1. Woven Fabric Calculations
Dr. Jimmy Lam
Institute of Textiles & Clothing

2. Agenda Calculations on weft consumption
Calculations on warp preparation
Calculations on warp/weft crimp percentage
Calculations on fabric weight (g/m2)

3. Weft consumption of a loom Question
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

4. Answer Weft consumption
A) Length of weft used per hour at 100% efficiency
=1.2 X 210 X 60 /1000km =15.12km per hour
B) At 82% efficiency, the length used in 8 hours
=15.12 X 0.82 X 8 =99.19km
C) Weft consumption, for 30 tex yarn is:
=30 X /1000kg =29.76 kg per 8 hours

5. 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?

6. Warp Preparation Answer
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
B) The total length of warp is given by
Number of pieces X piece length X (100+crimp)/100
=220X110X109/100 =26,378m

7. Crimp Percentage of Woven Fabric
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.

8. Example Crimp % Crimp % , (Formula 1) C=(L-S)/S * 100%
Where L is warp length, S is cloth length
Warp Length (L), (Formula 2)
L=(1+C)* S
Where C is crimp %, S is cloth length
Cloth length (S), (Formula 3)
S=L/(1+C)
Where L is warp length, C is crimp %

9. Question 1 Crimp %
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.

10. Answer Crimp Percentage: (21.2 – 20.0) / 20 = 6.0% Take up Percentage
( )/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%

11. 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%

12. 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

13. Answer Ex3 Warp Length, L =800m , find cloth length, s
S=L/(1+c) = 800/(1.08)
=740.8m

14. Fabric Weight Calculations (Areal Density)
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.

15. 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)

16. 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
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 = =108.8 g/m2

17. 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
= =108.8g/m2

18. Fabric Weight Calculation
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)

19. Answer
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

20. Fabric Weight (Weft yarn)
Mass of weft per meter
=28*106*14*100/1000 =41.6 g
Fabric weight (warp +weft) per square meter
= =110.5 g/m2

21. 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%

22. 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

23. 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

24. 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%

25. Ends/cm =ends per inch /2.54
Convert it to SI
Tex = Denier /9
Warp tex =45/9 =5
Weft tex =45/9=5
Ends/cm =ends per inch /2.54
Ends/cm= 104/2.54=40.9
Picks/cm =96/2.54=37.7

26. 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