**Indirect or Fixed System of Count: **

An indirect system of yarn numbering and calculation system is the count of yarn expresses the number of length units in one weight unit. Higher the count finer is the yarn. This system is generally used for cotton, worsted, woolen, linen (wet spun), etc.

The indirect system of yarn numbering and calculation covers which is the majority of the important types of yarns. The yarn count calculation is based on the number of length units in one weight unit. Thus if 20 length units weigh one weight unit, itscount is 20’s: if 80 length units weigh one weight unit, its count is 80’s, and so on. It may be noted that finer or less bulky the yarn, higher is its count number or in other words, the size or bulkiness of the yarn is inversely proportional to the count number and that is why the system is known as an indirect system.

The disadvantages of this system are that the count number does not express directly the size of the yarn. As explained above a coarse or bulky yarn will have a smaller count number than a finer or less bulky yarn. Secondly, when calculating counts of folded yarns, it is more difficult to calculate the resultant count, especially when the component threads are different counts. The advantage of this system is the comparative ease with which the weight of fabrics can be calculated. The twist of the yarn, the setting of cloth, etc., can be more easily calculated as they are directly proportional to the square root of the counts of the yarn.

The table shows the different length and weight units used in important indirect systems.

**Table:** Different length and weight units used in important indirect systems

**Table:**Different length and weight units used in important indirect systems

Name of System |
Unit of Weight |
Unit of Length |

English Cotton | 1 lb | Hank of 840 yards |

French Cotton | 1 kg | Hank of 1000 meters. |

Bump Cotton | 1 oz | 1 yard. |

Decimal (for all yarns) | 1 lb | Hank of 1000 yards. |

Metric | 1 kg | Hank of 1000 meters. |

Spun Silk | 1 lb | Hank of 840 yards. |

Spun rayon staple fibers | 1 lb | Hank of 840 yards. |

Worsted | 1 lb | Hank of 560 yards. |

Linen ( Wet spun) | 1 lb | Lea of 300 yards. |

Hemp (fine) | 1 lb | Lea of 300 yards. |

Woolen- Yorkshire Skein | 6 lbs | Skein of 1536 yards. |

Woolen- American Cut | 1 lb | Cut of 300 yards |

Woolen- American Run | 1 oz | Run of 100 yards |

Woolen- Dewsbury | 1 oz | 1 yard |

Woolen- Hawick | 26 ozs | Cut of 300 yards |

Woolen- Galashiels | 24 ozs | Cut of 300 yards |

Woolen- Alloa | 24 lbs | Spyndle of 11520 yards |

Woolen-West of England | 1 lb | Snap of 320 yards |

Asbestos- British | 1 lb | Hank of 50 yards |

Asbestos – American | 1 lb | Cut of 100 yards |

Fiber Glass | 1 lb | 100 yards |

**Indirect System of Yarn Numbering and Calculation**

**Calculations:**

In The indirect system, we have the following:-

**Count = Number of length units per weight unit **

Or,

…………………Length in appropriate length unit

Count= ……………………………………………………………… ……..(1)

……………..Weight in corresponding Weight Unit

By cross multiplication, we have the following:-

…………………Length in appropriate length unit

Weight = ………………………………………………………… …….(2)

………………………………………Count

Length = Count X Weight in appropriate length unit …….(3)

It will be seen from the above that there are factors, vix., Count, length, weight, of which two must be given to find the third one.

**English Cotton System**

Count = No. of hanks of 840 yards weighing 1 lb.

……………….Length in Hanks

Count = ………………………………. ……………….. (1)

………………….Weight in lbs

Again from the formula,

……………….Length in Hanks

Count = ……………………………..

………………..Weight in lbs

We have,

……………………Length in yards/840

Count = ……………………………………………. ……..(4)

………………..Weight in grammes/7000

……7000…………..Length in yards

= …………… X ..………………………….. ………(5)

………840…………..Weight in grains

………………………….1000

= ………………………………………………………….. …..(6)

…….Weight in grains of 1 lea of 120 yards

………25……………Length in yards

= …………… X …………………………….. ………..(7)

………3……………..Weight in grains

………………..Length in yards

= 8.33 X …………………………… ……..(8)

………………..Weight in grains

From (5) by cross multiplications, we have,

…………………………….25…………..Length in yards

Weight in grains = ………… X …………………………… ..…….(9)

……………………………….3……………….Count

………………….Length in yards

= 8.33 X ………………………….. ……….(10)

…………………………Count

……………………………….3

Or, Length in yds. = ……… X Count X Weight in grains ……..(11)

………………………………25

The formula (6) is generally used in spinning mills, where a complete lea of 120 yards is reeled out from a bobbin, and tested for count, as well as for tensile strength.

Example: If 240 yards of cotton yarn weight 40 grains, what is the count of the yarn?

Solution:

Here,

……………………240

240 yards = …….……. hanks

……………………840

………………….40

40 grain = ………… Lbs

……………….7000

……………………………..Length in hanks

Therefore, Count = ……………………………

………………………………..Weight in lbs

……240 / 840

= …………………

……40 / 7000

= 50’s Cotton

#### Also directly applying formula (2),

……Length in appropriate length unit

= ………………………………………………………

………………………Count

……………..7000 X 240

Count = ………………………

………………..840 X 40

= 50’s Cotton

Again Applying formula (7),

…….25……..length in yards

= ……… X ………………………..

……..3………weight in grains

…………….25…………….240

Count = ……… X ………………

………………3………………40

= 50’s Cotton

Example: Find the weight 270 yards of 60’s cotton yarn.

Solution:

Here,

…………………270

270 yds.= …………… hanks

…………………840

…………………………………………………….Length in Hanks

Applying Formula , Weight in lbs. = …………………………..

………………………………………………………………Count

We have,

……………………….Length in hanks

Weight in lbs. = ………………………

………………………………Count

….270/840

= …………… lbs.

………60

…..270 X 7000

= …………………… grains

……..840 X 80

= 37.5 grains

Also directly applying,

……………………………..25………..length in yards

Weight in grains = ………… X ………………………..

……………………………….3 ……………count

…….25…………..270

= ………… X ……………

………3……………60

= 37.5 grains (ANS)

Author of this Article: ]S.M. Bappy RanaDept. of Textile Engineering Bangladesh University of Business & Technology Cell: +8801781630519