Paper Cup Stack Height and Line Compatibility: Why a Magazine Runs Out
Stack-height questions arrive when a cup runs on one filler and jams or runs short on another, or when a magazine that should hold fifty cups only takes forty-four. The stack height is a product of cup height, wall thickness and the denesting gap, and it is usually specified only as a range without reference to the machine. The answers below cover what sets it and how to align it with a line.
What determines the height of a stack of cups?
The cup height plus the distance each cup sits above the one below it. That distance is set by the taper and by the rim geometry: two cups nest until their rims contact, and the amount of insertion depends on how the rim is formed. A cup with a thicker rim sits higher in the stack, so a change in rim design alters the stack height without altering the cup height at all. This is why stack height must be measured, not calculated from a drawing.
Why does a magazine care?
Because the magazine holds a fixed length. If a stack of fifty cups is taller than the magazine's usable length, the magazine holds fewer than fifty, and the line runs out at the wrong point in a cycle. If the stack is shorter, the cups rattle and the denesting pick can miss. Both failures look like machine faults and are actually product-fitting faults, which is why the magazine dimension belongs in the cup specification.
ISO 534 Paper and board — Determination of thickness, density and specific volume.
How should stack height be measured?
Assemble a stack of a defined count, let it settle under its own weight for a defined time, and measure the total length. Report it for the count the machine uses, not for a single cup, because the insertion varies along the stack as the lower cups compress. Measuring at the top, middle and bottom of a full magazine gives the distribution the line actually sees.
What does humidity do to stack height?
It changes both the cup height and the insertion. Paper absorbs moisture and the cup grows slightly; the rim also softens, so cups insert further and the stack becomes shorter even as each cup becomes taller. The two effects partly cancel, which makes the result hard to predict and easy to misdiagnose. A stack measured in a dry packing room and used in a humid filling hall can differ enough to change the magazine count.
How should stack height be specified?
As a range for a defined count, measured after a defined settling time, at a stated humidity. Then state the magazine's usable length and the count the machine needs. Those two numbers together define whether a cup will run, and either party can check them without a trial. Asking for a single stack height is not useful because the machine needs a window, not a point.
Standard Practice for Conditioning Containers, Packages, or Packaging Components for Testing.
What else changes the count in practice?
Two things that are easy to overlook. Cups that have been compressed in transport are shorter for a day or two as the rim recovers, so a batch measured on arrival reads low. And cups from different cavities in the same tool can nest slightly differently if the rim tools are not identical, producing a stack whose height depends on the order the cups were packed. Packing by cavity, or verifying cavity-to-cavity stack height, removes that source.
What should the purchase order state?
The stack height range for a defined count and settling time, the humidity at measurement, the cup height with tolerance, the rim design with its thickness, and the magazine dimensions the cups must suit. Add a requirement to re-measure stack height after any rim tool change, because the rim is the feature that sets insertion and therefore the only feature that can move the stack without moving the cup.