Your vessel displaces 869 tons and measures 136'L x33'B. You ship a large wave on the after deck which measures 52'Lx 33'B. The weight of the water is estimated at 52.8 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) • How to calculate the moment of inertia of a liquid surface in a rectangular tank (or on deck) • Relationship between free surface correction (FSC), moment of inertia, and vessel’s displacement
• How do you treat the shipped water on deck: as a weight in a tank or as a free surface? What formula applies to GM reduction in that case? • For a rectangular free surface, what dimensions do you use in the moment of inertia formula, and which dimension must you square? • Once you find the free surface correction, how do you convert that into feet of GM reduction using the vessel’s displacement in tons?
• Be sure you are using the correct formula for moment of inertia of a rectangle about its centerline and not confusing length and breadth. • Confirm that you use the vessel’s total displacement (869 tons) in the denominator of the GM reduction formula, not just the weight of the water. • Double-check your unit consistency: tons vs long tons, feet for all dimensions, and that the final GM reduction is in feet.
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