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Q1.  The load waterplane of a ship 144 m long, floating in sea water of density 1025 kg/m³, is defined by the half ordinates given in table Q1.

The following particulars are obtained from the ship’s hydrostatic curves:

Displacement= 13640 tonne

Centre of buoyancy above the keel (KB) = 3.84 m

Moment to change trim by one centimeter (MCT 1 cm) = 176.5 m

Calculate EACH of the following:

(a) The position of the longitudinal centre of floatation (LCF) from midships; (6)

(b) The second moment of area of the waterplane about a transverse axis through the centroid; (6)

(c) The height of the ship’s centre of gravity above the keel (KG) (4)

Q2. A ship has a lightship displacement of 9500 tonne and the height of the centre of gravity above the keel (KG) is 8.54 m.  Loading now takes place as detailed in Table Q2.

Table Q2

In this loaded condition, the height of the transverse metacentre above the keel (KM) is 10.38m.

(a) Draw a curve of statical stability for the loaded vessel, using the cross curves of stability provided in Worksheet Q2.  (12)

(b) Using the curve derived in Q 2 (a), determine the dynamical stability of the vessel up to an angle of  40^o.  (4)

Q3. A ship of length 110 m has draught marks 4.5 m aft of the forward perpendicular and 5.5 m forward of the after perpendicular. The draughts at the marks are 4.35 m aft and 3.85 m forward. For this condition, the following hydrostatic data are available:

LCF = 2.25 m aft of midships

Displacement= 6300 tonne

GML = 80 m

LCB = 0.6 m aft of midships

Calculate EACH of the following:

(a) The true mean draught;  (4)

(b) The draught at the perpendiculars;(4)

(c) The draught at the perpendiculars;(4)

Q4) A box shaped vessel of the length 100 m and breadth 12 m has a full breadth midship compartment 16 m long divided by a centreline watertight bulkhead to form equal tanks port and startboard.

The vessel loaded to a draught of 6 m in sea water of density 1025 kg/m³  and in this condition the KG is 3.611 m and the midship compartment has a permeability of 80%.

The vessel is now bilged below the waterline on one side only at midships.

Calculate the resulting angle of heel.  (16)

Q5) (a) Explain the procedure required to produce weight, buoyancy and load curves for a ship assumed to be floating in still water, stating any relevant features of the curves. (8)

(b) Describe how shear force and bending moment curves are produced from a load diagram, explaining how the features of EACH curve are connected. (8)

Q6. A single screw vessel with a service speed of 15 knots is fitted with an unbalanced rectangular rudder 6 m deep and 4 m wide with an axis of rotation 0.2 m forward of the leading edge. At the maximum designed rudder angle of 35^o the centre of effort is 30% of the rudder width from the leading edge.

The force on the rudder normal to the plane of the rudder is given by the expression:

F_n = 20.2 A v²  α newtons

where:A = rudder area (m²)

v = ship speed (  m⁄s)

α = rudder helm angle ( degrees)

The maximum stress on the rudder stock is to be limited to 70 MN/m²

Calculate EACH of the following:

(a) The minimum diameter of rudder stock required;(9)

(b) The percentage reduction in rudder stock diameter that would be achieved if the rudder was designed as a balanced rudder, with the axis of rotation 1.0 m aft of the leading edge. (7)

Q7.  A ship model of length 5 m has a wetted surface area of 4.6 m².  When tested in fresh water of density 1000 kg/m³, at a speed of 1.75 m/s, the total resistance was measured at 35 N. This tank speed corresponds with a trial ship seed of 17 knots in sea water of density 1025 kg/m³, which is achieved when the shaft power is 6000 kW, when the propulsive coefficient is 0.68.

Calculate the Ship Correlation Factor (SCF) for the ship in this trial condition. (16)

Note: The frictional coefficient for the model is fresh water is 1.694

The frictional coefficient for the ship in sea water is 1.419

Speed in m/s with the speed index (n) for ship and model 1.825

Q8.  (a) With respect to a ships propeller, explain the term thrust deduction.  (3)

(b) The following data were obtained during a ships acceptance trials:

Ship speed = 15.4 knots

Delivery power = 2500 kW

Effective power = 1730 kW

Thrust = 274 kN

Propeller efficiency = 64%

Apparent slip = 5%

Calculate EACH of the following:

(i) The thrust deduction factor; (3)

(ii) The Taylor wake fraction; (5)

(iii) The true slip; (3)

(iv) The hull efficiency. (2)