# Rieter

### The slenderness ratio (stiffness)

#### Index

Fig. 9 - Stiffness of fibers of different lengths

Fiber stiffness (Fig. 9) plays a significant role, mainly when rolling, revolving, and twisting movements are involved. A fiber that is too stiff has difficulty in adapting to these movements. For example, it is not properly bound into the yarn, produces hairiness, or is even lost in processing. Fibers that are not stiff enough have too little springiness. They do not return to shape after deformation. They have no longitudinal resistance. In most cases, this leads to the formation of neps. Fiber stiffness is dependent upon fiber substance and also upon the relationship between fiber length and fiber fineness. Fibers having the same structure and diameter will be stiffer, the shorter they are.

The slenderness ratio can serve as a measure of stiffness:

$Slenderness\ ratio = \frac{Fiber\ length}{Fiber\ diameter}$

Since the fibers must wind, as they are bound-in during yarn formation in the spinning machine, the slenderness ratio also determines to some extent where the fibers will finish up:

• fine and / or long fibers in the core;
• coarse and / or short fibers at the yarn periphery