Finding the Length, Hanks, and Weight of Yarn in a Given Length of Cloth
This calculation is used in weaving to find how much weft yarn is required to produce a cloth of a given width, length, and number of picks per inch.
In simple terms, it answers the question:
If I weave this much fabric, how many yards, hanks, or pounds of weft yarn will I consume?
1. What Is Being Calculated?
In woven fabric, there are two main sets of yarns:
| Yarn Direction | Meaning |
|---|---|
| Warp | Lengthwise yarns running along the length of the fabric |
| Weft | Crosswise yarns inserted across the width of the fabric |
This rule is mainly concerned with the weft yarn.
For example, if a fabric is 30 inches wide and has 60 picks per inch, it means that in every one inch length of cloth, there are 60 weft threads, and each weft thread runs across 30 inches of width.
Therefore, the weft yarn required for one inch length of cloth is:
\(30 \times 60 = 1800 \text{ inches of yarn}\)
This means that for every inch of cloth length, the loom consumes 1800 inches of weft yarn.
2. Main Rule
The basic rule is:
\[ \text{Yards of weft yarn in 1 yard of cloth} = \text{Width in inches} \times \text{Picks per inch} \]
In symbolic form:
\[ L = W \times P \]
Where:
- \(L\) = yards of weft yarn in one yard of cloth
- \(W\) = width of cloth in inches
- \(P\) = picks per inch
3. Example: Length of Yarn in One Yard of Cloth
Suppose:
- Width of cloth = 30 inches
- Picks per inch = 60
\[ 30 \times 60 = 1800 \]
Therefore:
One yard of cloth requires 1800 yards of weft yarn.
This may appear surprising at first, but it is correct. Each pick travels across the full width of the cloth, and there are many picks in every inch of cloth length.
4. Example: Length of Yarn in 50 Yards of Cloth
If one yard of cloth requires 1800 yards of weft yarn, then 50 yards of cloth will require:
\[ 1800 \times 50 = 90{,}000 \]
Therefore:
50 yards of cloth require 90,000 yards of weft yarn.
The general formula becomes:
\[ \text{Total yards of yarn} = W \times P \times Y \]
Where:
- \(W\) = width in inches
- \(P\) = picks per inch
- \(Y\) = length of cloth in yards
5. Converting Yarn Length into Hanks
After finding the total yarn length, it can be converted into hanks. Different yarn count systems use different hank lengths.
| Yarn System | One Hank Equals |
|---|---|
| Cotton | 840 yards |
| Worsted | 560 yards |
| Linen | 300 yards |
| Woollen | Varies according to the count system |
The formula for hanks is:
\[ \text{Number of hanks} = \frac{\text{Total yards of yarn}}{\text{Yards per hank}} \]
6. Example: Converting 90,000 Yards into Worsted Hanks
For worsted yarn:
\[ 1 \text{ hank} = 560 \text{ yards} \]
Therefore:
\[ \frac{90{,}000}{560} = 160.71 \]
So:
90,000 yards = approximately 160.71 worsted hanks.
7. Example: Converting 90,000 Yards into Cotton Hanks
For cotton yarn:
\[ 1 \text{ hank} = 840 \text{ yards} \]
Therefore:
\[ \frac{90{,}000}{840} = 107.14 \]
So:
90,000 yards = approximately 107.14 cotton hanks.
8. Finding the Weight of Yarn
Once the number of hanks is known, the weight can be found using the yarn count.
In indirect count systems, such as cotton count or worsted count:
\[ \text{Count} = \frac{\text{Number of hanks}}{\text{Weight in pounds}} \]
Therefore:
\[ \text{Weight in pounds} = \frac{\text{Number of hanks}}{\text{Count}} \]
9. Example: Weight of 20s Worsted Yarn
We have already found:
\[ 160.71 \text{ worsted hanks} \]
If the yarn count is 20s:
\[ \frac{160.71}{20} = 8.035 \]
Therefore:
The weight of 20s worsted yarn required is approximately 8.04 lb.
10. Example: Weight of 20s Cotton Yarn
We have already found:
\[ 107.14 \text{ cotton hanks} \]
If the yarn count is 20s:
\[ \frac{107.14}{20} = 5.357 \]
Therefore:
The weight of 20s cotton yarn required is approximately 5.36 lb.
11. Complete Formula Set
Let:
- \(I\) = width of cloth in inches
- \(P\) = picks per inch
- \(Y\) = length of cloth in yards
- \(N\) = yards per hank
- \(C\) = yarn count
Total Yarn Length
\[ \text{Total yarn length in yards} = I \times P \times Y \]
Number of Hanks
\[ \text{Hanks} = \frac{I \times P \times Y}{N} \]
Weight of Yarn
\[ \text{Weight} = \frac{I \times P \times Y}{N \times C} \]
12. Practical Example in One Table
Suppose the following details are known:
| Item | Value |
|---|---|
| Cloth width | 30 inches |
| Picks per inch | 60 |
| Cloth length | 50 yards |
| Yarn count | 20s |
| Cotton hank length | 840 yards |
| Worsted hank length | 560 yards |
Step-by-Step Calculation
| Calculation | Cotton | Worsted |
|---|---|---|
| Total yarn length | 90,000 yards | 90,000 yards |
| Hanks | \(90{,}000 / 840 = 107.14\) | \(90{,}000 / 560 = 160.71\) |
| Weight for 20s yarn | \(107.14 / 20 = 5.36\) lb | \(160.71 / 20 = 8.04\) lb |
Therefore, for the same cloth:
- If the yarn is 20s cotton, the required weight is about 5.36 lb.
- If the yarn is 20s worsted, the required weight is about 8.04 lb.
The difference arises because cotton and worsted systems define hank length differently.
13. Important Limitation: No Allowance for Shrinkage or Waste
The formula gives the theoretical yarn requirement. It does not include practical allowances such as:
- weaving waste,
- loom waste,
- selvedge waste,
- shrinkage,
- crimp,
- take-up,
- pattern effect,
- difference between reed width and finished width,
- yarn contraction,
- processing loss.
In actual weaving, the real yarn requirement will usually be higher than the theoretical value.
For example, if the theoretical requirement is 90,000 yards and a 5% allowance is added:
\[ 90{,}000 \times 1.05 = 94{,}500 \]
Therefore, the practical yarn requirement becomes:
94,500 yards
Similarly, for weight:
\[ 5.36 \times 1.05 = 5.63 \text{ lb} \]
So the practical cotton yarn requirement becomes approximately:
5.63 lb
14. Why No Fixed Allowance Is Given
A fixed wastage percentage cannot be applied universally because wastage and shrinkage depend on many variables.
| Factor | Effect |
|---|---|
| Yarn type | Cotton, wool, silk, and synthetic yarns behave differently |
| Yarn twist | High-twist yarn may contract differently |
| Fabric structure | Plain, twill, satin, dobby, and jacquard structures consume yarn differently |
| Picks per inch | Higher picks may increase crimp and take-up |
| Loom type | Handloom, powerloom, rapier, air-jet, and shuttle looms differ |
| Width in reed vs finished width | Fabric may contract after weaving |
| Finishing process | Washing, dyeing, calendaring, mercerising, and sanforising affect dimensions |
| Selvedge construction | Extra yarn may be consumed at the edges |
The best practical method is:
First calculate the theoretical yarn requirement, then add an allowance based on experience with that yarn, loom, fabric structure, and finishing route.
15. Difference Between Warp and Weft Calculation
For warp, the usual calculation is:
\[ \text{Total warp length} = \text{Number of ends} \times \text{Length of warp} \]
This is because warp threads run lengthwise.
But for weft, the yarn runs across the width of the cloth. Therefore, we calculate:
\[ \text{Total weft length} = \text{Width} \times \text{Picks per inch} \times \text{Length} \]
| Warp Calculation | Weft Calculation |
|---|---|
| Based on total number of ends | Based on picks per inch |
| Threads run along fabric length | Threads run across fabric width |
| Length of each warp end is known | Length of each pick equals cloth width |
| Formula uses ends × length | Formula uses width × picks × length |
16. Practical Use in Weaving and Merchandising
This calculation is useful for:
- estimating weft yarn consumption,
- costing fabric,
- planning yarn purchase,
- using up leftover yarn lots,
- deciding how many metres or yards can be woven from available yarn,
- checking whether a given yarn stock is enough for production,
- comparing fabric constructions,
- estimating fabric weight,
- planning small batch weaving.
17. Rearranged Formulae
The main formula is:
\[ \text{Weight} = \frac{I \times P \times Y}{N \times C} \]
From this, the formula can be rearranged depending on what needs to be found.
A. To Find Picks per Inch
\[ P = \frac{\text{Weight} \times N \times C}{I \times Y} \]
Use this when the available yarn weight, yarn count, cloth width, and cloth length are known, and the required picks per inch are to be found.
B. To Find Cloth Length
\[ Y = \frac{\text{Weight} \times N \times C}{I \times P} \]
Use this when the available yarn weight, yarn count, cloth width, and picks per inch are known, and the possible cloth length is to be found.
C. To Find Cloth Width
\[ I = \frac{\text{Weight} \times N \times C}{P \times Y} \]
Use this when the available yarn weight, yarn count, picks per inch, and required length are known, and the possible cloth width is to be found.
D. To Find Yarn Count
\[ C = \frac{I \times P \times Y}{N \times \text{Weight}} \]
Use this when the target yarn weight, width, picks per inch, and cloth length are known, and the required yarn count is to be found.
18. Practical Example: How Much Cloth Can Be Woven from Available Yarn?
Suppose:
| Item | Value |
|---|---|
| Available cotton yarn | 6 lb |
| Count | 20s cotton |
| Width | 30 inches |
| Picks per inch | 60 |
| Cotton hank length | 840 yards |
Formula:
\[ Y = \frac{\text{Weight} \times N \times C}{I \times P} \]
Substituting the values:
\[ Y = \frac{6 \times 840 \times 20}{30 \times 60} \]
\[ Y = \frac{100{,}800}{1800} \]
\[ Y = 56 \]
Therefore:
6 lb of 20s cotton yarn can theoretically weave 56 yards of cloth.
If a 5% allowance for waste and shrinkage is added, the practical cloth length will be slightly lower:
\[ 56 \div 1.05 = 53.33 \]
So practically, the weaver may expect about:
53 yards of cloth
19. Essence of the Calculation
To calculate the weft yarn required in a fabric, multiply:
\[ \text{Width} \times \text{Picks per inch} \times \text{Length} \]
This gives the total length of weft yarn. Then convert it into hanks using the hank length for that yarn system. Finally, divide by count to get weight.
Key Formula
\[ \boxed{ \text{Weight} = \frac{ \text{Width in inches} \times \text{Picks per inch} \times \text{Length in yards} }{ \text{Yards per hank} \times \text{Count} } } \]
Practical Note
\[ \boxed{ \text{Actual yarn required} = \text{Theoretical yarn required} + \text{Allowance for waste, shrinkage, and take-up} } \]
In weaving practice, the theoretical calculation should always be adjusted based on experience with the yarn, loom, fabric construction, and finishing process.
Conclusion
This rule is a simple but powerful textile calculation. It connects the geometry of woven cloth with yarn count systems and practical production planning. By knowing the width of the fabric, picks per inch, cloth length, yarn count, and hank length, a weaver or fabric planner can estimate the weft yarn required for production.
However, the calculation should not be treated as the final practical requirement. It gives the theoretical consumption. In actual weaving, shrinkage, crimp, take-up, loom waste, selvedge loss, and finishing effects must also be considered.
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