DieselShip's Online Content Library

Q1. A ship of length 180 m floats at its load draught with a displacement of 50000 tonne in sea water of density 1025 kg/m³ .

The longitudinal centre of buoyancy (LCB) is 1.80 m aft of midships.

In this condition, the forward of the ship displaces 23000 tonne and has a centre of displaced volume (lcb) 33.00 m forward of midships. This part of the ship is to be replaced with a new forward half of similar length, but having new immersed cross section areas, to the same load draught, as given in Table Q1.

For the new condition, calculate EACH of the following:

(a) The displacement of the ship; (6)

(b) The longitudinal position of the ship’s centre of buoyancy. (10)

Q2. The ‘ wall sided formula ‘ gives an expression for  righting lever ( GZ) as follows:

GZ=sinθ (GM+ 1/2  BM tan² θ)

(a) Using the wall sided formula, derive an expression for the angle of loll of a ship which is initially unstable in still water.(5)

(b) A box shaped vessel is 40 m long, 10 m wide and floats at a draught of 4 m in sea water of density 1025 kg/m³ with a KG of 3.883 m.

A beam wind acts on the exposed area of the vessel causing it to heel to an angle of 12^o.

The heeling moment caused by the wind is given by the expression:

Heeling moment = 850 v²  cos² θ Nm

where: v = wind speed in m/s

θ= angle of heel in degrees

Calculate the wind speed using the wall sided formula for GZ.  (11)

Q3. A ship 140m long floats at draughts of 6.8m aft and 4.4m forward when floating in river water of density 1012kg/m³

Using the hydrostatic curves provided in worksheet Q3, determine EACH of the following:

a) displacement (8)

b) the longitudinal position of the centre of gravity (8)

Q4. A vessel of constant rectangular section 80 m long and 12 m wide has a KG of 3.93 m and floats on an even keel draught of 5 m in water of density 1025 kg/m³ . The vessel is fitted with a transverse watertight bulkhead 10 m from the forward end.

The compartment forward of the transverse bulkhead, which has a permeability of 75 %, is now damaged and laid open to the sea.

Calculate the new end draughts of the vessel. (16)

Q5. With reference to the testing of a ship model in towing tank:

(a) define the term corresponding speed. (2)

(b) state Froude’s Law of Comparison. (2)

(c) explain how the effective power of a ship can be estimated from the model test. (12)

Q6. The force acting normal to the centreline plane of a rudder is given by the expression:

F_n=15.5 A v² α newtons

Where:      A=rudder area ( m²)

v=ship speed (m⁄s)

α=rudder helm angle ( degrees)

A ship travelling at a speed of 20 knots, has a rudder configuration as shown in Fig Q6.

The centre of effort for areas A1 and A2 are 32 % of width from their respective leading edges. The rudder angle is limited to 35 ^o from the ship’s centreline

Calculate EACH of the following:

(a) The diameter of the rudder stock required for a maximum allowable stress of 77 MN/m²  (12)

(b) The drag component of the rudder force when the rudder is put hard over at full speed. (4)

Q7. The speed of a ship is reduced by 20% when 600 nautical miles from port, thereby reducing the daily fuel consumption by 42 tonne. The ship arrives in port with 60 tonne of fuel on board. The fuel consumption in tonne per hour is given by the expression:

C = 0.14 + 0.001 v³

where v is the speed in knots.  Calculate EACH of the following:

(a) The reduced daily fuel consumption; (6)

(b) The amount of fuel on board when the speed was reduced; (4)

(c) The percentage decrease in fuel consumption for the reduced speed part of the voyage; (4)

(d) The percentage increase in time for this latter part of the voyage. (2)

Q8. A ship 156 m in length, 22 m breadth, displaces 19700 tonne when floating at a draught of 8 m in sea water of density 1025 kg/m³. The ship’s propeller has a diameter of 5.5 m, a pitch ratio of 0.9 and a blade area ratio of 0.45. With the propeller operating at 1.8 rev/s, the following results were recorded:

Apparent slip ratio = 0.05

Thrust power = 1250 kW

Propeller efficiency = 66 %

Calculate EACH of the following for the above condition:

(a) The ship’s speed; (3)

(b) The real slip ratio;(6)

(c) The thrust per unit area of blade surface; (4)

(d) The torque delivered to the propeller. (3)

Note: The Taylor wake function w, is given by w = 0.5 Cb – 0.05