(a) Free Surface Effect:

The free surface effect (FSE) is a reduction in the metacentric height (GM) of a vessel due to the movement of liquids within partially filled tanks when the ship heels. When a ship tilts, the liquid in a partially filled tank shifts to the lower side, causing the centre of gravity (CG) of the ship to move laterally. This lateral shift of the CG reduces the righting lever (GZ), effectively decreasing the ship's stability and increasing the angle of heel. This apparent loss of GM is the free surface effect.

Minimizing Free Surface Effect:

• Partially filled tanks should be avoided to minimize liquid movement.
• Tanks should be designed with longitudinal divisions or swash bulkheads to limit the movement of liquid.
• Install sluice valves to control the liquid movement between compartments in divided tanks.
• Fill smaller tanks at the bottom of the ship first to lower the centre of gravity and improve stability.
• Tanks should have reduced breadth to minimize the free surface's effect.

When a ship moves through water, resistance opposes its motion. The ship must exert an equal force to maintain speed.

Frictional resistance (Rf): This is caused by the friction between the hull and the water. The water immediately adjacent to the hull is dragged along, creating a boundary layer. This resistance depends on the water's viscosity, the ship's speed, and the wetted surface area of the hull. At lower speeds, frictional resistance can account for 70-90% of total resistance; however, at higher speeds, it can be less than 40%.

Residuary resistance (Rr): This is the resistance that remains after subtracting the frictional resistance. These are:

• Form drag: Resistance due to the shape of the hull and the flow of water around it, generating pressure differences.
• Wave-making resistance: This is a major component at higher speeds. The ship creates waves, and energy is expended in this process.
• Eddy resistance: Resistance caused by turbulent flow behind the ship, especially at sharp changes in the hull's shape. This is often minimized by optimizing the hull design.

Air resistance (Ra): This resistance is generated by the ship moving through the air. It depends on the shape of the superstructure, the projected area above the waterline, and wind speed and direction. Air resistance is typically a smaller component, usually around 2% but can be up to 10% for large container ships with extensive superstructure.

Total resistance (Rt): The total resistance experienced by the ship is the sum of frictional, residuary, and air resistance: Rt = Rf + Rr + Ra.