Your vessel displaces 585 tons and measures 128'L by 26'B. What is the reduction in GM due to free surface if the fish hold (30'L by 18'B by 9'D) is filled with 2.8 feet of water? (Each foot of water weighs 15.4 tons)
• Free surface effect (FSE) and how it reduces GM (metacentric height) • Formula for moment of inertia of a rectangular tank about its centerline: ( I = \frac{L \times B^3}{12} ) when breadth is across the ship • Relationship between free surface moment (FSM), vessel displacement, and reduction in GM
• How do you calculate the volume of water in the fish hold from the given depth and then convert that to tons using the weight per foot of water? • Once you know the tank’s dimensions, which dimension should you raise to the third power when calculating the moment of inertia for free surface: length or breadth? Why? • After finding the free surface moment, how do you relate it to the vessel’s total displacement to obtain a reduction in GM, and are your units consistent (feet vs tons-feet)?
• Be sure you’re using the breadth (across ship) of the hold in the ( B^3 ) part of the moment of inertia formula, not the length. • Confirm you have converted the free surface moment to the same unit system as the vessel’s displacement (tons) before dividing to get GM reduction. • Double-check that you used the actual water depth (2.8 ft) to find the water weight, not the full tank depth (9 ft).
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