tailieunhanh - Ship Hydrostatics and Stability 2010 Part 3

Tham khảo tài liệu 'ship hydrostatics and stability 2010 part 3', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | Basic ship hydrostatics 39 We conclude that the equilibrium of the floating body is stable if the metacentre is situated above the centre of gravity. For his contributions of overwhelming importance Bouguer was sometimes described as the father of naval architecture quotation in Stoot 1959 . It must be emphasized here that the definition of the metacentre is not connected at all with the form of a ship. Therefore the fact that in the above figures the metacentre is the intersection of the new line of action of the buoyancy force and the centreline is true only for symmetrical hulls heeled from the upright condition. For a general floating body we can reformulate the definition as follows Let us consider a floating body and its centre of buoyancy Bự . Let the line of action of the buoyancy force be R. If the body changes its inclination by an angle the centre of buoyancy changes its position to Bộ Srị and the new line of action of the buoyancy force will be say 5. When ốự tends to zero the intersection of the lines R and S tends to a point that we call metacentre. Readers familiar with elementary differential geometry will recognize that defined as above the metacentre is the the centre of curvature of the curve of centres of buoyancy. The notion of curvature is defined in Chapter 13. Metacentric height In the preceding section we learnt that a surface ship is initially stable if its initial metacentre is above the centre of gravity. For actual calculations we must find a convenient mathematical formulation. We do this with the help of Figure a . We choose a reference point K at the intersection of the centreline and the baseline and we measure vertical coordinates from it upwards. Thus defined K is the origin of -coordinates. A good recommendation is to choose K as the lowest point of the ship keel then there will be no negative z-coordinates. We remember easily the chosen notation because K is the initial letter of the word keel. In the same figure Mo is .