A Minimum-Freeboard Bound for Small Open Boats: Wave Height, Bow Immersion and a Hand-Span Rule

An open boat ships water when a wave encounter, at its worst moment, lifts the sea surface at the bow above the gunwale. This paper turns that moment into a simple bound that can be applied before leaving shore. The relative immersion at the bow is estimated as the sum of two parts: the crest height of a sinusoidal wave above still water, with no credit taken for the boat heaving with the wave, and the dip of the bow as the boat pitches with a stated fraction of the wave slope over a stated wavelength of 30 m. The sum is adjusted by a stated factor for bow shape. Boarding is taken to begin when this immersion reaches the loaded freeboard. For a 5.0 m boat of standard bow shape, a loaded freeboard of 0.30 m is exceeded at a wave height of 0.439 m; a freeboard of 0.20 m is exceeded at 0.293 m, and one of 0.40 m at 0.585 m. In units a fisherman can measure on his or her own hand, taking a stretched hand span as 0.20 m, the rule for the 5.0 m boat is that the largest wave that can be met without boarding is about 1.46 times the loaded freeboard, so one and a half spans of freeboard meet about 2.2 spans of wave. Bow shape matters at the same order as loading: at a length of 6.0 m and a freeboard of 0.30 m, a fine bow raises the limiting wave height to 0.490 m while a full, blunt bow lowers it to 0.362 m. Longer boats need more freeboard for the same wave, because the bow sits further from the pitching centre. The study is simulated, not measured, and the bound is deliberately conservative in the ways stated in the text.