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| PART - II |
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Chapter 6
Practical Application |
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The General Equation: a tool for economic cotton selection |
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In reading meaning out of fibre test reports, we have often mentally to balance the shortfall in one characteristic with the premium in another characteristic of the lot of cotton under consideration. The general equation provides us a means of performing this exercise quantitatively. The general equation, however, requires for its application the following fibre test data: |
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Effective length, %-age fibres shorter than 12-mm, %-age fibres longer than 24-mm; |
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Fibre fineness, millitex; |
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Fibre-bundle strength at zero- and 1/8th gauges. |
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Why? Because the general equation is founded on a set of logically tenable premises: |
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Yarn tenacity is dependent upon the number of fibres at the place of break. Now the number of fibres at the place of break is a fraction of the average numbers of fibres in the cross-section of the yarn. The number of fibres in the cross-section can itself be calculated only from yarn count and fibre fineness, millitex, not micronaire index. |
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The fraction, number of fibres at the place of break to the average number of fibres, is determined by yarn irregularity. Yarn irregularity is itself a function of yarn count, fibre fineness, and the abovementioned length parameters. |
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Of the total number of fibres at the place of break, the fraction that actually breaks in yarn testing is a function of yarn count, twist, fibre fineness, and the three length parameters. |
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The gauge length at which fibres break in yarn tenacity testing is not invariant, but a function of yarn count, twist and fibre fineness; therefore the yarn tenacity at any twist can only be calculated from a knowledge of yarn count and twist, and fibre fineness, zero-gauge tenacity and the gauge length parameter. |
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Table II - 6 - i provides these data for two cottons: F-414, the shorter and coarser, but stronger of the two, and S-4, the longer and finer, but weaker of the two. The Table also gives the CS estimates by the general equation for some yarns from these cottons. What do we learn from this exercise? Lord (3) states the conclusion succinctly: 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 spinnings of F-414 and S-4 cottons. The general equation correctly reflects this – Figure II – 6 - i. There is another interesting difference between these two cottons. Warp yarns from the stronger but shorter F-414 are comparable in strength to yarns from the longer but weaker S-4; however, hosiery yarns from F-414 are much weaker than hosiery yarns from S-4. The general equation again truthfully reflects this practical observation – Figure II – 6 - ii. |
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Yarns from Karnak and Interspecies cottons, Figure II – 6 - iii, and iv provide another illustration of Lord’s dictum; CS estimates from the general equation again correctly reflect the practical finding. |
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In other words, the equation convincingly delineates how fibre length and fibre fineness influence the contribution of drafting irregularity and ringframe twist to 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. |
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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 to quantify the compensation of extra strength for a shortfall in length. The general equation provides us with a tool to deal with this situation. |
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