Yarn irregularity is the outcome of thin and thick places in the yarn. Almost all thin places and most thick places in the yarn are the result of out-of-turn movement of fibres in the drafting zones. How do fibres move out of turn in the drafting zone? The length of most fibres is less than the distance between the nips of consecutive rollers. There is, therefore a duration of time between the trailing end of a fibre leaving the grip of the rear roller-nip and the leading end of that fibre getting gripped by the forward nip. During this period of transit between the nips, a fibre is prone to accelerate out of turn to the speed of the forward nip, if the a length of the fibre is sufficiently intermingled with other fibres that are already in the grip of the front rollers. In the front zone of roller drafting systems, aprons are provided to counter this out of turn movement of fibres. The pressure between the aprons restrains fibres from being pulled forward out of turn by their merely being entangled with other fibres; yet the fibres are free to move forward when once they are themselves gripped by the front rollers. Thus the provision of aprons has contributed to a significant reduction in the yarn irregularity. This is because with the provision of aprons, not all the fibres are likely to get pulled forward out of turn. Fibres that are longer than a critical length will have their trailing part under the restraining influence of the aprons for most part of their transit from the rear nip to the forward nip. They will change over to the speed of the front-roller nip only on their leading ends being gripped by the front nip. The aprons, however, are not effective in restraining the out-of-turn movement of all fibres, because their influence is effective only upto a certain distance forward of the middle roller nip. Fibres that are shorter than a critical length may not be under the restraining influence of the aprons for part of their transit between the roller-nips. They are quite likely to get pulled forward out-of-turn if they are sufficiently intermingled with fibres that are already under the grip of the front-roller nip. In some cases such fibres may, for a duration of time, move alternately at the speed of either the middle rollers or the front rollers. This out-of-turn and irregular movement of fibres in the drafting zone is what results in thick and thin places in the drafted strand flowing out of the front nip -- in other words, yarn irregularity. Thus the propensity of cotton fibres to incur thin and thick places can be quantified by two critical lengths. Fibres longer than the first critical length are very unlikely to incur irregular movement; fibres shorter than the second the critical length are most likely to incur irregular movement. We had to identify these two critical lengths.

For this we spun each of the 12 cottons representing the widely different types of length distribution encountered in Indian commercial cottons – Figure I – 4 -i -- to NE 22, 30, and 40. Using the fibre and yarn data, we derived regression equations to estimate Uster counts of thin and thick places in yarns from the fibre characteristics of the cotton.

The investigations led to an important conclusion: three length parameters, namely, effective length, the percentage of fibres shorter than 12-mm., and the percentage of fibres longer than 24-mm. can be used to construct a floating-fibre index, Q; this index can then be combined with fibre-fineness into a function f(Q;H), which can be used to estimate accurately the frequencies of Uster thin and thick places in the yarn. - - Table – I –4 -i.

The appropriateness of these two critical lengths to discriminate between cottons for their susceptibility to drafting irregularity is highlighted by comparing S-4 cotton with two others. The effective length of S-4 cotton is much less than that of VL and DCH-32 cottons. Naturally, therefore, VL and DCH contain some fibres of very long length, that are not present in S-4. S-4 is also much coarser than the other two cottons. However, S-4 cotton is superior to VL and DCH in a unique respect: it has much less percentage of fibres shorter than 12-mm, and also much more percentage of fibres longer than 24-mm, than the other two cottons. The regression equation based on these two percentages correctly anticipates the observed fact that, in the propensity to incur thin and thick places during drafting, S-4 is comparable to the longer and finer VL and DCH. We can, therefore, use Q as the appropriate length parameter in F1, the irregularity fraction of
of the tenacity equation.