Textile calculations

FIBER FINENESS, YARN COUNTS AND CONVERSIONS

Micronaire Value (Cotton): The unit is micrograms per inch. The average weight of one-inch length of fibre, expressed in micrograms(0.000001 gram). 

Denier (Man-Made Fibres): Weight in grams per 9000 meters of fibre. 

Micron (Wool): Fineness is expressed as fibre diameter in microns(0.001mm) 

Conversions: 

• Denier = 0.354 x Micronaire value
• Micronaire value = 2.824 x Denier

YARN COUNTS 
It is broadly classified into; 

1. INDIRECT SYSTEM
2. DIRECT SYSTEM

INDIRECT SYSTEM 

• English count (Ne)
• French count(Nf)
• Metric count(Nm)
• Worsted count

Metric system: Metric count(Nm) indicates the number of 1 kilometer(1000 meter) lengths per Kg.

• Nm = length in Km / weight in kg (or)
• Nm = length meter / weight in grams

DIRECT SYSTEM 

• Tex count
• Denier

CONVERSION TABLE FOR YARN COUNTS

	Tex	Den	Nm	Grains/yd
Tex		den/9	1000/Nm	gr.yd   x 70.86
Ne	590.54/tex	5314.9/den	Nm x .5905	8.33 / gr/yd
Den	tex  x  9		9000/Nm	gr/yd  x 637.7
Nm	1000/tex	9000/den		14.1 / gr/yd
Grains/yd	tex / 70.86	den / 637.7	14.1/Nm

Where, Nm – metric count, Nec – cotton count 

CONVERSION TABLE FOR WEIGHTS

	Ounce	Grains	Grams	Kilograms	Pounds
Ounce		437.5 grains	28.350 grams
Grains	0.03527 ounces		0.0648 grams
Grams	0.03527 grains	15.432 grains		0.001 kgs
Kilograms	35.274 ounces	15432 grains	1000 grams		2.2046 pounds
Pounds	16.0 ounces	7000 grains	453.59 grams	0.4536 kgs

CONVERSION TABLE FOR LINEAR MEASURES 

	Yard	Feet	Inches	Centimeter	Meter
Yard		3 feet	36 inches	91.44 cms	0.9144 meter
Feet	0.3333 yards		12 inches	30.48 cms	0.3048 meter
Inches	0.0278 yards	0.0833 feet		2.54 cms	0.254 meter
Centimeter	0.0109 yards	0.0328 feet	0.3937 inches		0.01meter
Meter	1.0936 yards	3.281 feet	39.37 inches	100 cms

CALCULATIONS 

• Grams per meter = 0.5905 / Ne
• Grams per yard = 0.54 / Ne
• Tex = den x .11 = 1000/Nm = Mic/25.4
• Ne = Nm/1.693
• DRAFT = (feed weight in g/m) / (delivery weight in g/m)
• DRAFT = Tex (feed) / Tex(delivery)
• DRAFT = delivery roll surface speed / feed roll surface speed
• No of hanks delivered by m/c = (Length delivered in m/min) / 1.605

WINDING 

1. Slub catcher settings : 

  a. Fixed Blade = Carded - (2.0 to 2.5) x diameter 
                          Combed - (1.5 to 2.0) x diameter 

  b. Electronic yarn clearer = 3 cm x 3 diameter

 Diameter in inch for Blended yarn   = 1/( 28 x √count ) 
                                                      = 10 to 15% more settings 

                                            Number of objectionable thick faults removed by slub catcher
2.Yarn clearer efficiency=...........................................................................................x 100 
                                            Total objectionable thick faults present in yarn before winding

                               Total breaks during winding (at faults) 
3. Knot factor =...............................................................................
                           No. of breaks due to objectionable yarn faults

                                                  Strength of spliced joint x 100
4. Retained splice strength = ........................................................... 
                                                       Strength of parent yarn 

5. Winding Tension = 0.1 x Single yarn strength in grams 

                                                  4500 x Y 
6. Expected efficiency E = ......................................................

                                               S x N (12 + 98)

7. Winder’s workload (0.17 min/operation on conventional winding m/c) = 2300 operations per shift of 8 hours 

Where, 

• 1 creeling or 1 piecing = 1 operation
• 1 doffing = 2 operations

8. Winder’s workload on autoconer (0.08 min per operation) = 4800 operations/shift of 8 hours 

Where, 

• 1 bobbing feeding = 1 operation
• 1 doffing (manual) = 4.5 operation

Y = Length/Bobbin (metres) 
B = Breaks per bobbin 
S = Winding speed (metres/min) 
C = English count 

9. Production in Kgs / 8 Hrs = (0.2836 x L x Effy x Nd) / (Ne) 

• L - delivery speed in m/min
• effy - efficiency
• Ne - english count
• Nd - No of delvieries

10. P =( L x 1.0936 x 60 x Effy ) / (Hank (Ne) x 36 x 840 x 2.2045) 

• P - production in kgs / hr
• L - delivery speed in m/min
• effy- efficiency
• Ne - English count ( number of 840 yards in one pound)
• 840 - constant
• 2.2045- to convert from lbs to kilograms

WARPING 

                                             R x 100 
1. Machine Efficiency E =............................. 
                                              R + S

R = Uninterrupted running time for 1,000 meters (in sec) 

                  1000 x 60 
= ................................................. 
         Machine speed in mtr/min.

S = Total of time in seconds for which the machine is stopped for a production of 1,000 meters 

               B X N X T1    T2          T3 
    = R + ---------------- + ------ + ----------- + T4 
                   400             L          L x C

• B = Ends breaks/400 ends/1,000 meters
• N = Number of ends
• L = Set length in 1,000 meters
• C = Beams per creel

Timing of activities in seconds are :

• T1 = To mend a break
• T2 = To change a beam
• T3 = To change a creel
• T4 = Miscellaneous Time loss/1,000 mtrs.  

2. Production in metres per 8 hrs. (K) = 480 x mtrs/min x E/100 kgs. 

3. Production in Kgs. per 8 hrs. = (K x N)/(1693 x English Count) 

4. Warping Tension = 0.03 to 0.05 x Single thread strength 


SIZING 

                                          Length in metre x 1.094 x Total ends 
1. Warp weight (in kg.) = ……………………………………………x 100 
                                                840 x 2.204 x Warp count 

                                   Sized warp weight - Unsized warp weight 
2. Size pick-up % =……………………………………………………… x 100 
                                                 Un-sized warp weight 

3. Weight of size = Warp Weight x Size pick up % 

                           Sized warp length - Unsized warp length 
4. Stretch % = …………………………………………………x 100 
                                      Un-sized warp length 

                                    Total-ends x Warp length in yards 
5. Sized yarn count = ……………………………………………………… 
                                      Sized warp weight (lbs) x 840 

                                            Wt. of sized yarn - Wt. of oven dried yarn 
6. % of Moisture content= ………………………………………………… x 100 
                                                            Wt. of sized yarn 


                               Deliver counter reading - Feed counter reading 
7. % of Stretch =……………………………………………………… x 100 

                                            Feed counter reading 


                                               840,000 x D x C 
8. % Droppings on loom = ……………………………. x 100 
                                                454 Y x N x P 

D = Dropping in gms. 

C = English Count 
Y = Length woven (yds.) 

N = Number of Ends 
P = % size add on

9. Invisible Loss% 

     Amount of size material issued - Amount of size added on yarn 
= ………………………………………………………….....................x 100 
                            Amount of size issued 

Steam, Consumption (Sizing M/c) = 2.0 kg/kg of sized yarn 
(Cooker) = 0.3 kg/kg of liquor 
(Sow box) = 0.2 kg/kg of yarn 

                                                 No. of Cylinder x 1,000 x English count 
10. Max. Speed of machine = ………………………………………………
                                                      (metres/min) Number of ends 

                                                Number of ends x 0.6 
11. Wt. of warp in gms/mtr = …………………………
                                                    English count 

WEAVING 

1. Reed Count : It is calculated in stock port system. 

                                      EPI 
Reed width = ……………………………… 
                          1 + Weft crimp %age 

No. of dents in 2 inches is called Reed Count 

2. Reed Width : 
                                            100 + Weft crimp %age 
Reed width = Cloth width x ……………………………… 
                                                       100 

3. Crimp % : 
                                       Warp length - Cloth length 
Warp Crimp %age =…………………………………………. x 100 
                                                Cloth length 

                                 Weft length - Cloth length 
Weft Crimp %age = ……………………………… x 100 
                                         Cloth length 

                                             EPI 

4. Warp cover factor = .................................... 
                                        √Warp Count 

                                            PPI 
5. Weft cover factor =……………………. 
                                        √Weft count

                                                                        Wp.C.F. x Wt. C.F. 
6. Cloth cover factor = Wp.C.F. + Wt.C.F. - ………………………………. 
                                                                                  28 

7. Maximum EPI for particular count : 

  a. For plain fabrics = 14 x √Count 

  b. For drill fabrics = √Count x 28 x 4/6 

  c. For satin fabric = √Count x 28 x 5/7 

                                     Ends/repeat x 1 / yarn diameter 
  d. Other design = ……………………………………………………….. 
                             No. of intersections / repeat + ends/repeat 

                                         1 
8. Yarn diameter = ……………………
                                 28 x √Count 

Weave Density 

1. Warp density = Ends/cm x √Tex x K 
                         = < 250 

2. Filling density = Picks/cm x √Tex x K 
                         = < 350 

                                            (Warp density - 100) x F.D.- 100 
3. Weave Density = 50 + …………………………………………… 
                                            (Weft density - 100) x F.D.- 100 

4. Effective weave density = W.D. x K of loom width x K of Design = < 72

Count Table

To change the count and number of thread/inch, keeping the same denseness of the fabric :

1. To change the EPI without altering the denseness : 

                               EPI in given cloth x √ Warp count in expected cloth 
EPI in Exp.Cloth =……………………………………………………………… 

                                         √ Warp count in given cloth

2. To change the count without altering the denseness : 

                                EPI in exp. cloth2 
EPI in exp. cloth = …………………………………x Count in given cloth 
                                EPI in given cloth 

Warp requirement to weave a cloth : 

                                                Total ends x 1.0936 x 453.59 x crimp% 
1. Warp weight in gms/mtrs. =…………..............................................x Wasteage% 

                                                                 840 x Count 

2. Weft weight in gms/mtrs.

    R.S. in inches x 453.59 x PPI 
=…………………………………x Crimp % x Waste % 
              840 x Count 

                                                                               

3. Cloth length in mtrs.with the given weft weight 

     Weft wt. in kgs. x Weft count x 1848 x 0.9144

=……………………………………………………….

                          PPI x R.S. in inches

For Silk and Polyester : 

1. Warp weight in gms/mtrs.

      Total ends x Count (Denier) 
= ……………………………..............x Crimp% x Waste %age 
                     9000 

2. Weft weight in gms/mtrs.

     RS in inches x PPI x Count (Denier) 
= …………………………………........ x Crimp% x Wasteage% 
                        9000 

Allowance for count in Bleached and Dyed Fabric : 

• Count becomes 4%
• Finer Dyed counts become max.6% Coarser

FABRIC PRODUCTION 

                                                    Motor pulley diameter 
1. Loom speed = Motor RPM x …………………………………. 
                                                    Loom pulley diameter 

                                         Actual production 
2. Loom Efficiency % = ------------------------------- x 100 
                                       Calculated production 

                                             Yarn weight - Dryed yarn weight 
3. Moisture Regain % = ----------------------------------------------------- x 100 
                                                      Dryed yarn weight 

                                          Yarn weight - dried yarn weight 
4. Moisture Content % = ----------------------------------------------- x 100 
                                                  Yarn weight 

                                        Total ends x Tape length in metre 
5. Warp weight in Kg. = ------------------------------------------------------ 
                                              1693.6 x Warp count 

                                      RS in centimetres x Coth length in metres x PPI 
6. Weft weight in Kg. = ------------------------------------------------------------------- 
                                                  4301.14 x Weft count 

                                             EPI                    PPI 
7. Cloth weight in GSM = ------------------ + -------------------- x 25.6 
                                      Warp count          Weft count 

                                              GSM (Grams per sq. metre) 
8. Oz (Ounce) per sq.yard = -------------------------------------------- 
                                                            34 

Material measurement : 
For calculating of length of any rolled fabrics : 

        0.0655 (D - d) (D + d) 
L = --------------------------------- 
                      t 

Where,

L = Length of material (feet) 
t = Thickness of fabrics (inches) 
D = Outside diameter (inches) 
d = Inside diameter (inches) 

Weight of yarn in a cloth : 
The weight of cloth manufactured on loom depends upon the weight of yarns in the warp and weft : ends/inch, picks/inch and the weight of size on the warp. 

Therefore, Cloth weight = Weight of warp + Weight of weft + Weight of size (All in lbs.) 

                                                        Total No. of Ends x Tape length in yds. 
Where as Weight of warp in lbs = ----------------------------------------------------- 
                                                                  840 x Warp yarn count 

Also Weight of weft in lbs.

    Length of cloth (yds) x Picks/inch in cloth x Reed width (inch) 
= -----------------------------------------------------------------------------------------------

                                840 x Weft yarn count