Your vessel displaces 840 tons and measures...

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Question 1 of 2066636eec28f7522a1c51d102

Your vessel displaces 840 tons and measures 146'L x 38'B. You ship a large wave on the after deck. What is the reduction in GM due to free surface before the water drains overboard, if the after deck measures 65'L x 38'B and the weight of the water is 76 tons?

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Question 1 of 20

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🔍 Key Concepts

• Free surface effect and how it reduces GM (metacentric height) • How to compute the second moment of area (moment of inertia) for a rectangular free surface • Relationship between free surface moment and vessel displacement (Δ) when finding GM reduction

💭 Think About

• Start by identifying which dimensions belong to the vessel and which to the free surface area of the shipped water. Which ones go into the free surface calculation? • Think about the standard formula for GM reduction due to free surface in a slack tank or water on deck. How does the moment of inertia of the free surface combine with the vessel’s displacement? • Estimate the size of the correction: with a displacement of 840 tons and a broad free surface on the after deck, should you expect a GM reduction of only a fraction of a foot, or several feet?

✅ Before You Answer

• Make sure you use the after deck dimensions (65' x 38') for the free surface, not the vessel’s overall length. • Confirm whether the weight of shipped water (76 tons) is used directly in the free surface correction, or whether the standard correction depends only on free surface geometry and displacement. • Double-check units: the moment of inertia for a rectangle uses breadth cubed; ensure you cube the correct dimension (usually the transverse breadth).

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