Textiles & Fabric formula solvers
Crimp and Take-up Conversion
Textiles & FabricCrimp and take-up describe the same waving of yarn in cloth and differ only in what they are measured against: crimp is the excess yarn as a fraction of the FABRIC length, take-up is the same excess as a fraction of the YARN length. Take-up is therefore always the smaller number, and the two are never interchangeable.
Crimp Percentage
Textiles & FabricA yarn in a woven cloth does not run straight — it waves over and under the threads crossing it, so a metre of cloth swallows more than a metre of yarn. Crimp is that excess, expressed as a fraction of the cloth length. It is measured by unravelling a marked length, straightening the yarn under a standard tension, and measuring what comes off.
Direct Count from Mass and Length — Tex, Decitex and Denier
Textiles & FabricThe whole of the direct count system in one division: weigh a measured length of yarn and divide. Tex is the grams in 1000 m, decitex the grams in 10 000 m, denier the grams in 9000 m — three names for one measurement made against three reference lengths, which is why denier = 9 × tex and dtex = 10 × tex exactly.
Fabric Cover Factor — Warp and Weft Combined
Textiles & FabricThe two thread systems of a woven cloth do not cover independently: where a warp thread crosses a weft thread, the same square millimetre is covered twice and must only be counted once. Subtracting the overlap gives a single figure for how much of the cloth is thread and how much is hole — the number that decides whether a fabric is a sheer, a shirting or a sailcloth.
Fabric Weight from Construction — GSM
Textiles & FabricWhat a square metre of woven cloth weighs, built from the specification rather than a scale: for each thread system, threads per unit length times mass per unit length, raised by the crimp because the yarn in the cloth is longer than the cloth it sits in. Threads per metre multiplied by kilograms per metre is kilograms per square metre — the arithmetic is dimensionally exact, with no conversion factor to lose.
Munden's Stitch Density for Plain Knit
Textiles & FabricMunden's 1959 finding, and one of the cleanest results in textile science: the dimensions a relaxed plain-knit fabric settles at depend on the STITCH LENGTH and on essentially nothing else — not the yarn count, not the fibre, not the machine gauge. Courses and wales per unit length each go as the reciprocal of the loop length, so stitch density goes as its reciprocal square, with constants that are properties of the knitted structure itself.
Surface Twist Angle of a Yarn
Textiles & FabricUnroll one turn of the outermost fibre and you get a right triangle: the circumference πd along one side, the length of one turn 1/T along the other. The angle between them is what twist actually does to a yarn, and it is the quantity the twist multiplier exists to hold constant across counts.
Twist Factor — Metric and Tex Systems
Textiles & FabricThe same square-root law as the English twist multiplier, expressed in turns per metre over the square root of the metric count. Typical values run near 60 for a soft knitting yarn, 100 for weft, 120 to 140 for warp — larger numbers than TM only because the length unit is a metre rather than an inch.
Twist Multiplier — English System
Textiles & FabricThe number a spinner actually specifies. Turns per inch alone says nothing useful, because a fine yarn needs far more turns than a coarse one to reach the same helix angle at its surface. Dividing by the square root of the English cotton count removes the fineness and leaves a figure that describes the CHARACTER of the yarn: about 3 for a soft hosiery yarn, 4 for weft, 4.5 to 5 for warp, 6 and up for a hard voile.
Warp or Weft Cover Factor from Setting and Count
Textiles & FabricOne thread system's contribution to how much of the cloth is covered: threads per inch divided by the square root of the English cotton count. The square root is there because the yarn's diameter goes as the square root of its linear density, so this ratio is really diameter over spacing in disguise.
Yarn Count Conversion — Direct and Indirect Systems
Textiles & FabricThe one relation that crosses between the two ways of numbering a yarn. Direct systems — tex, decitex, denier — state mass per unit length and get bigger as the yarn gets coarser. Indirect systems — English cotton count Ne, metric count Nm, worsted Nw, linen lea — state length per unit mass and get bigger as the yarn gets finer. Their product is a constant fixed by whatever hank length and unit of mass the system was built on.
Yarn Diameter from Linear Density
Textiles & FabricA yarn treated as a solid cylinder of uniform bulk density: linear density divided by bulk density is the cross-sectional area, and the diameter follows. This is the relation hiding inside the old rule d = 1/(28√Ne) inches, and writing it in full shows what that 28 was quietly assuming about how tightly the fibres are packed.