Q7. The load waterplane of a ship 120 m long, floating in sea water of density 1025 kg/m3, is defined by the following half-breadths given in Table Q1.
The following particulars are obtained from the ship's hydrostatic curves:
Displacement = 8450 tonne
Center of buoyancy above the keel (KB) = 3.21 m
Moment to change trim by one centimeter = 101.5 tm
Calculate EACH of the following:
(a) The position of the longitudinal center of flotation (LCF) from midships;
(b) The second moment of area of the waterplane about a transverse axis through the centroid;
(c) The height of the ship's center of gravity above the keel.
Q16. An inclining test carried out on a passenger vessel at a displacement of 8725 tonne in water of density 1012 kg/m3 resulted in an angle of heel of 1.5º when an inclining mass of 10 tonne was moved 15 m transversely across the deck.
To obtain the lightship condition for the vessel, corrections for the following masses are required:
40 tonne to be removed at Kg 9.2 m
65 tonne to be added at Kg 10.15 m
The following masses in Table Q2 are to be added to give the load condition:
In the above condition, free surfaces of liquid are present in one rectangular tank 8m long and 6m wide containing fresh water of density 1000 kg/m3 and in four rectangular tanks each 10 m long and 8 m wide containing oil fuel of density 950 kg/m3.
Using the hydrostatic curves provided in Worksheet Q2, determine EACH of the following:
(a) The lightship KG;
(b) The final mean draught in sea water;
(c) The final effective metacentric height.
Q3. A ship 150 m in length displaces 14000 tonne and floats at draughts of 6.25 m Forward and 6.6 m aft. The longitudinal metacentric height Is 165 m, the Centre of flotation is 1.8 m aft of midship and the TPC is 22. The vessel is required to enter dock with draught of 6.5 m and a trim of 1m by stern.
Calculate EACH Of the following
(a) mass of ballast to be discharged; (6)
(b) the distance its centre of gravity from midships. (10)
Q5. The force acting normal to the centerline plane of a rudder is given by the expression:
Fn = 15.5 A V2 α newtons
Where: A = rudder area (m2)
v = ship speed (m/s)
α = rudder helm angle (degrees)
A ship travelling at a speed of 20 knots has a rudder configuration as shown in Fig Q4. The center of effort for areas A1 and A2 are 32% of the width from their respective leading edges. The rudder angle is limited to 35º from the ship's centerline.
(a) The diameter of the rudder stock required for a maximum allowable stress of 77 MN/m2;
(b) The drag component of the rudder force when the rudder is put hard over at full speed.
Q6. The results in Table Q5 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 1000 kg/m3 at a temperature of 13ºC.
The following particulars are also available:
Ship correlation factor 1.22
Temperature correction ±0.43% per ºC
Calculate the effective power of a similar ship 160 m long travelling at a speed of 17.5 knots in sea water of density 1025 kg/m3 at a temperature of 15ºC. (16)
Note: frictional coefficient for the model in water of density 1000 kg/m3 at 15ºC is 1.655.
Frictional coefficient for the ship in water of density 1025 kg/m3 at 15ºC is 1.410.
Speed in m/s with index (n) for ship and model 1.825.
Q8. A ship 145 m long and 23 m beam displaces 19690 tonne when floating at a draught of 8 m in sea water of density 1025 kg/m3.
The following data are given for the service speed of 16 knots:
Effective power (naked) = 3450 kW
Appendage and weather allowance = 20%
Quasi-propulsive coefficient = 0.71
Thrust deduction fraction = 0.21
Transmission losses = 3%
Specific fuel consumption = 0.205 kg/kW hr
The Taylor wake fraction is obtained from: wt = 0.5 Cb - 0.05
(a) Calculate EACH of the following at the service speed:
(i) The delivered power;
(ii) The thrust power;
(iii) The fuel consumption per day.
(b) Calculate the maximum speed at which the ship must travel to complete a voyage of 3000 nautical miles, with only 200 tonne of fuel on board.
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