1. Abu Bakkar Marwat-Textile Engineer
LINEAR DENSITY
1/7
LINEAR DENSITY:
The thickness or diameter of a yarn is one of its most fundamental properties.
However, it is not possible to measure the diameter of a yarn in any meaningful way.
This is because the diameter of a yarn changes quite markedly as it is compressed.
 Yarn is a soft assembly of fibres
 There are voids spaces between the fibres within yarn
(Most methods of measuring the diameter of yarn involve compressing the yarn and
hence the measured diameter changes with the pressure used. So mechanical means, devices
can’t be used for measuring the diameter of the yarn.)
 yarn is thinner at twisted places and thicker where twist is less
 Yarn appears vivid because of the hairiness; it has protruding fibres upon its
surface and also sometimes loops of fibers (kinks).
(Due to undefined boundaries, optical methods e.g. microscope can’t be used to measure
yarn diameter)
 Also there are lots of differences in the structure and cross section of different
fibres
 Wool has nearly round cross-section
 Silk has a triangular cross-section
 Cotton is like flattened tube
 Man-made fibres are often made with trilobal (nylon), star or hollow
cross-section for particular purposes.
Due to these problems, there are no such devices to measure the diameter of a
yarn. Instead, systems of denoting the fineness of a yarn by weighing a known length
have evolved. This is known as the linear density. Simply it the yarn thickness or
coarseness. There are two systems:
1) Direct system
2) Indirect system
1: Direct System: w/l
In this system of counting, length unit is fixed and weight unit is variable. It is
defined as weight per unit length. When count increases, fineness decreases (count↑
fineness↓). It is further classified as:
a) Tex system
b) Denier system
c) Grex system
a) Tex System (Tt): It is defined as no of grams per 1000 meters length.
Multiples are based on weight unit and are as under
Milli-tex (mTex): no of mg per 1000 meters length. It is used for yarn and roving.
Deci-tex (dTex): no of decigrams per 1000 meters length. It is used for sliver.
Kilo-tex (KTex): no of kilograms per 1000 meters length. It is used for laps.
Tex is universal system either for spun or filament yarn.
b) Denier System (Td):
It is defined as no of grams per 9000 meters length.
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2. Abu Bakkar Marwat-Textile Engineer
LINEAR DENSITY
2/7
c) Grex System (Tg):
No of grams per 10000 meters length
2: Indirect System: l/w
In indirect count system weight unit is fixed and length is variable on which basis
measurement is done. When count increases, fineness increases. (count↑ fineness↑)
This includes:
a) English Count (Ne):
In this system, the weight unit is in lbs and length unit is hanks; No of hanks per
pound. Hank length varies for different fibers or yarns.





Cotton = 840yards
Wool = 256yards
Spun Silk = 840yards
Bast fibers (linen) = 300yards
Worsted = 560yards
b) Metric Count (Nm):
It is defined as no of 1000 meters length/Kg. It is commonly used for heavy yarns.
Count Conversion Table:
Ne=
Nm=
Tex=
Grex=
Denier=
Ne
1 xNe
1.693xNe
590.5 /Ne
5905 /Ne
5315 /Ne
Simplified calculations:
Calculations for Tex:
1000 m  1 g (1 Tex)
1m
 1 mg (1 Tex)
100 cm  1 mg (1 Tex)
50 cm  0.5 mg (1 Tex)
Calculations for Denier:
9000 m  1g
(1 denier)
9m
 1 mg (1 denier)
900 cm  1 mg (1 denier)
9 cm
 0.01 mg (1 denier)
Nm
0.5905 xNm
1 xNm
1000 /Nm
10,000 /Nm
9000 /Nm
Tex
590.5 /Tex
1000 /Tex
1 xTex
10 xTex
9 xTex
Grex
5905 /Grex
10,000/Grex
0.1 xGrex
1 xGrex
0.9 xGrex
Denier
5315 /Den
9000 /Den
0.111 xDen
1.111 xDen
1 xDen
Calculations for Grex:
10,000 m  1g (1 Grex)
10 m  1mg (1 Grex)
1m
 0.1mg (1 Grex)
50 cm
 0.05mg (1 Grex)
Calculations for Ne:
840 yd  1lb (1 Ne)
840 yd  453.6g (1 Ne)
1.85 yd
 1g (1 Ne)
66.67in
 1g (1 Ne)
33.33in
 0.5g (1 Ne)
Calculations for Nm:
1000 m * X(count)  1kg (X Nm)
1000 m * 1
 1000g (1 Nm)
1m
 1g (1 Nm)
50 cm
 0.5g (1 Nm)
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3. Abu Bakkar Marwat-Textile Engineer
LINEAR DENSITY
3/7
Effect of linear density on Hairiness:
Yarn linear density is statistically significant when evaluating both yarn counts
together with SPSS. We found a direct relationship between yarn linear density and
hairiness; the hairiness increases when the yarn linear density increases. In other
words, coarse yarns have more hairs than fine yarns for all the observed hair lengths.
This can be explained by the increase of fibres in the cross-section of yarn.
Designation/Nomenclature of Yarn:
 Single Yarn: (spun or cotton)
It is identified through one group of three symbols:
24/S/15
Where 24-count, S-direction of twist, 15-twist level or TPI
 Single Yarn: (filament yarn):
100(15)/S/80
Where 100-denier count, (15)-no of monofilaments in filament yarn,
S-direction of twist, 80-level of twist i.e TPM
 Plied Yarn:
It is identified through two groups of three symbols:
24/S/15, 2/Z/12
Where 24-Ne (cotton count), S-direction of twist, 15-TPI, 2-no of plies,
Z-direction of twist of "yarns", 12-TPI
 Cabled yarn:
It is identified by three groups of three symbols:
20/Z/10, 2/S/8, 2/Z/6
Where 20-Ne, Z-direction of twist in individual yarn, 10-TPI, 2-no of plies of single yarn, Sdirection of twist, 8-TPI, 2-no of plies of plied yarns, Z-direction of twist, 6-TPI
Measuring Linear Density:
Sampling:
For lots that contain five cases or less, the sample should consist of all the cases.
Ten packages are selected at random but in approximately equal number from each
case. For lots that consist of more than five cases, five cases should be selected at
random from each of these cases. In all cases, sampling ends up with ten cases.
Effect of Moisture Content:
Yarns contain a varying amount of moisture depending on the constituent
fibres and the moisture content of the atmosphere where they have been stored. The
additional moisture can make an appreciable difference to weight and hence the linear
density of yarn. So there are three conventional methods of expressing linear density.
Each of which has a different way of dealing with moisture content.
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4. Abu Bakkar Marwat-Textile Engineer
LINEAR DENSITY
4/7
a) Linear density as received:
In this method no allowance is made for the moisture content, the linear density
measured on the yarn as it is. Numbers of skeins are wound on a wrap reel which has
a circumference of a convenient length e.g., 1 meter. Then linear density is calculated
from the total length and total weight.
When measuring the length of a piece of yarn or when reeling a given length of
yarn it is important that the operation is carried out using a standard tension. On
wrap reel while reeling a hank of yarn, tension is set by introducing the correct
amount of friction into the yarn path.
Skein gauge:
The skein gauge shown in the fig checks the length of a 50 wrap skein under a
standard tension. The test hank is passed round the lower fixed peg and the upper peg
which forms one arm of a balance. The load on the other end of the balance is set at
50g x the nominal tex of the yarn. If the length of the hank is correct the pointer will be
opposite the zero mark. Any deviation from the correct length is shown directly as a
plus or minus percentage. The length of the skein should be within 0.25% of the actual
girth of the reel, the reeling tension of the wrap reel being adjusted to achieve this.
Because the yarn on a package may be under
Jaw
tension it is correct practice first to wind a hank from
the package of sufficient length for all the tests which
Hank
Load
are to be carried out. This is then allowed to relax
without any tension for 4h before winding the actual
test skeins from it.
Jaw
b) Linear density at standard testing atmosphere:
In this method the skeins of yarn are preconditioned for 4h by drying in an
oven at 50º C. They are then conditioned in the standard atmosphere (20±2 º C, 65±4%
RH) for 24 h. The reason for preconditioning the yarn is so that the equilibrium
moisture content is approached from the same side each time, thus avoiding the
effects of hysteresis. The reeling of the hanks and calculation of the linear density are
then carried out as above.
c) Linear density at correct condition:
This method is more accurate than the previous one as the amount of moisture
contained by the fibres in equilibrium with the standard atmosphere can vary. In the
method, the hanks are reeled as above and then dried to oven dry weight (105C-two
consecutive weighing the same) and weighed. The dry weight then has the
appropriate standard regain allowance added to it and the linear density is then
calculated from this weight.
Weight at correct condition
= dry weight x (100 + standard regain)/100
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5. Abu Bakkar Marwat-Textile Engineer
LINEAR DENSITY
5/7
Linear density from a fabric sample:
 When the linear density of a yarn has to be determined from a sample of fabric,
a strip of the fabric is first cut to a known size.
 A number of threads are then removed from it and their uncrimped length is
determined under a standard tension in a crimp tester.
 All the threads are weighed together on a sensitive balance and from their total
length and total weight; the linear density can be calculated.
Yarn from a finished fabric may have had a resin or other
type of finish applied to it so that its weight is greater
than that of the original yarn. Alternatively it may have
lost fibres during the finishing process so that its weight
may be lower than that of the original yarn. For these
reasons the linear densities of yarn from finished fabrics
can only represent an estimate of the linear density of the
yarn used to construct.
When yarn is removed from a fabric it is no longer straight but it is set into the
path that it took in the fabric as shown in fig. This distortion is known as crimp and
before the linear density of the yarn can be determined, the crimp must be removed
and the extended length measured.
Shirley crimp tester:
The crimp tester is a device for measuring the crimpfree length of a piece of yarn removed from a fabric. The length of the yarn is
measured when it is under a standard tension whose value is given in Table. The
instrument is shown diagrammatically in Fig. and consists of two clamps, one of
which can be slide along a scale and the other which is pivoted so as to apply tension
to the yarn. The sample of yarn removed fro the fabric is placed in the clamps with
each end a set distance into the clamp; this is because the length of yarn in the clamps
has to be allowed for in the measurement. The right hand clamp can be moved along
the scale and it has an engraved line on it at which point the extended yarn length can
be read. The left hand clamp is balanced on a pivot with a pointer arm attached. On
the pointer arm is a weight which can be moved along the arm to change the yarn
tension, the set tension being
indicated on a scale behind it.
At zero tension the left hand
clamp assembly is balanced
and the pointer arm lines up
against a fixed mark. As the
weight is moved along the
arm the clamp tries to rotate
around the pivot, so applying
a tension to the yarn.
When a measurement is
being made the movable
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6. Abu Bakkar Marwat-Textile Engineer
LINEAR DENSITY
6/7
clamp is slid along the scale until the pointer is brought opposite the fixed mark. At
this point the tension in the yarn is then the value which was set on the scale. The
length of the yarn can then be read off against the engraved line.
The crimp, which is the difference between the extended length and the length
of the yarn in the fabric, is defined as:
Percentage crimp: (Li + Lo)/Lo x 100
Lo = distance between ends of the yarn as it lies in the fabric
Li = straightened length of yarn
Yarn tensions for the crimp tester:
Yarn type
Woolen & worsted
Cotton
Man made continuous
filament yarn
Linear density
15 to 60 tex
61 to 300 tex
7 tex or finer
Coarser than 7 tex
All
Tension (cN)
(0.2 x tex) + 4
(0.07 x tex) + 12
0.75 x tex
(0.2 x tex) + 4
0.5 x tex
Applications of Linear density:
1) Total length on a yarn package:
1) Package wt: 2.5 lb & Ne 20:
Cotton:
840 x count = 1 lb
840 x 20 = 1 lb
16800 = 1 lb i.e 16800 yards length
weighs 1 lb
Then 2.5 lb cone length: 16800 x 2.5
= 42000 yards
Worsted:
560 x count = 1 lb
560 x 20 = 1 lb
11200 = 1 lb i.e. 11200 yards length
weighs 1 lb
Then 2.5 lb cone length: 11200 x 2.5
= 28000 yards
Woolen:
256 x count = 1 lb
256 x 20 = 1 lb
5120 = 1 lb i.e. 5120 yards length
weighs 1 lb
Then 2.5 lb cone length: 5120 x 2.5
= 12800 yards
2) Package wt: 2 lb, 80 spun polyester:
(Spun polyester means that it is cut
into small fibres like cotton)
840 x count = 1 lb
840 x 80 = 1 lb
67200 = 1 lb i.e. 67200 yards length
weighs 1 lb
Then 2 lb package length: 2 x 67200
= 134400 yards
3) Package wt: 2 kg, 100/2 denier
Nylon filament
(For filament yarn, 100/2=200,
50/2=100)
9000 m = 200 g
Then 2 kg cone length: (9000 x 2)/0.2
= 90,000 m
(30/2 viscose spun=15, 20/2=10)
4) Package wt: 3 kg, 100 denier
Polyester:
9000 m = 100 g
9000 m = 0.1 g
Then package weighing 3 kg have
length: (9000 x 3)/0.1
= 270,000 m
5) Package wt: 2 lb, Tex count = 20
1000 m = 20 g
1000 m = 0.0441 lb
2 lb package will have length:
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7. Abu Bakkar Marwat-Textile Engineer
LINEAR DENSITY
7/7
(1000 x 2)/0.041 = 45351 m
2) Fabric cost:
Fabric construction:
20 x 16/ 128 x 60 60”
3/1 S twill Leno
Warp crimp = 6%
Weft crimp = 8%
Total length = 36000 yards
Warp weight = (total ends x tape length)/(840 x warp count) {lbs} ----- (1)
Now for total ends, we have = (ends/in x width of fabric)+selvage ends + extra ends
= (128 x 63) + (2*24) + 10
= 8064 + 48 + 10
= 8122
For tape length:
Ly = Lf (1 + C) = 36000 (1+6%) = 36000(1.06) = 38160 yards
Putting values in equ. 1:
= (8122 x 38160)/(840 x 20) = 18448.54 lbs
Total bags = 18448.54/100 = 184.48
(one bag=100lbs)
Total cones = 184.48*40 = 7379 cones
(one cone=2.5lb & one bag = 40 cones)
Warp cost: price of cone x No of cones = 240*7379 = 1770960 rupees
Weft weight = (total picks x reeded width)/(840 x weft count)
----- (2)
Now for total picks, we have = picks/inch x fabric length + Extra picks
= (60*36) x 36000 + 10
= 77760010
For reeded width:
Ly = Lf (1 + C) = 63 (1+8%) = 63 (1.08) = 68.04” = 68.04/36 = 1.89 yd
Putting values in equ 2:
= (77760010 x 1.89)/(840 x 16) = 10935 lbs
Total bags = 10935/100 = 109.35 bags
Total cones = 109.35*40 = 4374 cones
Weft cost: price of cone x No of cones = 225*4374 = 984150 rupees
Total cost = 77760010 + 984150 = 2755110 rupees
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