
The metacentric height (GM) is a measurement of the initial static stability of a floating body. It is calculated as the distance between the centre of gravity of a ship and its metacentre. A larger metacentric height implies greater initial stability against overturning. Metacentric height also influences the natural period of rolling of a hull, with very large metacentric heights being associated with shorter periods of roll which are uncomfortable for passengers. Hence, a sufficiently high but not excessively high metacentric height is considered ideal for passenger ships. ==Metacentre== When a ship heeled, the centre of buoyancy of the ship moves laterally. It may also move up or down with respect to the water line. The point at which a vertical line through the heeled centre of buoyancy crosses the line through the original, vertical centre of buoyancy is the metacentre. The metacentre remains directly above the centre of buoyancy by definition. In the diagram to the right the two Bs show the centres of buoyancy of a ship in the upright and heeled condition, and M is the metacentre. The metacentre is considered to be fixed for small angles of heel; however, at larger angles of heel the metacentre can no longer be considered fixed, and its actual location must be found to calculate the ship's stability. The metacentre can be calculated using the formulae: :$KM\; =\; KB\; +\; BM$ :$BM\; =\backslash frac\; \backslash $ Where KB is the centre of buoyancy (height above the keel), I is the Second moment of area of the waterplane in metres^{4} and V is the volume of displacement in metres^{3}. KM is the distance from the keel to the metacentre. 〔Ship Stability. Kemp & Young. ISBN 0853090424〕 Stable floating objects have a natural rolling frequency like a weight on a spring, where the frequency is increased as the spring gets stiffer. In a boat, the equivalent of the spring stiffness is the distance called "GM" or "metacentric height", being the distance between two points: "G" the centre of gravity of the boat and "M", which is a point called the metacentre. Metacentre is determined by the ratio between the inertia resistance of the boat and the volume of the boat. (The inertia resistance is a quantified description of how the waterline width of the boat resists overturning.) Wide and shallow or narrow and deep hulls have high transverse metacenters (relative to the keel), and the opposite have low metacenters; the extreme opposite is shaped like a log or round bottomed boat. Ignoring the ballast, wide and shallow or narrow and deep means the ship is very quick to roll and very hard to overturn and is stiff. A log shaped round bottomed means slow rolls and easy to overturn and tender. "G", is the center of gravity. "GM", the stiffness parameter of a boat, can be lengthened by lowering the center of gravity or changing the hull form (and thus changing the volume displaced and second moment of area of the waterplane) or both. An ideal boat strikes a balance. Very tender boats with very slow roll periods are at risk of overturning but are comfortable for passengers. However, vessels with a higher metacentric height are "excessively stable" with a short roll period resulting in high accelerations at the deck level. Sailing yachts, especially racing yachts, are designed to be stiff, meaning the distance between the centre of mass and the metacentre is very large in order to resist the heeling effect of the wind on the sails. In such vessels the rolling motion is not uncomfortable because of the moment of inertia of the tall mast and the aerodynamic damping of the sails. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Metacentric height」の詳細全文を読む スポンサード リンク
