Trim, LCF, LCB and MCTC
1The lesson in plain words
Trim is the difference between the aft and forward draughts. The ship trims about the centre of flotation, and MCTC tells you how easily.
Trim
Trim is the draught aft minus the draught forward, at the perpendiculars. Deeper aft is trim by the stern; deeper forward, trim by the head; equal draughts, even keel. Most ships sail slightly by the stern for steering, propeller immersion and a drier forecastle. The best trim is ship-specific: use the booklet or the owner's trim tables.
Longitudinal centres
Positions along the ship are measured from the aft perpendicular (AP) or from midships: check your booklet's convention. LCG is the longitudinal centre of gravity. LCB is the centre of the underwater volume. LCF, the centre of flotation, is the centre of the waterplane area. The hydrostatic tables give LCB and LCF; you calculate LCG.
She trims about the LCF
For a small change of trim at constant displacement, the ship rotates approximately about the LCF, leaving its draught unchanged. The true mean draught is the draught there. Use it with even-keel hydrostatics only within the approved small-trim limits; otherwise use approved trim-dependent data.
MCTC
The moment to change trim one centimetre, MCTC, is the trimming moment in t·m that changes trim by 1 cm. MCTC ≈ Δ × GML ÷ (100 × LBP), where Δ is displacement in tonnes, GML is longitudinal metacentric height in metres, and LBP is length between perpendiculars in metres. For the same displacement and length, larger GML means larger MCTC and less trim change. Use the condition's tabulated MCTC.
Balance fore and aft
Use LCB from the even-keel hydrostatic table at the condition's displacement. LCG aft of that reference LCB gives trim by the stern; forward gives trim by the head. As the ship trims, buoyancy moves until G and B lie on one vertical.
2Step by step
Worked example: true mean draught
- 1
Data: LBP 140 m; draughts F 7.577 m, A 8.377 m; LCF 66.0 m forward of the AP.
Draughts already corrected to the perpendiculars.
- 2
Trim = 8.377 − 7.577 = 0.800 m by the stern.
The aft draught is deeper.
- 3
Mean of draughts = (7.577 + 8.377) ÷ 2 = 7.977 m.
This is the draught amidships, not at the LCF.
- 4
LCF lies 70.0 − 66.0 = 4.0 m aft of midships. Correction = 0.80 × 4.0 ÷ 140 = 0.023 m.
The waterline is deeper aft, and the LCF is aft of midships.
- 5
True mean draught ≈ 7.977 + 0.023 = 8.000 m.
Same as 8.377 − 0.800 × 66 ÷ 140, rounded. Use 8.000 m within approved small-trim limits.
3Key data
- Trim
- Trim = draught aft − draught forward
- True mean draught
- Draught at the LCF
- Draught at LCF
- dA − trim × (LCF from AP ÷ LBP)
- MCTC
- MCTC ≈ Δ × GML ÷ (100 × LBP), in t·m/cm
- Change of trim
- Trimming moment ÷ MCTC, in cm
4Key points
- 1
Trim = aft draught − forward draught; by the stern when deeper aft.
- 2
The ship trims about the LCF, so the draught there is the true mean draught.
- 3
MCTC is the moment that changes trim by 1 cm.
- 4
LCG aft of the even-keel LCB gives stern trim; forward gives head trim.
5Frequent mistakes
Wrong: The mean of the forward and aft draughts is the draught to use in the hydrostatics.
Right: Within approved small-trim limits, use the draught at the LCF. The simple mean is correct only when the LCF is amidships or she is on even keel.
Wrong: The ship trims about midships.
Right: She trims about the LCF, the centre of the waterplane, which moves with draught.
Wrong: MCTC is a fixed number for the ship.
Right: MCTC changes with draught. Read it from the hydrostatics for the condition.
6Practice case & exam keys
A cadet uses the mean, 7.977 m, from F 7.577 m and A 8.377 m. LBP is 140 m; LCF is 74 m forward of AP. They say stern trim always means adding a correction. Do you agree, and what draught should you use?
Show the answer
No. LCF is 4 m forward of midships, where this stern-trimmed waterline is shallower. Use 7.977 − 0.800 × 4 ÷ 140 ≈ 7.954 m. Choose the correction sign from the position of LCF and the direction of trim.
Exam keys
- Trim = dA − dF.
- True mean draught = draught at the LCF.
- MCTC = moment to change trim 1 cm ≈ Δ × GML ÷ (100 × LBP).
- LCG aft of the reference even-keel LCB: trim by the stern.
Finish this unit
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