Two lots of one cloth drift apart down a drop

A patterned cloth has to be matched wherever two pieces of it meet. Across the width that is a question of where the repeat lands between the selvedges; along the length it is a whole repeat per panel, paid so that every panel starts at the same phase. That arithmetic took the match itself as exact — a match within a few millimetres reads as a match, and the slop is small against a repeat.

Within one lot of cloth it is. Two lengths cut from the same piece have the same repeat to the pick, and once they are matched at one height they stay matched at every height. Two lengths from two lots do not, and the reason is not carelessness at the cutting table. It is that a repeat has no fixed length.

A repeat is a count of picks. Its length on the loom is that count times the pick spacing, and its length in the finished cloth is what the loom length became when the cloth gave back the crimp the weaving had pulled out of it. How much it gave back depends on how hard the warp was held. Two lots woven a tenth apart in warp tension have repeats a hundredth apart in length — and matched at the top of a curtain drop, they are three centimetres apart at the hem.

A repeat’s length is decided after it is woven #

A drawn pattern has a size on the design paper, and the weaver translates it into picks. What comes off the loom is a cloth whose warp is still stretched: the loom held the warp under tension through the whole of weaving, pulling a fraction of its crimp out, and the cloth has not yet had the chance to take it back.

It takes it back in finishing. Wetting, washing and relaxing the cloth let the warp re-crimp until its threads stop pushing, and the cloth shortens along its length by the fraction of its length the loom had borrowed. Every repeat shortens with it. The finished repeat is the loom repeat times one minus the relaxation shrinkage, and that shrinkage belongs to the lot rather than to the design.

That is the omission a dimension without a state names in general: a length quoted without the state the cloth was in is not yet a measurement. A pattern repeat is a dimension like any other, and “a 32 cm repeat” is a length in one particular lot’s relaxed state.

How hard the warp was held decides how much it gives back #

The relaxation model computes the shrinkage from the crimp geometry of the relaxed cloth and the fraction of each crimp the loom pulled out. For the ordinary sheeting geometry it uses, a warp held at a tension that pulls out six tenths of its crimp relaxes by 6.80 per cent along the length, and one held at seven tenths by 7.94 per cent.

The relation is a straight line: each tenth of warp tension is 1.13 more points of shrinkage, up to a ceiling of 11.3 per cent where the loom would have pulled every last bit of crimp out and the cloth cannot shrink past its crimp. The weft is held more lightly and more consistently between the temples, and it gives back a steady 2.8 per cent whatever the warp does, so the difference between lots lives almost entirely along the length.

A tenth of warp tension is not a large difference between two looms, two warps or two weavers. Neither is it one anybody records on a piece ticket. Two lots of the same design woven at different times can differ by that much without any fault in either.

Matched at one height, two lots drift apart at the rate their shrinkages differ #

Hang a length from each lot side by side and match the pattern at the top. A repeat that is 32 centimetres in lot A is 31.61 in lot B, because B gave back more of its length. At the first mark down the two are 3.9 millimetres apart; at the second, 7.8; and the offset grows by the same amount at every repeat.

Measured per unit of drop, the offset grows at the difference in the two shrinkages divided by what is left of lot A: 12.2 millimetres for every metre. At the hem of a 250 cm curtain the two lengths are 30.4 millimetres apart. A pattern that matched perfectly across the seam at the heading is, at the hem, out by more than the width of a finger.

The rate is in proportion to the difference in warp tension. Lots five hundredths apart drift at half the rate, fifteen millimetres at the same hem; lots two tenths apart at twice it, sixty.

The repeat does not enter #

The offset at the hem is a length times a fraction. The size of the pattern is not in it. A two-centimetre sprig, a 32 cm damask and a 64 cm floral drift apart by the same 30.4 millimetres over the same drop, because each is the same cloth giving back the same share of its length.

What the size of the repeat changes is what the offset looks like. Against a 64 cm repeat, thirty millimetres is a twentieth of the pattern, a motif visibly stepped across a seam. Against a 32 cm repeat it is a tenth. Against a two-centimetre sprig it is one and a half repeats — and there the offset does something the large patterns never do within a drop: it comes back into register. Once lot B has fallen a whole repeat behind lot A, which for a two-centimetre sprig happens 164 centimetres down, the marks line up again, one repeat out of step, and the eye reads a match.

So a small repeat’s lot mismatch is a slow beat: matched at the top, stepped halfway down the first metre and a half, matched again, stepped again. A ten-centimetre repeat beats once in 8.2 metres, and a 32 cm repeat once in 26 — which is to say never, on any curtain.

Matching in the middle halves it #

A hanger who matches the two lengths at the middle of the drop rather than the top splits the offset: at the heading lot B is ahead by half the total and at the hem behind by half. For the 250 cm drop that is 15.2 millimetres at each end instead of 30.4 at one.

That is the only free lever, and it is worth exactly a factor of two. The two lengths still drift at the same rate; matching in the middle only chooses where the zero is. And it chooses it at eye height on a full-length curtain, which is where a mismatch is noticed first, so it spends the lever where it is most needed.

How long a drop stays matched #

Turn the question round. If a mismatch of three millimetres across a seam still reads as matched, how far down does a match made at the top survive? For lots a tenth apart in warp tension, 25 centimetres. Matched in the middle, 49 centimetres, split between the two ends. A tolerance of five millimetres buys proportionally more: 41 centimetres from the top, 82 from the middle.

Lots only five hundredths apart stay matched for 49 centimetres from the top and nearly a metre from the middle; lots two tenths apart, for 12 and 25. None of those is a curtain. On any drop long enough to be worth matching, two lots differing by the smallest tension anybody could notice will show the seam.

No cutting allowance can take it out #

A cutting room’s allowance of a repeat per panel exists to let every panel start at the same point in the repeat. It works because a panel’s length is free to be rounded up: cut long enough, any panel can be trimmed to start where the next one does.

The lot drift is not an offset in where the pattern starts, and rounding up does nothing to it. Both lengths can be cut to begin at exactly the same point in the pattern, and they will still disagree by a hundredth of every repeat below that point, because their repeats are different lengths. An allowance fixes where two patterns start; it cannot fix how long each repeat is.

There are three things that can. The first is to hang every length of a pair from one lot, which is why pattern-matched furnishings are ordered from a single lot and why a lot number is printed on the ticket. The second is to ease one length onto the other while making up — stretching the shorter or gathering the longer by a hundredth — which is possible in a soft cloth and not in a stiff one. For the 250 cm drop that is thirty millimetres of lot A worked into the same seam as lot B, about one millimetre in every eight centimetres of seam: well within what a soft furnishing cloth gives under a machinist’s hand, and more than a firm, closely set cloth will take without puckering along the whole seam. The ease has to be spread evenly, too, because a mismatch corrected at the hem and not in between is still a mismatch everywhere between. The third is to take the difference out before either lot is cut, by shrinking both to the same state — which works only as far as the residual shrinkage that remains is the same in both, and a cloth shrinks most the first time and differently thereafter.

Across the width the lots agree #

The same arithmetic run the other way says a seam across the width is safe. The weft is laid under a light tension that the temples hold nearly constant from pick to pick and lot to lot, so it gives back the same 2.8 per cent whatever was done to the warp. A pattern’s width repeat is a count of ends, and two lots with the same count of ends at the same reed relax to the same width within the weft’s own small variation.

So the mismatch has a direction. Two lengths hung side by side, joined by a seam that runs down the drop, disagree by the warp’s difference and show it more the further down the seam goes. Two pieces joined end to end, by a seam that runs across the width, meet along a line where both are cut at the same phase and their widths agree; the lot difference never has a length to accumulate over. That is why pattern matching across lots fails on curtains, wall hangings and upholstered panels whose widths are joined vertically, and very rarely on a table runner joined across its middle.

A printed pattern drifts by a different route #

Everything above is about a woven pattern, whose repeat is a count of picks and so is decided on the loom before the cloth relaxes. A printed pattern is laid on after. The cloth is scoured, relaxed and set before it reaches the printing table or the rotary screen, and the screen puts down a repeat of a fixed length in centimetres on cloth that has already given back most of what it borrowed.

For a printed pattern the lot difference in relaxation has therefore mostly been spent before the repeat exists, and what separates two lots is only the residual shrinkage each has left to give after printing — the part that a cloth gives back on its later washings, and which a finishing works can control far more tightly than a weaving shed can hold a warp. The same design printed on two lots drifts by a fraction of what the same design woven into two lots does.

That is also why a woven motif is drawn at the wrong shape on purpose: its designer knows the repeat will shrink by the relaxation along the length and less across it, and draws the motif taller on the paper so that it finishes the right shape. That correction is made once, for a stated relaxation. The lot drift is what happens when a second lot relaxes to a different number than the one the design was corrected for.

What was counted, and how #

The two shrinkages come from the relaxation model, the relaxed cloth from Peirce’s circular geometry at the default sheeting spacings, and the loom state from that cloth with a stated fraction of each crimp pulled out. A lot’s finished repeat is the reference repeat times the ratio of what is left of each lot after relaxation.

The offset was confirmed to double with the drop, to halve when the match is made in the middle, to reach the tolerance exactly at the computed longest matched drop, to be the same for repeats of 2, 10 and 64 cm, and to be nothing for two lots woven alike. A two-centimetre repeat was confirmed to drift exactly one repeat at its computed rematch drop. The numbers for lots a tenth apart — 1.13 points of shrinkage, 30.4 mm at a 250 cm hem, a 3 mm match lost 25 cm down — were checked against stated bounds rather than quoted.

Where the model stops #

Warp tension is one cause among several. Lots also differ in pick density, in the tension a stenter holds them at in finishing, in the moisture they were measured at and in how long they rested before cutting. Each moves the finished repeat by its own route. Warp tension is modelled because its effect is exact in the relaxation geometry and because it is enough, on its own, to break a match.

The cloth is the model’s sheeting. A heavier cloth with more crimp to give back has a steeper line and a higher ceiling; a cloth woven close to jamming has less. The slope of 1.13 points a tenth is this geometry’s, and the method, not the number, is what transfers.

The tolerance is a stand-in for an eye. Three and five millimetres are round numbers for how far a pattern can step across a seam before it reads as stepped. A high-contrast stripe shows less; a busy floral hides more. The longest matched drop scales in proportion to whatever the right number is.

And a hung length is not in its relaxed state for ever. Hanging stretches a curtain along its drop under its own weight, and humidity moves it daily. Both act on both lots alike, to first order, and so leave the difference between them where the relaxation put it.

Still open: how different two lots really are #

The model says a tenth of warp tension is enough to break a match on any curtain. What it cannot say is how much two lots of one design actually differ in a mill, and that is measurable with a tape before anything is cut. Ten repeats of a 32 cm pattern are 3.2 metres, and two lots differing by 1.13 per cent are 36 millimetres apart over that length — far more than a tape’s reading error.

A cutting room that measured ten repeats of every lot and recorded the length would have, within a season, the distribution of lot-to-lot repeat differences for each design and loom. That distribution, set against the longest matched drops here, would say how often an unmatched pair of lots is a real risk and how often it is a label printed out of caution.

Who worked it out #

That patterned cloth must be bought from one lot for matched work is trade knowledge as old as printed and woven furnishings, and the lot number on the ticket exists for it. Relaxation shrinkage as crimp coming back is Peirce’s geometry applied to the loom state. The drift rate, its independence of the repeat, the rematch of small repeats and the longest matched drops were computed directly.