In the year 2002 Chellamani, Thanabal, Basu and Ratnam (4) collected extensive data to modify the earlier SITRA CSP equation (18) to render it usable with cotton test data from HVI. They first postulated a fibre quality index:

where,              L=mean length,
                        s=fibre-bundle strength,
                        f=Micronaire value.
They then derived the algebraic expression for CSP in terms of this fibre quality index:

Where, CSP=yarn count (NE) x lea-strength (lbs.)

The authors concluded: “The prediction expression gives a very close fit with the actual CSP with a high correlation of 0.986.” “The error of estimate was found to be about 150 at 95% confidence limits.”

Calculation of errors in individual estimates of CSP of each of the 123 (=41 x 3) yarns, Table – II – 6 -iv, however, brings out some disturbing facts:-

Equally importantly, the way it is constructed, the SITRA equation can not tell us anything about how fibre length and fibre fineness govern the contributions of yarn irregularity and twist to the translation of fibre-tenacity into yarn-tenacity. On the contrary it gives us an erroneous conclusion. According to the equation, the yarn tenacity of a NE 45.4 (13 tex) yarn at optimum twist is given by

Therefore a 25% increase in either fibre tenacity or fibre length of the cotton used to spin a NE 45.4 yarn will result in a 5% increase in the CS of the yarn. This is contrary to what one would expect. One would expect that a 25% increase in fibre tenacity would result in a proportionate increase, or a near 25% increase, in yarn CS; but one would expect a 25% increase in fibre length would result in a rather smaller increase in yarn CS. Also one would expect that the increase in CS with increasing length would be more in the short to medium staple range than in the case of long to extra long staple range. The increase in yarn tenacity with increasing fibre length will understandably be in the nature of a growth curve.

We decided to examine how far these shortcomings of the SITRA equation can be overcome by modifying the general equation to estimate CS of ring-spun yarns of optimum twist from HVI data.

Curiously, in the SITRA fibre data, tenacity shows a remarkable increasing trend with length -- Figure II – 6 - vi. Analysis of available data from conventional fibre-bundle tenacity test does not exhibit this prominent trend. There are some short-staple cottons of low tenacity, but there is no clear increasing trend of tenacity with length – Figure II – 6 - vii. What could possibly be the reason for this peculiar feature of SITRA data? This is because of a fundamental difference between the manual and the HVI tests in the fibre bundle subjected to tensile loading, that results in 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. In this test, therefore, all the fibres in the tuft, without exception, share the applied load.

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. If 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. In other words, in the tuft under tensile loading in the HVI tenacity test, some fibres 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.

Logically, one can estimate the percentage of non-contributing fibres in tenacity testing, and therefore, the error can be corrected. But as of now the instrument does not seem to have been programmed to apply such a correction.

Let us now recall the steps in the derivation of 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 fraction is a function of A, C, H, and M; the gauge-length fraction is a function of G, H, C, and M.

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

Figure II - 6 - ix 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.