When a ship is at rest in calm water, the COB & the COG
will be in a vertical line as illustrated by figure X on the Below pic.
Pitch: If waves cause an increase in the under water volume aft, and a decrease fwd,
the COB will shift aft. The forces of gravity and buoyancy now get separated by a fore and aft distance and form a couple which will cause the bow to dip downwards and the stern to lift upwards as shown in figure Y on the below Pic.
If waves cause an increase of underwater volume forward, and a decrease aft, COB will shift forward, and the forces of gravity and buoyancy will form a couple which will cause the bow to lift upwards and the stern to dip downwards as shown in figure Z on the previous pic. This up and down movement of the ship's ends, due to longitudinal shift of COB resulting from wave action, is called pitch.
During pitch, the COG of the ship does not move because no weights are loaded, discharged or shifted. Pitching is the longitudinal equivalent of rolling.
Trim:
The difference between the drafts fwd and aft, expressed in metres or in centimetres, is called trim. If the draft aft is greater than the draft fwd, the ship is said to be trimmed by the stern. If the draft fwd is greater, the ship is said to be trimmed by the head. If the drafts fwd and aft are equal (if trim is zero), the ship is said to be on an even keel.
Trim is the longitudinal equivalent of list, but with three main differences:
1) List is measured in degrees. Trim is expressed in metres or centimetres only.
2) In the sailing condition, the ship is usually upright but rarely on an even keel. In other words, list is normallyabsent whereas trim is normally present.
3) If the ship is listed, it is not important whether it is to port or to stbd.Trim must be by the stern, never by the head. If trimmed by the head, the steering qualities and speed, especially the former, would be adversely affected.
Consider a ship at rest, on an even keel in calm water. The COB and the COG would be in a vertical line as shown in figure 1 on the below pic. If a weight of 'w' tonnes is shifted aft by a distance 'd' metres, the COG of the ship would shift by GGi metres, as shown in figure 2 on the below pic. The forces of gravity and buoyancy would form a couple and cause the stern to sink and the bow to rise. This would increase the underwater volume aft and decrease it forward - the COB will shift aft. This would continue until the COB comes vertically under Gl, as shown in figure 3 on below pic.
In figure 3, ML is the longitudinal metacentre - the point of intersection of
the verticals through the COB when on an even keel and when trimmed. KML is the
sum of KB and BML. KML is a function of draft and is given in the hydrostatic
table/curves of the ship against draft.
Referring to figure 3 on above pic:
Trim = GG1 (since both = tanθ)
L GML
but GGI = wd So trim = wd
W L W x GML
So trim (in metres) = wd x L
W x GML
Or trim (in cm) = wd x 100 x L
W x G ML
= wd / W x GML = wd
100L MCTC
Trim caused (in cm) = trimming moment
MCTC
MCTC is called the moment to change trim by 1 cm. Since GML is very large (more than the ship's length), use of BML instead of GML will not make any appreciable change in the value of MCTC.
MCTC = W.GML/IOOL ≈ W.BML/lOOL
MCTC is calculated by using BML for the various salt water drafts and given in the ship's hydrostatic table/curves.
Center of flotation (COF)
COF is that point about which the ship would pivot, when the trim is changed. COF is also called the tipping centre. It is the geometric centre of the waterplane area of the ship at that draft. The position of COF is indicated by its distance from the after perpendicular of the ship (AF) or by its distance forwa~d or abaft amidships (HF). AF or HF, as the case may be, depends on the hydrostatic draft of the ship. Hence the values of COF are indicated against draft in the hydrostatic tables/curves of the ship.
Change of draft fwd & aft
If COF is amidships, the change of draft fwd and the change of draft aft would be equal. So if the trim caused (or Tc) is 40 cm by the stern, the stern would sink by 20 cm and the bow would rise by 20 cm.
If COF is not amidships, the change of draft at each end would be unequal:
Change of draft aft (or Ta) = AF x Tc.
LBP
Change of draft fwd (or Tf) = Tc - Ta.
Pitch: If waves cause an increase in the under water volume aft, and a decrease fwd,
the COB will shift aft. The forces of gravity and buoyancy now get separated by a fore and aft distance and form a couple which will cause the bow to dip downwards and the stern to lift upwards as shown in figure Y on the below Pic.
If waves cause an increase of underwater volume forward, and a decrease aft, COB will shift forward, and the forces of gravity and buoyancy will form a couple which will cause the bow to lift upwards and the stern to dip downwards as shown in figure Z on the previous pic. This up and down movement of the ship's ends, due to longitudinal shift of COB resulting from wave action, is called pitch.
During pitch, the COG of the ship does not move because no weights are loaded, discharged or shifted. Pitching is the longitudinal equivalent of rolling.
Trim:
The difference between the drafts fwd and aft, expressed in metres or in centimetres, is called trim. If the draft aft is greater than the draft fwd, the ship is said to be trimmed by the stern. If the draft fwd is greater, the ship is said to be trimmed by the head. If the drafts fwd and aft are equal (if trim is zero), the ship is said to be on an even keel.
Trim is the longitudinal equivalent of list, but with three main differences:
1) List is measured in degrees. Trim is expressed in metres or centimetres only.
2) In the sailing condition, the ship is usually upright but rarely on an even keel. In other words, list is normallyabsent whereas trim is normally present.
3) If the ship is listed, it is not important whether it is to port or to stbd.Trim must be by the stern, never by the head. If trimmed by the head, the steering qualities and speed, especially the former, would be adversely affected.
Consider a ship at rest, on an even keel in calm water. The COB and the COG would be in a vertical line as shown in figure 1 on the below pic. If a weight of 'w' tonnes is shifted aft by a distance 'd' metres, the COG of the ship would shift by GGi metres, as shown in figure 2 on the below pic. The forces of gravity and buoyancy would form a couple and cause the stern to sink and the bow to rise. This would increase the underwater volume aft and decrease it forward - the COB will shift aft. This would continue until the COB comes vertically under Gl, as shown in figure 3 on below pic.
Referring to figure 3 on above pic:
Trim = GG1 (since both = tanθ)
L GML
but GGI = wd So trim = wd
W L W x GML
So trim (in metres) = wd x L
W x GML
Or trim (in cm) = wd x 100 x L
W x G ML
= wd / W x GML = wd
100L MCTC
Trim caused (in cm) = trimming moment
MCTC
MCTC is called the moment to change trim by 1 cm. Since GML is very large (more than the ship's length), use of BML instead of GML will not make any appreciable change in the value of MCTC.
MCTC = W.GML/IOOL ≈ W.BML/lOOL
MCTC is calculated by using BML for the various salt water drafts and given in the ship's hydrostatic table/curves.
Center of flotation (COF)
COF is that point about which the ship would pivot, when the trim is changed. COF is also called the tipping centre. It is the geometric centre of the waterplane area of the ship at that draft. The position of COF is indicated by its distance from the after perpendicular of the ship (AF) or by its distance forwa~d or abaft amidships (HF). AF or HF, as the case may be, depends on the hydrostatic draft of the ship. Hence the values of COF are indicated against draft in the hydrostatic tables/curves of the ship.
Change of draft fwd & aft
If COF is amidships, the change of draft fwd and the change of draft aft would be equal. So if the trim caused (or Tc) is 40 cm by the stern, the stern would sink by 20 cm and the bow would rise by 20 cm.
If COF is not amidships, the change of draft at each end would be unequal:
Change of draft aft (or Ta) = AF x Tc.
LBP
Change of draft fwd (or Tf) = Tc - Ta.
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