EQUILIBRIUM: when a vessel, inclined at a small angle tends to further heel over, the situation is called unstable equilibrium. When the vertical position of G is higher than that of the transverse metacenter. If the condition of stable equilibrium is not reached till the time the deck is immersed, the vessel may capsize.

Ships vary greatly in various terms like shape, size, operational profile and the environmental conditions, which makes it difficult to have a generic stability criterion for the assessment of all kinds of ships. There are certain ships that have greater risks of encountering unstable conditions in waves than others. The IMO is currently in the process of promulgating a performance-based criteria for assessing five dynamic stability failure modes in waves, namely dead ship, excessive acceleration, parametric rolling and broaching.

### DAMAGE STABILITY

• CHANGE OF DRAFT: When a ship compartment is damaged, water is likely to enter in if flooded. This will hence create a difference in draft, where displacement of intact part will be equal to displacement of the ship before damage less the weight of ship after water seeped in.

Damaged displ. = Intact displ. – Weight of water in damaged part.

• CHANGE OF TRIM: Ingress of water in a compartment can be an addition to the weight of the ship at any point. This in turn causes a change in the trim.
• HEELING: If the damaged compartment of the ship is unsymmetrically positioned, it will cause the ship to heel. If the metacentric height of the ship is negative, the ship may even capsize.
• CHANGE IN FREEBOARD: The increase in draft of the ship due to flood shall result in the increase of draft and thereby reducing the freeboard which is a threat to the residual buoyancy of the ship. Even if the metacentric height is positive, reduction of freeboard may reduce the ship’s range of stability and hence the vessel could capsize due to external factors.

EVALUATION OF DAMAGED STABILITY EQUILIBRIUM CONDITIONS:

1. LOST BUOYANCY METHOD: In this method it is assumed that the damaged part does not contribute in the total buoyancy of the vessel, hence it loses a part of it’s total waterplane, therefore reduced stability (buoyancy is also reduced). Although the results obtained from this method are not very reliable, but this is an easy method.

2. ADDED WEIGHT METHOD: This method is a more accurate method as it involves some iterations of trim and draft. In this the flooded weight is considered as a weight added but to a certain point only. It is adopted by various stability calculating software.

With this I end my article on stability. Do not restrain yourself to only this as stability topic itself is a vast domain, the more you explore the wider it gets and more interesting it becomes. Keep reading, keep exploring.

By Resham Pandey

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