🔍 Key Concepts

• 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

💭 Think About

• 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)?

✅ Before You Answer

• 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).