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Fabric Design · Lecture 12
Fabric Analysis II – Yarn Diameter
Estimating the diameter of a yarn from its count and specific volume — the number behind every cover and crimp calculation.
Specific volumed = √tex / 26.7d = 0.9 / √Ne
From count to diameter
Treat the yarn as a cylinder of specific volume v (cm³ per gram; about 1.1 for a cotton yarn in cloth). One metre of yarn of N tex weighs N/1000 g and occupies N·v/1000 cm³; equate that to the cylinder volume π d² l / 4 and solve:
d = √( 4 v N / (π l) ) ⇒ d (mm) = √tex ÷ 26.7 · d (mm) = 0.9 ÷ √Ne · d (in) ≈ 1 ÷ (28 √Ne)
| A | B | C | D | |
|---|---|---|---|---|
| 1 | Yarn A | Yarn B | Yarn C | |
| 2 | Count Ne | |||
| 3 | Specific volume (cm³/g) | |||
| 4 | Tex | 29.53 | 19.69 | 14.77 |
| 5 | Diameter from v (mm) | 0.203 | 0.166 | 0.144 |
| 6 | Diameter, √tex ÷ 26.7 (mm) | 0.204 | 0.166 | 0.144 |
| 7 | Diameter, 0.9 ÷ √Ne (mm) | 0.201 | 0.164 | 0.142 |
| 8 | Threads per inch if touching (25.4 ÷ d) | 126.2 | 154.6 | 178.5 |
blue = input (edit me)grey = formula (click to see it)
An Ne 20 yarn is about 0.2 mm across: 126 of them touching fill an inch, which is why the maximum cover factor per direction is about 28 (126 ÷ √20). A 1 cm³/g assumption makes the yarn 5% thinner; real cotton yarns in cloth are flattened and cover more than the circular model predicts.
Original lecture material
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