You are hoisting a heavy lift with the jumbo boom. Your vessel displaces 8560 T. The 45-ton weight is on the pier and its center is 65' to starboard of the centerline. The head of the boom is 95' above the base line and the center of gravity of the lift when stowed on deck will be 55' above the base line. As the jumbo boom takes the strain the ship lists to 5.5°. What is the GM with the cargo stowed?
• Virtual rise of G when lifting a weight off the pier with a jumbo boom • How to use list angle and displacement to find GM from a suspended weight (GZ = (w × horizontal shift of G) / W) • Difference between GM during the lift and GM after stowage on deck (final GM)
• First, think about what happens to the ship’s center of gravity when the weight is still on the pier but hanging from the boom. How far and in what direction does G move? • Use the 5.5° list and the ship’s displacement to find the metacentric height during the lift. Which formula links GZ, GM, and the list angle (in radians)? • After you know how much G moved when the load was hanging, how does G move again when the weight is brought inboard and stowed at 55 ft above the baseline? Compare the initial and final vertical positions of G.
• Be sure you’re using radians, not degrees, when relating GZ and GM via the sine of the angle for small angles. • Keep track of which displacement to use: always use the ship’s total displacement (ship + cargo) once the cargo is lifted clear, not the cargo weight alone. • Carefully separate the two stages: (1) weight hanging at boom head, (2) weight stowed on deck. Compute the change in KG between these stages before deciding on the final GM.
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