Naval architecture -Initial-Stability.pptx

Naval architecture for marine engineering

1. Initial stability By: 4/c manuel jade carlo b. 4/c lipana , melson 4/c Montemayor, josept 4/c Fernandez, raphael 4/c dela cruz , David michael

2. Objectives: Uses of hydrostatic curves to find the height of the metacenter above the keel (km) at given draughts. States that km is only dependent on the draught of a given ship. Given the values of kg, uses the values of km obtained from hydrostatic curves to find the metacenter heights, gm STATES, THAT FOR A CARGO SHIP, THE RECOMMENDED INITIAL GM SHOULD NOT NORMALLY BE LESS THAN 0.15

3. Hydrostatic curves A series of graphs drawn to a vertical scale of draught and a base of length, which gives values such as the centre of buoyancy, displacement, moment causing unit trim, and  centre of flotation. In practice tables with hydrostatic parameters calculated for different draughts are used.

4. Sample problem Analysis: Height of the metacenter is also called KM. While metacentric height is also called GM. Keep in mind that the height of the metacenter and the metacentric height are not the same thing. To find for the height of the metacenter, we have to add GM and KG. So the formula is KM = KG + GM. In the problem we are given a value of KG, so we have to solve for the GM first, and then add it to the KG to get the value of K Find The Height Of The Metacenter Above Keel When a ship of 12,000 tons displacement is heeled 5° 25' the moment of statical stability is 300 tons-meters, KG = 7.5 m. Find the height of the metacenter above the keel. Given: Angle of heel = 5° 25' Displacement = 12,000 tons MSS = 300 tons-meters KG = 7.5 meters What is asked: Height of the metacenter above the keel.

5. Solution: Solving for metacentric height (GM) GM = Moment of Statical Stability Displacement x Sin Ɵ = 300 tons-meters 12,000 tons x Sin 5° 25’ = 300 tons –meters 1132.77 tons GM = 0.26 meters

6. Solution: 2. Solving for the height of the metacenter (KM) KM = KG + GM = 7.5 m + 0.26 m = 7.76 m is the height of the metacenter above keel

7. KM is the distance from Keel to Metacenter, which depends on the vessel draft, displacement and hull form. Typical KM for a Panamax cruise vessel is 18 m. High KM means more stability, but often at the expense of speed and sea keeping capabilities .

8. Ship stability can be defined in simple terms as its characteristics or tendency to return to its original state or upright state, when an external force is applied on or removed from the ship. A ship is at equilibrium when the weight of the ship acting down through centre of gravity is equal to the up thrust force of water acting through centre of buoyancy and when both of these forces are in same vertical line. A Stable Ship

9. B is center of buoyancy and G is center of gravity A ship will come to its upright position or will become stable, when an external force is applied and removed, if the centre of gravity remains in the same position well below metacentric height of the ship. When ship is inclined, centre of buoyancy shifts from B to B1, which creates a movement and the righting lever returns the ship to its original position and makes it stable.

10. Intact stability The Area of the GZ curve should be at least: a)      0.055 m radian up to Ѳ = 30̊ b)      0.090 m radian up to Ѳ = 40̊ c)     0.03 m radian between 30̊ and 40̊ or between 30̊ and angle of down flooding. For a cargo vessel, the intact stability requirements are follows- Initial GM or metacentric height should not be less then 0.15 m. Righting lever GZ should be at least 0.2 m and angle of heel Ѳ ≥ 30̊. Maximum righting lever should occur at heel >30̊ preferably but not less than 25̊.