The expression for irregularity fraction in The General Equation contains the floating fibre index that is obtained by compounding three parameters from the Baer diagram of cotton, namely, effective length, percentage fibres shorter than 12-mm and percentage fibres longer than 24-mm. The ATIRA spinning that was carried out to derive this expression includes cottons that cover a wide range of fibre-length distribution and fibre-fineness. Is the irregularity fraction capable of extrapolation to values beyond the range of values met with in these cottons?

Like with cotton, for any count of yarn, a plot of CS against M yields an inverted parabola for viscose too. There is, however, a very important difference between the viscose and cotton curves: the viscose curve peaks up much faster than the cotton curve. There are two important differences between cotton and viscose  that can possibly explain this difference:

Also the constant in Bogdan’s expression for the obliquity fraction, namely 0.014, may not be applicable to viscose. From available published data (9), we determined the value of d for viscose to be 0.0225. The cotton equation

thus simplifies itself to

for viscose.

Now the question is whether the cotton based expression for , together with the revised expression for obliquity fraction, can predict the fact that viscose yarns reach their maximum CS at a much smaller value of M than cotton yarns. Obviously

will be the maximum when

is the maximum. There is, thus, a simple method to verify the applicability of the cotton based expression to viscose: we compare the experimentally observed value of M (9) for maximum CS with the value of M that gives the maximum value of  the expression

Table I – 8 - ii  gives the results. The agreement is very close indeed. There are two important points to note here.

Therefore, two important inferences emerge. Firstly, the partitioning of the effect of twist on CS into the two components, F2 and F3 is not a computational artifice, but is based on reality. Secondly, the numerical values that we get from the algebraic expressions for F2 and F3 are not altogether arbitrary, but reflect the actual.

We have, now, to check the overall accuracy of the viscose CS equation: -

For this we have to derive afresh, by regression, the constants in the expression for the irregularity fraction. We did this from published data (9). Table I –8 -ii compares the estimated and experimentally observed values of CS. The accuracy of estimates is good enough to conclude that The General Equation accounts for the way in which fibre-length and fibre-fineness influence the translation of fibre tenacity into yarn tenacity in the case of viscose yarns too.

We, therefore, have parameters derived from fibre-length test data that help us in characterizing cotton as well as viscose for susceptibility to irregularity in drafting, and in delineating the role of fibre length and fibre fineness in the translation of fibre tenacity into yarn tenacity.

Table I - 8 -i : Application Of General Equation To Hand-Ginned CottonsOBS:experimentally observed; ERR:  error in estimate
fg factory-ginned; hg hand-ginned.

Table I –8 –ii:  Application Of Equation To Viscose Yarns
OBS: experimentally observed;  EST: estimated from general equation.
NA: not available