Inclining Experiment and Lightship Verification Project

This project produces an inclining-experiment and lightship verification package for a small vessel after construction changes. The objective is to determine whether the vessel’s measured displacement and vertical center of gravity are consistent with the stability documentation used for operation.

An inclining experiment is not only a calculation of metacentric height. It is a controlled measurement exercise. Draft readings, water density, loose weights, slack tanks, mooring forces, wind, pendulum geometry, test-weight positions, and onboard condition all affect the result.

Project Objective

Plan, execute, and reduce a simplified inclining experiment for a workboat after a deck-crane upgrade and machinery-room modification.

The deliverable must include:

• test condition and exclusions;
• draft, trim, and water-density correction;
• test-weight shift log;
• pendulum readings and heel angles;
• observed metacentric height;
• free-surface correction;
• updated lightship KG;
• comparison with design estimate;
• uncertainty and acceptance statement;
• handover actions for the stability booklet or loading computer.

Test Boundary

Use this representative vessel condition:

Quantity	Value
vessel type	small workboat
hydrostatic displacement from draft curves at reference density	522.5\ \text{t}
reference seawater density	1.025\ \text{t/m}^3
measured harbor water density	1.020\ \text{t/m}^3
hydrostatic transverse metacentric height reference	use KM_T from curves
KM_T at test displacement	5.20\ \text{m}
design lightship displacement estimate	512\ \text{t}
design lightship KG estimate	3.66\ \text{m}
residual free-surface correction	0.06\ \text{m}

The experiment uses movable test weights. Tanks are either pressed full, empty, or documented. Loose gear is secured or removed. Mooring lines are slack enough not to restrain heel, and wind conditions are recorded.

Acceptance Criteria

Use these acceptance criteria for the project review:

Check	Acceptance criterion
difference between measured and estimated lightship displacement	\le 2.0\% or engineering disposition
difference between measured and estimated KG	\le 0.10\ \text{m} or stability model update
pendulum repeatability	readings within 5\ \text{mm} for repeated equivalent shifts
heel angle range	large enough for measurement, small enough for small-angle assumptions
free-surface state	controlled, documented, and corrected
final evidence	sufficient for stability documentation update

These criteria are project screening values. Real vessel acceptance must follow the applicable class, flag, owner, and regulatory procedure.

Step 1: Correct Displacement for Water Density

The draft readings are reduced using hydrostatic curves prepared for reference seawater density:

The curve gives:

The measured harbor density is:

Correct the displacement:

Use:

Engineering Comment

Density correction matters because the same draft does not imply the same displacement in fresh, brackish, and seawater. A small density error can become a significant weight error when the vessel displacement is large.

Step 2: Record Weight Shift and Pendulum Data

Use one test weight:

The transverse shift distance is:

Pendulum length:

Recorded deflections for equivalent port and starboard shifts are:

Run	Deflection
1	72\ \text{mm}
2	75\ \text{mm}
3	73\ \text{mm}
4	74\ \text{mm}

Average deflection:

Convert to meters:

For small heel angles:

Therefore:

Engineering Comment

The repeated readings are close enough for a screening reduction. If port and starboard results were asymmetric, the team would investigate mooring restraint, wind, hull contact, pendulum friction, loose liquid, or a test-weight position error before accepting the data.

Step 3: Calculate Observed GM

The inclining moment is:

For a small heel angle:

Substitute the measured values:

Engineering Comment

This is the observed metacentric height under the test condition. It reflects the vessel, the test loading, and any free-surface effects present during the experiment. It is not yet the clean lightship vertical center of gravity.

Step 4: Apply Free-Surface Correction

A residual slack tank cannot be fully pressed or emptied for the test. Its calculated free-surface correction is:

The solid-condition metacentric height is:

Engineering Comment

Free surface reduces observed stability. When deriving the vessel’s solid-condition lightship KG, the correction is added back to the observed GM. For loading-condition checks with slack tanks, the correction is subtracted from the uncorrected GM of that condition.

Step 5: Derive Lightship KG

From the hydrostatic curves at the corrected test displacement:

The relationship is:

Therefore:

The measured lightship vertical center of gravity is:

Engineering Comment

The result is a vessel property only if the test condition has been reduced correctly. Temporary loads, missing stores, unrecorded tools, trapped water, and onboard personnel must be accounted for in the lightship correction.

Step 6: Compare with Design Estimate

Measured displacement:

Design estimate:

Difference:

Percent difference:

Measured KG:

Design KG estimate:

Difference:

Both differences are within the project screening criteria:

Engineering Comment

The measured vessel is heavier and has a slightly higher KG than the design estimate. The difference is small enough to accept after engineering review, but the stability documentation should use the measured values rather than the older estimate.

Step 7: Check Measurement Uncertainty

Assume pendulum deflection uncertainty:

Relative deflection uncertainty:

Because:

the deflection contribution to relative GM uncertainty is approximately:

For:

the deflection-related uncertainty is:

Use a rounded screening uncertainty:

Engineering Comment

This is not a full uncertainty budget. A formal reduction should also consider weight calibration, shift distance, draft readings, water density, hydrostatic interpolation, tank state, mooring restraint, wind, and pendulum alignment. The simple check shows that the KG margin is not dominated by one unreadable pendulum measurement.

Failure Modes to Control

Failure mode	Effect on result	Control
slack tank not corrected	KG appears too low or too high depending on reduction method	tank status log and free-surface correction
mooring line restrains heel	measured deflection is too small, GM appears too high	slack mooring check and repeat shifts
test weight position error	inclining moment is wrong	marked deck positions and survey measurement
wind gust during reading	inconsistent pendulum data	weather limit and repeated readings
unrecorded onboard weights	lightship displacement and KG are biased	weight survey and removal/addition log
wrong water density	displacement is biased	hydrometer or density measurement record

Handover Package

The final deliverable should contain:

1. vessel identification, test date, location, weather, water density, and responsible engineer;
2. test condition drawing or table showing all onboard weights and tank states;
3. draft readings, trim, hydrostatic interpolation, and density correction;
4. test-weight certification and measured shift distances;
5. pendulum geometry, raw readings, averaged deflections, and heel calculation;
6. observed GM, free-surface correction, corrected GM, and derived KG;
7. comparison with design lightship estimate and disposition of differences;
8. uncertainty notes and rejected readings, if any;
9. stability-booklet or loading-computer update requirement;
10. sign-off by naval architecture, operations, and owner or class representative as applicable.

Decision

The project result is acceptable for the screening criteria:

• displacement difference is below 2 percent;
• KG difference is below 0.10 m;
• pendulum readings are repeatable;
• free-surface correction is documented;
• measured values should replace the design estimate in the stability record.

The vessel should not rely on the older lightship estimate after the modification. The correct engineering action is to update the stability documentation with the measured displacement and KG, preserve the inclining evidence, and require a new review after any future modification that changes weight, vertical center of gravity, tank configuration, or operating envelope.