Differential Equations Governing the Geometry of a Diamond Mesh Cod-end of a Trawl Net

A new surface, made up of an infinite number of infinitesimal meshes, is defined to approximate the cod-end. The force balance on a mesh element of this surface is considered in the limit as the mesh size tends to zero and the differential equations governing the geometry of a diamond meshed cod-end of circular cross section are derived in cartesian coordinates. The parametric form of the equations in terms of a, the distance along the cod-end profile, is then deduced and some special cases examined. In particular the case of a partially filled cod-end hanging under gravity is investigated and experimental measurements are compared with numerically obtained theoretical predictions. The numerical results are shown to provide a good description of the cod-end geometry except where the cod-end diameter is at its narrowest where there is a systematic departure of the predicted values from those measured. It is demonstrated that a probable explanation of this discrepancy is the assumption that the knots are simple points of intersection rather than finite well-defined structures.