Twist Factor — Metric and Tex Systems

The metric twist factor is the same square-root law wearing metric clothes: turns per metre divided by the square root of the metric count. Typical values run near 60 for a soft knitting yarn, 100 for a weft, 120 to 140 for a warp — larger numbers than the English twist multiplier only because a metre is a great deal longer than an inch.

Three factors are in circulation and they are all bound to their units. $TM$ uses turns per inch and $N_e$. $\alpha_m$ uses turns per metre and $N_m$. $\alpha_{\mathrm{tex}}$ uses turns per centimetre and multiplies by $\sqrt{\mathrm{tex}}$ rather than dividing, because tex is a direct system and runs the other way. The ratios between them are fixed and exact:

$$\frac{\alpha_m}{\alpha_{\mathrm{tex}}} = \frac{100}{\sqrt{1000}} = \sqrt{10}, \qquad \frac{\alpha_m}{TM} = \frac{39.370\,079}{\sqrt{1000/590.541\,247}} = 30.254\,599.$$

The $\sqrt{10}$ looks like a coincidence and is not. Write $\alpha_m = T_{\text{m}}/\sqrt{N_m}$ and substitute $N_m = 1000/\mathrm{tex}$: you get $T_{\text{m}}\sqrt{\mathrm{tex}}/\sqrt{1000}$. Write $\alpha_{\mathrm{tex}} = T_{\text{cm}}\sqrt{\mathrm{tex}} = T_{\text{m}}\sqrt{\mathrm{tex}}/100$. Divide, and the tex and the twist both cancel, leaving $100/\sqrt{1000}$.

$\alpha_{\mathrm{tex}}$ is the worst of the three for unit hygiene, and it is worth saying plainly why. Its dimensions are $\mathrm{tex}^{1/2}\,\mathrm{cm}^{-1}$ — the square root of a mass per unit length, multiplied by a reciprocal length. That is a real physical dimension, but it is a half-power of one, and no units engine converts half-powers of composite units. There is no conversion that rescues an $\alpha_{\mathrm{tex}}$ whose system was not written down. This is the same problem Taylor's cutting-speed constant has on the machining pages, and it has the same solution: write the system beside the number, every time, and never lift a bare figure out of a table without knowing which table it was.

On the machine, twist is not typed anywhere. On a ring frame it is the ratio of spindle speed to front-roller delivery, so it lives in a gear or a drive setting, and the honest check is to untwist a measured length on a twist tester and count the turns back. Rotor spinning puts twist in by a different mechanism and the resulting yarn behaves as though it had rather more than its nominal twist, because of the wrapper fibres bound round its surface — which is one reason rotor and ring yarns of the same count and the same nominal twist do not weave the same.