Yarn diameter:
The cross section of cotton yarn is more or less circular. Therefore, as the count of cotton yarn is equal to the number of length unit per weight unit it can be shown that for practical purposes, the diameter of yarns are approximately inversely proportional to the square root of the counts.
The diameter of cotton yarn for practical purposes,
1
= ………………………………… × inch approximately
√ (count × 840) – 8%
Example 01:
Find out the diameter of 25s cotton yarn.
Solution:
Diameter,
1
= ………………………………… inch
√ (count × 840) – 8%
1
= ………………………………. inch
√ ( 25 × 840) – 8%
1
= ……………. inch
133
= 0.0075188 inch
So, the diameter of 25s cotton yarn is 0.0075188 inch.
Cloth setting:
For cloths of ordinary structure the number of threads per inch that can be conveniently inserted will depend on the diameter of the yarn used and the number of insertions the threads make per repeat of the weave which is used in the cloth. As described above, the diameters of yarns can be found out if their counts are known. The number of insertions are can also be found out if the weave is known. The above factors being shown, the maximum setting for a square cloth, i.e. a cloth in which warp and weft threads bend to the same extent, can be found by the following formula,
Number of threads per repeat × Reciprocal of diameter of yarn
= ……………………………………………………………………………………
Number of insertions per repeat × Number of threads per repeat
And,
For a plain cloth the maximum setting,
2 × Reciprocal of diameter
= ………………………………………
2 + 2
2 × Reciprocal of diameter
= ……………………………………..
4
Reciprocal of diameter
= ……………………………………..
2
Example 02:
Find out the maximum setting for a warp of 40s cotton yarn that can be woven into a plain square cloth.
Solution:
Maximum setting,
Reciprocal of diameter
= …………………………………….. (1)
2
Now,
Diameter,
1
= ………………………………… inch
√ (count × 840) – 8%
1
= ………………………. inch
√ (40 × 840) – 8%
1
= ……… inch
168
Now, from (1) we have,
Maximum setting,
168
= ………
2
= 84
So, the maximum setting for a warp of 40s cotton yarn is 84.
