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Calculating KB, BM, and metacentric diagrams 113
Exercise 12
1 A box-shaped vessel 75 m long, 12 m beam and 7 m deep, is ¯oating on an even keel at 6 m draft. Calculate the KM.
2 Compare the initial metacentric heights of two barges, each 60m. long, 10 m beam at the waterline, 6 m deep, ¯oating upright on an even keel at 3 m draft, and having KG 3 m. One barge is in the form of a rectangular prism and the other is in the form of a triangular prism, ¯oating apex downwards.
3 Two box-shaped vessels are each 100 m long, 4 m deep, ¯oat at 3 m draft, and have KG 2.5 m. Compare their initial Metacentric Heights if one has 10 m beam and the other has 12 m beam.
4 Will a homogeneous log of square cross-section and relative density 0.7 have a positive initial Metacentric Height when ¯oating in fresh water with one side parallel to the waterline? Verify your answer by means of a calculation.
5 A box-shaped vessel 60m 12 m 5m is ¯oating on an even keel at a draft of 4 m. Construct a metacentric diagram for drafts between 1 m and 4 m. From the diagram ®nd:
(a) the KM's at drafts of 2.4 m and 0.9 m, and
(b) the draft at which the minimum KM occurs.
6 Construct a metacentric diagram for a box-shaped vessel
65m 12m 6m for drafts between 1m and 6m. From the diagram ®nd: (a) the KM's at drafts of 1.2 m and 3.6 m, and
(b) the minimum KM and the draft at which it occurs.
7 Construct a metacentric diagram for a box-shaped vessel 70 m long and 10 m beam, for drafts between 1 m and 6 m. From the diagram ®nd:
(a) the KM's at drafts of 1.5 m and 4.5 m, and
(b) the draft at which the minimum KM occurs.
8 A box-shaped vessel is 60 m long, 13.73 m wide and ¯oats at 8 m even-keel draft in salt water.
(a) Calculate the KB, BM and KM values for drafts 3 m to 8 m at intervals
of 1 m. From your results draw the Metacentric Diagram.
(b) At 3.65 m draft even keel, it is known that the VCG is 4.35 m above base. Using your diagram, estimate the transverse GM for this
condition of loading.
(c) At 5.60 m draft even keel, the VCG is also 5.60 m above base. Using
your diagram, estimate the GM for this condition of loading. What state of equilibrium is the ship in?
Draft(m) 3 4 5 6 7 8 KM (m) 6.75 5.94 5.64 5.62 5.75 5.96