Jacquard Cards and Cloth

What is modelled

On a Jacquard loom each card is read as one row of holes. A hole raises the hook, and its warp thread, for that pick of the weft; no hole leaves the thread down. Twelve cards of twenty-four holes repeat across the cloth. The page weaves the pattern pick by pick and works out what the pattern means for the cloth.

Equations

• Float length: the run of consecutive picks over which a warp thread stays on the same side of the weft, counted cyclically along the card chain.
• Output L = speed × efficiency × 60 / (picks per cm × 100) metres per hour.
• Cloth weight 0.1 (EPC Tw (1 + cw) + PPC Tf (1 + cf)) in g/m², with crimp c estimated from how often the threads change side.
• Thread diameter d = 0.0357 √(tex / 0.9) mm and cover factor K = e + p − e p with e = EPC d, p = PPC d, both at most 1.

Checks run in the page

• Float runs counted two ways, and their lengths summing to every cell of the pattern.
• A stepped hour of weaving against the output formula.
• Yarn masses in one square metre against the weight formula.
• Jamming warp density by bisection against 1 / d.

Honest simplifications

The crimp is a simple linear estimate from the interlacing frequency, not Peirce geometry solved for the actual thread bending; yarn density is taken as 0.9 g/cm³; the cloth is drawn as flat coloured cells with no shed geometry, beat-up or tension; and the pattern is limited to six built-in cards.

• Press Satin 12 and see the longest float jump compared with Plain.
• Press Fine silk, dense and watch the cover factor reach one as the threads touch.
• Press Heavy furnishing and read the cloth weight in g/m2.