The Escape Length of a Stretched Mesh: An Inscribed-Circle Rule Linking Mesh Size, Opening Shape, and Fish Girth

Fishermen and gear designers routinely need to answer a plain question: given a netting mesh of a stated size, what is the largest fish that will still get through it, and what is the smallest fish that will be held? This paper originates a simple geometric rule for that question. A mesh is treated as a rhombus of four bars, and the widest fish cross-section that can pass is identified with the circle inscribed in the opening, whose diameter is the altitude of the rhombus. Combining that diameter with a stated girth-to-length relation for a fusiform fish (maximum girth equal to half the length) and a stated allowance for body compression gives two thresholds for every mesh: a nominal escape length and a larger escape length that a fish can reach by compressing its girth by one tenth; fish longer than the second value are reliably retained. For a 100 mm stretched mesh the rule gives an escape length of 335.1 mm for a square opening and 288.3 mm for a diamond opening, a ratio of 0.86, so opening shape alone changes the escaping size by about one seventh at fixed mesh size. Across stretched mesh sizes from 25 mm to 150 mm the escape length rises from 73.3 mm to 509.6 mm for square openings and from 61.6 mm to 439.5 mm for diamond openings. The full table is provided so that a mesh can be chosen directly from the length of fish to be released or held. The study is simulated, not measured.