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The effect of the short fiber content of a cotton on yarn and fabric properties and processing efficiency, long a speculative and controversial subject, is investigated to a limited extent in this paper by the technique of cutting sliver into and ¼- and ½-in. segments and adding the resulting short fibers to the parent cotton. The results indicate that increases in short fibers are detrimental to virtually all yarn and fabric properties and require increased roving twist for efficient drafting during spinning. A 1% increase in fibers shorter than 3/8 in. causes a strength loss in yarns of somewhat more than 1%. The quantities of cotton processed for this paper were insufficient to draw conclusions on neps, waste, or processing efficiency. The effect of short fibers on these properties will be considered in subsequent papers.

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By differentially ginning a single lot of Acala 44 cotton, various short fiber content levels were obtained. Yarns produced from these cottons showed the effects of increases in short fiber content; namely, reduced strength, elongation, and appearance grade. The twist required for maximum strength was found to be largely unaffected by changes in short fiber content, except for a medium yarn number for which a relationship was demonstrated. A graph showing the close relationship between the percentage of fibers less than 3/8 in. and those less than 1/2 in., calculated for a wide number of cottons, is included. Spinning efficiency is shown to be adversely affected by changes in short fiber content.

Mathematical models of cotton fiber length distribution under various breakage models are discussed. Theoretical analyses are given, including the demonstration of certain factors, capable of measurement. which afford the possibility for numerical con firmation of the respective models. For example, the model for random fiber breakage independent of length shows that where μ F and μ G are the means and γ F and γ G are the absolute second moments about the origin of the parent and daughter populations, respectively. In addition, mathematical models, somewhat more complicated, are given when breakage is proportional to length and for the case where the fibers are held and then subjected to breakage.