# Rieter

### The staple diagram

#### Index

The fibers in the boll do not exhibit extremely great length differences. Noticeable shortening of many fibers arises before the spinning process owing to mechanical working, for example, ginning and cleaning. The effect is such that fiber length exhibits the greatest irregularity of all the fiber characteristics.

In even the smallest tuft of cotton taken up in the hand, there will be all lengths from the absolute minimum (2 mm) to the absolute maximum (between 30 and 60 mm depending on origin). If the fibers of such a tuft are arranged next to each other with their ends aligned and sorted according to length in a coordinate system, then the staple diagram (Fig. 1) typical of cotton is obtained, the so-called numerical diagram . If the diagram is derived abstractly from the masses of the length groups, then the weight-based diagram is obtained (Fig. 2). This has a notably higher curve compared with the numerical diagram, because long fibers have more mass than short fibers and therefore a greater effect. The weight-based diagram corresponds to the distribution of fibers in the yarn cross-section. This diagram should therefore be referred to in considerations and calculations relating to the yarn. On the other hand, the numerical diagram emphasizes the proportion of short fibers. It provides in visual form a good assessment of the running behavior in the process. The two average staple lengths are related as follows:

$\overline{l}_W = \overline{l}_N +\frac {s^2}{\overline{l}_N}$

Where $\overline{l}_W$  is the average fiber length based on the weightbased diagram; $\overline{l}_N$ is the average fiber length based on the numerical diagram; s is the standard deviation of the fiber length distribution. In addition, in relation to fiber materials, five types of diagrams can be distinguished according to their form (Fig. 3 - Fig. 7). Measurment of the staple diagram is possible by AFIS-Systems.

Fig. 1 - The staple diagram, by number

Fig. 2 - The staple diagram, by weight