Knowledge / Maritime cargo

Draught surveys: from draught readings to cargo mass and uncertainty

Separate density, tank quantities, sign conventions and uncertainty when estimating bulk-cargo mass from displacement change.

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A draught survey estimates cargo quantity from changes in a vessel's displacement rather than weighing the cargo directly. Its strength is the ability to assess large shipments; its difficulty is separating every non-cargo mass change within the same calculation. Writing more decimal places in a draught reading does not improve the answer if water density or ballast quantity is wrong.

Begin with the mass balance

Let corrected displacements before and after loading be Δ1 and Δ2. Let separately assessed ballast, fuel, fresh water and other variable non-cargo masses be D1 and D2. Cargo increase is C = (Δ2 − D2) − (Δ1 − D1). Lightship and genuinely unchanged constants cancel in the difference. A changing item treated as constant becomes an error in cargo quantity.

UK P&I Club's 2023 draught-survey chapter explains correcting displacement differences for variable shipboard masses. It is professional practice guidance, not a guarantee of a particular accuracy under all conditions or a legal resolution of a commercial dispute.

A draught reading is not yet a hydrostatic condition

Port and starboard readings forward, amidships and aft contain different information about heel, trim and hull deflection. One average does not automatically eliminate all these effects. The positions of marks relative to perpendiculars and the reference conventions in the hydrostatic tables must be known. A mark-to-perpendicular correction translates a local reading to the hydrostatic reference position; a trim correction accounts for the immersed-volume relationship differing from the reference even-keel condition. LCF is the longitudinal centre of flotation, the longitudinal position of the waterplane centroid. Misinterpreting the vessel tables' LCF sign can make apparently correct arithmetic produce an incorrect correction.

A vessel stationary in a current still experiences water flow relative to its hull, so the observed level may not represent ideal static hydrostatics. Waves, viewing angle and mark visibility also matter. A sophisticated formula cannot recover missing condition information. Corrections should be consistent with the vessel's approved hydrostatic information and the accepted survey method.

Density and hydrometer type

If hydrostatic tables give displacement at a reference density, the actual mass associated with the same immersed volume changes with actual water density. A simplified relation is Δ actual = Δ table × ρ actual / ρ reference. Sampling location, depth and timing can matter because of stratification and tidal changes alongside.

Density, relative density and corrections associated with apparent weighing in air are not interchangeable concepts. Adding a fixed correction without knowing the hydrometer scale and calibration temperature is unsuitable. UNECE's official overview identifies the harmonisation purpose of its 1992 coal-cargo draught-survey code. The existence of that code does not justify combining instrument readings without understanding their definitions.

Cargo quantity and sensitivity examples

For a wholly hypothetical loading, assume initial displacement after all hydrostatic and density corrections is 18,000 t and initial variable non-cargo mass is 6,000 t. If the final values are 50,000 t and 5,000 t, cargo increase is (50,000 − 5,000) − (18,000 − 6,000) = 33,000 t. Looking only at displacement change gives 32,000 t, missing the 1,000 t reduction in non-cargo mass during loading.

In a separate sensitivity example, assume a tabulated displacement of 50,000 t at reference density 1.025 t/m³. A density change of 0.001 t/m³ changes mass at the same immersed volume by approximately 50,000 × 0.001 / 1.025 = 48.8 t. TPC means tonnes per centimetre immersion for a parallel sinkage at the stated condition. In another condition with local TPC of 30 t/cm, a 0.5 cm error in mean draught corresponds to approximately 15 t. These are small-change sensitivities, not the error of the whole survey or acceptance tolerances.

Errors hidden in ballast and fuel quantities

Tank volume depends on matching a sounding or ullage to the applicable trim and heel table. Even a correct volume gives the wrong mass if density is wrong. Fuel, ballast and fresh water cannot share one assumed density. Part-filled tanks, liquid remaining in pipes or an undocumented transfer can compromise comparison between initial and final conditions.

A command to empty a tank does not establish that no measurable liquid remains. Timing matters too: draughts read at one time and tanks measured at another while transfer continues may not represent one physical condition. When the inferred ship's constant is unexpected, inventory, signs and measurements should be reassessed rather than forcing the result to match a historical value.

Report uncertainty as part of the result

NIST's uncertainty-propagation explanation accounts for sensitivity coefficients and covariance together. Initial and final measurements may share instruments, tables or assumptions. Treating every source as independent, or assuming every error cancels in subtraction, is therefore unjustified without evidence.

For an illustrative independent-input calculation only, let standard uncertainties in Δ1, Δ2, D1 and D2 be 25, 40, 30 and 30 t respectively. The root sum of squares gives a combined standard uncertainty of approximately 63.4 t. This is not a worst-case bound or automatically a 95-percent interval. The report should explain measurement conditions, corrections, density definitions and uncertainty scope. Extra decimal places cannot replace that explanation.

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