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Q1.  A ship 160 m in length has a load displacement of 20500 tonne and floats in water of density 1025 kg/m³. The load waterplane is defined by equally spaced half breadths as shown in Table Q1.

The following particulars are also available:

Centre of buoyancy above the keel (KB) = 4.264 m

Centre of gravity above the keel (KG) = 7.561 m

Centre of lateral resistance above the keel = 4.050 m

A rectangle tank, partially filled with oil of relative density 0.89 has overall dimensions of 10 m by 10 m, but is divided into two equal tanks by an oiltight longitudinal bulkhead.

Calculate EACH of the following:

(a) The effective metacentric height; (12)

(b) The angle to which the ship will heel when turning on a circular course of 400 m diameter at a speed of 16 knots. (4)

Q2. A ship of 25420 tonne displacement floating in sea water has 800 tonne of bunker fuel of density 895 kg / m³ in double bottom tanks which are pressed up full. In this condition the metacentric height is 0.25 m and the ordinates of the statical stability curve

Corresponding to this displacement are as shown in Table Q2.

 Table Q2

The oil is transferred to a deep tank 4.85 m long by 18.2 m wide, situated on the ship's centreline. The centre of gravity of the fuel after transfer is 6.8 m above the original centre Determine EACH Of the following for the new condition:

(a) the final effective metacentric height; (3)

(b) the angle to which the ship lists; (7)

(c) the dynamical stability at 200 angle Of heel.  (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)

Q6. A single screw vessel with a service speed of 16 knots is fitted with an unbalanced rectangular rudder 6 m deep and 3.5 m wide with an axis of rotation 0.25 m forward of the leading edge. At the maximum designed rudder angle of 350 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:

Where:

20.2 A v2 a newtons

A rudder area (m2)

v ship speed (m/s)

- 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  (7)

if the rudder was designed as a balanced rudder, with the axis of rotation 0.85 m from the leading edge.

Q7. A ship 137 m long displaces 13716 tonne. The shaft power required to maintain a speed of 15 knots is 4847 kW, and the propulsive coefficient based upon shaft power is 0.67.

wetted surface area = 2.58

propulsive coefficient = ep/ sp

Values of the Froude friction coefficient for Froude’s Formula are given in Fig Q7, with speed in m/s and speed index (n) =1.825

Calculate the shaft power for a geometrically similar ship which has a displacement of 18288 tonne and which has the same propulsive coefficient as the smaller ship, and is run at the corresponding speed. (16)

Q8) The following data applies to a ship operating on a particular voyage with a propeller of 6 m diameter having a pitch ratio of 0.9.

Propeller speed = 1.85 revs/s
Real slip = 33%
Apparent slip = 6%
Shaft power = 11000kW
Specific fuel consumption = 0.205 kg/kWhr

Calculate EACH of the following:

(a) the ship speed in knots; (3)

(b) the taylor wake fraction; (3)

(c) the reduced speed at which the ship should travel in order to reduce the voyage consumption by 30%; (2)

(d) the voyage distance if the voyage takes 30 hours longer at the reduced speed; (4)

(e) the amount of fuel required for the voyage at the reduced speed. (4)

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)