Your vessel displaces 689 tons and measures 123'L x 31'B. You ship a large wave on the after deck which measures 65'Lx 31'B. The weight of the water is estimated at 62 tons. What is the reduction in GM due to free surface before the water drains overboard?
• Free surface effect and how it reduces GM (metacentric height) • Using the second moment of area of the free surface: ( I_T = \frac{L \times B^3}{12} ) for a rectangular surface • The relationship: loss of GM = (free surface moment) / (ship’s displacement)
• First, identify which dimensions belong to the free surface of the shipped water and which belong to the ship. Which dimension is used as breadth in the ( B^3 ) term? • Think about whether the ship’s displacement in the denominator should be the original displacement only, or original + weight of shipped water. • After computing the free surface moment from the shipped water, how do you convert that into a reduction in GM using the ship’s displacement?
• Be sure you are using the free surface dimensions of the water on deck (65' x 31'), not the ship’s full length, when calculating ( I_T ). • Confirm that your breadth is raised to the third power and your length is not: ( I_T = L \times B^3 / 12 ). • Double-check that the displacement in your final division is in consistent units (long tons) and reflects the condition after the 62 tons of water is on board, if required by your method.
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