A study of the wool fibre cross-sectional area profile in a selection of New Zealand Romney ewe hoggets : A thesis submitted in partial fulfilment of the requirements for the degree of Master of Applied Science at Lincoln University

Abstract

It was proposed that a method of measuring the cross-sectional area profile of wool fibres should be developed. Statistics from the cross-sectional area profile of fibres from fleeces with known differing staple strengths could be gathered to address a hypothesised relationship between staple strength and the cross-sectional area profile. It was proposed that mathematical functions of summary crosssectional area profiles should be developed, to fulfil a need to account for fibre morphology in fibre breakage computer simulations. A method was developed to derive cross-sectional area, from multiple-view diameter measurements, using an approximation theory based on the parametric equations for an ellipse. Image analysis technology enabled diameter to be sampled at 3.2 μm intervals along the length of Romney fibres. Sample intervals of approximately 19 μm were used when deriving cross-sectional area, to produce cross-sectional area profiles at a resolution previously unattained in the relevant literature. Summary statistics of cross-sectional area profiles of fibres from sheep with high and low levels of staple strength and an unselected control flock, were subject to an analysis of variance. A cycloid and a discrete form of Fourier series were used to approximate summary cross-sectional area profiles. No significant difference between strength lines was revealed for any of the summary statistics of cross-sectional area, including minimum, mean, standard deviation, mean minus minimum or the average absolute rate of change of cross-sectional area along discrete sections of fibres. A strong repeatable pattern was revealed between cross-sectional area profiles within sheep and between sheep. A clear pattern of seasonality was observed in the high, low and control summary crosssectional area profiles, evident as a major and two secondary troughs. There were significant differences between summary cross-sectional area profiles at certain regions, including the major and secondary troughs. These differences were assumed to depend on the phase of the respective profiles and the slopes of the profiles at the region of comparison. The cycloid equations gave a poor fit to the summary profiles, based on high mean square errors associated with fitted functions, and a limited biological basis. The discrete form of Fourier series was shown to be less sensitive to the underlying nature of the data. Good fits to the summary profiles were achieved with ten terms in the Fourier series, although further work is required before any physical significance can be ascribed to the constants associated with the terms. This study has contributed considerable new work to its field. This includes: a unique and theoretically sound method of deriving cross-sectional area from diameter measurements, at a high sampling frequency along fibres; the first detailed published analysis of variance for cross-sectional area variability in Romney wool fibres; and, proof that a discrete form of Fourier series can be used to summarise cross-sectional area profiles in Romney wool.