# Textile Calculation

## Some Useful Formulas for Determining Fiber Properties

Some Useful Formulas for Determining Fiber Properties
Amit Kumar Das
Founder of "টেক্সটাইল ম্যানিয়া" Blog
Pabna Textile engineering college, Pabna, Bangladesh
Cell: 01770 456240
Email: amitptec6th@gmail.com

Introduction:

Today we will discuss about some easy formula aims to determine some important properties of fiber like diameter of fiber, fiber maturity, spinning limit, spinning value of cotton fiber, standard fiber fineness etc. Those properties are necessary to know before taking decision about production. So lets have a look how can we determine those?
Diameter of Fiber:

(I) Diameter of fibre in microns = 2000 = √ { X ÷ ( Y x π x 9000 ) }

Where,

X = Fibre denier
Y = Fibre specific gravity

Denier is the mass in grams of 9 kilometres of the material.

Also ,

1 denier = 0.05315 grains and
Denier = 5315
÷ cotton count

(II) Fiber diameter in microns = 20 √ { Denier ÷ (3.14 x specific gravity)}

Fibers per cross section of yarn (T),
T = 20√ [ { 53.15 x sum of ( % of each denier ÷ each denier) } ÷ ( yarn count to be spun ) ]

Fiber maturity:

Fibre maturity ratio = (Normal – Dead ) /200 + 0.7

Maturity coefficient = ( N + 0.75T + 0.4 D) / 100

Where,

N = normal coefficient
T = Thin walled of half mature fibers

Spinning limit:

Spinning limit = 5315 / (Denier of fibre x Actual fibres per cross section)

The ratio should be about 3200 for fine yarn counts and about 3000 for course counts.

Neps:

Neps per 100 square = { (1.531 – log (34-x)) x 100 } / 0.434 inches of web

Where X is the number of cells containing neps (Shirley template method) and 34 is the total number of cells.

Spinning value of cotton:
The formula given by Indian Central Cotton Committee is

C = 78.2X2  -  79.2X3 - 24.8

Where ,
C = highest standard warp count.

X2 =Mean fibre length In inches
X3 = Mean fibre weight per inch (106 oz. )

Another formula to predict spinning value from fibre properties is:

X1 = 71.6X2 - 70.8X3 – 20.8X4 + 17.9X5 + 0.037X6 + 4.4 X7-14.1

X1 = Highest standard warp count
X2 = Fibre length (inches)
X3 = Fibre weight per inch (10-6 oz.)
X4  = Fibre width(10-3 inch)
X5 = Fibre strength
X6 = Fibre convolutions
And
X7 = Fibre rigidity (oz./inch2 x 10-6)

Standard fiber fineness :
Standard fiber fineness = Measured fineness / Maturity ratio