In naval stability, what does metacentric height (GM) describe?

In naval stability, what does metacentric height (GM) describe?

• A. The distance between the center of gravity and the metacenter.
• B. The distance from the hull to the waterline.
• C. The ship's overall length.
• D. The distance from the keel to the center of buoyancy.

Answer: (A)

Metacentric height is the vertical distance between the center of gravity and the metacenter. It tells you how stable the ship is at small angles of heel. When the hull heels, the center of buoyancy shifts and the buoyant force intersects the centerline at the metacenter; the weight acts through the center of gravity. The outer righting moment that tends to restore upright position is proportional to the weight times GM times sin(heel). If the center of gravity sits below the metacenter (positive GM), a restoring moment develops; if it sits above (negative GM), the ship tends to capsize. The larger the GM, the stronger the initial stability. The other quantities mentioned describe different measurements—distance from hull to waterline, ship length, or keel to buoyancy—and do not define metacentric height.

Metacentric height is the vertical distance between the center of gravity and the metacenter. It tells you how stable the ship is at small angles of heel. When the hull heels, the center of buoyancy shifts and the buoyant force intersects the centerline at the metacenter; the weight acts through the center of gravity. The outer righting moment that tends to restore upright position is proportional to the weight times GM times sin(heel). If the center of gravity sits below the metacenter (positive GM), a restoring moment develops; if it sits above (negative GM), the ship tends to capsize. The larger the GM, the stronger the initial stability. The other quantities mentioned describe different measurements—distance from hull to waterline, ship length, or keel to buoyancy—and do not define metacentric height.