TPC (Tonnes Per Centimetre Immersion) is the weight of cargo, in tonnes, required to change a vessel’s mean draft by exactly one centimetre at a given waterline.
The Actual Formula
TPC = (A × ρ) / 100
Where:
- A = waterplane area (the area of the ship’s cross-section at the current waterline, in square meters)
- ρ (rho) = density of the water the vessel is floating in (1.025 t/m³ for seawater, 1.000 t/m³ for fresh water)
The division by 100 converts from meters to centimeters for the 1cm draft change reference.
Why Waterplane Area Is the Key Variable
TPC depends directly on waterplane area because a wider ship (or one with more hull area at the waterline) requires more weight to sink it the same 1cm, compared to a narrower vessel — more waterplane area means more buoyant support spread over more surface, so the same added weight produces a smaller draft change.
Practical Use: Calculating Cargo Weight for a Target Draft
TPC is used directly in everyday cargo planning — if a Chief Officer needs to increase draft by a specific amount (say, to reach a target load line), multiplying the desired draft change (in cm) by the vessel’s TPC gives the approximate cargo weight needed to achieve it.
Example logic: If TPC = 25 tonnes/cm, and you need to increase draft by 10cm, you’d load approximately 250 tonnes (25 × 10) to achieve that change — a real, practical calculation used during loading operations, not just an exam formula.
TPC Changes With Draft
Since waterplane area itself can change somewhat as draft changes (depending on hull shape), TPC isn’t necessarily identical at every draft — vessel-specific hydrostatic tables (in the stability booklet) provide the correct TPC value for the vessel’s actual current draft, rather than using a single fixed number throughout the entire loading range.
Freshwater vs Saltwater TPC
Since TPC depends on water density, the same vessel has a different TPC in freshwater versus saltwater — genuinely relevant when loading in a freshwater port versus a seawater port, and factored into related concepts like Fresh Water Allowance (FWA).
Exam Relevance
TPC’s correct formula, its practical use in loading calculations, and its relationship to waterplane area are core, heavily-tested Ship Stability topics in deck officer competency exams.