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Q1. A spade type rudder, supported only at the rudder head, has a depth of 3.6 m, with the following widths at equal intervals commencing from the top of the rudder:

2.10 m, 2.05 m, 1.80 m, 1.45 m and 1.00 m

The top of the rudder is 0.4 m from the bearing at the rudder head.

The centre of effort of the rudder can be taken to act at the vertical centroid of the rudder and at a distance of 0.15 m from the axis of rotation.

The force on the rudder (F_n ), normal to the plane of the rudder is given by the expression:

Where:

F_n  = 18.32Av² α Newtons

A = rudder area (m²)

v = ship speed (m/s)

α = rudder angle (degrees)

The equivalent twisting moment (T_E) is given by:

T_E  = M + √(M²+T² )

Where: M = bending moment

T = twisting moment

Calculate the required diameter of the rudder stock, assuming a maximum allowable stress of 70 MN/m², for a ship speed of 18 knots and rudder angle 35^o. (16)

Q2. A vessel floating in sea water of density 1025 kg/m³ with a displacement of 6600 tonne has the following particulars:

Mean draught = 7.0 m

Centre of buoyancy above the keel (KB) = 3.845 m

Transverse metacentre above the centre of buoyancy (BM) = 4.025 m

Transverse metacentric height (GM) = 0.850 m

Tonne per centimetre immersion (TPC) = 16

Assuming the vessel to be wall-sided over the affected range of draught, calculate the mass to be added to the vessel at a KG of 2. 5 m, to give a final transverse metacentric height of 1.2 m. (16)

Q3) A ship of length 136 m has a light displacement of 4850 tonne with the longitudinal centre of gravity 1.64 m aft of midships.

Loading now takes place as shown in Table Q3.

Using the relevant data extracted from the hydrostatic curves provided on worksheet Q3, determine the final end draughts of the vessel in sea water of density 1025 kg/m³. (16)

Q4. A ship of displacement 6600 tonne in sea water of density of 1025 kg/m³ has a breadth of 16 m and a draught of 5.6 m.

The area of waterplane is 1600 m², KB is 3.4 m, KG is 5.1 m and the second moment of area of the waterplane about the centreline is 23180 m⁴.

A rectangular wing tank of length 12 m and breadth 4 m is situated above a double bottom of depth 1.2 m as shown in Fig Q4.

Calculate the angle of heel that would occur if the wing tank were bilged. (16)

Q5. A ship has a length of 130 m and floats in the sea water of density 1025 kg/m³.  A model of this ship has a length of 5 m and a wetted surface area of 6 m2.  The model has a total resistance of 45 N when towed at 1.85 m/s in fresh water of density 1000 kg/ m³.

(a) Using the data below, calculate EACH of the following:

(i) the ratio of residuary resistance to total resistance for the model; (5)

(ii) the ratio of residuary resistance to total resistance for the ship at the corresponding speed. (8)

(b) State why the two ratios should be different. (3)

The frictional coefficient for the model in fresh water is 1. 694

The frictional coefficient for the ship in sea water is 1. 418

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

Q6. A model propeller of mean pitch 0.4 m is tested in a tank under conditions of constant speed of advance 2 m/s in fresh water of density 1000 kg/m³ and the results for a range of rotational speeds are as shown in Table Q6.

(a) Plot a curve of propeller efficiency against real slip. (12)

(b) Determine EACH of the following at maximum propeller efficiency:

(i) real slip; (1)

(ii) rotational speed. (3)

Q7. A box shaped barge of length 70 m has a full mass of 420 tonne which is evenly distributed throughout its length. Bulkheads are located 5 m from the barge ends to form peak tanks which are empty.

The remainder of the barge is divided by two transverse bulkheads to form three holds of equal lengths. These holds are loaded with a total of 1680 tonne of level stowed bulk cargo, 480 tonne of which is loaded in the centre hold and the remainder is equally distributed in the other two holds.

Using graph paper, draw EACH of the following curves on a base of ship length:

(a) Weight and buoyancy curves;    (5)

(b) Load curve;(3)

(c) Shear force curve;(4)

(d) Bending moment curve. (4)

Q9. A ballast tank watertight bulkhead 6.0 m deep is stiffened by vertical angle bar stiffeners 255 mm x 100 mm x 12.5 mm thick, spaced 0.6 m apart.

The ends of the stiffeners in contact with the tank top are welded all around as shown in Fig Q9 and the thickness of the weld is 5 mm.

The bulkhead has sea water of density 1025 kg/m³ on one side to a depth of 4.85 m. Calculate the shear stress in the weld metal. (16)