Hanging Ratio Moves a Gillnet's Catch Band but Cannot Narrow It: A Geometric Selection Rule

Gillnetters often speak of the hanging ratio — the length a net is hung to, divided by its stretched length — as a way of tuning which fish the net takes, and it is natural to hope that slackening or tightening the hang might narrow the range of sizes caught around a target length. This paper tests that hope with a geometric model. The mesh opening at a given hanging ratio is a rhombus whose width for a fish's body is set by its altitude; a fish is caught when the mesh can be pushed over its gills but cannot pass over its greatest girth. Both edges of the caught-length band turn out to be proportional to the same quantity, so their ratio is fixed at 1.4238 for every hanging ratio from 0.30 to 0.70: hanging ratio moves the band and stretches it, but cannot change its relative width. The result is then worked in the form a fisherman actually needs. On a fixed 100 mm mesh, raising the hanging ratio from 0.30 to 0.70 moves the band from 172.9–246.2 mm to 302.0–430.0 mm. If instead the mesh is re-chosen at each hanging ratio so the band stays centred on a 300 mm target, the band is 247.5–352.5 mm at every hanging ratio — a width of 104.9 mm that no choice of hanging ratio reduces. What hanging ratio does change, once the target is held fixed, is the bill: twine per hung metre falls from 6.67 m at a ratio of 0.30 to 2.86 m at 0.70, and a 50-mesh-deep net hangs 6.83 m deep at 0.30 against 2.93 m at 0.70. The selection rule is therefore to set the band with mesh size and the target, and to spend hanging ratio on depth and twine cost, where it genuinely has leverage. The study is simulated, not measured.