Cotton cost has always been the single major contributor to the cost of grey yarns. Consequently, economic cotton selection for meeting yarn specifications continues to be one of the major concerns of a spinner. Most often, the spinner has to decide upon the purchase of cotton on the basis of fibre-test reports. This is by no means an easy task. Why?

We know that yarn tenacity is the manifestation of fibre tenacity. However, we come across instances wherein length plays a decisive role. We find that of two cottons, the weaker but longer cotton spins a yarn that is as strong as, or even stronger than, the yarn spun from stronger but shorter cotton. We explain this by reasoning that the longer cotton spins a more even yarn than shorter cotton. In other words, for any one given yarn count, along the axis, the longer fibre yarn has less variation in the number of fibres in the cross-section than the shorter-fibre yarn. This means that, at the place of yarn break in tenacity testing, the yarn from the longer fibres will contain more number of fibres in cross-section than the yarn from the short fibre. The extra number of fibres that break in the case of the long fibre yarn possibly more than compensates for the deficiency in fibre strength itself. This explains why the yarn from the longer, but weaker fibre is stronger than the yarn from the stronger but shorter fibre.

Implicit in the situation is a trade off: there must exist instances in which a shorter, but stronger cotton spins yarn of the same tenacity as the yarn from a longer, but weaker cotton. In the early nineteen-eighties ATIRA investigations showed that the stronger but shorter F-414 can spin warp yarns comparable in strength to yarns from the longer but weaker S-4. Discerning spinners used this finding, and thereby achieved considerable savings in yarn cost. Such instances are, however, rare, and remain unexplored by default. There are two reasons for this. The first is psychological: the persistence in memory of cotton evaluation by hand stapling. The second is real: the non-availability of a method toquantify accurately the compensation of extra strength for a shortfall in length.

This is where equations that help estimate yarn tenacity from fibre test data are useful. Consequently, research workers have, over the years, published many yarn tenacity equations.

It is for these reasons that we have constructed the General Equation for estimating yarn tenacity. With the availability of computers it is possible to perform even very complex calculations instantaneously. In the construction of the equation, therefore, we do not shirk the use of complex expressions where these decidedly enhance the fulfilment of the spinner’s twin expectations of a tenacity equation: accuracy of estimates of yarn tenacity; elucidation of the specific manner in which fibre-length and fibre-fineness contribute to the translation of fibre-tenacity to yarn tenacity.

In its original form, the general equation requires for its application the following fibre test data: effective length, %-age fibres shorter than 12-mm, %-age fibres longer than 24-mm; fibre fineness, millitex; fibre-bundle strength at zero- and 1/8th gauges.

We have successfully modified the General Equation to use HIV data for estimating CSP of ring-spun yarns of optimum TM; there is a possibility of extending this method to the estimation of CSP at values of TM other than the optimum. We have also modified the General Equation to predict rotor spun yarn CSP from HVI length, uniformity ratio, and micronaire values.

The General Equation for estimating cotton yarn tenacity is the outcome of work that I carried out in ATIRA during the period of 1985 to 1991.

TAS with inputs from,
Ashok Hirway