Draft Survey · Explainer
Trim Correction in a Draft Survey: First, Second and the Sign Errors
Why a draft survey needs two trim corrections, how each one is calculated, and how a sign convention applied the wrong way quietly moves the cargo figure.
Draft Survey · Knowledge Note
What Is TPC in a Draft Survey?
TPC is the weight needed to change a vessel's mean draft by one centimetre. What it means, how it is derived, and where the figure is used on board.
In short
TPC — tonnes per centimetre immersion — is the weight that must be added or removed to change a vessel's mean draft by one centimetre at a given draft. It comes from the waterplane area and the water density, and in a draft survey it converts a difference in draft into a difference in weight.
Key points
- TPC depends on waterplane area and water density, so it changes with draft and with the water the vessel is floating in.
- It is read from the hydrostatic particulars at the quarter mean, alongside displacement.
- It converts the first trim correction from a draft difference into tonnes.
- Tabulated TPC assumes the table's density; in fresh water the true value is about 2.5% lower.
Pending technical review
The following statements have not yet been cleared by a named technical reviewer. Treat them as provisional and verify against the primary source before relying on them.
- The 2.5% figure for the difference between TPC in salt water at 1.025 t/m³ and fresh water at 1.000 t/m³ is arithmetic from the definition rather than a sourced value, and assumes the particulars are tabulated at 1.025.
TPC is tonnes per centimetre immersion: the weight that changes the vessel’s mean draft by one centimetre at a given draft.
Where it comes from
Adding weight increases the immersed volume. If the draft changes by a small enough amount that the hull sides can be treated as vertical over that distance, the added volume is the waterplane area multiplied by the change in draft.
TPC = (A_w × ρ) / 100where A_w is the waterplane area in square metres and ρ is the water density in tonnes per cubic metre. The 100 converts one centimetre into metres.
So a vessel with a waterplane area of 6,050 m² in water of 1.025 t/m³ has a TPC of about 62 t/cm.
Two things follow directly from the definition:
- TPC increases with draft, because the waterplane area of a typical hull grows as it becomes more deeply immersed. It is tabulated against draft for that reason.
- TPC depends on the water, because density is in the expression. The tabulated figure assumes the density the particulars were computed for.
Where it is used
Two places.
The first trim correction. The correction works out how much deeper or shallower the vessel is floating at her LCF than the quarter mean suggests, and TPC turns that draft difference into tonnes:
First trim correction (t) = (Trim × d_LCF × TPC × 100) / LBPSanity-checking a discrepancy. When a calculated figure and an expected one differ, dividing the difference by TPC converts it into centimetres of draft. That is the quickest way to tell whether a discrepancy is plausibly a draft-reading error. A 500 tonne difference at 62 t/cm is about 8 cm of draft — far more than a careful reading would be out by, so the problem is somewhere else, most likely in the deductibles.
The density trap
If the particulars tabulate TPC for 1.025 t/m³ and the vessel is lying in fresh water at 1.000 t/m³, the true TPC is lower in the ratio of the densities — roughly 2.5% lower. The tabulated figure over-states how much weight one centimetre of draft represents.
Within the first trim correction the effect is second order and usually immaterial. Where TPC is used directly to convert a weight into a draft change — loading the last parcel to hit a target draft, for instance — it is worth correcting for.
Related
TPC is one of three figures read from the particulars at the quarter mean, the others being MCTC and the LCF position. All three are used in trim correction, and they sit inside the full survey procedure.
This article has not yet been signed off by a named technical reviewer. Written and maintained by SurveyEra Editorial. Corrections: report an error.
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