Author
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Robert Jr, Kearny |
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Submitted to: National Cotton Council Beltwide Cotton Conference
Publication Type: Proceedings Publication Acceptance Date: 11/4/2004 Publication Date: 6/5/2005 Citation: Robert Jr, K.Q. The original cotton fiber length distribution. CD-ROM. Memphis, TN. National Cotton Council Beltwide Cotton Conferences. 2005. Interpretive Summary: The general form of cotton fiber’s mathematical length distribution has been discovered. One of the most important characteristics of cotton fiber as a raw material for spinning of textile yarns is the fact that cotton has a continuous distribution of staple fiber lengths. In other words, the fibers are not all equally long. The length of cotton, therefore, cannot be characterized by a single value, but must be described as a length distribution. The ability to describe cotton length more meaningfully now allows us to link mechanical processes of fiber breakage quantitatively to changes in the length distribution, which in turn can be measured by modern laboratory instruments. These advances in mathematical interpretation constitute a revolution in our thinking about cotton fiber length. Since the degradation of cotton fiber length by breakage is crucial to features of bale production and textile greige processing, whole new aspects of cotton quality are opened for marketing exploitation and optimization. In the present work, the cotton length distribution is traced back to the seed, and the mathematical form of the unbroken seed fiber is revealed and confirmed by re-analysis of archival experimental data. These results have profound importance for many aspects of cotton breeding, ginning, classing, and international marketing of U.S. cottons as raw material for textile manufacturing. Technical Abstract: The mathematical form of the cotton fiber length distribution has been discovered. Cotton fiber length distributions are now known to belong to a specific family of mathematical curves. These types of probability density functions (Robert distributions) are defined by the mathematical property that differences between their shapes are generated by different degrees of random fiber breakage having occurred within the finite number of fibers comprising a batch being described by that distribution. Reported here are length dispersion characteristics of cotton fibers that were separated painstakingly from the seed at the seed coat surface and individually measured, one at a time. Three crucial results are reported here: (1) that the form of the cotton fiber length distribution is linked to an originating Gaussian distribution by mass bias (not number bias); (2) that the relevant number of parameters required to adequately describe the range of fiber length potential is two for seed cotton and four for ginned cotton lint; and finally, (3) that cotton length depends upon both biological growth environment and physical breakage factors. Observed cotton fiber length distributions can thus be explained mathematically to result from physical changes imposed by mechanical breakage upon original parent length distributions. These parent distributions have a higher degree of inherent biological symmetry and uniformity than ginned lint. Depending upon the degree of breakage, the asymmetric physical breakage influences can dominate the inherent symmetric genetic influences by the time the cotton is processed into a bale. Cotton, therefore, is a two-component mixture consisting of broken fiber fragments and unbroken (full potential length from the seed) fibers. The prevalence of short fibers is associated overwhelmingly with the broken fibers, not the unbroken fibers. Short fibers are the tail of the broken fiber distribution. |
