Measuring Fineness Characteristics of Wool Fibres

This chapter covers four topics.

Mean Fibre Diameter

Diameter Distribution Histogram

Standard Deviation

Coefficient of Variation of Fibre Diameter

You can access each one individually using the links provided above or in the index, or simply scroll down this page.

Mean Fibre Diameter

Wool fibres are not uniform cylinders, nor is the thickness of the fibres exactly the same. The fibre cross-section is roughly circular, but can vary from ovoid (egg-shaped) to elliptical and a range of shapes in between. Some fibres actually have concave cross-sections. The magnified cross sections of some fibres selected from a 19-micron top¹ are shown below (Figure 1). Coarser wool can exhibit even greater variation than is illustrated here. This non-uniform geometry means that defining Mean Fibre Diameter (MFD) is not as simple as it may at first seem.

Figure 1 Photograph provided by Peter Turner, CSIRO Division of Wool Technology, Belmont, Victoria, Australia

Consider these fibre cross sections, and the range of shapes exhibited. How then do we determine the Mean Fibre Diameter? Clearly, if we use a ruler to measure the “diameter” of these images, the “diameter” we obtain for each image will depend where we place the ruler. We could of course use a ruler to measure a very large number of transects across each fibre cross section, and then calculate the average of all these transects, but that would be unbelievably tiresome. And in doing so, we would not have taken account of any variation in the dimensions of the cross section along the length of each fibre. We could only do this by taking a very large number of cross sections and making a large number of measurements – an even more tedious exercise.

Alternatively, we could define the fibre fineness in terms of the area of the cross section. Once again, if conducted manually, the measurement would be slow and tedious because many cross sections would have to be measured to obtain a reasonable estimate of the “area” or fineness of each fibre, and thus the average fineness of the sample.

Clearly, if fibre fineness is to be measured, the definition of fibre fineness must be related to some geometrical dimension of the fibre. There are effectively only four geometrical dimensions that are suitable. These are:

	the area of the cross section;
	the width of a 2-dimensional projected image;
	the area of the surface; or
	the area of a 2-dimensional projected image

The Wool Industry has chosen to define Fibre Diameter in terms of the average thickness or width of a two- dimensional projected image of a large number of fibre snippets , measured using a Projection Microscope (IWTO-6). This choice is fundamentally one of convenience, because in practice it is the simplest and fastest way to obtain a direct measurement of the fineness of the fibres. Measurements based on fibre cross-section first require cross-sections to be obtained. The accuracy of the measurement is then determined by whether or not the cross-sections are taken perpendicular to the longitudinal axis of the fibre. Any deviation from perpendicular will distort the shape of the cross-section and make it increasingly elliptical. The fineness of wool fibres and the curvature of the fibres makes obtaining such cross-sections extremely difficult.

But what is a snippet and why measure Mean Fibre Diameter using snippets?

Within any mass of wool there is considerable variation in fibre fineness between fibres and along the length of individual fibres. To complicate things even further, there is also variation in the lengths of individual fibres. Any measurement of fineness must take this variation into account. The method used to obtain the sample to be measured is therefore of paramount importance.

Measuring fibre snippets is one way to take account of the variation of fibre length, as well as the variation in thickness along and between fibres. Fibre snippets are short lengths of fibre (0.8 - 2 mm long) cut from individual fibres at random positions along the length of the fibres. The precise mechanism for doing this generally involves using a mini-core (in the case of raw wool) or a microtome (in the case of wool sliver). The key issue is the randomness inherent in the sampling. Using these techniques the population of snippets so obtained will be biased towards the longer fibres i.e. more snippets will be obtained from longer fibres. Therefore, it is only necessary to measure the width of each snippet once, at a point randomly located along its length, and calculate the average of all these individual measurements, to obtain a reliable estimate of the average thickness, or the Mean Fibre Diameter of the wool. In practice, not all snippets need to be measured - a sample selected at random from the total population of snippets is usually sufficient. In scientific language, the Mean Fibre Diameter of wool is therefore a length-weighted mean.

The fibre snippets are spread on a glass slide in a mounting fluid under a glass cover-slip. They are magnified using a Projection Microscope and the widths of the magnified images of the snippets are measured using a graduated scale (basically a ruler). Care is taken to ensure that the snippet is in focus, and each snippet is measured only once.

The procedure followed is designed to ensure that the point at which each snippet width is measured is randomly located along the snippet. Because the magnification factor is known, these measurements can be readily converted into actual dimensions. For convenience, the Wool Industry expresses these dimensions as micrometres (microns). This results in values of fineness ranging from 10 to 50 micrometres (microns), where one micron is equivalent to one millionth of a metre.

Diameter Distribution Histogram

Measurements made on individual snippets using a Projection Microscope are classified into class intervals. A class interval is a range of diameters within which the measurements lie. The Projection Microscope technique uses class intervals of 2 microns. By recording the number of measurements that fall within each class interval, a diameter frequency distribution table is developed (see Table 1).

Table 1: Distribution Data

This frequency distribution table provides the information required to construct a pictorial image of the range of diameters and their relative proportions in the wool from which the fibre snippets were obtained. The class intervals are plotted on one axis and the numbers of fibre snippets (or their frequency expressed as a percentage) on the other axis. It is usual to use solid bars or lines to illustrate the number of fibres or their frequency. The Diameter Distribution Histogram derived from the information in the table is shown in Figure 2. 

Figure 2: Diameter Distribution Histogram

Note that in Figure 2, the histogram uses the percentage of fibre snippets rather than the number of snippets. Although either is satisfactory, in practice the number of fibre snippets can vary quite substantially and this makes comparisons of different histograms quite difficult. Using the percentage overcomes the difficulty.

In the particular situation illustrated, the largest snippet proportion (approximately 33%) has diameters in the range 12 to 14 microns. However this example of very fine wool has a small number of fibres in the range 24 to 26 microns.

Calculating the Mean Fibre Diameter (MFD) from a Diameter Distribution Histogram is a relatively simple exercise. The calculation is illustrated in the table on the previous page.

For each class interval, select the middle of the range (for example for 12 to 14 microns select 13 microns) and multiply this by the number of fibre snippets. Add the products so obtained for all the class intervals and then divide by the total number of fibre snippets. For this example:

Standard Deviation

The Standard Deviation of Fibre Diameter (SD) is a measure of the dispersion or spread of the distribution. If the distribution is very narrow (the range from the highest to the lowest diameter is small) then, for the same Mean Fibre Diameter, the Standard Deviation will be smaller. Conversely, if this range is large then the Standard Deviation will be larger.

This is illustrated in Figure 3 on the next page, where two idealised symmetrical Distribution Histograms are shown1 , each with the same Mean Fibre Diameter, but with different Standard Deviations. To present this more simply, the histograms are shown as continuous curves, instead of solid bars as in the first example above.
In this illustration it has been assumed that the same number of fibre snippets has been measured in both cases, and therefore the areas under both curves are actually identical. Note that the curve with the higher Standard Deviation is both wider and flatter.

Calculation of the Standard Deviation (SD) from the distribution data is a little more complex as it also involves a further calculation in multiplying the square of the diameter by the number of fibre snippets in each class interval. From the earlier table (Table 1):

Figure 3: Standard Deviation

 

Coefficient of Variation of Fibre Diameter

While the Standard Deviation is useful in describing the dispersion of a Fibre Diameter Distribution it is of limited usefulness in comparing different lots of wool, unless the Mean Fibre Diameters are identical. As the Mean Fibre Diameter of wool increases, so does the Standard Deviation.
In part this is due to the fact that the diameter distribution of wool fibres is rarely symmetrical. Most distributions are skewed towards the coarse end of the distribution. This must occur because as the Mean Fibre Diameter is reduced, the cellular structure of the wool fibres becomes a limiting factor determining the diameter of the finest fibres in the distribution.
Commercial use of distribution statistics requires a measure of dispersion that is comparable, even for different Mean Fibre Diameters. The Coefficient of Variation of Diameter (CVD) is such a measure.
The Coefficient of Variation (CVD) is derived from the Standard Deviation (SD) and the Mean Fibre Diameter (MFD) as follows:

Because the Standard Deviation is linearly related to Mean Fibre Diameter the Coefficient of Variation is, on average, independent of the Mean Fibre Diameter.
This is illustrated in Figure 4 showing the dependency of Coefficient of Variation of Diameter and Standard Deviation of Diameter on Mean Fibre Diameter for sale lots of Australian wool. The illustration is based on measurement of 2500 Australian sale lots during 1998/99.
Note that over the range of diameters in this illustration the Standard Deviation is steadily increasing. However the Coefficient of Variation of Diameter is essentially constant.
The lines in the illustration are average conditions. Individual sale lots will vary above and below these lines. The constancy of the average Coefficient of Variation of Diameter provides a benchmark for ranking individual sale lots using this particular measurement.

Figure 4: Coefficient of Variation