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Q12. A RO-RO ferry of length 80 m has a displacement of 3800 tonne in sea water of density 1025 kg/m³ with BM = 3.4 m. The breadth of the ship at the waterline, between sections 3 and 7 is constant at 13 m. To increase stability, sponsons, 1.8 m deep and of constant plan area are to be fitted as shown in Fig Q1.

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

For the new condition, there is no change in draught and the load waterline is at mid-depth of the sponson.

Calculate the increase in BM due to the sponsons.

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)

Q4. A ship of displacement 11000 tonne has a length 120 m and an even keel draught of 5.5 m in sea water of density 1025 kg/m³.

The area of the waterplane is 1440 m² and the second moment of area of the waterptane about a transverse axis through midships is 1.2 x 106 m4 with the LCF at midships. The ship has a full depth empty rectangular compartment having a length 12 m and breadth 10 m. The centre of the compartment is on the centretine of the ship 40 m forward of midships. Calculate the end draughts after the compartment is bilged.

Note: For the purposes of calculating the MCT1cm it can be assumed that GML= BML. (16)

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. The values of effective power (naked hull) given in Table Q7 refer to a ship which is to have a service speed of 17.75 knots.

The following data also apply:

appendage allowance = 8%

weather allowance = 15%

quasi propulsive coefficient = 0.7

transmission losses = 3%

engine mechanical efficiency = 85%

ratio of service indicated power to maximum indicated power = 0.9

(a) Determine the indicated power of the engine to be installed.  (8)

(b) Determine the speed obtained if all the available power of the engine is used in EACH of the following:

(i) when the ship is running on acceptance trial in calm conditions; (4)

(ii) when operating under actual service conditions. (4)

Q13. A ship 160 m in length, 24 m breadth, displaces 24800 tonne when floating at a draught of 9 m in sea water of density 1025 kg/m^3.

The ship's propeller has a diameter of 5.8 m, a pitch ratio of 0.9 and a blade area ratio of 0.45.

With the propeller operating at 1.9 rev/sec, the following results were recorded:

Apparent slip ratio = 0.06

Thrust power = 3800 kW

Propeller efficiency = 64%

The Taylor wake fraction wt is given by: wt = 0.5 C_b − 0.05

Calculate EACH of the following for the above condition:

(a) The ship's speed;

(b) The real slip ratio;

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

(d) The torque delivered to the propeller.

Q6) (a) With the aid of an outline sketch explain EACH of the following:

(i) unbalanced rudder; (2)

(ii) semi-balanced rudder; (2)

(iii) balanced rudder. (2)

(b) State the principal advantage of fiiting a balanced rudder. (1)

(c) A ship travelling at full speed has its rudder put hard over to port, where it is held until the ship completes a full turning circle.

Describe, with the aid of a sketch, how the ship will heel from the upright condition during the manoeuvre. Illustrate the moments produced by the forces acting on the ship and the rudder. (9)