Lesson s Ship brium, stability and trim The basis for ship equilibrium Consider a ship floating upright on the surface of motionless water. In order to be equilibrium, there must be no unbalanced forces or moments acting on it. There are two forces that maintain this equilibrium(1)the force of gravity, and(2)the force of buoyancy. When the ship is at rest, these two forces are acting in the same perpendicular line, and, in order for the ship to float in equilibrium, they must be exactly equal numerically as well as opposite in direction The force of gravity acts at a point or center where all of the weights of the ship may be said be concentrated: i.e. the center of gravity. Gravity always acts vertically downward The force of buoyancy acts through the center of buoyancy, where the resultant, of all of the buoyant forces is considered to be acting. This force al ways acts vertically upward. when the ship is heeled, the shape of the underwater body is changed, thus moving the position of the center of buoyancy Now, when the ship is heeled by an external inclining force and the center of buoyancy has been moved from the centerline plane of the ship, there will usually be a separation between the lines of action of the force of gravity and the force of buoyancy. This separation of the lines of action of the two equal forces, which act in opposite directions, forms a couple whose magnitude is equal to the product of one of these forces(i.e. displacement) and the distance separating them In figure 1(a), where this moment tends to restore the ship to the upright position, the moment is called the righting moment, and the perpendicular distance between the two lines of action is the righting arm(Gz) Suppose now that the center of gravity is moved upward to such a position that when the ship s heeled slightly, the buoyant force acts in a line through the center of gravity. In the new position there are no unbalanced forces. or in other words. a zero moment arm and a zero moment I figure 1(b), the ship is in neutral equilibrium, and further inclination would eventually bring about of the state ofequilibrium If we move the center of gravity still higher, as in figure 1(c), the separation between the lines of action of the two forces as the ship is inclined slightly is in the opposite direction from that of figure 1(a). In this case, the moment does not act in the direction that will restore the ship to the upright but will cause it to incline further. In such a situation, the ship has a negative ighting moment or an upsetting moment. The arm is an upsetting arm, or negative righting arm These three cases illustrate the forces and relative position of their lines of action in the three fundamental states of equilibriumLesson Seven Ship Equilibrium, Stability and Trim The basis for ship equilibrium Consider a ship floating upright on the surface of motionless water. In order to be at rest or in equilibrium, there must be no unbalanced forces or moments acting on it. There are two forces that maintain this equilibrium (1) the force of gravity, and (2) the force of buoyancy. When the ship is at rest, these two forces are acting in the same perpendicular line, and , in order for the ship to float in equilibrium, they must be exactly equal numerically as well as opposite in direction. The force of gravity acts at a point or center where all of the weights of the ship may be said to be concentrated: i.e. the center of gravity. Gravity always acts vertically downward. The force of buoyancy acts through the center of buoyancy, where the resultant, of all of the buoyant forces is considered to be acting. This force always acts vertically upward. When the ship is heeled, the shape of the underwater body is changed, thus moving the position of the center of buoyancy. Now, when the ship is heeled by an external inclining force and the center of buoyancy has been moved from the centerline plane of the ship, there will usually be a separation between the lines of action of the force of gravity and the force of buoyancy. This separation of the lines of action of the two equal forces, which act in opposite directions, forms a couple whose magnitude is equal to the product of one of these forces (i.e. displacement) and the distance separating them. In figure 1(a) ,where this moment tends to restore the ship to the upright position, the moment is called the righting moment, and the perpendicular distance between the two lines of action is the righting arm (GZ). Suppose now that the center of gravity is moved upward to such a position that when the ship is heeled slightly, the buoyant force acts in a line through the center of gravity. In the new position, there are no unbalanced forces, or, in other words, a zero moment arm and a zero moment. In figure 1 (b) ,the ship is in neutral equilibrium, and further inclination would eventually bring about a change of the state of equilibrium. If we move the center of gravity still higher, as in figure 1 (c) ,the separation between the lines of action of the two forces as the ship is inclined slightly is in the opposite direction from that of figure 1 (a) .In this case, the moment does not act in the direction that will restore the ship to the upright but will cause it to incline further. In such a situation, the ship has a negative righting moment or an upsetting moment. The arm is an upsetting arm, or negative righting arm (GZ). These three cases illustrate the forces and relative position of their lines of action in the three fundamental states of equilibrium