After discharging cargo a ship rides too high to handle safely, so deck officers take on ballast water to restore an adequate sailing draft. This tool sizes that ballast: it turns the gap between your present and target draft into a tonnage using the vessel’s TPC, then converts that mass to a pumping volume.
How it works
The required mass follows directly from the draft change and the tonnes-per- centimetre immersion, and volume follows from density:
draft change (cm) = (target draft − current draft) × 100
ballast mass (t) = draft change (cm) × TPC
ballast volume (m³) = ballast mass / water densityA positive draft change means you must add ballast to sink the ship; a negative result means you are already deeper than target and would need to deballast. Because mass equals volume times density, dividing the required mass by the ballast water density gives the cubic metres to pump aboard.
Worked example
A ship sitting at 6.20 m mean draft after discharge needs 7.00 m to sail legally in the next port’s harbour entrance channel. The TPC at the working draft is 25 t/cm, and the dock water density is 1.010 t/m³.
draft change = (7.00 − 6.20) × 100 = 80 cm
ballast mass = 80 × 25 = 2,000 tonnes
ballast volume = 2,000 / 1.010 ≈ 1,980 m³The ballasting operation requires approximately 2,000 tonnes of dock water, equivalent to 1,980 m³ to pump into the ballast tanks.
Why water density matters
Fresh water (rivers, freshwater ports) has a density of approximately 1.000 t/m³, whereas open-sea salt water is typically 1.025 t/m³. Dock and harbour water varies between these extremes. The difference of 2.5% matters over large ballast volumes: the same mass of salt water occupies about 2.4% less volume than fresh water, which affects how much tank capacity you need and how long the pumping operation takes.
Entering the correct dock water density also affects TPC accuracy indirectly — TPC itself changes with waterplane area and is read from hydrostatic tables constructed at a standard seawater density. A vessel in fresh water sits slightly deeper for the same displacement, so the tabular TPC may be slightly higher than the effective value.
TPC accuracy over a large draft range
TPC is derived from the waterplane area, which changes as the hull immerses. Over a modest draft change (a metre or less) a single TPC value at the mean working draft gives adequate accuracy. For large ballasting operations spanning several metres of draft, the recommended practice is to apply the mean TPC between the initial and final drafts, or to divide the operation into stages and re-read TPC at each intermediate draft from the hydrostatic tables in the vessel’s stability booklet.
Trim is a separate step
This calculation gives the total ballast mass and volume needed to reach a mean draft. Distributing that ballast across forward, aft, and wing tanks to achieve the desired trim and zero heel is a separate planning step that uses each tank’s longitudinal centre (frame position) and cross-sectional position relative to the ship’s centreline. Most vessels have a loading computer or a stability software tool for the trim and heel optimisation; this tool handles the simpler total-ballast sizing step.