DRAFT

The draft of a ship's hull is the vertical distance between the waterline and the bottom of the hull (keel). Draft determines the minimum depth of water a ship can safely navigate. The draft can also be used to determine the weight of the cargo on board by calculating the total displacement of water and then using Archimedes' principle. A table made by the shipyard shows the water displacement for each draft. The closely related term "trim" is defined as the difference between the forward and aft drafts.

• The draft aft (stern) is measured at the perpendicular of the stern.

• The draft forward (bow) is measured at the perpendicular of the bow.

• The mean draft is obtained by averaging the stern and bow drafts.

  

  

Displacement calculation

Displacement of a vessel can be obtained directly from Archimedes’ principle by multiplying its underwater volume by the density of water. Ship’s displacement may be expressed either in terms of weight (tonnes) or measured capacity (cubic meters). It should also be noted that salt and fresh water have different densities.

The formula to find ship displacement in either sea water or fresh water: Displacement = density of fluid × volume of displaced fluid

Example 1. A solid block of cast iron has a mass of 500 kg. When it is completely immersed in fresh water the mass appears to be reduced to 430 kg. Calculate the relative density of cast iron.

Solution:

• Step 1: Find the apparent loss of mass. Apparent loss of mass = (Mass in air) - (Apparent mass in water) = 500 kg - 430 kg = 70 kg (This 70 kg represents the mass of the displaced fresh water)

• Step 2: Calculate the relative density. Relative density = (Mass of object) / (Mass of equal volume of fresh water) = 500 kg / 70 kg = 7.143

Example 2. A piece of brass (rd 8.4) 0.06 m³ in volume is suspended in oil of rd 0.8. Calculate the apparent mass of the brass.

Solution:

• Step 1: Calculate the mass of the brass. Mass of brass = 1000 kg/m³ × 8.4 × 0.06 m³ = 504 kg

• Step 2: Calculate the mass of the displaced oil. Mass of equal volume of oil = 1000 kg/m³ × 0.8 × 0.06 m³ = 48 kg

• Step 3: Calculate the apparent mass in oil. Apparent mass in oil = (Mass of brass) - (Mass of displaced oil) = 504 kg - 48 kg = 456 kg

Example 3. A block of wood 4 m long, 0.3 m wide and 0.25 m thick floats at a draught of 0.15 m in sea water. Calculate the mass of the wood and its relative density.

Solution:

• Step 1: Calculate the mass of the wood (which equals the mass of displaced sea water). Mass of wood = (Density of sea water) × (Volume of displaced water) = 1025 kg/m³ × (4 m × 0.3 m × 0.15 m) = 1025 kg/m³ × 0.18 m³ = 184.5 kg

• Step 2: Calculate the total volume of the wood block. Total volume = 4 m × 0.3 m × 0.25 m = 0.3 m³

• Step 3: Calculate the mass of an equal volume of fresh water. Mass of equal volume of fresh water = (Density of fresh water) × (Total volume of wood) = 1000 kg/m³ × 0.3 m³ = 300 kg

• Step 4: Calculate the relative density of the wood. Relative density = (Mass of wood) / (Mass of equal volume of fresh water) = 184.5 kg / 300 kg = 0.615

Example 4. A box barge 40 m long and 9 m wide floats in sea water at a draught of 3.5 m. Calculate the mass of the barge. (Density of sea water = 1025 kg/m³)

Solution:

• Step 1: Calculate the underwater volume of the barge. Volume = Length × Width × Draught = 40 m × 9 m × 3.5 m = 1260 m³

• Step 2: Calculate the mass of the barge (which equals the mass of displaced sea water). Mass of barge = (Density of sea water) × (Underwater volume) = 1025 kg/m³ × 1260 m³ = 1,291,500 kg

• Step 3: Convert the mass to tonnes. Mass in tonnes = 1,291,500 kg / 1000 kg/tonne = 1291.5 tonnes

Example 5. A ship displaces 12240 m³ of sea water at a particular draught. (a) Calculate the displacement of the ship. (b) How many tonnes of cargo would have to be discharged for the vessel to float at the same draught in fresh water?

Solution: (a) Calculate the displacement (mass) in sea water. Displacement = (Volume of displaced water) × (Density of sea water) = 12240 m³ × 1.025 t/m³ = 12546 tonnes

(b) Calculate the displacement (mass) in fresh water for the same volume. Displacement = (Volume of displaced water) × (Density of fresh water) = 12240 m³ × 1.000 t/m³ = 12240 tonnes

• Calculate the cargo to be discharged. Cargo to discharge = (Displacement in sea water) - (Displacement in fresh water) = 12546 tonnes - 12240 tonnes = 306 tonnes

Tutorials

1. A piece of metal 250 cm³ in volume is attached to the bottom of a block of wood 3.5 dm³ in volume and having a relative density of 0.6. The system floats in fresh water with 100 cm³ projecting above the water. Calculate the relative density of the metal.

2. A raft 3 m long and 2 m wide is constructed of timber 0.25 m thick having a relative density of 0.7. It floats in water of density 1018 kg/m³. Calculate the minimum mass which must be placed on top of the raft to sink it.

3. A box barge 65 m long and 12 m wide floats at a draught of 5.5 m in sea water. Calculate: (a) The displacement of the barge, (b) Its draught in fresh water.

4. A cylinder 15 m long and 4 m outside diameter floats in sea water with its axis in the waterline. Calculate the mass of the cylinder.

5. A vessel 40 m long has a constant cross-section in the form of a trapezoid 10 m wide at the top, 6 m wide at the bottom and 5 m deep. It floats in sea water at a draught of 4 m. Calculate its displacement.