Section 2: Inertia Flashcards
What is COB?
COB is the point where the force of buoyancy is considered to act vertically upwards and is the geometric centre of the underwater portion of the ship.
Therefore, this position depends on the underwater shape of the ship.
If the ship is box-shaped, her geometric centre will be at a point that is half the draft from the keel - see Figure A. For a prismatic shape, it will be the point of intersection of the medians; see Figure B.
What is KB?
KB for a box-shaped underwater is = ½ draft
KB for a prism-shaped underwater is = 2/3 draft
For any other shape (that is, a shape that is not standard), KB can be determined by taking moments about the keel or by using Simpson’s Rules.
What is BM?
BM is calculated by the formula:
V - underwater volume (sometimes referred to as “volume of displacement”)
I - “moment of inertia”
What is inertia and moment of inertia?
Inertia, “I”, is usually calculated either with reference to the axis through the centre of flotation, either in the longitudinal direction or in the transverse direction.
“Moment of Inertia” / “2nd moment of area”. According to Newton’s 1st Law of Motion, a body at rest will remain at rest unless some external force is exerted on it, while a body in motion will continue to move unless some external force is exerted. This reluctance for a body at rest to move and a body moving to stop is known as the INERTIA of that body.
“Moment of Inertia” is the resistance of an area to rotate about a given axis, therefore known as the Second Moment of Area.
LL, in the figure is the longitudinal axis through the waterplanes centre of floatation, TT is the athwartship axis through the waterplanes centre of floatation.
Calculate the second moment of area (I) about the transverse axis through the centre line of a box-shaped barge having the following dimensions:
Length 40 m
Breadth 6 m and
Draft 3.5 m
32,000 m4
Calculate the second moment of area (I) about the longitudinal axis through the centre line of a box-shaped barge having the following dimensions:
Length 40 m
Breadth 6 m and
Draft 3.5 m
720 m4
A rectangular-shaped vessel 130 m long, 12 m beam and 6 m depth is floating in salt water at a 4 m draft. Calculate the vessel’s MCTC.
173.225 tm
A box-shaped vessel 45 m long and 9 m beam is floating at a displacement of 1200 tonnes in dock water (R.D. 1.008). Calculate the vessel’s KM.
3.766 m
A vessel is of length 120 m, maximum beam 15 m and block co-efficiency 0.78. The vessel is floating on an even keel draft of 6 m in salt water. KB = 3.2 m and KG = 6.5 m
The water plane area at the 6m draft is rectangular. Determine the vessel’s GM.
0.706 m
The second moment of area of a ship’s waterplane area about the fore and aft centreline is 15,000 m4. The vessel’s displacement is 6575 tons whilst floating in dock water of Relative Density 1.012.
Calculate the metacentric height if KB = 5.2 m and KG = 7 m
0.509 m
