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Doubling buys exactly the square root of the ends. Everything worse than that was made in the drafting zone.
Drafting-Wave CV
—%
The irregularity doubling does not explain
Draft Split & Irregularity
Total Draft
—x
Main Draft
—x
CV Doubling Alone Would Give
—%
Limit Irregularity
—%
Index of Irregularity
—x
Fibres in the Cross-Section
—
Doubling Improvement Factor
—x
Production
—kg/h
The decomposition assumes the feed ends are independent, which is the basis of the square-root rule. They are not independent if several ends come from the same card or the same can, and correlated feed is a real and common condition that makes the doubling improvement smaller than predicted - in that case the drafting-wave residual computed here is overstated, because the shortfall is being blamed on drafting. The limit irregularity is the Martindale figure for a random assembly of fibres of uniform linear density; a real fibre population has a spread of fineness, which raises the true limit slightly above the value shown. Measured CVs must be taken at the same cut length on the same instrument - a CV at 1 m and a CV at 1 cm are different quantities and cannot be combined. The drafting wave is periodic in nature and a CV alone does not locate it: use the spectrogram to identify the roller, and this figure to size the problem.
Using this calculator
About the Drawframe Draft, Doubling & Drafting-Wave Decomposition
The formula
This is the expression the tool evaluates. Every term is named underneath, with the unit it must be supplied in.
Draft across the whole machine and across the main zonetotalDraft = doublings x feedKtex / deliveryKtex mainDraft = totalDraft / breakDraft
Eight ends of 5 ktex entering and 4.5 ktex leaving means the machine drafted 40 ktex down to 4.5. The break draft is then split off, because the two zones do completely different jobs: the back zone only straightens and tensions, the front zone does the attenuation.
The irregularity no process can beatfibresInSection = deliveryKtex x 1000 / ( fibreDtex / 10 ) limitCv = 100 / sqrt( fibresInSection )
Fibres arrive in the cross-section at random, so the count follows Poisson statistics and its coefficient of variation is one over the square root of the mean. This is a floor set by the fibre and the linear density alone - no machine, however good, produces a sliver more even than this.
What doubling buysdoublingCv = inputCv / sqrt( doublings )
Combining independent ends averages their variation, and averaging n independent quantities divides the standard deviation by the square root of n. Eight ends therefore improve evenness by 2.83 times - exactly, and with no dependence on the machine.
Subtracting in variance, not in CVdraftingWaveCv = sqrt( measuredOutputCv^2 - doublingCv^2 )
Independent sources of variation add as variances, so they subtract as variances too. The residual is the irregularity the drafting zone introduced: roller settings, break draft, top-roller loading and apron condition all act here, and nothing else does.
Symbols used above
Symbol
Stands for
Unit
CV_lim
Limit irregularity, the Poisson floor for this sliver and fibre
%
I
Index of irregularity, measured CV over limit CV
x
n
Fibres in the sliver cross-section
—
D_b
Break draft, the back-zone draft
x
How the result is derived
Step by step, from the values you type to the figure on screen.
The 9 inputs are read from the form on every keystroke: Ends at the Creel, Feed Sliver, Delivered Sliver, Break Draft, Delivery Speed, Machine Efficiency, Feed Sliver CV, Delivered Sliver CV and Fibre Linear Density.
Each value is checked against the accepted range in the input table below. A value outside its range stops the calculation rather than producing a misleading figure — the results blank out and a message appears.
The validated values are substituted into the expression above, which resolves Drafting-Wave CV together with every supporting figure in one pass — no value is carried over from a previous entry.
The supporting outputs — Total Draft, Main Draft, CV Doubling Alone Would Give, Limit Irregularity, Index of Irregularity, Fibres in the Cross-Section, Doubling Improvement Factor and Production — come from the same pass, so they always describe the same case as the headline figure.
Results are rounded for display only. The full-precision value is used throughout the chain, so reading a rounded intermediate figure back into the tool by hand can shift the last digit.
What each input means
Where to read each value on the floor, the unit it must be in, and the range the tool accepts.
Input
Unit
Accepted range
Default
What it means
Ends at the Creel
—
1 to 16
8
Feed Sliver
ktex
0.5 to 20 ktex
5
Delivered Sliver
ktex
0.5 to 20 ktex
4.5
Break Draft
x
1 to 3 x
1.35
Draft in the back zone, before the main zone
Delivery Speed
m/min
50 to 1200 m/min
450
Machine Efficiency
%
20 to 100 %
85
Feed Sliver CV
%
0.3 to 15 %
3.8
Delivered Sliver CV
%
0.2 to 15 %
2.4
Fibre Linear Density
dtex
0.5 to 20 dtex
1.7
Cotton of 4.0 micronaire is about 1.7 dtex
What the tool returns
The headline figure and every supporting value it is built from.
Doubling alone would have given 1.34%; the limit is 0.61%
3
Index of irregularity 3.90 against 26,471 fibres in the section
4
Production 103.28 kg/h
The drafting wave at 1.99% is larger than the 1.34% the feed contributes after doubling - so most of what is wrong with this sliver was created by this machine, not inherited. That is a roller setting and top-roller loading conversation, and no amount of better card sliver will fix it.
How to use it
Work through the input groups in order — Draft & Doubling and Evenness. The defaults are a realistic case, so you can change one value at a time and watch what moves.
There is no calculate button. Every figure recalculates as you type or drag, which is what makes this usable for a what-if sweep rather than a single answer.
Read Drafting-Wave CV in the dark results panel — that is the headline figure, expressed in %.
Check the supporting rows underneath (Total Draft, Main Draft, CV Doubling Alone Would Give, Limit Irregularity, Index of Irregularity, Fibres in the Cross-Section, Doubling Improvement Factor and Production) before acting on the headline — they are where an implausible input usually shows itself first.
Reset to defaults returns every field to the reference case, which is the quickest way to check whether a surprising result came from the tool or from an input you had changed earlier.
Where this is used
Process planning — establishing Drafting-Wave CV before a trial is booked, so machine time and material in Blowroom, Carding, Drawing & Roving Control are committed against a calculated figure rather than an estimate.
Costing and quotation — Drafting-Wave CV is an input to the cost sheet, and quoting from a worked number rather than a remembered one is what keeps a margin intact.
Troubleshooting — when the floor result drifts from plan, entering the measured values (starting with Ends at the Creel) shows how much of the gap in Drafting-Wave CV each variable explains.
Teaching and study — the accepted ranges bracket normal Blowroom, Carding, Drawing & Roving Control practice, so moving one variable at a time shows the shape of the relationship rather than a single answer.
Reading the result
Typical bands and what each one is telling you.
Value
What it indicates
Index 1.0
The theoretical floor. Never reached by a real machine.
Index 2.0 - 3.0
Excellent drawframe sliver.
Index 3.0 - 4.5
Normal commercial drawn sliver.
Break draft 1.15 - 1.5
The usual window for cotton. Too low leaves fibres uncontrolled; too high starts the drafting wave in the back zone.
Assumptions and limits
The decomposition assumes the feed ends are independent, which is the basis of the square-root rule. They are not independent if several ends come from the same card or the same can, and correlated feed is a real and common condition that makes the doubling improvement smaller than predicted - in that case the drafting-wave residual computed here is overstated, because the shortfall is being blamed on drafting. The limit irregularity is the Martindale figure for a random assembly of fibres of uniform linear density; a real fibre population has a spread of fineness, which raises the true limit slightly above the value shown. Measured CVs must be taken at the same cut length on the same instrument - a CV at 1 m and a CV at 1 cm are different quantities and cannot be combined. The drafting wave is periodic in nature and a CV alone does not locate it: use the spectrogram to identify the roller, and this figure to size the problem.
Every input is bounded to the range normal practice occupies (Ends at the Creel 1 to 16, Feed Sliver 0.5 to 20 ktex and Delivered Sliver 0.5 to 20 ktex, and so on for the rest). Those bounds are guard rails against typing errors, not a claim that the formula fails one unit outside them.
The calculation is deterministic: the same inputs always give the same result. It carries no allowance for machine condition, operator skill, ambient conditions or lot-to-lot material variation unless an input above explicitly represents one.
Nothing is sent anywhere. The maths runs in your browser, so the numbers you type never leave the page.
Standards and further reading
ASTM D1425 - Unevenness of Textile Strands Using Capacitance Testing Equipment.
ISO 16549 - Textiles, Unevenness of textile strands, Capacitance method.
Martindale, J. G. (1945) - the derivation of the limit irregularity from fibre count statistics.
USTER Statistics, for the index of irregularity benchmarks by process stage.
Questions people ask
Why subtract in variance rather than subtracting the CVs directly?
Because variances of independent sources add, and CVs do not. Subtracting 1.34 from 2.4 directly gives 1.06%, where the correct answer is 1.99% - a 47% understatement of the drafting wave, which would make a machine with a real drafting problem look nearly clean. The same rule governs every irregularity budget in spinning, and getting it backwards is one of the more expensive arithmetic errors available.
What is the index of irregularity actually for?
Comparing across counts and materials. A 2.4% CV is excellent on a fine roving and poor on a coarse sliver, because the limit itself moves with the fibre count in the cross-section - the raw CV cannot be compared between them. Dividing by the limit removes that dependence, so an index of 3.9 means the same thing on any linear density and any fibre. It is the only fair way to compare two machines running different articles.
Does more doubling always give a better sliver?
It always improves the inherited part, but with diminishing returns, and it costs elsewhere. Going from 6 ends to 8 improves the doubling factor from 2.45 to 2.83 - about 14%; going from 8 to 12 gains another 22%, but the total draft rises in step and a higher draft makes a larger drafting wave. Since the drafting wave here is already the larger term, adding ends would make the sliver worse. That is the trade this decomposition exists to expose.
How should break draft be set?
By what the back zone is for, which is straightening rather than attenuating. Too little and the fibres enter the main zone hooked and uncontrolled; too much and the back zone starts drafting properly, without the fibre control the front zone has, and generates its own wave. For cotton the window is roughly 1.15 to 1.5, and it should be raised for longer fibre and for heavier feed. If the drafting-wave residual moves when break draft is changed, the setting was the cause - that is the experiment this figure makes possible.
