Investigation of the Minimum Length of Cotton Fiber Effective in Single Yarn Tenacity

A systematic investigation of the translation of cotton fiber length distribution and fiber bundle tenacity into single yarn tenacity is reported. The mathematical model proposed is: Y = af (l, x) × S + b where Y is single yarn tenacity, a and b are constants, S is fiber bundle tenacity, l is length distribution of the cotton, x is critical length, and f( l, x) is a numerical value termed “effective weight” which is dependent upon the entire fiber length distribution. The investigation was carried out over a wide range of twists and yarn numbers, the latter ranging from 15/1 (40 tex) to 80/1 (7.2 tex). The optimum f( l, x) was selected, and it was found that fibers shorter than about 1/8 in. do not contribute to yarn tenacity. Similarly, a 1/8-in. portion of each longer fiber is ineffective. This may be viewed as implying physically that, on the average, the 1/8-in. tip at each end of each fiber does not contribute to the yarn tenacity. Hence, the degree of translation of fiber bundle tenacity to yarn tenacity is a function of the entire length distribution. An interesting finding of this investigation is that the “zero”-gauge fiber bundle test is superior to the ⅛-in.-gauge length test as a criterion for relating bundle to yarn tenacity if the zero-gauge value is modified by the effective weight, i.e. f( l, x) above.