Can The General Equation Predict CSP  Of Yarns Spun From Mixings Of Cottons?

Table - A - vi : Application Of General Equation
To Estimate CSP Of Yarns From Mixings Of Disparate Cottons
OBS:experimentally observed; ERR: error in estmated CS

We spun two cottons, one short and coarse, and the other long and fine, in isolation as well as in mixings containing varying proportions of the two. The CSP estimates from the General Equation are in agreement with the corresponding test values on yarns; this is true of yarns from the two individual cottons as well as mixings of the two cottons –Table A – vi. This is of great practical significance. We can use the general equation to estimate the CSP of yarns from mixings of cottons by making use of the fibre test data on the individual component cottons.

In reading meaning out of fibre test reports on cottons, one has often to do a mental exercise: balance the shortfall in one quality aspect with the premium in another quality aspect of the lot of cotton under consideration. We posed the problem in the very beginning of this abstract, Tables A-i and A-ii, only to stress how tricky it is to quantify, mentally, the trade-off between fibre length and fibre strength. We now know that the fibre data available in Table A-i are not adequate to complete Table A-ii. We also know that we can complete Table A-ii by  making use of The General Equation. and for this the following fibre data are required:-

Fibre effective length, percentage fibres, by number, that are less than 12.5 mm/, percentage fibres that are longer than 24 mm.;

Fibre fineness, millitex;

Fibre-bundle strength at zero- and 1/8th gauges.

Table A – vii provides these data for cotton XX and cotton ZZ; the Table also gives the CSP estimates for the two yarns. What do we learn from this exercise?

Lord (3) states, succinctly, the observation regarding the tenacity of yarns from a short, but strong cotton, in comparison to the tenacity of yarns from a long and weak cotton : the CS – C line of a strong, but short and coarse cotton could be above that of a relatively weak, but long and fine cotton in  coarse counts, but below the latter in fine counts. This is what happens in actual spinning with F-414 and S-4. The model correctly reflects this--Figure A - iv. There is another interesting difference between these two cottons. The stronger but shorter F-414  spins warp yarns comparable in strength to yarns from the longer but weaker S-4, but  the F-414 hosiery yarns are much weaker than the S-4 hosiery yarns. The model again truthfully reflects this practical finding – Figure A  -  v.

The General Equation, thus, accounts for the important practical observations concerning the performance of the two cottons. Often in commercial evaluation of cotton one overlooks this mutually compensating aspect of cotton fibre-characteristics, and one accords, erroneously, fibre-length a premium. There are two reasons for this error of judgment. 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 the compensation of extra strength for a short-fall in length. The General Equation provides us with a tool to deal with this situation.

In other words, the Equation convincingly delineates how fibre length and fibre fineness govern the translation of cotton fibre-tenacity into yarn-tenacity. The Equation can, thus, expose hidden options that can secure the economic selection of cotton to meet specification of yarn tenacity.