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 PART - I

Chapter 13

The General Equation: A Tool for Economic Cotton Selection

 

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 now return to the discussion in the very beginning as to how tricky it is to quantify, mentally, the trade-off between fibre length and fibre strength. We now know that the commonly tested fibre characteristics, namely 2.5 % span length, micronaire, and fibre tenacity at 1/8-in. (3.2 mm) are not adequate to quantify this trade off. We also know that we can carry out this by making use of The General Equation, and that, to do 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 I – 13 - i provides these data for cotton XX and cotton ZZ; the Table also gives the CSP estimates of yarns from these two cottons. 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 I – 13 – i. 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. The model again truthfully reflects this practical finding – Figure I – 13 - ii.

 

Brown’s data provide another example of the fascinating phenomenon. The CS – C line of the strong, but short and coarse Interspecies cotton is above that of the relatively weak, but long and fine Karnak cotton in coarse counts, but below the latter in fine counts. Also, the stronger but shorter Interspecies spins warp yarns comparable in strength to yarns from the longer but weaker Karnak, but the Interspecies hosiery yarns are much weaker than the Karnak hosiery yarns. The model again truthfully reflects both these practical findings – Figure I – 13 – iii and iv.

 

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 shortfall 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.

 

In this context one remembers USTER AFIS, as it provides the fibre array diagram from which the effective length, % fibres shorter than 12 mm., and % fibres longer than 24 mm. can be determined; further AFIS provides fibre fineness, milllitex. These are essential for the use of the general equation to estimate yarn CS. One wishes instrument makers consider the provision of two facilities: i) application of a correction factor to remove the bias in the fibre tenacity test values of high volume instruments, and ii) tenacity values at two gauge lengths.

 
                

Cotton

XX
S-4

ZZ
F 414

Effective length, mm

32.3

27.1

% fibres shorter than 12-mm

19.8

19.7

% fibres longer than 24-mm

56.1

37.8

Stelo g/t at zero gauge

35.42

43.40

Stelo g/t at 1/8-inch

19.29

21.43

Fibre fineness, millitex

130

150

Cost index

100

84

T.M.

CSP at NE

30

50

30

50

3.25

2144

1853

1639

1297

3.75

2307

2044

2121

1781

4.25

2300

2056

2278

1974

4.50

2270

2034

2288

2000

4.75

2231

2001

2273

1998


TABLE I – 13 – i CS Estimates of Yarns from Short but Long cotton and
of Yarns from Strong but Short Cottons

 
  Figure I – 13 – I: CS – C Plots of yarn from S – 4 and F 414 Cottons
 
 
 

Figure I – 13 – ii: CS – M Plots of Yarns from S-4 and F414

   
 
 

Figure I – 13 – iii: CS – C Plots of Yarns from Karnak and Interspecies

 
 

Figure I – 13 – iv: CS – M Plots of Yarns from Karnak and Interspecies

Part - I
 
Understanding And Making Use Of The Equation
   
Chapter 1

Why Do We Need Another Equation for the Prediction of Yarn Tenacity?

Chapter 2

Strcturing the General Equation for Yarn Tenacity

Chapter 3

The Algebraic Expressions for the General Equation

Chapter 4

The Choice of Parameters of Fibre-Length Distribution for Use in the Irregularity Fraction

Chapter 5
Chapter 6

Making Use of the Equation in a Mill

Chapter 7

What Does the General Equation Tell Us?

Chapter 8

How General Is The General Equation ?

Chapter 9

Can We Use the General Equation to Estimate the CSP of Yarns from Mixings of Cottons?

Chapter 10

Can We Modify the General Equation to Estimate CSP Of Combed Yarns?

Chapter 11 A Note of Caution
Chapter 12
Chapter 13 The General Equation, A Tool for Economic Cotton Selection
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