ship structureSixty tonnes moved twenty metres aft, but the end readings will not each change five centimetres
TRIM LEDGER · WEIGHT MOMENT, MCT AND LCF
Solve total trim change first, then distribute it about the LCF
The example assumes 100 m LBP, LCF 4 m aft of amidships and locally constant MCT 1 cm. It exposes the calculation structure; it does not replace the vessel's loading manual or loading computer.| Item | Value | Meaning |
|---|---|---|
| Initial F / A draught | 6.300 / 6.700 m | Initial trim 0.400 m by stern |
| Weight shifted | 60 t × 20 m aft | Trimming moment 1,200 t·m |
| MCT 1 cm | 120 t·m/cm | For this example condition only |
| Change of trim | 1,200 ÷ 120 = 10 cm | Adds 0.100 m by stern |
| LCF position | 4.0 m aft of amidships | 54 m from FP; 46 m from AP |
| F / A draught change | −0.054 / +0.046 m | Distributed about LCF |
| New F / A draught | 6.246 / 6.746 m | New trim 0.500 m by stern |
Δtrim(cm) = w × d / MCT₁cm = 60 × 20 / 120 = 10 cmδTF = −10 × 54 / 100 = −5.4 cm · δTA = +10 × 46 / 100 = +4.6 cmDisplacement stays constant; LCG moves and the waterline rotates principally about LCF.
There is bodily sinkage or rise as well as trim; a shift-only formula is insufficient.
Also check free surface, tank limits, transfer sequence and structural load.
Trim uses the difference between end draughts to describe longitudinal attitude
In ship stability, trim is the fore-and-aft floating attitude, usually expressed as the difference between forward draught TF and aft draught TA rather than first as a very small angle. When TA exceeds TF, the vessel is trimmed by the stern. When TF exceeds TA, she is trimmed by the bow, also called by the head. Sign conventions differ among manuals and loading systems, so an auditable record states both the arithmetic and the direction—for example, TA minus TF equals plus 0.40 metre, by the stern—instead of leaving an unexplained positive number.
Trim is distinct from three neighbouring meanings. A list, or steady heel, is transverse and makes port and starboard draughts unequal. Pitch is dynamic fore-and-aft angular motion in a seaway. Sail trim means adjusting sail shape and angle to the apparent wind. Mean draught is also not trim: a vessel can keep nearly the same displacement and reference draught while changing the difference between its ends. The U.S. Navy damage-control handbook accordingly treats longitudinal inclination separately from transverse inclination and defines ship trim from the forward and after draughts.
The relative positions of LCG and LCB create a trimming moment
Longitudinal centre of gravity, LCG, is the combined position of every weight aboard, each multiplied by its longitudinal coordinate. Longitudinal centre of buoyancy, LCB, is the geometric centre of the displaced volume. In static equilibrium, weight and buoyancy must produce no remaining longitudinal moment. If loading places LCG abaft the LCB for the current upright form, the vessel tends to trim by the stern. Rotation reshapes the immersed volume and moves LCB until the buoyant and weight lines of action regain equilibrium. The reverse arrangement tends to produce trim by the bow.
LCB is therefore not a permanently fixed mark, and moving one parcel aft does not merely push the stern down in isolation. A wedge of immersed volume is transferred from one end to the other while displacement stays constant in a pure shift. The MCA stability-booklet method first derives LCG from longitudinal weight moments, then combines it with LCB, LCF, MCT and reference draught at the applicable displacement. Those hydrostatic quantities change with hull form, draught and sometimes trim. Values copied from another vessel—even one of similar length—have no technical basis.
The waterline rotates near LCF and lever arms divide the change between the ends
LCF is the longitudinal centre of flotation, the centroid of the present waterplane area. For a small change, the waterplane can be treated as rotating about a transverse axis through LCF. If LCF is not at the midpoint between perpendiculars, the changes of forward and aft draught are unequal. MCA guidance also notes that calculated trim commonly belongs to the length used in the hydrostatics, usually length between perpendiculars. Draught marks located appreciably away from FP or AP need a further geometric correction before their expected readings can be compared with observation.
Take an illustrative 100-metre LBP with LCF 4 metres abaft amidships: LCF is 54 metres from FP and 46 metres from AP. If stern trim increases by 10 centimetres, small-angle geometry gives a 10 times 54 divided by 100, or 5.4-centimetre, reduction forward and a 10 times 46 divided by 100, or 4.6-centimetre, increase aft. The difference between end draughts grows by exactly 10 centimetres. Their simple average falls by 0.4 centimetre although the vessel has not risen bodily; the apparent mismatch occurs because the equal-displacement rotation point is not the midpoint of the two readings.
MCT 1 cm converts a longitudinal weight moment into change of trim
Moment to change trim one centimetre, written MCT 1 cm or MCTC, is the trimming moment required to change the end-draught difference by one centimetre. Its common unit is tonne-metres per centimetre. Moving 60 tonnes through 20 metres aft creates 1,200 tonne-metres. If MCT 1 cm for that loading condition is 120 tonne-metres per centimetre, the change is 1,200 divided by 120, or 10 centimetres by the stern. Starting from 6.300 metres forward and 6.700 metres aft, the LCF division above gives approximately 6.246 and 6.746 metres.
MCT is not a permanent nameplate constant. It follows from the longitudinal second moment of the waterplane and the vessel's displacement relationship, so it changes with draught, hull geometry and significant trim. The UK Workboat Code calls for intermediate-trim hydrostatic data when the maximum anticipated trim exceeds 0.3 metre so that reasonably accurate interpolation is possible. That requirement exposes the danger of extending one MCT value across a large change. Approved loading software iterates the hydrostatics and checks stability, shear force, bending moment, draught and operational limits together.
Trim changes clearance, freeboard, sight lines and propulsion conditions
The operational question is not whether the sheer line looks level but which limit an altered waterline approaches. Stern trim may increase propeller and rudder immersion, yet reduce after freeboard and deepen the aftermost fixed point. Bow trim may immerse the forebody, change slamming or shipping-water exposure and alter the blind sector ahead of the bridge. MCA manoeuvring information includes propeller immersion, rudder-area ratio, bow and stern profiles and forward and after blind zones for full-load and normal-ballast conditions because flotation state changes visibility and handling inputs.
No universal maxim predicts the net benefit. Optimum resistance trim, propeller ventilation risk, rudder effectiveness, bulbous-bow immersion and shallow-water response differ by hull and speed. Squat can add bodily sinkage and dynamic trim. The Queen Elizabeth 2 grounding investigation described both mechanisms and warned that the trim component could further reduce under-keel clearance. Passage planning therefore uses the predicted dynamic deepest point, not merely static mean draught, and does not assume that adding stern trim always improves manoeuvrability.
Weight shifts, added loads, liquid transfer and flooding require different ledgers
A pure longitudinal shift preserves displacement and suits the w times d divided by MCT exercise. Adding or removing weight produces bodily sinkage or rise as well as trim, so TPC, loading-point moment and LCF must enter together. Transferring liquid between fore and aft tanks also brings tank capacity, pump sequence, free-surface effect and structural loading into the decision. Concentrating cargo at an end can change trim quickly while worsening longitudinal weight distribution and hull-girder bending. A satisfactory pair of end draughts is not by itself proof of an acceptable loading condition.
Unexpected trim can also be evidence of a casualty. The MAIB investigation of Kirsteen Anne connected heavy after loading, reduced after freeboard and water ingress in a reinforcing sequence. A later MAIB safety-digest case described a fishing vessel settling farther by the stern; shifting deck gear forward could not correct it because flooding, not misplaced cargo alone, was increasing displacement aft. Historical experimental sailing adds another scale of evidence: the Viking Ship Museum weighs stone ballast, drinking water, equipment and crew positions on Sea Stallion, adjusting longitudinal balance while avoiding heavy ends that worsen motion. In every period, the useful record identifies each weight, its coordinate and the physical reason for the observed change.
Questions
Continue exploring this subject
What does trim by the stern mean?
It means aft draught exceeds forward draught. Record both end readings and the stated direction because positive and negative sign conventions vary between sources.
What is the difference between trim and list?
Trim compares forward and aft draught and is longitudinal. List or steady heel compares port and starboard immersion and is transverse. Pitch normally describes dynamic longitudinal motion.
How does MCT 1 cm give the change of trim?
Calculate the trimming moment w × d and divide it by MCT 1 cm for the applicable displacement and condition. Then distribute the total difference to FP and AP using their distances from LCF.
Do forward and aft draught each change by half after moving a weight?
Only when LCF is at the midpoint under the chosen simplification. Normally the changes follow the actual distances from LCF, with additional correction when draught marks do not coincide with the perpendiculars.
What is the best trim for a ship?
There is no fleet-wide value. Hull form, displacement, propulsion, steering, visibility, freeboard, strength, stability, resistance, channel and speed all matter; use the vessel's approved data and operating limits.
Sources
Continue the research
- Safety practices related to small fishing vessel stabilityFood and Agriculture Organization
- MCA Stability Information Booklet (MSF 2231)UK Maritime and Coastguard Agency
- Workboat Code Edition 3UK Maritime and Coastguard Agency
- Handbook of Damage Control, Chapter X: Longitudinal stability and trimU.S. Navy via Historic Naval Ships Association
- MGN 301 Amendment 1: Manoeuvring information onboard shipsUK Maritime and Coastguard Agency
- Loss of fishing vessel Kirsteen AnneUK Marine Accident Investigation Branch
- MAIB Safety Digest 2/2015, Case 21UK Marine Accident Investigation Branch
- Why does the Sea Stallion sail with ballast?Viking Ship Museum Roskilde