Woven Fabric
Calculations
Dr. Jimmy Lam
Institute of Textiles & Clothing
Agenda
Calculations on weft consumption
 Calculations on warp preparation
 Calculations on warp/weft crimp percentage
 Calculations on fabric weight (g/m2)
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Weft consumption of a loom
Question
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A loom runs at 210 picks/min at an overall
efficiency 82%. The warp width in the reed is
1.2m and the linear density of the weft is 30 tex.
What is the weft consumption per 8 hours
Answer
Weft consumption
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A) Length of weft used per hour at 100% efficiency
=1.2 X 210 X 60 /1000km =15.12km per hour
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B) At 82% efficiency, the length used in 8 hours
=15.12 X 0.82 X 8 =99.19km
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C) Weft consumption, for 30 tex yarn is:
=30 X 99.19 /1000kg =29.76 kg per 8 hours
Warp Preparation
Question

An order for 220 pieces of woven fabric, each
110m in length and 1.2m in wide, is received. In
the finished fabric, the warp crimp is 9% and
there are 38 ends/cm. The creel of the direct
warping process has a maximum capacity of
500 cones.
– A) How many back beams are required
– B) What length of warp is on each?
Warp Preparation
Answer
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A) Total number of ends:
– Ends/cm x finished width in cm
– =38 x 120 =4560 ends
– Since the creel can hold 500 cones, the number of ends per
back beam could be 456, and 10 back beams should be used
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B) The total length of warp is given by
– Number of pieces X piece length X (100+crimp)/100
– =220X110X109/100 =26,378m
Crimp Percentage of Woven Fabric
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The crimp percentage is the difference between
straightened thread length and the distance between
the ends of the thread in the fabric.
Crimp % = (l-s)/s x 100
Measuring crimp practically is not always a simple
procedure. The length of the crimped yarn may be
easily measured, but to decide when the crimped
yarn removed no longer retains crimp is not easy.
Example
Crimp %
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Crimp % , (Formula 1)
C=(L-S)/S * 100%
– Where L is warp length, S is cloth length
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Warp Length (L), (Formula 2)
L=(1+C)* S
– Where C is crimp %, S is cloth length
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Cloth length (S), (Formula 3)
S=L/(1+C)
– Where L is warp length, C is crimp %
Question 1
Crimp %
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A cotton cloth is analysed, and from a tested
strip of 20cm, the mean warp length is 21.2cm.
Determine both the crimp and take-up
percentage.
Answer
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Crimp Percentage:
(21.2 – 20.0) / 20 = 6.0%
Take up Percentage
(21.2-20.0)/21.2 = 5.66%
N.B In many fabrics, there is not too great difference between the
warp and weft crimps, but there are examples of quite large
differences. E.g. in cotton poplin, the warp cirmp could be 14%
and the weft crimp in only 2%
Example 2
Crimp %
Ex2:
 Calculate the length of warp required to weave
160m of cloth if the warp crimp is 12%
 Ex3
 What length of cloth can be woven from 800m
of warp if the warp crimp is 8%

Answer
Ex2
 S= cloth length = 160m
 Crimp = c = 0.12 and therefore warp length will
be:
 C= (l-s)/s X100%; and c =l/s -1 and l=(1+c)*s
 L=(1+0.12)*160 = 179.2m
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Answer
Ex3
 Warp Length, L =800m , find cloth length, s
 S=L/(1+c) = 800/(1.08)
 =740.8m
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Fabric Weight Calculations
(Areal Density)
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In the imperial system, fabric weight is expressed in
ounces per square yard.
In SI, the mass per unit area is grams per square meter.
If we get a 10 cm x 10 cm fabric, the fabric is easy to
measure and multiplied by 100 to give fabric weight
(g/m2).
However, if we don’t have the fabric, the fabric weight
can be calculated by fabric density (sett), yarn count
and crimp percentage.
Fabric Weight
Calculation
Question 1:
 A cotton fabric is woven from 18 tex warp and
21 tex weft. The fabric has 28 ends/cm and 25
picks/cm, and the warp and weft crimp
percentages are 2.5 and 9.0 respectively.
Estimate the areal density (fabric weight g/m2)

Answer

Mass of warp per square meter
– =(ends/m)/1000 x (100+crimp%)/100 x tex
– =(28 x 100)/1000 x (102.5 *18)/100
– =51.5 g
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Note factor 1000 is introduced because tex is defined in
terms of g/km
Mass of weft per square meter
– =(picks/m)/1000 x (100+crimp%)/100 x tex
– = (25*100)/1000 x (109*21)/100
– =57.2g

Fabric weight =51.5 + 57.2 =108.8 g/m2
If we use ends/cm in the formula, we could omit
the factor of 100 on the bottom line, the total
mass per square meter will be written:
 {(ends/cm x 100+crimp% x tex) + (picks/cm x
100+crimp x tex)} /1000
 ={(28*102.5*18) +(25*109*21)}/1000
 =51.6+57.2 =108.8g/m2
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Fabric Weight
Calculation
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Question 2
A satin strip cotton fabric is woven from a warp of 25
tex in the plain sections and from one of 12 tex in the
satin weave. There are 40 repeats of the pattern in a
fabric width of 1.28m, each repeat being made up of 48
ends of plain weave and 72 ends of satin weave.
The crimp is 8% in the plain weave and 5% in the satin
weave. The weft is 14 tex, with 28 picks/cm and has 6%
crimp.
Calculate the aerial density of this fabric (g/m2)
Answer
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For this patterned fabric in which varied yarns are used,
each type of yarn will require separate treatment.
Number of pattern repeats per meter width= 40x1/1.28
=31.25
Fabric Weight (Warp Yarn)
Hence, number of plain weave ends/m =31.25 x 48; and
Mass of plain weave ends/m
(31.25*48)/1000 *(108*25)/100 =40.5g
Similarly, mass of satin weave ends/m
(31.25*72)/1000 * (105*12)/100=28.4 g
Fabric Weight (Weft yarn)
 Mass of weft per meter
 =28*106*14*100/1000 =41.6 g
 Fabric weight (warp +weft) per square meter
 =40.5+28.4+41.6=110.5 g/m2
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Fabric Weight
(Imperial System)
Sometimes, we need to express fabric weight in
Imperial System (oz/yd2), the calculation is as
follows:
 Question 3
 Calculate the fabric weight (oz/yd2) for the
following cotton cloth:
 22s x18s, 64 x 60 and 6.5% x 8.5%

Convert the system to SI
 Tex = 590.5/cotton count
 Warp =590.5/22 =26.8 tex
 Weft=590.5/18=32.8 tex
 Sett /cm =Ends per inch /2.54
 Ends/cm =64/2.54=25.2
 Picks/cm =60/2.54 =23.6
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Fabric Weigth (g/m2)
 {(25.2*106.5*26.8)+(23.6*108.5*32.8)}/1000
 =155.g/m2
 Since 1 g/m2 =0.029 oz/yd2
 Fabric Weight (oz/yd2) = 155*0.029
 =4.52 oz/yd2
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Fabric Weight
Denier
Question 4
 Calculate the weight of the fabric (oz/lb2) for
the following nylon fabrics:
 45 denier x 45 denier; 104 x 96 and 4% x 5%

Convert it to SI
 Tex = Denier /9
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– Warp tex =45/9 =5
– Weft tex =45/9=5
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Ends/cm =ends per inch /2.54
– Ends/cm= 104/2.54=40.9
– Picks/cm =96/2.54=37.7
Fabric Weight (g/m2)
 {(40.9 x 104 x 5) + (37.7 x 105 x 5)}/1000
 41 g/m2
 Since g/m2 =0.029 oz/lb2
 Fabric Weight (oz/lb2) = 41 x 0.029
 =1.19 oz/lb2
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