The yarn is yours; the warper makes the beam. In between, there is only one sure way to account for the yarn: the beam's weight. The formula tells you how much yarn should be on the beam; the scale tells you how much is.
The formula
Why 9,000,000?
Denier is the weight in grams of 9,000 m of yarn. Every end on the beam is as long as the beam, so the total yarn length is ends × metres. Divide that by 9,000 and multiply by the denier to get grams; divide by 1,000 again for kilos. 9,000 × 1,000 = 9,000,000 (90 lakh). That's all there is to it.
Example 1 — plain filament yarn
6,400 ends, a 7,500 m beam, 75 denier warp.
- 6,400 × 7,500 × 75 ÷ 9,000,000 = 400 kg
Example 2 — two-ply (two yarns twisted together)
4,800 ends, a 6,000 m beam. The warp is two 75 denier yarns twisted into one.
- Two-ply denier ≈ 75 × 2 = 150 denier
- 4,800 × 6,000 × 150 ÷ 9,000,000 = 480 kg
Twisting shortens the yarn a little, so the real denier comes out slightly above 150. Ask the supplier for the resultant (after-twist) denier — that is the most accurate.
Example 3 — a count yarn (2/40s cotton)
3,000 ends, a 5,000 m beam, 2/40s warp — two plies of 40s, about as thick as a 20s.
- Denier = 5,315 ÷ 20 = 265.75
- 3,000 × 5,000 × 265.75 ÷ 9,000,000 = 442.92 kg
Take "40" as the denier by mistake and you get 66.67 kg — almost seven times too little. Get the denier from a count in the yarn count converter; the full story is in denier vs count.
Checking a warper's beam
Put the beam on the scale as soon as it arrives. You need to know the empty beam's weight (with flanges) beforehand — it can differ from beam to beam, so paint it on the flange.
Gap % = (net yarn − formula kg) ÷ formula kg × 100
Actual metres (about) = net yarn × 9,000,000 ÷ (ends × denier)
Example
The beam from Example 1: 400 kg by the formula. On the scale the full beam is 532 kg and the empty beam 140 kg → net 392 kg.
- Gap: (392 − 400) ÷ 400 × 100 = −2%
- Actual metres: 392 × 9,000,000 ÷ (6,400 × 75) = 7,350 m — the card says 7,500, so about 150 m short
When there's a gap, check these one by one:
- Ends. How many cones were on the creel and how many sections were made — match them with the ends on the beam card.
- Metre counter. If the warping machine's counter is off, every section is short or long.
- Denier lot. A finer or coarser new lot changes the weight even when ends and metres are right.
- Sizing. A sized beam carries the weight of the size too, so it comes out heavier than the formula. Set the normal gap for sized beams from your own past beams.
Reconcile the yarn as well: yarn given to the warper − net yarn on the beam − yarn returned = wastage. Write this down for every beam and you'll see which warper shows more wastage.
Common mistakes
- Guessing the empty beam weight. A 5 kg wrong guess on a 400 kg beam is already a 1.25% gap.
- Using cloth metres. The formula takes the warp metres on the beam, not cloth metres. Crimp makes the cloth shorter — that calculation is in the takas from a beam guide.
- Treating a count as denier. See Example 3 — the gap is nearly sevenfold.
- Giving two-ply a single yarn's denier. A 2 × 75 warp is not 75 denier but at least 150.
- Forgetting selvedge ends. Count the edge ends too — see ends from reed and picks.
In Loomiro
In Loomiro's Beam Stock, enter each beam's ends, metres and denier — leave the weight blank and it is worked out as ends × metres × denier ÷ 9,000,000, or type in the weight from the scale. Beam cards print, and when the beam goes on a loom, Bhidan shows the expected takas. To see how many takas a beam will give, use the Beam → Taka calculator — it gives the beam's kilos as well.
The formula gives the weight of dry, unsized yarn. Moisture and size make a real beam a little different — set your unit's normal gap from past beams.