Home › Weaving Calculations › Lecture 07
Weaving Calculations · Lecture 07
Beam Calculations
How much yarn fits on a beam — volume of the yarn annulus, packing density, weight, length and the fabric one beam will weave.
Beam volumePacking densityLength per beam
Yarn on a beam is a hollow cylinder
A beam full of yarn is a cylinder of diameter D (the yarn diameter at the flanges) with the barrel of diameter d removed, over the length L between the flanges:
Yarn volume = π/4 × ( D² − d² ) × L
Yarn packs at a known density — about 56 in³ per lb for a warped (unsized) beam and 60 in³/lb for a sized beam, which is bulkier because of the size film. Weight = volume ÷ density, and then the familiar count relation gives length:
Length on beam (yd) = weight × 840 × Ne ÷ ends on the beam
Beam worksheet
| A | B | C | |
|---|---|---|---|
| 1 | Warper’s beam | Sized beam | |
| 2 | Diameter with yarn, D (in) | ||
| 3 | Barrel diameter, d (in) | ||
| 4 | Length between flanges, L (in) | ||
| 5 | Packing density (in³ per lb) | ||
| 6 | Ends on the beam | ||
| 7 | Count Ne | ||
| 8 | Warp contraction (for fabric length) | ||
| 9 | Volume of full beam (in³) | 67,180 | 67,180 |
| 10 | Volume of barrel (in³) | 16,795 | 16,795 |
| 11 | Volume of yarn (in³) | 50,385 | 50,385 |
| 12 | Weight of yarn on beam (lb) | 899.7 | 839.7 |
| 13 | Length of yarn on beam (yd) | 23,741 | 3,693 |
| 14 | Fabric from one sized beam (yd) | 3,357 | |
| 15 | Fabric from one sized beam (m) | 3,070 |
blue = input (edit me)grey = formula (click to see it)
The same beam holds 23,700 yd of a 637-end warper’s beam but only 3,700 yd once all 3,820 ends are sized onto it — about 3,070 m of fabric A per weaver’s beam. The 20,000 m order of Lecture 6 therefore needs about 7 sized beams.
Original lecture material
Open the file this page was built from: