Lection3船舶原理英文版.doc

Lection 3 Investigation of equilibrium conditions. Weight of ship and co-ordinates of centre of gravity. Displacement and co-ordinates of centre of buoyancy. P. 1 – 38. Investigation of equilibrium conditions. Weight of ship and co-ordinates of centre of gravity. Only two forces, the force of ship weight and the force of buoyancy act upon the ship in position of equilibrium in still water. Module of the weight force is determined by the formula where is the mass of the ship and is the absolute value of the gravitational acceleration. is the volume of the ship body immersed portion. The weight force acts vertically downwards. The line of action of this force goes through point, which is the ships centre of gravity or the centre of the ship mass. Co-ordinates of the point in the system of co-ordinates oxyz, linked with the ship, are denoted through, and. For projections of the force into the axes of the co-ordinate system oxyz are introduced the following designations, , . The Archimedean force or buoyancy force acts vertically upwards, going through the point, which is a centroid of the ship immersed volume. By co-ordinates of the point, as is known, are the values, and. Projections of the buoyancy force into the axes of the system oxyz are designated by expressions , , . The force of ship weight and the buoyancy force form moments and , which are calculated concerning an origin of co-ordinates, the point о. By projections of the moments and into the axes of the co-ordinate system oxyz are values , , and , , accordingly. Static moments , and of ship mass , calculated concerning the planes yoz, zox and xoy of co-ordinate system, linked with ship, are defined by expressions For static moments of immersed volume , calculated concerning the plane yoz, zox and xoy of co-ordinate system oxyz, the following designations, and are introduced. The calculation of these static moments is realised with the he