Paper cup bottom reel yield connects purchased material to usable bottom discs. Reel weight alone cannot predict output without net board mass, width, basis weight and the actual punching layout. A transparent estimate helps plan reel changes and investigate consumption differences without confusing theoretical geometry with accepted production.
This article provides arithmetic for a defined single-lane layout. The examples are hypothetical, not recommended feed settings or tooling dimensions. Confirm reel compatibility, pitch, margins and disc geometry with the machine supplier. Never change punching pitch or guarding based on a yield calculation alone.
Decision worksheet
| Input | Unit | Evidence |
|---|---|---|
| Net board mass | kg | Gross mass less verified tare |
| Reel width | m | Measured usable stock width |
| Basis weight | g per square metre | Defined full material construction |
| Feed pitch | m per cycle | Approved layout and machine record |
| Usable length | m | Net of documented unusable sections |
Confirm what the purchased mass includes
Remove core, wrapping and other packaging from gross reel mass using verified tare values. Check whether the stated basis weight covers the complete coated construction or only the paper substrate. If the mass includes coating but the denominator excludes it, the estimated length will be biased.
Use actual width and an appropriate representative basis-weight value. Record the material lot and measurement method. Nominal values can support an early estimate, but do not treat them as measured production evidence. Where width, moisture or basis weight varies meaningfully, present a range rather than a precise-looking single number.
Convert net mass into estimated reel length
For uniform material, estimated length in metres equals net mass in kilograms multiplied by 1,000, divided by width in metres times basis weight in grams per square metre. The units matter: entering millimetres as metres creates a thousand-fold error. Keep the unit conversion visible in the worksheet.
For an illustrative 12 kg reel, 0.08 m width and 250 g per square metre full-construction basis weight, estimated length is 600 m. This assumes uniform material and accurate inputs. A supplier’s measured length, when available and traceable, provides a useful independent cross-check.
Apply the approved layout and usable length
For a single lane producing one disc per cycle, theoretical cycles equal usable reel length divided by approved feed pitch. If 10 m of the illustrative 600 m is unusable and pitch is 0.07 m, 590 divided by 0.07 gives about 8,428 complete cycles after rounding down.
The example does not specify a disc diameter or prove that the layout is physically suitable. The actual pitch must allow the approved geometry and web support. Multi-lane or staggered layouts require the correct discs-per-repeat and repeat-length calculation. Obtain that layout rather than extending the single-lane equation by guesswork.
Distinguish theoretical discs from accepted cups
Deduct or separately record failed punches, misfeeds, setup use and rejected cups after bottom insertion. A correctly punched disc is not automatically a saleable cup. Keep the stages visible so a forming-quality problem is not misreported as poor reel-length yield.
Reconcile reel changes with residual stock still on the core, splices, damaged sections and end-of-roll restrictions. Avoid counting the same startup material both as unusable length and as rejected punched discs. Compare actual cycle counts and scrap streams against the estimate, then investigate the largest supported difference first.
Use yield information in purchasing and scheduling
Translate the verified disc yield into expected reel changes for a planned order, with documented uncertainty. Check whether more frequent changes affect staffing and downtime. Do not purchase a wider or heavier reel solely to reduce change frequency; shaft, handling, unwind and material compatibility must be confirmed.
Send HANNAI the reel width, core and outside dimensions, full material basis weight, net mass, drawing and approved feed layout. When actual yield differs, include counters, residual mass and scrap categories. Keep the calculation revision linked to the relevant cup format and material lot so comparisons remain meaningful.
Related equipment and next checks
Review the HN-M100 automatic paper cup machine and the related guide to bottom-roll slitting and feeding preparation. The Engineering Notes archive connects these checks with wider machine planning.
Frequently asked questions
Can gross reel weight be used directly?
Not for net board yield; subtract core and packaging tare.
Does substrate basis weight include coating?
Not necessarily. Confirm which material construction the declared value describes.
Can feed pitch be reduced to improve yield?
Only after supplier-approved tooling and process review; the arithmetic does not authorize a setting change.
Why is actual cup output below estimated disc count?
Setup, punching, transfer and downstream quality losses occur at different stages.
Review the evidence with HANNAI
Send the bottom-stock construction, net reel mass, width, core dimensions and approved punch layout. Include actual counts and residual material when investigating a yield difference.