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Q2. A vessel of 10000 tonne displacement floats at a draught of 7.2 m in sea water of density 1025 kg/m³.

Further hydrostatic data for the above condition are:

centre of buoyancy above the keel (KB) = 3.844 m

transverse metacentre above the keel (KM) = 7.186 m

tonne per centimetre immersion (TPC) = 18

The vessel in the above condition is unstable and heels to an angle of 80. To restore positive stability, ballast Of 540 tonne is now loaded at a Kg of 0.5 m.

Calculate EACH Of the following for the final condition:

(a) the transverse metacentric height; (13)

(b) the righting moment when the vessel is heeled to an angle of 150.  (3)

Note: The vessel may be considered wall-sided between the limits of draught, hence:

GZ = sin θ (GM + ½ BM tan² θ)

Q3. A ship 140m long floats at draughts of 6.8m aft and 4.4m forward when floating in river water of density 1012kg/m³

Using the hydrostatic curves provided in worksheet Q3, determine EACH of the following:

a) displacement (8)

b) the longitudinal position of the centre of gravity (8)

Q6. A single screw ship with a service speed of 15 knots is fitted with a rectangular rudder, 5.5 m deep and 3.5 m wide with the axis of rotation 0.4 m aft of the leading edge. At a rudder angle of 35^o, the centre of effort is 32 % 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=577 A v²  sin⁡ α newtons

Where;

A=rudder area ( m² )

v=ship speed ( m⁄s)

α=rudder angle ( degrees)

The maximum stress in the rudder stock is to be limited to 70 MN/m².

Determine EACH of the following:

(a) The minimum diameter of the rudder stock required for ahead running;     (9)

(b) The speed of the ship, when running astern, at which the maximum stress level would be reached.(7)

Q5) (a) Explain the procedure required to produce weight, buoyancy and load curves for a ship assumed to be floating in still water, stating any relevant features of the curves. (8)

(b) Describe how shear force and bending moment curves are produced from a load diagram, explaining how the features of EACH curve are connected. (8)