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.
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 KM.
Solution:
1. 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
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
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.
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 KM.
Solution:
1. 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
1132.77
GM = 0.26 meters
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
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