A cop winder rotates a tube or spindle to take up yarn while a guide distributes the yarn along it. The historic mechanism shown here uses an arm pivoted to the frame, with a thread eye at its moving end. The calculator finds circumferential surface speed from the current cop diameter and spindle RPM.
Cop Winder Interactive Calculator
Adjust the cop diameter and spindle RPM to calculate circumferential winding speed. The rotating cop and supported guide arm show how rotation takes up yarn while traverse distributes it along the package.
Equation Used
- No slip between yarn and the selected cop surface.
- Diameter is the current winding diameter, not the bare tube diameter.
- Guide traverse, package taper and bearing geometry are illustrative.
- Actual permissible RPM depends on the machine, yarn, tension and package build.
- Animation spindle speed is reduced by 600; guide motion has a separate illustrative 12-second period.
The circumference result is the distance around the cop at the selected winding diameter. No safe speed, yarn tension or breakage probability is inferred from diameter and RPM alone.
A rotating cop and a rocking thread guide
The spindle and cop rotate together inside stationary supports. Yarn passes through the eye on a pivoted arm and onto the cop. Rocking the arm moves the winding location along the package.
Hiscox illustrates this arrangement as mechanism 1438. The guide-arm movement is illustrative because the traverse drive and gearing are not specified. The spindle rotation responds to RPM, and cop width responds to diameter.
Preparing a yarn package
Cop winding prepares a compact yarn package for subsequent textile operations. Winding rotation takes up the yarn, while traverse distributes successive turns. Tension and package-build control also matter but are outside this two-input calculator.
This is an explanatory historic mechanism, not a dimensioned replica or a performance model for a particular modern winding machine.
Diameter, circumference and surface speed
One revolution carries a surface point through the circumference πD. With D in millimetres and spindle speed N in revolutions per minute, the circumferential speed is πDN/1000 metres per minute. Multiply by 3.28084 for feet per minute. The spindle rate in revolutions per second is N/60.
This excludes the axial component of a helical winding path. A traverse rate and winding geometry would be needed to calculate the total yarn-path speed and winding pitch.
Example at 50 mm and 5000 rpm
The circumference is about 157.1 mm per turn. At 5000 rpm the circumferential speed is 785.4 m/min, or about 2577 ft/min. The spindle makes 83.3 revolutions per second.
At the same RPM, increasing diameter from 50 to 90 mm increases surface speed by a factor of 1.8. Reducing spindle RPM in inverse proportion to diameter would hold that surface speed constant.
What the result does not predict
Diameter and RPM determine surface speed. They do not establish an overspeed-risk percentage or a universal safe winding speed. Yarn properties, tension, equipment and package build affect acceptable operating conditions.
The animation slows spindle rotation 600 times so it can be seen. The guide has a separate illustrative cycle: its relation to spindle speed is not a measured gear ratio. Package shape remains fixed during playback, rather than claiming to simulate layer-by-layer growth.
Cop-winder questions
Which diameter should I enter?
Use the current package diameter where yarn is being wound. The bare tube diameter gives a different surface speed.
Why does a larger cop wind faster at the same RPM?
Each turn covers a larger circumference, so πDN increases in proportion to diameter.
Does the animation calculate winding pitch?
No. The guide movement illustrates traverse. A traverse-rate input and a package-build law would be needed for pitch.
What does the circumference result mean?
It is the distance around the cop at the selected diameter: pi times diameter. Multiplying by spindle revolutions per minute gives circumferential surface speed.
Is the shown speed a safe operating limit?
No. It is a calculated surface speed, not a machine or yarn rating.
References
Gardner D. Hiscox, Mechanical Movements, Powers, Devices and Appliances,1901, mechanism 1438, printed page 344: cop tube and pivoted thread-guide arm.
Rieter Autoconer X6 specifications, for the distinction between calculated speed and equipment-, yarn- and build-dependent operating conditions. This modern package rewinder is not the historic mechanism illustrated above.
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