魚体を網目通過させるための目合と縮結の必要十分条件 Necessary and sufficient conditions of mesh size and hang-in ratio and hang-out ratio for fish to pass through the mesh

魚体を網目通過させるためには,網目内周長を最低でも最大胴周長と同じにする必要がある。最大胴周長を最大体高D_mと最大体幅W_mから計算される楕円周長とみなし,魚を網に羅網させることなく逃がすために最低限必要な目合L_nと網地に接する程度の十分な大きさの目合L_s,およびそのときお内割縮結S_i,外割縮結S_oを導いた。L_nは楕円周長の半分としてL_n=(π/4)(1.5(D_m+W_m)-√<D_mW_m>),L_sは最大体高と最大体幅の合計値としてL_s=D_m+W_m,S_i,S_oはS_i=1-√<W_m/(D_m+W_m)>,S_o=√<(D_m+W_m)/W_m>-1で表された。体長30cm前後のホッケを測定した結果,各々平均でL_n=94.7mm,L_s=119.0mm,S_i=0.376,S_o=0.604であった。

For a fish to pass through the mesh of a net, the mesh perimeter must be at least equal to the fish's maximum girth. Assuming the maximum girth as the circumference of an ellipse calculated from the maximum body depth (D_m) and maximum body width (W_m), We assessed the necessary conditions of the mesh size (L_n) for a fish passing through the mesh without entanglement and the sufficient conditions of the mesh size (L_s) for the cross-sectional shape of the fish body encountering the four sides of the mesh at four tangential points. For mesh size in a sufficient condition, the hang-in ratio (S_i) and hang-out ratio (S_o) were assessed. The necessary conditions of the mesh size can be expressed as, L_n=(π/4)(1.5(D_m+W_m)-√<D_mW_m>), that is as half the circumference of the ellipse. Sufficient condition of the mesh size can be expressed as L_s=D_m+W_m, that is as the total of the maximum body depth and maximum body width. The hang-in ratio and hang-out ratio were obtained as S_i=1-√<W_m/(D_m+W_m)>, S_o=√<(D_m+W_m)/W_m>-1. Based on measurements of the maximum body depth and maximum body width of Arabesque greenling, Pleurogrammus azonus, of about 30 cm standard length, the average values of the approximation were : L_n=94.7 mm, L_s=119.0 mm, S_i=0.376, S_o=0.604.