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Q6. A fine form vessel of length 120 m, having immersed transverse sections in the form of semi-circles, floats in sea water of density 1025 kg/m³.

The load waterplane is defined by half widths as shown in Table Q1.

Calculate EACH of the following:

(a) The load displacement;

(b) The height of the transverse metacenter above the center of buoyancy (BM);

(c) The block coefficient (C_b).

Q2. An inclining test carried out on a passenger vessel at a displacement of 10860 tonne in water of density 1012 kg/m³ resulted in an angle of heel of 0.85^o when an inclining mass of 10 tonne was moved 20 m transversely across the deck.

To obtain the lightship condition for the vessel, corrections for the following masses are required:

80 tonne to be removed at Kg 8.25 m.

60 tonne to be added at Kg 9.05 m.

The follov6ng masses in Table Q2 are to be added to give the load condition:

In the above condition, free surfaces of liquid are present as follows:

• fresh water of density 1000 kg/m³, in one rectangular tank, 10 m long and 10 m wide;

• oil fuel ot density 925 kg/m³, in four rectangular tanks, each 8 m long and 10 m wide.

Using the hydrostatic Curves provided in Worksheet Q2, determine EACH Of the following:

(a) the lightship KG; (8)

(b) the final mean draught in sea water; (2)

(c) the final effective metacentric height.  (6)

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

Fn = 20.2 A V² a newtons

Where :         A = rudder area (m²)

V = ship speed (m/s)

a = rudder angle (degrees)

A manoeuvrability specification for a ship that requires a transverse rudder force of 92 kN is generated when the angle of helm is 35^o with the ship travelling at 5 knots.

(a) Determine suitable dimensions for a rectangular rudder having an aspect ratio (depth to width ratio) of 1.5.  (6)

(b) The rudder stock is designed to have a diameter of 360 mm with the allowable shear stress in the material limited to 70 MN/m² at its service speed of 16 knots. At the maximum helm angle of 35^o, the centre of effort is 35% of the rudder width from the leading edge of the rudder.

Calculate the maximum distance of the axis of rotation from the leading edge of the rudder so that the stock is not overstressed at the service speed. (10)

Q7. (a) State TWO of the MINOR components of the residuary resistance.  (2)

(b) A ship has a length of 140 m and floats in sea water of density 1025 kg/³. A geometrically similar model of this ship has a length of 5 m and a wetted surface area of 5.8 m².  The model has a total resistance of 29.55 N when towed in fresh water of density 1000 kg/m³ at a speed corresponding to 15 knots for the ship. Calculate EACH of the following:

(i) the ratio of residuary resistance to total resistance for the model at the corresponding speed; (6)

(ii) the ratio of residuary resistance to total resistance for the ship. (6)

(c) State why the TWO ratios calculated in Q7(b) should be different.  (2)

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

The frictional coefficient for the ship in sea water is 1.415

Speed in rms with the speed index (n) for ship and model 1.825

Q8. A ship 145 m long, 24.5 m beam displaces 24910 tonne when floating at a draught of 9.5 m in sea water of density 1025 kg/m³.

The propeller has a diameter of 6.0 m and a pitch ratio of 0.95.

With the propeller operating at 1.75 revs/sec, the following results were recorded:

propeller thrust = 1300 kN

real slip = 35 %

propeller efficiency = 67 %

transmission losses = 3 %

fuel consumption per day = 63 tonne

Calculate EACH of the following:

(a) the ship speed; (6)

(b) the apparent slip; (2)

(c) the specific fuel consumption; (4)

(d) the mass of fuel required to travel 3500 nautical miles at a constant speed of 17.5 knots including a reserve of 10%. (4)

Note: Wake fraction = 0.5 C_b-0.05