Q4 (10 Marks) Ship Stability
SC&S • Written Exam

When a ship moves into water of different density, there will a change in its draught and trim. List out the minimum information required to calculate the final draughts. Also briefly outline the procedure involved. (16)

Appeared In: Jul 2018

Verified Model Answer (Text Solution)

Structured for DG Shipping MEO Class II examination scoring criteria.

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If the specific gravity of the water in which the ship is floating changes without any changes to the ship's displacement, the ship's draft will change. The draft will change because the ship must displace the same mass of water, which no longer has the same density.

$$\Delta=V\times\rho$$

If the displacement ( Δ ) remains constant and the density ( ρ ) changes, the underwater volume must change; therefore, the ship's draft will change automatically.

If a ship goes from fresh water to salt water, buoyancy will increase and the draft will decrease. Inversely, a ship that goes from salt water to fresh water will see its draft increase.

A ship that loads to its marks (summer load lines S ) in salt water, will see its draft increase as it goes into fresh water and will exceed its marks. This situation is accepted because the absence of heavy weather on bodies of fresh water compensates for the ship's increased draft. This situation has even been made official by adding an additional mark ( F ) to the load lines.

Minimum Information Required to Calculate Final Draughts:

  1. Displacement (Δ): The mass of water displaced by the ship in tons.
  2. Densities (ρ₁, ρ₂): Densities of the initial and final liquids (e.g., seawater = 1.025 t/m³, freshwater = 1.0 t/m³).
  3. TPC (Tonne Per Centimeter Immersion): The mass required to change the mean draught by 1 cm.
  4. MCTC (Moment to Change Trim by 1 cm): The moment required to cause a 1 cm change in trim.
  5. LCB and LCF (Longitudinal Center of Buoyancy and Floatation): To determine the trimming effect.
  6. Length of Vessel (L): Used in trim calculations.

Procedure to Calculate Final Draughts:

1. Determine Change in Mean Draught:

$$Change\:in\:draught\:=\:\frac{\Delta}{TPC}\:\times\:\frac{\rho_1-\rho_2}{\rho_2}\:\left(in\:cm\right)$$

2. Determine Change in Trim:

$$Change\:in\:trim\:=\:\frac{\Delta\:\times\:FB}{MCTC}\times\frac{\rho_1-\rho_2}{\rho_2}$$

where:

$$FB\:=\:LCB\:+\:LCF$$

3. Determine the change in forward/aft draught:

$$Change\:in\:Fwd/Aft\:=\:\frac{Change\:in\:trim}{Length\:of\:vessel}\:\times Distance\:from\:CF$$

4. Calculate the new forward and aft draughts

$$New\:draught\:Fwd/Aft\:=\:Even\:keel\:draught\:-\:change\:in\:mean\:draught\:+\:change\:in\:Fwd/aft$$

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