Textile Structure
how cloth is put together
Concept

Shaft — where it appears

A frame carrying the heddles of every end that is always lifted together, so a draft needs one per distinct column of its matrix. Their count is the number of distinct columns the matrix has, which is decidable from the draft alone and is what a loom budget is spent on.

Named by 6 essays across 4 fields — each of them below, with the objects they name alongside it.

What four notations can say. Four ways of writing a weave down, with how many of the 426 four-by-four cloths each can express and whether expressing one identifies it: point paper, 426, identifies; a four-part draft on 3 shafts and 4 treadles, 110, identifies; a fraction name, 5, does not identify; a longest-float specification, 426, does not identify. A longest-float specification names every cloth and separates them into only 3 classes.

Four ways to write a weave down

A weave's name in the trade is a pair of numbers — 2/2, 3/1, five-end satin — and the notation is so universal that it is easy to forget it is a notation. It has an image and the image is computable: of the 426 cloths at four by four, five have a name of that kind, and there are four names for the five.

cloth · Notation The shed in section. A warp line 1200 mm from the fell of the cloth at the left to the back rest at the right, with 8 shafts at 300 mm and every 16 mm behind it. Each shaft lifts its ends in proportion to its own distance from the fell, which is what gives the same 30 mm clear opening at the reed from every shaft. The resulting extension is 0.460 per cent at the front shaft and 0.722 per cent at the back, a ratio of 1.57. Vertical scale exaggerated 4 times.

The shed is an extension

Every model of a finished cloth treats a thread as inextensible, and every one of them is about a fabric that has left the loom. On the loom the warp is stretched thousands of times a minute by the shed itself, and the amount is exact trigonometry with nothing fitted in it: the square of the shed's tangent, times the shaft's own distance from the fell, over twice what is left behind it.

mechanics · Shed What a figure costs in shafts. Two families of block designs in 8-end satin on 8-end sateen at blocks of 8. One repeats three block-columns however wide it gets and costs 24 shafts at every width from 24 to 120 ends. The other gives every block-column a different pattern and costs 16, 24, 32, 40, 48 shafts as it grows — exactly 8 more per new column. Shafts are counted as distinct columns of the composite matrix.

What a figure costs the loom

A block design's shaft count does not depend on how wide the figure is, or how deep, or how many blocks it has. It depends on how many *different* block-columns it has, and each new one costs exactly one repeat of the ground weave — 8 shafts, then 16, then 24, in a straight line with no slope to fit.

pattern · Blocks The strain across a harness. The warp strain each shaft of a 24-shaft harness puts into its own ends, from 0.460 per cent at the front to 1.728 per cent at the back. Shafts within a budget of 1.0 per cent are drawn in one colour and those outside it in another; the budget is reached at shaft 13.

The back shaft works hardest

How hard the loom is on a warp end is the product of two numbers from different worlds — how often its column changes sides, which is a property of a binary matrix with no millimetre in it, and the strain of the shaft it happens to be on, which is a property of a machine with no weave in it. Neither knows about the other, and the threading that joins them is a decision nobody makes on structural grounds.

mechanics · Shed The harness a strain budget buys. How many shafts stay inside a 1.0 per cent warp-strain budget, against the clear shed opening the loom needs at the reed: 12 mm gives 43, 16 mm gives 36, 20 mm gives 28, 24 mm gives 21, 30 mm gives 13, 36 mm gives 7, 44 mm gives 1. The shed's tangent enters the strain squared, so the opening is much the strongest thing a loom builder controls.

The harness has a depth

Why does a dobby carry sixteen or twenty-four shafts rather than two hundred? The usual answers are about the mechanism — how many jacks a box can drive, how many hooks a dobby has — and they are real limits that are not the binding one. A stated tolerance on warp strain is a stated distance from the fell, and a stated distance is a whole number of shafts. One per cent buys thirteen.

fancy · Shafts Twelve eight-shaft lifting plans' silent errors, nested. The double threading errors silent under twelve eight-shaft lifting plans, over every threading that puts one end on each of eight shafts: 1/7 twill, 2/6 twill, 3/5 twill, 1/2/3/2 twill, satin, move 3, satin, move 5: 1,536; 4/4 twill: 1,888; 3/1/1/3 twill: 448; 2/1/1/4 twill: 256; broken 4/4 twill: 384; point 4/4 twill: 576; unrelated rows: 0. Plans in one box hide exactly the same errors. An arrow means every error silent under the first is silent under the second: 1/7 twill into 4/4 twill, 3/1/1/3 twill into 4/4 twill, 2/1/1/4 twill into 1/7 twill, 2/1/1/4 twill into 3/1/1/3 twill, broken 4/4 twill into point 4/4 twill, point 4/4 twill into 4/4 twill. The order is not total — the 3/1/1/3 twill and the satins each hide errors the other does not — but it has a top, the 4/4 twill, which hides every error any of the others hides. The plan of unrelated rows hides none.

An eight-shaft error hides in the row's mirror

At four shafts the lifting plans nest, with the 2/2 twill hiding every threading error the others hide. An eight-shaft loom has satins as well as twills, and their slides are different slides, so the order was expected to break. It does not. Over every threading that puts one end on each of eight shafts, the 4/4 twill hides every double error any of eleven other plans hides, and a satin hides exactly what a 1/7 twill hides, error for error. What decides it is not the slide. Every silent error is an exchange that turns the threading into a copy of itself, the slide accounts for one in six of them, and the rest hide in the row's mirror.

cloth · Notation

Named alongside it

The objects these essays reach for when they reach for this one.

HarnessLifting planLoomShedThreadingWarp strainBack restHeddleJacquardReedShift-ruleAbrasion

All concepts