The reader is now most likely to raise two questions.  i) Can we modify The General Equation to calculate CSP of ring-spun yarn from HVI data? i ) Can we modify The General Equation to estimate rotor yarn CSP from HVI data?

Before we begin to answer these questions, let us recapitulate some basic considerations that have been used to structure The General Equation:

Now HVI does not provide data on any of the following: the %-ages of fibres at the two critical lengths; fibre-tenacity at two different gauge-lengths; fibre millitex. Furthermore, in the fibre-tenacity testing by HVI there is a likelihood of some percentage of fibres in the bundle under test having a free end within the test length - - please see Appendix I – 12 - i. Would not this %-age be more for a short-fibre cotton than for a comparatively long cotton? Again, between two cottons of the same effective length, would not this %-age be more for a cotton that is much more variable in length than that for a very uniform cotton? One can argue that this very feature of the fibre-bundle test by HVI, of there being free fibre-ends in the bundle that breaks, can perhaps make it quite suitable for estimating yarn tenacity, the test for which shares the feature with HVI fibre-tenacity test. One has, then, to rewrite the expression for F ₃ taking this aspect into consideration. One has to ponder over these points and questions before one rushes to modifying The General Equation, for use with HVI data.
Having said this, let us yielded to the exigency in the situation.

We made use of SITRA data (4) in our attempt to modify The General Equation to estimate CSP  of ring-spun yarns of optimum T.M. from HVI data. In these data a plot of the fibre-tenacity against fibre-length shows a remarkable increasing trend of tenacity with length -- Figure I – 12 - ii. Data from conventional fibre-bundle tenacity test does not exhibit this trend. There are some short-staple cottons of low tenacity, but there is no clear increasing trend of tenacity with length – Figure I – 12 – iii, iv, v and vi. What could possibly be the reason for this peculiar feature of SITRA data? This is of course the earlier mentioned feature of fibre-bundle tenacity by the HVI: the presence in the bundle under test of fibres with free ends inside the test length. We have to adjust for this, and for the earlier mentioned differences between ATIRA and SITRA spinnings in the fibre characteristics tested, while undertaking the modification of The General Equation for using it to estimate the CSP of ring-spun yarns from HVI data.

In deriving the General Equation for ATIRA data, we first compounded the effective length and percentages of fibres shorter than 12-mm and longer than 24-mm into a single parameter, A. We then used this parameter to construct the expression for Q, the floating fibre index. The irregularity fraction is, itself, a function of Q, C and H. The contributing-fibres function is a function of A, C, H, and M.

Keeping these in mind, we proceeded along the following steps to modify the General Equation to accept HVI data.

This is quite similar to the corresponding ATIRA spinning data expression.

We substituted the I, H, Z and G values derived from the HVI data in the ATIRA spinning expressions to calculate the numerical value of F2  and F3 .

We evaluated, by multiple regression, the numerical coefficients in the correction factor to convert the HVI tenacity value to the conventional one, and the constants in F1, the expression for the irregularity fraction, so as to minimize the percentage errors in the estimates of CSP.

In constructing expressions for transforming the HVI data to the corresponding values of manual measurements of fibre length, fineness and tenacity, our criterion for choice between alternatives was very simple: maximum compatibility between the transformed values and the available manual measurement values on similar cottons. Tables I – 12 - i and ii and figure I- -12 -vii reflect the measure of our success in the exercise. This validates the use of A, Q, H, Z and G derived from the HVI data in the algebraic expressions for F1,F2and F3 of the General Equation.

Figure I - 12 - viii compares the errors in the estimates of CSP by the two methods, the SITRA equation and the General Equation. In spite of the numerous correlations that have been used to make it possible to substitute the SITRA HVI data in the general equation, this equation yields much more accurate estimates than the SITRA equation. This is not surprising: the SITRA equation does not take cognizance of fundamental aspects of the phenomenon of yarn-breakage in tenacity testing. Even with the General Equation there is bias in the CSP estimates of at least one cotton. The extent of bias is, however, within the known limits of maximum possible error in the determination of fibre-bundle strength.

The inference is clear: we can successfully modify HVI data for using them in The General Equation to estimate the CSP of ring-spun yarns of optimum T.M. There is a possibility of extending this method to estimate the CSP at values of TM other than the optimum, but considerable work needs to be done  to realize this.

On the basis of published data (16), an attempt was also made an attempt to modify The General Equation to use it to predict rotor yarn CSP from HVI data. For these data the increasing trend of fibre-tenacity with increasing fibre-length is rather less pronounced than in the case of SITRA data – Figure I – 12 -xi. The modified equation (17) gave estimates of acceptable accuracy for cottons ranging in yarn CSP from 1232 to 2807 at NE 10.1, and T.M. 5.3. – Table I – 12 – iii.

The modification of the General Equation to predict rotor yarn CSP from HVI length, uniformity ratio, tenacity and micronaire seems a distinct possibility.

Figure I – 12 –iii Lack of trend between tenacity by manual method
and fibre length

Cottons: DCH, VL, MCU5, MCU7, S-4, F414, Jyoti, Somnath, J34(1),

 J34(2), CJ, CO2~~ Source of data: My project work in ATIRA during 1985 to 1990.

Figure I – 12 – iv   Lack of trend between tenacity by manual method and fibre length
Cottons: Suvin, VL, MCU5, S-4, 1007, CO-2, CJ-73,
DV ~~ Tenacity by manual method
            Source: Data collected by me for project

Figure I – 12 – v Lack of trend between tenacity by manual method and fibre length
Source Brown, J.J., Howell, N.A., Fiori, L. A., Sands, J. E. and Little. H. W., Tex. Res. J, 27, 332-339 (1957).  

Figure I – 12 – vi Lack of trend between tenacity by manual method and fibre length
Cottons: American El Paso, twelve US cottons ranging in staple
 from 7/8-in to 13/32-in, three Ugandan, two Brazilian, three Pakistani
Source Lord, E., The Characteristics of Raw Cotton, Vol. I, Part I, Manual of cotton Spinning, The Textile Institute, Butterworths, Manchester and London, 1962, 310

Figure I – 12 – vii Adjusted SITRA HVI Fibre-tenacity and Manually Tested Tenacity of Similar Cottons VS Length:

Adjusted: Tenacity values after correcting for length related bias
Manual: Data from ATIRA Spinnings in which tenacity was determined by manual testing and did not incur the bias.

Figure I – 12 –xi Plot of Fibre-tenacity VS Length: ITB Data
Source of Data: Zhang Hongwei, Relationship Of Cotton Fibre HVI Properties

Table – I – 12 - i  Estimates of Conventional Fibre Test Data from HVI Data
SITRA Cottons

EST: estimated; EL: effective length; H: fibre fineness, millitex;
Z: zero-gauge Stelo level fibre-bundle tenacity;
G: gauge-length parameter of tenacity; F: Stelo level 1/8-in gauge tenacity;Q: floating fibre index, a function of HVI UHML

Table – I –12 - ii  Conventional Fibre Test Data
on Cottons Comparable to those in Table – A - viii

Table I –12 - iii  Percentage Error in Estimate of CS Of Rotor-Yarns
By General Equation Modified To Accept HVI Cotton Test Data

** Cotton 7-A could not be spun to these counts.
Source of fibre and yarn data :
Zhang Hongwei pp 44-46, ITB (1/2003)

APPENDIX I – 12 –i:  A SPURIOUS UNDER-ESTIMATION OF THE TENACITY
OF SHORT STAPLE COTTONS BY THE HVI

The manual determination of cotton fibre tenacity is performed on a specially prepared tuft. When this tuft is held between the two clamps for tenacity test, all the fibres between the two clamps, without any exception, bridge the distance between the clamps.

As against this, the HVI determination of tenacity makes use of the beard that is prepared for the measurement of span lengths. Evidently, in such a beard, the number of fibres that protrude into the field of scan, beyond the comb used to hold it, goes on reducing as one moves away from the comb. This is the fact that span length measurement makes use of. Therefore, when the two clamps for HVI tenacity test are applied on the fibre beard in the scanning zone what happens? The number of fibres in the grip of the clamp farther from the comb will be less than the number of fibres in the grip of the clamp near the comb.

The use of a fibre beard for the determination of fibre tenacity in the HVI, we have seen, results in the presence in the tuft under tensile loading of fibres that do not stretch the full distance between the two clamps. In the HVI tenacity test, therefore, some fibres in the tuft under tensile loading will not share the applied load. However, the calculation of tenacity (g/tex) from the breaking load (grammes) makes use of the weight of the tuft between the two pairs of clamps. The HVI tenacity test will, therefore, tend to underestimate cotton fibre bundle tenacity.

The percentage of fibres that do not stretch the full distance between the two clamps used to hold the tuft under loading will, naturally, increase as the 2.5% span length decreases. Consequently, the under estimation of fibre tenacity by the HVI will be more for short staple cottons than for long staple cottons. Now, some short staple cottons are quite strong, but by nature short staple cottons tend to have a lower 1/8-inch (3.2 mm) gauge tenacity than long staple cottons. The HVI tenacity test will accentuate this difference in tenacity between short and long staple cottons: the test will render the strong short staple cottons look weak, and the weak short staple cottons weaker than they really are. If one plots a graph of HVI tenacity against HVI 2.5% span length, one will get a striking increasing trend.

The Error Can Be Corrected

APPENDIX I – 12 –ii:  Procedure for Adjusting SITRA HVI Test Data For Use In The Modified General Equation For Estimating CSP Of Rotor Yarns