Principles of naval engineering - Historic Naval Ships Association

PRINCIPLES OF NAVAL ENGINEERINGm DIRECTION OFRIGHTING MOMENT8.52Figure 3-8. — Development of righting momentwhen a stable ship inclines.is exaggerated in the drawing), establishing ametacenter at M. The ship's righting arm GZis one side of the triangle GZM. In this triangleGZM, the angle of heel is at M. The side GMis perpendicular to the waterline at even keel,and ZM is perpendicular to the waterline whenthe ship is inclined.It is evident that for any angle of heel notgreater than 7°, there will be a definite relationshipbetween GM and GZ because GZ = GMsin . Thus, GM acts as a measure of GZ, therighting arm.GM is also an indication of whether the shipis stable or unstable at small angles of inclination.If M is above G, the metacentric heightis positive, the moments which develop whenthe ship is inclined are righting moments, andthe ship is stable (part A of fig. 3-11). But ifM is below G, the metacentric height is negative,the moments which develop are upsetting moments,and the ship is unstable (part B of fig.3-11).INFLUENCE OF METACENTRIC HEIGHTFORCE OF BUOYANCYDIRECTION OFUPSETTINGMOMENTWhen the metacentric height of a ship islarge, the righting arms that develop at smallangles of heel are also large. Such a ship resistsroll and is said to be stiff. When the8.53Figure 3-9.— Development of upsetting momentwhen unstable ship inclines.initial position is referred to as M. The distancefrom the center of buoyancy (B) to the metacenter(M) when the ship is on even keel is themetacentric radius.METACENTRIC HEIGHT (GM)The distance from the center of gravity (G)to the metacenter is known as the ship's metacentricheight (GM). Figure 3-11 shows aship heeled through a small angle (the angleFigure 3-10.— The metacenter.8.5438