LCB and LCF Explained: Their Role in a Ship’s Stability

LCB (longitudinal center of buoyancy) and LCF (longitudinal center of flotation) are reference points read straight off a ship’s hydrostatic particulars. Together they explain how a vessel trims under a given load and why neither is the same as the center of gravity. This guide covers what each point means, how they differ, and how officers and surveyors apply them.

What Is the Longitudinal Center of Buoyancy (LCB)?

The LCB is the longitudinal position of the centroid of the ship’s underwater volume, measured from a reference point such as the aft perpendicular. It marks where the total upward buoyant force effectively acts. Every draft and trim condition has its own LCB value, tabulated in the hydrostatic particulars.

For an object to float in equilibrium, per Archimedes’ principle, its weight and the buoyant force must act along the same vertical line. That means LCB and the longitudinal center of gravity (LCG) must coincide at any floating condition. If they don’t, the ship trims until they do.

When a ship heels rather than trims, the same buoyant force shifts sideways instead of fore-and-aft. That sideways shift, relative to the center of gravity, produces the ship’s metacentric height. LCB and LCF describe the longitudinal picture; metacentric height describes the transverse one.

LCB is expressed as a distance forward or aft of a stated reference, usually the aft perpendicular or midships. On most hydrostatic tables, it’s given in meters, alongside the corresponding mean draft and displacement. A change in draft moves the underwater volume’s shape, so LCB shifts slightly with every loading condition.

What Is the Longitudinal Center of Flotation (LCF)?

The LCF is the geometric centroid of the ship’s waterplane area at a given draft. It is the point about which the ship trims when weight is added, removed, or shifted. Unlike LCB, it depends only on hull shape at the waterline, not on the underwater volume.

LCF position is usually expressed in the hydrostatic particulars as a distance forward or aft of the after perpendicular, or from midships. Because waterplane shape changes with draft, LCF shifts slightly as a vessel loads deeper or lighter. Ships with fine ends and full midship sections typically show more LCF movement across their draft range than boxier hull forms.

A tanker or bulk carrier with a long parallel midbody tends to keep a fairly stable LCF across its normal draft range. A fine-lined containership or naval hull, with more curvature fore and aft, shows a larger LCF shift between light and loaded conditions. This is one reason hydrostatic tables list LCF at multiple drafts rather than a single fixed figure.

How Do LCB and LCF Differ from LCG?

LCB, LCF, and LCG measure three different things, and confusing them is a common source of calculation errors. LCG is the centroid of the ship’s weight, fixed by how cargo, fuel, and stores are distributed. LCB is the centroid of underwater volume, and LCF is the centroid of waterplane area.

	LCB	LCF	LCG
What it measures	Centroid of underwater volume	Centroid of waterplane area	Centroid of the ship’s weight
Depends on	Underwater hull shape at that draft	Waterplane shape at that draft	Cargo, fuel, and stores distribution
Role	Force-balance point (with LCG)	Geometric pivot point for trim	Set by the current loading condition
Equals LCG at equilibrium?	Always	No requirement	—

At equilibrium, LCB always equals LCG. LCF is different, since it isn’t a force-balance point but a geometric pivot for trim changes. Mixing up LCF with LCG is the most common error officers make when working trim calculations by hand.

Why Do LCB and LCF Matter for a Ship’s Trim?

A ship trims whenever the LCG moves away from directly above the LCB, and it rotates about the LCF while doing so. Load cargo aft of the LCF and the stern goes down; load forward of it and the bow goes down. This is the mechanical link between weight distribution and the trim an officer reads on the draft marks.

This is also why trim by the head or by the stern is defined relative to the LCF, not the ship’s midships. A weight placed exactly at the LCF changes draft evenly, fore and aft, without altering trim at all. That’s the practical test officers use to judge whether a cargo shift will affect trim.

Cargo planning software and manual trim calculations both rely on this relationship. Every tonne loaded or discharged is checked against its distance from the current LCF, not from midships or from the aft perpendicular. Getting that reference point wrong is a common source of trim errors in manual stability calculations.

How Do Officers Use LCB and LCF in Hydrostatic Calculations?

Officers use LCB and LCF together with two other hydrostatic values: TPC (tonnes per centimeter immersion) and MCT1cm (moment to change trim one centimeter). TPC gives the parallel rise or sinkage from adding or removing weight. MCT1cm, combined with the distance of that weight from the LCF, gives the resulting change of trim.

• TPC: tonnes needed to change the mean draft by 1 cm, read at the current waterplane.
• MCT1cm: the trimming moment, in tonne-meters, needed to change trim by 1 cm.
• Distance from LCF: the lever arm between where a weight is loaded and the current LCF position.
• Change of trim = (weight × distance from LCF) ÷ MCT1cm.

A worked example makes this concrete. Say a ship’s MCT1cm is 150 tonne-meters, and 50 tonnes of cargo is loaded 20 meters aft of the LCF. The trimming moment is 50 × 20, or 1,000 tonne-meters, giving a change of trim of roughly 6.7 cm by the stern.

A surveyor doing a draft survey uses LCF the same way. It’s the point hydrostatic tables assume when correcting observed drafts to a true mean draft. Getting it wrong produces a small but real error in the calculated displacement.

Where Do You Find LCB and LCF for a Specific Ship?

LCB and LCF values live in the ship’s approved trim and stability booklet, alongside the hydrostatic curves or tables for that hull. Each is listed against a range of drafts, usually in half-meter or one-meter steps. For any working draft in between, the officer interpolates between the two nearest tabulated values.

Modern loading computers pull these values automatically once a draft or displacement is entered, and interpolate them internally. Even so, officers are expected to know how to read the same figures from the paper tables. Class surveys and cargo-plan checks are often verified by hand.

A stability booklet without current, class-approved hydrostatic data isn’t valid for cargo planning.

These hydrostatic curves come from the naval architect’s calculations at the design stage, then get confirmed against the actual, as-built hull through an inclining experiment. Any later structural change, such as a major conversion or a bulbous bow retrofit, can shift LCB and LCF enough to require updated hydrostatic data. A class society reviews and re-approves the stability booklet whenever that happens.

How Does LCF Affect a Draft Survey?

A draft survey reads drafts at marks placed near the perpendiculars, not at the LCF itself. That offset means the observed mean draft needs a trim correction before it can be converted into an accurate displacement figure. The correction uses the distance between the LCF and midships, together with TPC and the ship’s length between perpendiculars.

The correction grows with both the trim and the offset between LCF and midships. It matters most on a fully loaded ship trimmed well by the stern. Surveyors pull the LCF figure from the current hydrostatic table for the ship’s actual draft, never from a previous survey at a different displacement.

Reusing an outdated LCF value is a quiet, recurring source of error in cargo-quantity disputes.

Do LCB and LCF Change with Loading, Water Density, or Draft?

Both LCB and LCF shift with draft, because both depend on hull shape below or at the waterline. LCF does not shift with water density on its own. Density changes draft, and any LCF movement follows from that new draft, not the density itself.

The same hydrostatic table works in fresh or salt water, as long as the draft used to enter it is correct. TPC and displacement change directly with density, since a ship floats higher in denser water for the same weight. LCF’s position, by contrast, is a geometric property of the waterplane at the ship’s actual draft.

Loading or discharging weight doesn’t move the LCF directly either, since LCF is a function of waterplane geometry, not weight. It only moves indirectly, when the resulting change in draft alters the shape of the waterplane. On most merchant hull forms this shift is small enough over normal operating drafts that a single LCF value is used for quick calculations.

What Happens If a Ship Is Loaded Without Checking LCF?

Ignoring LCF during cargo planning doesn’t cause instability by itself, but it produces trim the plan didn’t predict. A cargo plan built around even keel can still end up trimmed several centimeters by the head or stern. That happens whenever loading isn’t checked against the current LCF.

On a ship close to its maximum permissible drafts, that unplanned trim can push one end past the load line.

Excessive trim by the head also increases the risk of slamming and reduces rudder and propeller immersion aft. That’s a large part of why it’s generally avoided on ocean passages. Checking each parcel’s distance from LCF during planning, before cargo is loaded, catches this early.

When Are LCB and LCF Equal on a Ship?

LCB and LCF coincide only for a hull with vertical, wall-sided topsides and a rectangular waterplane, like a barge or a pontoon. Real ship hull forms taper toward the bow and stern, so LCB and LCF sit at different longitudinal positions almost everywhere else. The gap between them tends to widen on fine-lined, high-speed hull forms and narrow on full-bodied bulk carriers.

What is LCB in ship stability?

LCB is the longitudinal center of buoyancy, the centroid of a ship’s underwater volume at a given draft. It marks where the total buoyant force acts, and at equilibrium it sits directly below the center of gravity.

What is LCF in ship stability?

LCF is the longitudinal center of flotation, the centroid of the ship’s waterplane area. It’s the point about which the ship trims when weight is added, removed, or shifted longitudinally.

What is the difference between LCB and LCF?

LCB is based on underwater volume and must equal the center of gravity at equilibrium. LCF is based on waterplane area and serves as the pivot point for trim, with no requirement to match either LCB or LCG.

Does LCF change with water density?

Not directly. Density changes the ship’s draft for a given displacement, and any shift in LCF follows from that change in draft, not from the density itself.

When are LCB and LCF equal on a ship?

Only on hull forms with vertical sides and a rectangular waterplane, such as barges or pontoons. On tapered ship hulls, LCB and LCF sit at different positions along the length.

Does LCF change when a ship is loaded or discharged?

Only indirectly. Loading or discharging cargo changes the ship’s draft, and that new draft can bring a slightly different waterplane shape and LCF position with it.

What is MCT1cm and how does it relate to LCF?

MCT1cm is the moment, in tonne-meters, needed to change a ship’s trim by one centimeter. It’s applied together with a weight’s distance from the LCF to calculate the resulting change of trim.