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The righting lever is a measure of a ship's stability in water. It is the distance between the ship's center of gravity (G) and its metacentre (M), which is the point at which the ship would balance if it were tilted from upright. The larger the distance between G and M, the more stability the ship has, and the greater its ability to resist capsizing.

The righting lever is important for ships because it affects the ship's ability to maintain its upright position in various conditions, such as heavy seas or high winds. A ship with a large righting lever is able to resist being overturned, while a ship with a small righting lever is more susceptible to capsizing.

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righting lever GZ is equal to GMsintheta as GZ is perpendicular to Centre of buoyancy.

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righting lever GZ is equal to GMsintheta as GZ is perpendicular to Centre of buoyancy.

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Righting lever (GZ) is defined as the horizontal distance, measured in metres, between the centre of gravity (G) and the vertical line of action of the buoyancy force (Bf) acting through the centre of buoyancy (B1) when the ship is heeled

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Archimedes’ principle states that a body immersed in a fluid is subjected to an upwards force equal to the weight of the displaced fluid. This is a first condition of equilibrium.

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The hull is a ship’s watertight enclosure, engineered to provide sufficient protection for the cargo, machinery, and passenger accommodations. Its most basic purpose is to safeguard against weather, flooding, and/or structural damage.

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The basic idea of Archimedes' principle is that the buoyant force acting on an object submerged in a fluid is equal to the weight of the fluid that the object displaces.

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Archimedes Principle states that when a body is floating freely
in a fluid, the weight of the
body equals the buoyancy
force, which is equal to the
weight of the fluid displaced.

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A body, wholly or partially immersed in a fluid, will experience an upward force

Specifically buoyancy force  equal and opposite to the weight of the fluid displaced by it.

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The free surface effect is a phenomenon that occurs in ships and other vessels when liquid in an unsealed or partially-sealed tank sloshes back and forth due to the movement of the ship. This sloshing of liquid can cause the ship to become unstable and increase the risk of capsizing.

The free surface effect is a result of the liquid in the tank having a tendency to move in response to the ship's motions, creating an unpredictable shifting weight within the ship. This can cause the ship to become unbalanced and increase the risk of capsizing.

One way to reduce the free surface effect is through the subdivision of tanks. This involves dividing a large tank into smaller, separate tanks, which restricts the movement of the liquid and reduces the sloshing effect. By reducing the size of the liquid surface area, the free surface effect is reduced, and the stability of the ship is improved.

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Bow
Stern
Waterline
Freeboard
Deck
Superstructure
Bilge
Keel

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When a compartment is not completely filled with liquid it is said to have a free surface that tends to remain horizontal. As the ship inclines,the liquid flows to the lower side (in the direction of inclination)thereby increasing the inclining moment.
Consider a compartment/tank containing a solid weight. when the ship is inclined, the center of gravity remains the same. Only the center of buoyancy shifts towards the direction of the inclination and righting arms (GZ) are formed.

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Righting lever GZ is the perpendicular distance between the weight (W ship) and  for buoyancy
Righting moment, RM: Moment caused by weight and buoyant force

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Normally. 4 equal groups of weights are used - 2 to each side of the ship and preferably at the amidships or near the centre of flotation. The groups of weights are shifted to the opposite sides, one group at a time.  Angles of heel are measured after each mass shift by using suspended plumblines. There should be at least 3 plumblines - normally positioned at the forward-end, the amidships and the aft-end. Plumblines should be as long as practicable to minimise experimental error. The forward, amidships and aft draughts are read, and the SG of the water in which the ship floats is gauged to determine its displacement with the aid of the ship's hydrostatic data

The ship must be able to heel freely - ie, there should be as few attached mooring ropes as possible, and they must be slack. There should be as little deadweight as possible, as weights and their CGs are difficult to ascertain. No liquid free surfaces if possible as FSE may be difficult to determine accurately. All movable objects must be secured. Only required personnel are to be allowed to stay on board. Underwater current and wind should be minimal, and the sea calm. The ship should initially be upright.

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One example of a primary hull feature is camber.

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Calculate the center of gravity: The CG is a critical factor in determining a ship's stability, and the inclining experiment is used to calculate its position.

Assess the stability of the ship: By calculating the ship's displacement and CG, the inclining experiment helps to assess the stability of the ship in different conditions and to ensure that it meets the required safety standards.

Confirm compliance with regulatory requirements: Inclining experiments are often required by international maritime regulations, and the results are used to confirm that a ship complies with the stability requirements set by these regulations.

Provide data for stress analysis: The results of an inclining experiment provide important data for stress analysis, which is used to design and evaluate the structural components of a ship.

SCENARIOS:
New ship construction: An inclining experiment is usually performed on a new ship before it is put into service to verify its stability and ensure that it meets regulatory requirements.

After a major incident: If a ship is involved in a major incident, such as a grounding or collision, an inclining experiment may be performed as part of the investigation to assess the impact on its stability and make any necessary repairs.

Change in regulations: If international maritime regulations change, an inclining experiment may be required to confirm that a ship complies with the updated requirements.

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Find Actual G location from Incline test
Find Lightship weight(Lightship survey)

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The distance between the

forces of buoyancy and gravity.The righting lever curve represents a ship's ability to withstand external heeling moments.Force of buoyancy

and gravity are equal and act along parallel

lines, but in opposite directions, hence a

rotation is developed

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Free surface effect is when ship rolling and pitching in the sea causes liquid to flow according to the
motion. The liquid behaves like moving masses, affecting the CG of ship, & stability.
With more subdivision tanks, it can help minimise the FSE.

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The inclining experiment, involves causing the ship to heel to small angles by moving known weights known distances transversely across the deck and observing the angles of inclination.

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When a body is freely floating on a liquid , it displaces an amount of fluid and the mass of the Fluid displaced is thus equals to the mass of the body acting on the fluid 

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When a body is freely floating on a liquid , it displaces an amount of fluid and the mass of the Fluid displaced is thus equals to the mass of the body acting on the fluid 

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.... Reduce bow wave and resulting drag on ship hull