GLASGOW COLLEGE OF NAUTICAL STUDIES
SHIP STABILITY 1
D78A 34
TUTORIAL 7: Initial Transverse Metacentre
1. Construct the metacentric diagram for a box-shaped vessel, length 64 m, breadth 10 m, depth 6 m, between the light draught of 1 m and the load draught of 5 m (use 0.5 m intervals). From the diagram find:
(a) the minimum value of KM and the draught at which it occurs.
(4.08 m; 4.00 m)
(b) the draughts at which the vessel is unstable when the KG is 4.15 m.
(3.42 m to 5.00 m)
(c) the righting moment when heeled to 5 degrees by external forces in salt water when the upright draught is 2.8 m and the KG is 4.0 m.
(60.2 t-m)
(d) the maximum KG when loaded to a draught of 5.0 m in SW to ensure that a righting moment of 100 t-m is available at 4 degrees heel.
(3.73 m)
2. Draw a curve of transverse metacentres for a box vessel, length 100 m, breadth 12 m, between the draughts of 2.0 m and 8.0 m (at 0.5 m intervals). From the curve find:
(4.90 m; 5.00 m)
(b) the draughts at which the vessel is unstable when the KG is 5.20 m.
(3.50 m to 7.00 m)
(c) the righting moment when heeled to 7 degrees by external forces in salt water when the upright draught is 2.5 m and the KG is 4.0 m
(768.2 t-m)
(d) the maximum KG when loaded to a draught of 7.50 m in water RD 1.015 to ensure that a righting moment of 100 t-m is available at 4 degrees heel.
(5.193 m)
3. Draw a curve of transverse metacentres for a box vessel, length 76 m, breadth 14 m, between the draughts of 2.0 m and 9.0 m (at 0.5 m intervals). From the curve find:
(5.72 m; 5.50 m to 6.00 m)
(b) the draughts at which the vessel has neutral stability when the KG is 6.00 m.
(4.20 m and 7.75 m)
(c) the righting moment when heeled to 10 degrees by external forces in water RD 1.012 when the upright draught is 5.86 m and the KG is 5.44 m.
(303.8 t-m)
(d) the maximum KG when loaded to a draught of 5.10 m in water RD 1.022 to ensure that a righting moment of 86 t-m is available at 2 degrees heel.
(5.308 m)
4. A box-shaped barge is 40 m in length and 12 m wide. Construct a metacentric diagram for the range of draughts 2.0 m to 8.0 m at 0.5 m intervals.
(a) If the KG is 4.90 m determine the minimum value of GM and the draught at which it occurs.
(0.00 m; 5.00 m)
(b) If the barge is floating at the draught in (a) in salt water, how much weight should be shifted from Kg 4.00 m to Kg 2.00 m to ensure a minimum GM of 0.20 m.
(246 t)
(c) Having shifted the weight in (b) calculate the available moment of statical stability if the vessel is heeled 5 degrees.
(42.9 t-m)
(d) If the barge is floating at a draught of 3.6 m in water RD 1.002, what is the maximum KG required to ensure that at 2 degrees heel there is a righting moment of at least 200 t-m.
(1.824 m)
5. A box-shaped vessel has length 160 m, breadth 20 m and depth 14 m. If it floats at an even keel draught of 8.0 m in fresh water, calculate the change in GM that occurs when the barge is towed into salt water.
(0.006 m increase)
6. A box vessel, length 160 in, breadth 20 m has a light draught of 4.0 m and a load draught of 10 m. Determine the range of draughts for which the GM will be less than 0.50 m when the KG is 8.00 m.
(6.137m or less)
7. A box-shaped vessel length 100 in, breadth 16 m and depth 10 m has a draught of 5.0 m on an even keel in salt water. Calculate the change in GM that will occur if the barge is towed into fresh water.
(0.042 m decrease)
8. Draw a metacentric diagram for a box vessel of length 120 m, breadth 14 in and depth 8 m for the range of draughts 2.0 m to 6.0 m (using 0.5 m draught intervals). If the box is in a neutral condition of stability at a draught of 5.0 m in salt water, calculate the GM after filling a double bottom tank with 200 tonnes of oil at Kg 1.0 m. (0.092 m)
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TUTORIAL 7 – Initial Transverse Metacentre (MAR Rev.18/11/03)
dariusz.lipinski