About this calculator
Every tonne loaded makes the ship sink a little (sinkage) and, unless it is placed right above the centre of flotation (LCF), also changes the trim. Officers and planners work this out again and again: is the aft draft still within the channel limit, will the ship trim by the head once the forward hold is full, or where must the remaining cargo go to finish on even keel?
This calculator uses three figures from the hydrostatic table at the ship's mean draft: TPC (tonnes per centimetre immersion), MTC (moment to change trim 1 cm, t·m/cm) and LCF (longitudinal centre of flotation measured from the aft perpendicular). Sinkage = Σ weight ÷ TPC. Trimming moment = Σ weight × (position − LCF); cargo forward of the LCF trims the ship by the head, and change of trim = moment ÷ MTC. The change of trim is shared between the ends in proportion to their distance from the LCF: the aft draft changes by trim × LCF ÷ LBP, the forward draft by the rest.
You can enter several load, discharge and shift lines at once. The calculator also shows the position where extra cargo does not change the aft draft (or the forward draft) — the classic trick when the ship is already at its aft draft limit. The formulas are accurate for small changes (usually below ±25 cm of sinkage); for large changes, repeat with TPC/MTC/LCF at the new draft.
Worked example
Ship LBP 100 m, forward draft 5.00 m, aft 5.60 m, TPC 15 t/cm, MTC 120 t·m/cm, LCF 48 m from AP. Load 150 t at 80 m from AP:
- Sinkage = 150 ÷ 15 = 10 cm
- Moment = 150 × (80 − 48) = 4,800 t·m forward → change of trim 4,800 ÷ 120 = 40 cm by the head
- Aft: 10 − 40 × 48/100 = −9.2 cm → 5.508 m; forward: 10 + 40 × 52/100 = +30.8 cm → 5.308 m
- Final trim 0.20 m by the stern; position that keeps the aft draft unchanged: 48 + 120 × 100 ÷ (15 × 48) = 64.67 m from AP
How to use it
Enter ship data
Enter LBP, the current forward and aft drafts, then TPC, MTC and LCF from the hydrostatic table at the mean draft.
Add weight lines
For each load/discharge enter weight and LCG (metres from the aft perpendicular); for a shift enter the from and to positions.
Read the new drafts
See sinkage, change of trim, new forward/aft drafts and the trim sketch, updated as you type.
Find the neutral position
Use the "aft draft unchanged" position to place extra cargo without increasing the aft draft.