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# Textile Calculations and Equations

Production = no. of needle x no of feeder x RPM x stitch length/ yarn count
Production per shift in KG at 100% efficiency

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### Textile Calculations and Equations

1. 1. TEXTILE CALCULATION & EQUATION
2. 2. Name : MAZADUL HASAN SHESHIR ID: 2010000400008 Batch: 13th Batch (Session 2009-2013) Department: Wet Processing Technology Email: mazadulhasan@yahoo.com Blog: www. Textilelab.blogspot.com Southeast University Department of Textile Engineering PREPARED BY ©right
3. 3. Spinning Calculation and Equation
4. 4. Basic Conversions (Spinning) No Length Weight Time 1. 1 in = 2.54 cm 1 lb = 7000 gr 1 min = 60 sec 2. 1 yd = 36 in 1 lb = 16 oz 1 hr = 60 min 3. 1 m = 1.0936 yd 1 oz = 437.5 gr 1 shift = 8 hr 4. 1 Hk = 840 yd 1 kg = 2.2046 lb 1 day = 24 hr 5. 1 Hk = 7 leas 1 bag = 100 lb 1 day = 3 shifts
5. 5. Count Conversion Table (Spinning) Ne Nm Tex Grex Denier Ne= 1 xNe 0.5905 xNm 590.5 /Tex 5905 /Grex 5315 /Den Nm= 1.693xNe 1 xNm 1000 /Tex 10,000/Grex 9000 /Den Tex= 590.5 /Ne 1000 /Nm 1 xTex 0.1 xGrex 0.111 xDen Grex= 5905 /Ne 10,000 /Nm 10 xTex 1 xGrex 1.111 xDen Denier= 5315 /Ne 9000 /Nm 9 xTex 0.9 xGrex 1 xDen
6. 6. Draft & TPI Formulas
7. 7. Efficiency Percentage (Spinning) Cleaning Efficiency (%) Efficiency (%) Twists per inch
8. 8. PRODUCTION CALCULATION FORMULAS
9. 9. PRODUCTION FORMULAS
10. 10. Yarn Count in Direct system System Unit weight Unit length Uses Tex Grams 1,000m Polyester Denier Grams 9,000m Lycra D-Tex Grams 10,000m Lycra Pounds/Spyndle Pounds 14400yds Jute Yarn Count in Indirect system System Unit weight Unit length Uses English (Ne) 1 lb 840 yds Cotton yarn Metric (Nm) 1 kg 1 km Cotton yarn Worsted 1 lb 560 yds Worsted yarn Woolen 1 lb 256 yds Woolen yarn
11. 11. Excellence of fiber quality by combing:
12. 12. Fabric (Knitting & Weaving) Calculation and Equation
13. 13. SIZING
14. 14. Calculation:
15. 15. Required Chemical &no. of Mixing of Sizing Recipe:
16. 16. Production is calculated in accordance with the following equation-
17. 17. Production calculation: 1. Production = no. of needle x no of feeder x RPM x stitch length/ yarn count Production per shift in KG at 100% efficiency Where, Ks = knitting constant Count = linear density of yarn GSM = gm per square meter Another formulae is : Stitch length = (Tex × Ks) / GSM Ks is a constant. Its value is different for different fabric structure and fabric type. Ks is calculated and estimated as below: Ks = (GSM x Stitch length) / Tex
18. 18. Production calculation: Fabric type Color Value of Ks Single jersey Average 19.55 Single lacoste Average 22.4 Double lacoste Average 22.75 Polo pique Average 25 Plain interlock Average 39.3 1 X 1 rib Light 24.5 1 X 1 rib Average 26.5 Ks = (GSM x Stitch length) / Tex
19. 19. Relation between yarn count and m/c gauge seen in different m/c.:
20. 20. GSM Calculation
21. 21. DIFFERENT FABRIC GSM AND THEIR REQUIRED YARN COUNT S/J without lycra - Fabric G.S.M Yarn Count 110 - 120 40 S – 36 S 120 - 130 36 S - 32 S 130 - 140 32 S – 28 S 140 - 150 28 S 150 - 160 26 S 170 - 210 24 S Rib without lycra - Fabric G.S.M Yarn Count 180 - 190 36 S - 32 S 190 - 200 30 S 200 - 215 28 S 215 - 230 26 S 230 - 250 24 S 250 - 300 24 S
22. 22. Interlock without lycra - Fabric G.S.M Yarn Count 200 - 220 34 S 220 - 230 32 S 230 - 250 30 S 250 - 300 26 S Lacoste without lycra - Fabric G.S.M Yarn Count 180 - 190 30 S 190 - 210 28 S 210 - 230 26 S 230 – 250 26 S 40D Lycra Rib - Fabric G.S.M Yarn Count 230 - 240 32 S 240 - 250 30 S 250 - 280 26 S 280 - 300 24 S 40D Lycra S/J – Fabric G.S.M Yarn Count 180 - 190 34 S 190 - 210 32 S 210 - 220 30 S 220 – 240 28 S 240 - 250 26 S DIFFERENT FABRIC GSM AND THEIR REQUIRED YARN COUNT
23. 23. Yarn Dyeing Calculation and Equation
24. 24. Production Calculation of Yarn singeing machine: Length = Count * Weight = Count * Weight * 840 yards = (Count * Weight * 840) / rpm yards per minute = (Count * Weight * 840) / rpm * 60 * 8 * 3 yards per day = (Count * Weight * 840) / rpm * 60 * 8 * 3 * 0.914 =……X…meter/day.
25. 25. Production Calculation of reeling machine:
26. 26. Production Calculation of hank to cone winding machine: Machine Parameter Yarn quality Speed (rpm) 58/2, 60/2 450 All single count 500 to 550 Length = Count  Weight = Count * Weight  840 yards = (Count  Weight  840) / rpm yards per minute = (Count  Weight  840) / rpm  60  8  3 yards per day = (Count  Weight  840) / rpm  60  8  3  0.914 =……X…meter/day.
27. 27. GSM Calculation: WPI = 32 CPI = 45 Stitch length = 3 mm Yarn Count = 20’S Ne
28. 28. No. of Needle = π × Machine Diameter (D) × Machine Gauge (N) = 3.1416 × 30 × 24 = 2262 Yarn Count = 30/1 Ne No. of Feeder = 96 Machine RPM = 28 Stitch length = 3 mm Efficiency = 85% = 0.85 Shift = 8 hr. = 8 × 60 = 480 min Production Calculation Of Yarn Dyeing Machine : Production of the machine is 146.407 Kg/Shift. Note: If any parameter in this calculation is changed then production capacity per shift will be changed.
29. 29. Package Density Calculation (Yarn Dyeing): Formula
30. 30. Density Calculation for Several Counts (Yarn dyeing): 1**Before Pressing • Yarn Quality: 30/1 cc • Package Height (H) = 162mm = 16.2cm • Total Package Dia (D1) = 162mm = 16.2cm • Total Package Weight (W1) = 1.38kg = 1380gm • Spring Weight (W2) = 0.185kg = 185gm • Spring Dia (D2) = 65 mm = 6.5cm
31. 31. 2 **After Pressing Yarn Quality: 30/1 cc Package Height (H) = 145mm = 14.5cm Total Package Dia (D1) = 165mm = 16.5cm Total Package Weight (W1) = 1.38kg = 1380gm Spring Weight (W2) = 0.185kg = 185gm Spring Dia (D2) = 65 mm = 6.5cm **So we can sure that after pressing for every count, yarn package density will be increase. Density Calculation for Several Counts (Yarn dyeing):
32. 32. Length Calculation in Package: To maintain the constant package density same length of yarn should be wound to all the packages of a batch or lot. The dyeing machine capacity is calculated on weight, so it is necessary to maintain the uniform weight throughout the packages. To do this for a definite count of yarn following calculation is followed, In this machine length is pre selected. For different count of yarn different length of yarn is pre selected. This is due to maintain the constant package weight and package density.
33. 33. Package density Calculation We know package density ρ =mass (m)/volume (v) gm/cc Volume= π (R2-r 2) h R= outer radius of package R= inner radius of package h= height of package Now we consider a sample of 40/1 cotton yarn whose R=4.138 r= 1.59 h=15.24 Mass m=1000gm So package density ρ=1000/π (4.1382-1.592)15.24 gm/cc =1.433 gm/cc Production calculation: We know production= speed (m/min) ×60×24 ×1.09/(840×40×2.2045) Kg/day/head When speed is 800m/min at 80% efficiency Production=800×60×24×1.09/ (840×40×2.2045)kg/day/head =10.5976kg/day/head Total production=10.5976×54×12kg/day =6867.2448kg/day
34. 34. Production calculation of RF Dryer : Length of RF Dryer = 13m At 28rpm it takes 21 min 9 sec to pass this length Along this length it can accommodate 416 package 416kgs So at 21 min9sec or 1269sec it can dry 416kgs So in 1hr or 3600sec it can dry = 416×3600/1269 kg/hr = 1180.14 kg/hr So Production per day = 1180.14×24kg = 22658.688 kg = 22.66 tons Production calculation of RF Dryer
35. 35. Knit Dyeing Calculation and Equation
36. 36. Calculations related to batch section: Now, when a gram per linear meter is low then meters per chamber will be more. Thus, fabric loading should be reduced to avoid jamming in the winch. In this case 80-85% fabric loading is given. But when gram per linear meter is more then rope length will reduce and in this case up to 90% fabric loading can be given.
37. 37. Calculating the chamber loading In the following table are listed general recommendations covering rope cycle times and speeds for a wide range of fabrics: Fabric Rope cycle times in minutes (Cycle Time) Rope circulation speed m/min (Reel speed) Knit fabric PES unfixed 1 250 PES heat set 1-1.5 200 PC 1-2 250 Co - reactive 2-3 225-275
38. 38. Preparation and storage of stock dyes and chemicals Available stock solution: 1. Red-0.1%, 0.5%, 1%, 2% 2. Yellow-0.1%, 0.5%, 1.0%, 2.0%, 3. Blue- 0.1%, 0.5%, 1.0%, 2.0%. Preparation:  To prepare 0.1% stock solution, it necessary to mix 0.1 gm dye with 100cc water.  To prepare 0.5% stock solution, it necessary to mix 0.5 gm dye with 100cc water.  To prepare 1.0% & 2.0% stock solution similar procedure is followed.  To prepare 10% stock solution of soda ash, it necessary to mix 10 gm soda with 100cc water. SHADE % STOCK SOLUTION % 0.0001-0.009 0.1 0.10-0.99 0.5 1-1.99 1 2-3.99 2 4 ( or above) 4 Stock solution preparation:
39. 39. Stock Solution Making Procedure (Dyeing lab) For solid, X gm chemicals/dyes/auxiliaries in the 100 ml water is called x% stock solution. For liquid, X ml/cc chemicals/dyes/auxiliaries in the (100 - x ml/cc) water is called x% stock solution. Conversion formula from percentage to g/l is as g/l = Required amount (%)× 10
40. 40. Recipe Calculation
41. 41. Dyes and chemicals measuring formula for laboratory: The amount of dye solution (ml) is calculated as follow – The amount of chemical soln (ml) is measured as follow –
42. 42. Fabric Type GSM Pump Speed % Reel Speed(MPM) Single Jersey Up to 140 80 250 140 – 180 85 230 180 – above 90 210 Polo Pique, Back Pique & Bubble Knit Up to 160 85 280 160 – 200 90 260 220 – above 90 240 Interlock Up to 180 85 260 180 – 220 90 240 220 – above 90 220 Machine Setup On The Basis Of Fabric Type & GSM
43. 43. MONTHLY EFFICIENCY OF KNITTING FLOOR: Daily production – 6500 kgs. Approx. Daily production capacity – 10000 kgs approx. So, monthly production – 6500 x 30 kgs. Monthly production capacity – 10000 x 30 kgs. So, Monthly production efficiency = (6500x30x100)/ (10000x30) % = 65%
44. 44. Garments Calculation and Equation
45. 45. COSTING OF THE PRODUCT: Let price of yarn is \$ 3.00/ kg. Process loss of yarn for knitting (10%) = \$0.30 Knitting fabric cost = \$3.30 Cost of dyes & chemicals = \$2.50 Process loss for dyeing (12%) = \$0.30 Dyed fabric cost = \$ 6.10 Packing cost = \$0.05 Production cost of fabric=\$6.15 Fabric price (with 25% margin) =\$7.79 Fabric consumption/ doz. = (Body length + Sleeve length +10) x Chest length x 2 x GSM x12 /10000000
46. 46. Garments specification: Body length=78 cm Sleeve length=33 cm Chest length=62 cm GSM=210 Fabric consumption/ doz. = {(78+33) x62x2x210x12}/ 10000000 = 3.469 kg Fabric consumption/doze (with 10% wastage) = 3.816 kg Body fabric cost / doz. =\$(7.79x 3.816) = \$29.73 Cost of collar& cuff/doz = \$ 4.00 Cost of Trims=\$ 2.25 Cost of Trims (with 5% Process loss) = \$2.36 Production Cost of Garments/ doz=\$36.09 Garments Price/doz (with 25% Profit) =\$45.12 COSTING OF THE PRODUCT:
47. 47. Costing of Men’s shirt Fabric consumption for a dozen of shirt π × L ═ size of basic shirt. Width of body of shirt ═ 1/2 chest ═ 24"+1"(sewing allowance) ═ 25" Body length ═ 32"+1"(sewing allowance) ═ 33" Sleeve length ═ 23"+2.5(cost) +1.5"(sewing allowance) ═ 27" Consumption of a body shirt: ═{1/2 chest× (body length) ×2} / 36× fabric width. (Sq. inch) ═25"×33"×2 (Sq. inch ). {Let assume fabric width 25"effective width ═25"−1" ═ 24"} Fabric length ═25×33×2 / 44 inch
48. 48. Fabric consumption ═25×33×2 / 44×36 yds Consumption of sleeve ═ (length of sleeve × width sleeve) ×2 sq. inch ═27"×24"×2" (Sq. inch) Fabric consumption in length width ═ 27×24×2 / 44×36 sq. inch Total fabric consumption of one dozen shirt ═ [(25×33×2 / 44×36 + / 27×24×2 / 44×36) ×2+ wastage of 8%] ═ 22.75 yds + 8% wastage ═24.6 yds Sewing threads consumption: It is calculated by measuring the total of different kind of seam. Normally sewing threads consumption per shirt , 120m. So, sewing threads consumption per dozen, ═ 120 × 12 ═ 1440m Costing of Men’s shirt
49. 49. Costing of T- shirt Fabric Type :Single jersey G.S.M :180 Yarn count :24/1 Measurement of Garments: Body length : 54 cm Chest length : 43 cm Sleeve length : 15 cm Fabric Consumption = {(Body length + sleeve length + allowance) *(Chest length + 3)} * 2 /10,000 * G.S.M / 1000 * 12 * 10 % (+) = {( 54 + 15 + 10 ) * ( 43 + 3 )} * 2 / 10,000 * 180 / 1000 * 12 * 10% (+) =1.72 kg =1.72* 0.18 = 1.90 kg / doz. Costing Fabrics cost : 17.10 Cost of making : 4.5 Print cost : 3.5 Lab cost : 0.20 Accessories cost : 2.5 Washing cost : 1 Total = \$ 28.80 / Doz. = \$ 2.40 / pcs.
50. 50. How can we get Fabric Consumption & Fabrics Price? Say: ** Body Length = 85, Chest Width = 52, Sleeve Length = 44 & G.S.M = 240 Fabric Description: 100 % Cotton S/J Fabric Need = [(85+5+44+5)  52+5]  2  12  240/10000000+10% = [(90+49)  57]  2  12  240/10000000+10% = (13957)  2  12  240/10000000+10% = 7923 12  240/10000000+10% = 45636480/10000000 + 10% = 4.563648 +10% = 4.563648 + .4563 = 5.02 Kgs Fabrics Say Per Kgs Price: US\$ 6.00/Kgs
51. 51. Poly bag costing : Total Length X width X Thickness = 36cm X 28cm X 10mm = 10080/72000 = 0.14pcs/lb Fabrics Price: Total Fabric Need 5.00 Kg  \$ 6.00 = \$ 30.00 Trim/ Accessories (Minimum Charge) = \$ 2.50 Cutting & Making Charge (C.M) = \$ 5.00 Printing Charge (If any) = \$ 0.00 Embroidery Charge (If any) = \$ 0.00 Buying Commission (If necessary) 5% = \$ 1.97 Final/Total = \$ 39.47/12 Costing of a garment: Fabric cost + Accessories cost + Trimming cost + Production cost + Transport cost + Commission + Profit
52. 52. Consumption of T-Shirt: Equation: {(Body length + Sleeve length)  Chest}  2  GSM  10000  1000  5000 Solution: Body Length = 50 + 6 (Allowance) = 56 cm Sleeve Length = 15 + 3 (Allowance) = 18 cm Chest = 37 + 3 (Allowance) = 40 cm GSM = 180 cm = {(56 + 18)  40}  2  180  10000  1000  5000 = 532.8 kg.
53. 53. Consumption of Collar: Equation: {(Neck width + Front neck drop)  collar depth}  2  GSM  10000  1000  5000 Solution: Neck width =22  2 = 44 cm Front neck drop =5 cm Collar depth =2.5 cm  2 = 5 cm GSM = 240 = {(44 + 5)  5}  2  140  10000  1000  5000 = 58.8 kg. Total = 532.8 + 58.8 kg = 591 kg
54. 54. Collar & Cuff measurements Size Collar measurement (cm) Cuff measurement (cm) S 40 x 9 40 x 3.5 M 42 x 9 40 x 3.5 L 44 x 9 40 x 3.5 XL 46 x 9 40 x 3.5 XXL 48 x 9 44 x 3.5 XXXL 50 x 9 44 x 3.5
55. 55. Consumption of bottom part: Equation: Length*(width*4)*G.S.M÷10000÷1000*12 Length=53=8=2=63cm Width= 18*4+6= 78cm G.S.M= 260 Solution [(63*78*260)÷10000÷1000*12 =1.53kgs
56. 56. Consumption of Pocket: Equation: Length*width*G.S.M÷10000÷1000*12 Length=11+2=13cm Width=10cm G.S.M= 260 Solution (13*10) *260÷10000÷1000*12 =0.04056kg Total= 1.53+0.04056 1.5705kg
57. 57. Costing process: Finish fabric cost: (Yarn price + Knitting cost + dyeing cost) Body fabric cost: (Total fabric consumption + Total yarn consumption) Cost of making (CM):……………………………\$ Accessories cost:…………………………………..\$ Overhead cost………………………………………\$ Others cost:………………………………………….\$ Buyer commission:……………………………….\$ Total cost..................................................\$ Costing process: PRICE OF THE PRODUCT: Generally price of product is determined by the required profit adding to the total expenses. So, Price of products = (Direct expenses + Indirect expenses + Factory Overhead) + Required profit
58. 58. MARKER EFFICIENCY: The marker planner measures his success by the efficiency of the marker plan. The following formula is used to measure the efficiency: Marker efficiency=Area of the pattern in the marker plan/ Total area of the marker plan X 100%. MARKER EFFICIENCY:
59. 59. STANDARD TIME = Normal time + Allowances = Normal time + (Normal time ×Allowances) = NT (1+ Allowances). In garments production world, the terms SMV or SAM used frequently.  SMV stands for Standard Minute Value.  SAM for Standard allocated minute or Standard Allowed Minute. SMV CALCULATION: SMV calculation of a basic T-shirt from a time study sheet of a garments industry. Following formulas are use-  Normal time = (Average observed time) × (Performance rating factor).  SMV (Standard Minute Value) = Basic Time + (Allowances × Basic time). = Basic Time× (1+ Allowance).  Allowances are assumed for this calculation is 20%. SMV
60. 60. SMV Target Production /Hour = (No Of worker -1) x 60 / SMV SMV= standard Mean Value (the Time Required to Complete garments by sewing ) SMV=( Basic time +Allowance )
61. 61. To select sewing thread, thread size or number is very important. The number which is used to express the fineness of a sewing thread is called sewing thread number or ticket number. It has 2 system as follows- Cotton system : It is derived from English cotton system. Cotton ticket number in Ne = ( Yarn count in Ne / Number of ply ) x 3 Metric system : It is derived from Metric count system. Ticket number in Nm = ( Yarn count in Nm / Number of ply ) x 3 sewing thread number or ticket number
62. 62. Equation For Find Yarn Count (If GSM is Known)  Single Jersey = 4300 /GSM  Pique = 5200 / GSM  Fleece = 7200 / GSM  Interlock = 7200 / GSM  1x1 rib = 6000 / GSM  Locoest =5500 / GSM  2x2 rib = 6250 / GSM  Terry = 6240 / GSM
63. 63. Find out Required Yarn Count (If GSM is Known) Equation : S/j Ne = (0.141x GSM) + 50.22 Pique Ne = (0.146x GSM) + 57.16 Double Lacost Ne = (0.167 X GSM) + 64.36 1X1 Rib Ne = (0.123X GSM) + 54.57 Interlock = (0.206X GSM) + 80.56 Lycra 1X1 Rib = (0.119 X GSM) + 59.12 Lycra 2X2 Rib = (0.108X GSM) + 56.62
64. 64. Conversion of (GSM Equation ) Kg To Yards Equation : = GSM / 39.37 X 36 X fabric Width =Result .Kg =1000/ Result .yds [It is converted Kg To yards ] Per Yards Fabric price Equation : = GSM / 43” X Width / 1000 X Per kg Prize =Result . [This the Equation define per yards Fabric price ]
65. 65. Conversion of (GSM Equation ) Yards To meter Equation : = Length X 36 X 2.54 /1000 =Result [It is converted yards to Meter ] Meter To Yards Equation : = Length /36 / 2.54 X 1000 =Result [ It is converted Meter To yards ]
66. 66. Conversion of (GSM Equation ) Find Out How many Yds / Kg Equation : = 714//GSM =Result (yds in Kg) [Only For 58’’/60’’ Width] Price/Yards Equation : = GSM /43 / 2.54 X Width =Result / 1000 X Price = price/yds
67. 67. Textile Testing Calculation and Equation
68. 68. Four point grading system Size of defects Penalty 3 inches or less 1 point Over 3 inch but not over 6 inch 2 point Over 6 inch but not over 9 inch 3 point Over 9 inch 4 point Four point grading system
69. 69. Shrinkage Test:
70. 70. Spirality test: