# Mathematical Problems and Solutions of Sizing in Textile Weaving

Textile Sizing:
Sizing is known as the heart of weaving in textile. Size% calculation is very important to achieve maximum weaving efficiency specially for blended and filament yarns. As its importance, this article has presented some important mathematical problems and solutions of sizing, which will be very useful for all the persons related with textile weaving sector. Sizing calculation in weaving
Textile Sizing Calculations:

Problem-01:
The weight of sized yarn on a beam was 80. The beam contains 1000 yds of warp, before sizing which count was 45s. Calculate the following if the number of ends in warp is 2800.

a. The weight of the sized yarn,
b. Size% put on the yarn,
c. Sized yarn count.

Solution:
Here,
Weight of sized warp in pounds= 80,
Yarn count= 45,
Number of ends= 2800,
Length of warp in yds= 1000,

Now,

a. Weight of the sized yarn calculation:

Weight of the sized yarn in pounds,
= (weight of sized warp – weight of unsized warp)…………………….. (1)

Again,

Weight of unsized warp,
Length of warp in yds × Number of ends
=……………………………………………………………….
840× yarn count
1000×2800
=……………………
840×45
= 74.07 pounds

Now, from equation (1), we get,
Weight of the sized yarn in pounds= (80-74.07) = 5.93 pounds

So, weight of sized yarn stands at 5.93 pounds.

b. Size% put on the yarn calculation:

Size% put on the yarn,
Weight of size
=…………………………………….. × 100%
Weight of unsized warp
5.93
=………………… × 100%
74.07
=     8%

So, Size% put on the yarn is 8%.

c. Sized yarn count calculation:

Sized yarn count,
Length of warp in yds × Number of ends
=…………………………………………………..
Weight of sized warp in pounds × 840
1000×2800
=…………………..
80×840
=  41.67s

So, Sized yarn count for this calculation stands at 41.67s

Problem-02:
A beam of 300kg contains sized yarn of 20% take up. Calculate the unsized yarn count if the sized yarn count is 45s.

Solution:
Here,
Size%= 20%,
Sized yarn count= 45s,
Unsized yarn count=?

So,
Count of sized yarn,
Count of unsized yarn×100
=…………………………………………………
100+ Size%

Or,
Count of unsized yarn,
Count of sized yarn × (100+ Size%)
=……………………………………………………….
100
45 × (100+20)
=…………………………..
100
= 54s

So, unsized yarn count for this calculation is 54s.