Crimp Percentage

A yarn in a woven cloth does not run straight. It climbs over one crossing thread, dives under the next, and traces a wave whose amplitude is set by how thick those crossing threads are and how far apart they sit. So a metre of cloth swallows more than a metre of yarn, and crimp is the excess, expressed as a fraction of the cloth length:

\[ c = \frac{L_y - L_f}{L_f} \]

Measured by unravelling a marked length from the fabric, straightening the removed yarn under a standard tension, and measuring what comes off. The tension matters more than it looks: too little and the yarn keeps some of its wave, giving a crimp that reads low; too much and the yarn extends, giving one that reads high. Ten ends, averaged, is a reasonable specimen.

Crimp is not shared equally between the two systems — it is a competition. The warp is held under tension on the loom; the weft is inserted slack and then beaten up. So the weft normally does most of the waving and the warp stays comparatively straight: something like 5 to 8% weft against 3 to 6% warp in a plain cotton cloth, and much more lopsided in anything woven under high warp tension. The total is roughly conserved. Push one system flatter and the other has to bend more to keep the cloth together, which is why a "crimp interchange" happens whenever a fabric is stretched, relaxed, wetted or finished, and why cloth off the loom is never quite the cloth in the shop.

Peirce made this quantitative, in the paper that founded the whole subject: F. T. Peirce, "The Geometry of Cloth Structure", Journal of the Textile Institute Transactions, 28(3), 1937, T45–T96. (Two corrupted versions of that citation circulate — one giving the wrong journal, Textile Research Journal, and one giving the pages as T45–112. Neither is right. And it is P-e-i-r-c-e.) His model treats each thread as a circular arc over its crossing thread joined to a straight length between, and it closes with relations linking the crimps, the thread spacings and the modular lengths.

His crimp relation uses crossed indices, and this is a real error in some secondary sources:

\[ c_1 = \frac{l_1}{p_2} - 1 \]

— warp modular length $l_1$ over weft spacing $p_2$. The crossing has to be there once you see what governs what: a warp thread's waving is set by how far apart the picks are that it climbs over, not by how far apart its neighbouring ends are. Writing $c_1 = l_1/p_1 - 1$ puts a thread's crimp under its own spacing and gets the geometry backwards. If a derivation you are reading has uncrossed indices, it has been copied from someone who copied it.

Practically, crimp is where warp ordering goes wrong. To weave 1000 m of cloth at 6% warp crimp you need 1060 m of warp on the beam, before loom waste, knotting-on and the ends of the piece. Underestimate it and the beam runs out with the order unfinished, which is the most expensive arithmetic mistake available in a weaving shed. And check which measurement the 6% was: crimp or take-up.