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Q1) A RO-RO ferry of length 120 m has a displacement of 12800 tonne in sea water of density 1025 kg/m³ with BM = 4.6 m.

The breadth of the ship at the waterline, between sections 3 and 7 is constant at 20 m.

To increase stability, sponsons, 2.7 m deep and of constant plan area to be fitted as shown in Fig Q1. For the new condition there is no change in draught and the load waterline is at mid-depth of the sponson.

The sponsons extend over the midship length between Sections 3 and 7, with sponson widths as shown in Table Q1.

Table Q1

Calculate the increase in BM due to the sponsons. (16)

Q2). A ship of length 150 m and breadth 20 m floats upright at a draught of 7.5 m in sea water of density of 1025 kg/m³ and the height of centre of gravity above the keel (KG) is 5.388 m.

Further hydrostatic data for this condition are as follows:

centre of buoyancy above the keel (KB) = 3.956 m

height of metacentre above the keel (KM) = 7.014 m

water plane area coefficient ( C_w) =  0.82

block coefficient ( C_b) = 0.72

In the above condition there is an empty rectangular wing tank 16 m long, 5 m  wide and 5 m deep, adjacent to the hull and directly above a double bottom tank 1.2 m deep.

Calculate the angle to which the ship will heel when the tank is completely filled with fresh water of density 1000 kg/m³, assuming the ship to be wall sided over the change of draught. (16)

Q3. A ship of length 130 m is loaded as shown in Table Q3(a).

Table Q3(a)

The following hydrostatic data in Table Q3(b) can be assumed to have a linear relationship between the draughts shown.

Table Q3(b)

Calculate the final end draughts.   (16)

Q4) With reference to the inclining experiment:

(a) state the purpose of the experiment and when the experiment should be performed during the life of a ship; (2)

(b) explain the procedure immediately prior to the experiment; (4)

(c) describe the procedure for the experiment; (4)

(d) list SIX precautions to ensure acceptable accuracy of results. (6)

Q5) A box shaped barge of uniform construction is 80 m long , 10 m wide and has a light displacement of 720 tonne. It is divided into three compartments by two transverse watertight bulkheads so that the end compartments are of equal length. The barge is loaded to draught of 6 m in water of density 1025 kg/m³ with cargo evenly distributed over the two end compartments.

The empty midship compartment, extending the full width and depth of the barge is now bilged and the draught increases to 8 m.

(a) Determine the length of the midship compartment. (3)

(b) For the original intact condition:

(i) plot curves of mass and buoyancy distribution; (5)

(ii) determine the longitudinal still water bending moment at midships. (4)

(c) Determine the longitudinal still water bending moment at midships for the final bilged condition. (4)

Q6. A spade-type rudder has an area of 6.33 m². At its maximum designed rudder angle of 35^o, the centre of effort is 0.12 m aft of the axis of rotation and 1.6 m below the lower edge of the rudder stock bearing.

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

F_n=18.32 A v²  α newtons

where:    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=torque

The maximum stress in the rudder material is to be limited to 77 MN/m².

Calculate EACH of the following:

(a) the diameter of the rudder stock required for a ship speed of 16 knots (10)

(b) the speed to which the ship must be restricted, given that the effective diameter of the stock is reduced by wear and corrosion to 375 mm. (6)

Q7. The results in Table Q7 were obtained from resistance tests on a ship model 6 m in length having a wetted surface area of 7.5 m² in fresh water of density 1000 kg/m³ at a temperature of 13^o C.

The following particulars are also available:

Ship correlation factor  1.18 ; Temperature correction

Calculate the effective power of a similar ship 160 m long travelling at a constant speed of 17.5 knots in sea water of density 1025 kg/m³ at a temperature of 15^oC. (16)

Note:

frictional coefficient for the model in water of density 1000 kg/m³ at 15^oC is 1.655.

frictional coefficient for the ship in water of density 1025 kg/m³ at 15^oC is 1.410.

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