The Tonnes You Signed For: Soundings, Density and the ROB Ledger

Bunkering, the trade will tell you, has two halves: quantity is the paperwork half, quality the technical half. The chief signed for 1,162.0 tonnes, the note went into the file, and the interesting arguments start weeks later when the laboratory report arrives. That figure is not a measurement of anything: it is an arithmetic product of a sounding read against somebody else's tank table, a temperature nobody on your side took, and a density the seller declared, and this lesson prices all three on one stem.

Which is worth doing, because the cheapest bunker decision on this ship is made with a pen before the barge arrives, and the dearest with a lawyer after the engine stops. This course walks from one to the other, starting with the tonnes, because every claim you might bring and every performance figure your office builds rests on a number made in a few minutes at a manifold.

The chain that makes a tonne

Take one stem and follow it. The barge's opening sounding is 11.60 m, which reads 1,468.0 m³ against her calibrated tank table, the certified list turning a depth of liquid in that tank into a volume. The closing sounding is 2.40 m, or 272.0 m³. Both are corrected for the barge's trim and list first, because a tank read while she sits down by the stern is not the tank the table describes. The difference, 1,196.0 m³, is the gross observed volume: the space the fuel occupied, at the temperature it happened to be, here 48 °C.

Volume at 48 °C is not volume at 15 °C, and the trade sells at 15 °C, so it is scaled by a volume correction factor. Worked as a straight line, 1 less 0.00038 times the 33 degrees of difference gives 0.98746, and 1,196.0 m³ becomes 1,181.0 m³ at 15 °C. That line is a teaching approximation, good for the shape of the correction and not good enough to put in a claim. A surveyor never computes the factor: he reads it out of the petroleum measurement tables, ASTM D1250 and ISO 91:2017, against density at 15 °C and observed temperature, as this worked bunker survey calculation (open) does table by table.

Then the mass. Multiply 1,181.0 m³ by the seller's declared density of 985.0 kg/m³, less the 1.1 kg/m³ air-buoyancy correction that turns a mass in vacuum into the weight in air the trade invoices, so 983.9, and you get 1,161,986 kg. The note reads 1,162.0 tonnes. Notice what it therefore is: under BIMCO Bunker Terms 2018 the receipt warrants the delivered quantity in volume units, the density at 15 °C and the delivery temperature. The seller warrants the ingredients. The tonnes are your arithmetic.

Where the chain breaks

Three of its links move real money on an ordinary stem.

The sounding. Between the two soundings this barge tank holds 130 m³ per metre: 1,196.0 m³ over 9.2 m of depth. Five centimetres of honest disagreement on the closing sounding, a tape read against a swell by two tired people, is 6.5 m³, and through the same chain 6.3 tonnes, about 3,500 USD at 550 USD/t. Nobody has cheated, which is why a surveyor sounds both sides and applies trim and list rather than taking one figure from one side of one tank.

The temperature. Now delete the correction, which is what a hurried tally at three in the morning does. The same 1,196.0 m³ times 983.9 kg/m³ is 1,176.7 tonnes: about 14.8 tonnes more than the corrected figure, 8,100 USD, and not one kilogram of fuel moved to create them. Ranked by money this is the largest of the three, and the only one that costs nothing to prevent: either the correction was made, or it was not.

The density. The note used 985.0 kg/m³ because that is what the seller declared. The laboratory, testing your manifold sample, returns 979.0. Six kilograms per cubic metre is 0.61 per cent of 985.0, and across 1,181.0 m³ that is 7,086 kg: 7.09 tonnes, 3,897 USD. Two rules, one general and one local. Generally, a declared density half a per cent above the tested one is half a per cent of tonnes that never existed. On this stem, every kilogram per cubic metre of declared density is 1.18 tonnes on the invoice.

This is density's third job, and the one nobody teaches. The first is energy, where density is the largest term in the specific-energy calculation: lesson 4. The second is separation, which belongs to our course Marine Engineering & Main Engines and its lesson "Fuel Quality: What Actually Arrives in the Bunker Tank", where the 991 kg/m³ ceiling and the separator train are taught. Neither is re-taught here. The third job is the multiplier that turns cubic metres into invoiced tonnes, and it is the only one of the three where the figure that counts is the one the seller wrote down.

The cappuccino effect

There is a fourth way a sounding goes wrong, and it is not honest. Blow compressed air into the fuel and it froths. Aerated fuel occupies more space than the fuel in it, so the level rises, the sounding agrees with the paperwork, the note is signed, and hours later the air comes out of suspension and the level falls back. The surveyors behind the bulletin Cappuccino Bunkers (free PDF) describe it exactly so, a frothing caused by compressed air blown through the delivery hose, and report being called to the next port to explain 30 to 40 tonnes that vanished overnight.

The tells are physical, and the bulletin lists them: froth on the barge tanks at the opening gauge, bubbles on the sounding tape before, during and after the delivery, a hose that jerks or whips about, a delivery rate slower than agreed, a gurgling at the manifold, a pressure gauge that will not settle. It adds that hose jerking, and superficial bubbles after line blowing or tank stripping, are common and not on their own evidence of malpractice: this is a suspicion built from several signs at once. Mass metering removes the argument altogether, which is lesson 2.

This is why surveyors exist. The UK Defence Club's guide Bunkers: a guide to quality and quantity claims (free PDF) puts the job in a sentence: a competent member of the crew attends the barge before and after the delivery to sound or ullage the tanks, take temperatures, establish her trim and use the calibration tables to determine volumes. All the tanks, not the ones the barge crew nominate. The Club's own case file says why: a crew was persuaded to measure only the tanks the fuel came from; the closing figures were 40 tonnes adrift of the ship's; the barge sailed before a surveyor arrived; and the supplier, relying on a term making its own figures binding, pursued the owner for 40 tonnes never received.

The ROB ledger

All of that produces one number, and that number goes into a ledger. Opening ROB, the fuel remaining on board, plus delivered, less consumed, equals closing ROB: four quantities, three measured imperfectly and one a residual, and the residual is the number nobody owns.

If the delivered figure is 7 tonnes optimistic, the ledger reports no error. It reports 7 tonnes the ship must now appear to burn, and they surface somewhere: a consumption a little high, a closing ROB a little low, an argument at redelivery. Unexplained ROB drift poisons everything built on it, because everything built on it assumes it.

What happens to the number afterwards is not this lesson's ground. The reconciliation of the noon fuel figure against the flow meters, and the unit slip in which cubic metres are logged as tonnes, belong to our course Fleet Data & Performance Monitoring and its lesson "The Onboard Data Landscape: Noon Reports and Autologging". Traceability back to the sounding is owned by our course The Road to Efficiency in "Data Quality Is the Ultimate Form of Compliance". This lesson owns the creation of the number, not its handling. One consequence follows: the tonne you did not receive but signed for is also a tonne you will report, because three regulatory ledgers count tonnes and multiply them by a factor, which is the territory of our course Compliance Calculations & Life-Cycle Emissions.

So the decision, taken while the hoses are still connected. Name which of the three inputs you are contesting and with what evidence: the sounding, whether both sides were read and trim and list applied; the temperature, whether the correction was made at all; the density, whose figure it is. Then write it down. Under BIMCO Bunker Terms 2018 a quantity dispute must be noted at the time of delivery under sub-clause 6(c), as a remark on the delivery note or a separate letter of protest acknowledged in writing by the seller's representative, and the claim must reach the seller in writing within fourteen days. Miss either and the contract treats the claim as given up and barred. That letter is the only instrument that survives the hoses being disconnected. The one argument you cannot win on paper is about volume itself, and there is a machine that settles it by weighing the fuel: Singapore made it compulsory in 2017, Rotterdam and Antwerp-Bruges in 2026, which is where lesson 2 begins.