Buoyancy and the load line

A floating ship pushes aside its own mass of water (Archimedes). Its displacement is that mass. The heavier the load, the deeper it floats. The load line painted on its side marks how deep it may legally go, in each season and in each kind of water.

The ship

Length L Breadth B Summer draught T Block coefficient C_B Waterplane coeff. C_W Water density

The arithmetic

The block coefficient C_B says how much of the box L × B × T the hull fills (about 0.8 for a tanker, 0.6 for a fast container ship); C_W does the same for the waterplane. With sea water at 1.025 t/m³:

TPC, tonnes per centimetre immersion, is the load that sinks the ship one centimetre deeper. The fresh water allowance is how much deeper the same ship floats in fresh water (density 1.000) than in the sea: for a wall-sided hull it comes to exactly 1/40 of the draught, because fresh water is 1/40 less dense. In dock water between the two densities the allowance is taken in proportion (Convention, article 12).

The marks

The deck line marks the freeboard deck. Below it, by the assigned summer freeboard, the centre of the ring (300 mm across, 25 mm wide) sits at the summer load line, with a 450 mm bar whose upper edge runs through its centre. Beside it, lines 230 mm long mark the other load lines. The upper edge of each line is the limit. Tropical (T) is 1/48 of the summer draught above summer (S), winter (W) the same below, and Winter North Atlantic (WNA), only for ships of 100 m or less, 50 mm below winter. The fresh-water lines (F, TF) lie aft of the vertical line, raised by the fresh water allowance. The letters beside the ring identify the authority that assigned the freeboard. Sizes and rules: the Load Lines 1966 Convention, Annex I, regulations 4 to 8 and 40.

Then and now

Samuel Plimsoll’s campaign against overloaded “coffin ships” led to compulsory load-line marks in British law in 1876; the first international convention came in 1930, the present one in 1966. Older handbooks give the fresh-water rule as 1/48 of the draught: the 1966 Convention still allows that figure, but only when the displacement at the summer waterline cannot be certified. Otherwise the allowance is Δ / 40 TPC. Before metric units, the same rules were written with tons of 2240 lb, and with 35 cubic feet of sea water to the ton.