• Fashion & Textile Research Journal
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• v.1 no.4
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• pp.387-392
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• 1999

The effects of the ratio of warp diameter to filling diameter (${\beta}$-ratio) and warp thread crash on the crimp factor and the yarn curvature were studied theoretically in this paper. The models of 2/2 twill fabric derived square cloth and sinusoidal curved cloth were used for the theoretical analysis. The crimp factors (C) for the models were given theoretically as follows; (1) Derived square cloth(general equation for b) $$C=\frac{(1+{\beta})({\theta}-sin{\theta})}{(1+{\beta})sin{\theta}+{\alpha}}$$ (2) Sihusoidal curved cloth $$C=\frac{(1+{\beta})sin{\theta}\[1+\{\frac{{\pi}(1-cos{\theta})}{4sin{\theta}}\}^2\]+{\alpha}}{(1+{\beta})sin{\theta}+{\alpha}}-1$$ The curvatures(${\kappa}$) for the models were given theoretically as follows; (1) Derived square cloth $${\kappa}=\frac{2}{d_w+d_f}$$ (2) Sinusoidal curved cloth $${\kappa}=\|{^{\;\;\prime\prime} \atop r}(s)\| \\ where \;s=\frac{p^'}{{\pi}}\(u+\frac{k^2u}{4}+\frac{k^2}{8}sin2u\)$$.