Case study
Ballast Free-Surface GM Loss Case Study
Naval engineering case study on ballast free-surface effect, slack tanks, corrected metacentric height, heel response, roll-period change, ballast sequencing, and validation evidence.
A vessel can lose a large part of its initial stability without taking on more weight. The mechanism is free-surface effect: liquid in partly filled tanks shifts as the vessel heels, creating a heeling moment and reducing effective metacentric height. The problem is operational as well as hydrostatic. A loading plan may be acceptable when tanks are pressed full or empty, then become unsafe when several tanks are left slack during transfer.
This case study follows an offshore support vessel preparing for departure after ballast transfer. The loading computer initially shows acceptable stability, but the tank status in the calculation does not match the actual soundings. Three ballast tanks are slack. Correcting for free surface reduces the effective GM enough to require an operational hold.
The case is a screening calculation for engineering judgement. Final vessel decisions must follow the approved stability booklet, loading software, class rules, flag requirements, and company operating procedures.
Case Context
The vessel has completed cargo loading and is trimming for departure. Ballast has been shifted to improve propeller immersion and forward draft. A watch officer notes that the loading computer still shows the port and starboard wing tanks as pressed, but manual soundings indicate they are about half full.
| Item | Value |
|---|---|
| Displacement mass | \Delta=8000\ \text{t} |
| Uncorrected metacentric height | GM=0.85\ \text{m} |
| Minimum operating GM used for departure screen | 0.35\ \text{m} |
| Beam used for roll-radius estimate | B=20\ \text{m} |
| Roll radius of gyration estimate | k=0.38B=7.6\ \text{m} |
| Operational transverse heeling moment | M_H=320\ \text{t m} |
| Departure heel-screen limit | 8^\circ |
| Actual tank state | three ballast tanks slack |
The transverse heeling moment represents a combined small-angle screen for wind, minor cargo offset, and operational asymmetry. It is not a substitute for a full righting-arm curve or weather criterion.
Field Evidence
The issue is discovered before departure because the loading records do not agree:
| Evidence | Engineering interpretation |
|---|---|
| remote level trend shows two wing tanks between 45 percent and 55 percent | tanks are slack, not pressed |
| manual sounding confirms the remote level trend | the level signal is credible |
| ballast valve lineup shows a transfer was stopped mid-sequence | procedural interruption created multiple slack tanks |
| loading computer status still marks tanks as pressed | model state is wrong |
| vessel roll feels slow during berth movement | low effective GM is plausible |
| no structural overload or flooding alarm is present | problem is stability margin, not hull damage |
The most important finding is the mismatch between actual tank condition and the stability model. A stability calculation with the wrong tank state can be worse than no calculation because it creates false confidence.
Free-Surface Correction
The loading computer gives uncorrected:
The actual slack tanks have free-surface corrections:
| Slack tank | Free-surface correction |
|---|---|
| port wing ballast tank | FSC_1=0.31\ \text{m} |
| starboard wing ballast tank | FSC_2=0.24\ \text{m} |
| forepeak ballast tank | FSC_3=0.15\ \text{m} |
Total correction:
Corrected metacentric height:
The corrected value is positive, but it is far below the departure screening minimum:
This is enough to stop departure. A positive GM is not the same as an acceptable loading condition.
Heeling Response Screen
For a small-angle screen, use:
Solving for heel angle:
With the corrected GM:
Therefore:
The estimated heel exceeds the departure screen:
If the original uncorrected GM had been used, the same heeling moment would give:
That difference explains why the tank-state error matters. The vessel did not become heavy; it became tender because the liquid was free to shift.
Roll-Period Screen
A simplified roll-period estimate is:
Using:
and corrected:
gives:
This is only a screening estimate, but it is consistent with a tender vessel. A very long roll period can be a warning sign when it appears after a ballast transfer and is not part of the planned loading condition.
The same estimate with uncorrected GM=0.85\ \text{m} gives:
Roll period alone is not a stability approval method, but the change reinforces the free-surface diagnosis.
Engineering Decision
The vessel should not depart in the actual tank condition. The engineering decision is:
Hold departure, restrict nonessential deck operations, correct the loading computer tank states, press or empty the slack ballast tanks according to the approved sequence, and release the vessel only after soundings, valve lineup, loading software, and stability criteria agree.
Immediate controls:
- stop ballast transfer until the officer, chief engineer, and master agree on the current tank state;
- enter actual tank soundings into the loading computer;
- avoid additional transverse cargo or crane operations while GM_{corr} is low;
- press up or empty tanks in a sequence that avoids creating more slack tanks;
- maintain port-starboard symmetry unless the stability plan explicitly approves otherwise;
- record final soundings and valve positions before removing the hold.
The operational issue is not solved by “adding more ballast” in a generic sense. Ballast placement and tank fill state decide whether the correction improves or worsens stability.
Corrective Ballast Sequence
The approved correction is to press up the two wing tanks and empty the forepeak to the required departure state. After completion, only a small service tank remains slack.
Corrected free-surface state:
| Tank condition after correction | Free-surface correction |
|---|---|
| port wing ballast tank pressed | 0.00\ \text{m} |
| starboard wing ballast tank pressed | 0.00\ \text{m} |
| forepeak ballast tank emptied | 0.00\ \text{m} |
| service tank slack | 0.12\ \text{m} |
New total correction:
New corrected metacentric height:
Heeling response under the same operational moment:
Roll-period screen:
The corrected condition restores margin for the departure screen. The loading computer must still confirm all applicable criteria, including trim, draft, freeboard, downflooding, longitudinal strength, and any route or weather limits.
Validation Evidence
Release should require evidence, not only an instruction that tanks were corrected.
| Evidence | Acceptance purpose |
|---|---|
| manual soundings for affected tanks | confirms actual liquid levels |
| remote level trend | confirms sensors agree with soundings |
| valve lineup record | confirms transfer path is closed and stable |
| loading-computer printout or controlled electronic record | confirms corrected tank state and stability criteria |
| total free-surface correction register | makes slack-tank contribution visible |
| departure draft and trim readings | confirms the loading model matches the vessel |
| master/chief engineer sign-off | assigns operational responsibility for release |
If any of these disagree, the vessel remains in a restricted state. A single loading-computer green status is not enough when the inputs are uncertain.
Uncertainty Check
Assume the uncorrected GM has uncertainty:
and the combined free-surface correction has uncertainty:
Combined uncertainty in corrected GM is:
The estimated corrected GM before action is:
The lower bound is:
The condition is not close to the departure requirement in a useful way. It is below the screening minimum even before considering uncertainty, and the uncertainty shows that the real condition could be extremely tender. The correct decision is operational hold and correction, not debate over a few centimetres of GM.
Risk Screen
A risk-priority-number screen helps document the operational hold:
Before correction:
Severity is high because low effective stability can lead to excessive heel, downflooding exposure, cargo movement, or loss of operational control. Occurrence is moderate because interrupted ballast transfers are credible. Detection is weak because the loading computer can look acceptable when tank states are wrong.
After corrected ballasting, tank-state verification, and release controls:
The severity of a future recurrence remains high, but the occurrence and detection scores improve when slack-tank combinations are controlled and recorded.
Lessons for Marine Operations
The transferable lessons are:
- Free-surface effect is an operational condition, not only a design note.
- Several modest slack tanks can remove most of the usable GM margin.
- Loading software is only as reliable as the tank states entered into it.
- Roll-period observations can support diagnosis but cannot replace stability criteria.
- Release after ballast correction requires soundings, valve lineup, loading records, and sign-off.
The engineering decision is to treat tank state as a stability-critical configuration. A vessel should depart only when the actual ballast condition and the approved stability model describe the same vessel.