 
I It is desirable that the calculations connected with cotton manufacturing in all its bearings be treated in a separate chapter. This is not only necessary from their number, but from their great variety and difficulty of classification under different chapter headings, inasmuch as many are applicable to more than one process. Yarn Calculations.The fineness of cotton yarn is indicated by the counts (otherwise numbers or grist). The counts refer to the number of hanks in a pound (avoirdupois). The cotton hank is always 840 yards; and, therefore, if we speak of 10’s, we refer to yarn of which 10 hanks or 8400 yards weigh one pound; or in referring to 36’s, of that which 36 × 840 or 30,240 yards weigh one pound. This applies to either twist or weft. The cotton yarn measure is—
and the cotton yarn weight is peculiar, being an avoirdupois pound divided into pennyweights and ounces as in the troy weight.
Wrapping.1’s are taken as the standard with 840 yards in 7000 grains, and a higher count means finer yarn; then 840 yards of, say 2’s, would weigh 3500 grains, or of 70’s, would weigh 100 grains. If we measure a hank of yarn, and find that it weighs 100 grains, then 7000, divided by 100, gives the counts. It is inconvenient in wrapping yarn to measure 840 yards, therefore a lea of 120 yards is taken as the standard length for 1’s, and also the proportionate weight = 1000 grains. Instead of taking 840 yards and 7000 grains it is usual, then, to take 120 yards and 1000 grains. A wrap reel is 1-1/2 yards in circumference, and, by revolving it 80 times, we can wind 120 yards from a cop placed in the machine. Suppose this lea of 120 yards weighs 25 grains, then 10000/25 = 40’s. Should less than a lea be taken, say 60 yards, then 500 grains must be the dividend. Generally, however, to obtain the counts of any yarn, 120 yards are weighed, and the weight, in grains, divided into 1000. Having the Length and Counts given, to find the Weight.—9240 yards of 44’s weft = 9240 yards ÷ 840 = 11 hanks. In the given counts 44 hanks weigh 1 lb., then 11 hanks weigh 11/44 or 1/4 of a lb. Counts of Silk, Worsted, Linen.—Single silk is counted same as cotton, except that in two-fold patent silk the actual wrapping is given—say, 30’s/2 in silk will wrap 30’s. In cotton, 2/30’s would wrap 15’s. The worsted hank is 560 yards. The linen “lea” is 300 yards. The French cotton standard is 1000 metres in 500 grammes—equivalent to 992·4 yards in 1 lb. Thus, 1·181’s in English would be 1’s in French. To transfer cotton measure to any other take the cotton count, proportion it inversely to the number of yards in the hanks, say— 20’s cotton equals 30’s worsted, Double Yarns (Cotton).—Two-fold yarns are numbered according to the single yarn counts—thus, 2/80’s = two ends of 80’s twined together, which would wrap 40’s. Actually, to make the resultant count 40’s, the single yarn should be finer than 80’s, because the twist put in the folded yarn contracts it in length and causes the two-fold to be really coarser than would appear. However, neglecting this, suppose we twine one end of 40’s and one of 20’s, the counts would not be 15’s, as a first glance would indicate, but 13·33. This can be proved by taking the weight of a lea of 40 = 25 grains, and of 20’s = 50 grains; total, 75. 75 divided into 1000 gives the counts as 13-1/3. Another rule is, multiply the two counts and divide by their sum—
Or take the highest count and divide it by each of the others and by itself, then divide the total of the quotients into the highest—
Testing Yarns.In addition to wrapping warp yarn to ascertain actual counts, it is frequently tested as to strength; the lea from the reel is placed between two hooks on a testing machine, and by a wheel worm and screw the lower hook is moved downwards, increasing the tension on the yarn. By an index finger this tension is indicated on a face plate, and when the lea is broken the finger stops at the highest weight or strain that the yarn has stood. Below is a table, which will give a general idea of the comparative strength of mule twists, having, for the American cotton, the standard turns in—i.e., square root of counts multiplied by 3-3/4.
In yarn the diameters of the threads do not vary inversely as the counts, but inversely as the square root of the counts. Thus, 16’s is not four times as thick as 64’s, but twice as thick, the square roots being four and eight respectively. Reed Counting.Before entering into the calculations regarding the weight of cloth, it is necessary to familiarise ourselves with some method of counting the ends of warp in the cloth. On the Exchange the system adopted both for ends and pick is their number per quarter inch—e.g., a 16 by 14 means 16 ends per 1/4-inch, or 14 picks per quarter. The methods used in the manufactory are based on the counts of reed. Formerly many systems of reed counts prevailed, each town or district having a method peculiar to itself; thus, Blackburn counts, Preston counts The Bolton counts is still used in some mills in that town and also in Bury and some few other districts. It is based on the number of beers in 24-1/4 inches—a beer comprising 20 dents. A Stockport 40’s reed would have 485 dents on 24-1/4 inches, or 24-1/4 beers Bolton. A Bolton 24-1/4 reed is then equal to a Stockport 40’s. To find the number of splits per inch in a reed having Bolton counts given, multiply those counts by ·8249, or vice versÂ. This rule shows the number of dents and decimal parts; 8·245 is more often taken, but it gives the number with less exactitude. The fraction is only taken to two places of decimals, showing thus the 100th parts of dents—e.g., a 300 Bolton has 24-74/100 splits per inch (8·249 × 30 = 24·747). To convert Stockport into Bolton counts multiply by ·60625. To convert Bolton into Stockport multiply by 1·6495. This rule gives the number of ends per inch in Bolton counts, supposing the cloth to be wrought two ends in a dent. The Scotch systems are to take the number of dents or splits in the old Scotch ell, 37 inches, or by the number of porters on the same length. The Scotch porter is equal to the Lancashire beer—20 splits. In the first system, the splits per ell are expressed in hundreds—thus, 1700 indicates 1700 splits on 37 inches, almost equal to a 92 reed, Stockport; or a 46 on the Scotch inch scale, which is the number of splits in one inch, and corresponding to the old Radcliffe and Pilkington method in Lancashire. By the porter system, a 40-porter reed would give 40 × 20 dents = 800 on 37 inches, equal to a 43 reed, Stockport, In Scotland (as in Lancashire) the old In the reed table given below, the first row of figures shows the proportion which these reeds bear to one another, and the lower rows indicate the fineness of the different systems for 33 and 40 splits per inch respectively—the calculation results being given, which same might not frequently appear in practice—
Healds.In Stockport counts four healds are considered as a set, and having one thread through each eye are dubbed of similar counts to the reed—e.g., a 60’s set of healds has 15 stitches per inch in each set, equalling 60 ends per inch in the reed, which is a 60’s reed, Stockport. In spaced healds some are knitted finer than others and consequently numbered differently. In this point draft:—
twelve ends are drawn on five healds, one end on the 1st heald, two on the 2nd, three on the 3rd, four on the 4th, and two on the 5th. Four different degrees of fineness are required in the five heald staves, and the above draft is given to the knitter with instructions for so many patterns to the inch. Say five patterns per inch: 5 × 12 would give a 60 reed, and the number of stitches per inch would be respectively 5, 10, 15, 20 and 10—the front one being equal to a Stockport 20’s, for if there were four similar to it in a set, the number of ends would be 20. Weight of a Piece.In calculating the weight of a piece, the warp weight is obtained from the number of ends, based upon the width in the reed. This is multiplied by the sizing length and brought into hanks, from which the weight can be obtained by dividing by the counts. The weft is calculated from the picks to the inch, the reed width, and the actual length of piece. Example—A piece has to be made full dimensions, 36 inches wide, 36 yards long, 16 square (1/4 inch)—i.e., 64 ends per inch and 64 picks; yarns 30’s/36’s, the first number being the warp, sized 25 per cent. In the reed it would stand 38 inches, about six per cent. being allowed for contraction. Of course, if the yarn were coarser, the pick heavier, and the reed finer, more than this would be allowed. Supposing that a 60’s reed (Stockport) is used, the number of ends would be 38 × 60 = 2280; the length of warp, say 38 yards, allowing six per cent.—then (2280 × 38)/840 = 103-1/7 hanks, Weft.—The weft, 37-1/2 inches wide, 64 picks; length of piece, 36 yards. (37-1/2 × 64 x 36)/(840 × 36’s) = 2lb. 13-3/4oz. 37-1/2 × 64 gives the number of inches of weft in one inch of cloth, or, what is the same, yards of weft in one yard of cloth. Size.— 3lb. 7oz. = 55oz. The weight of the piece is then—
When the piece is measured by the long stick, about half an inch more to the yard must be reckoned—e.g., 38-inch: 14/14, 37-1/2 yards L.S., 38’s weft, to be 8-1/4lb. in weight; this would be perhaps 38-1/4 yards long S.S. Weft.— (40 × 56 × 38-1/4)/(840 × 38) = 2 : 10-3/4 Leaving 5: 9-1/4 for twist and size, say of the latter 100 per cent., then 2: 12-1/2 would be twist— (40 × 52 × 41)/840 = 101-1/2 hanks required to be found in 2: 12-1/2 of yarn; then if 2: 12-1/2 = 101-1/2 hank:: 1lb. equals 36’s twist about. This cloth would then be composed of— Warp2 : 12-1/4 For quoting purposes the weight of the yarn is taken at the market price, say that of the cloth No. 1— lb. oz. To this is added a sum sufficient to cover cost—winding, warping, sizing, power, miscellaneous expenses, waste (which sum varies considerably, and depends mainly upon the situation of the producers as regards the amount at The examples given are supposititious ones, for, as has been said, the exact details of weight and quoting prices are decided purely by local or temporary position, and fixed data cannot be given as a standard for every case. Stripe Patterns.In case of stripes with two counts of warp yarn, for example, the number of ends of each must be obtained. If there are 38 stripes each of 15 ends, 40’s twist, with a ground cloth between each of 45 ends warp, 60’s T, separate calculations for each must be made. 38 × 15 = 570 stripe ends. Altering.When the pick or reed is altered, the weight of the weft or warp is altered in proportion; when the length or width is altered, the weight of the piece is altered in proportion; when the counts of yarn are altered, the weight alters inversely proportionately. Other Reeds.Although the 1/4-inch scale is mostly used for calculating warps in Lancashire, we give an example of a calculation with the Bolton reed. To get the number of ends, multiply the reed counts by the width of your warp in the reed, and by 1·6495—thus, Bolton 36’s, 39 inches in the reed, would give 2238 ends. The calculation is then proceeded with in the ordinary manner. In the Scotch ell standard system, the dimensions of the cloth before-mentioned would be 36 inches wide, 36 yards (1100 × 38)/37 = 1130. Multiply by 2, as it is always understood that there are two ends in a split, and we get 2260 ends. The calculation is then continued in the usual way. (2260 × 38)/(840 × 30) = 3·407lb. Weft.—— The meaning of shots on the glass refers to a counting glass used in Glasgow district, one two-hundredth part of a yard in width; 11-1/2 shots will then give 11-1/2 × 200 = 2300 picks in a yard. (2300 × 37-1/2 inches wide)/(36’s × 36 inches to the yard × 840) = 2·85lb. If required to be left in hank, omit to divide by the counts in each case. In other materials, the length of the hank varies, and, in the case of single worsted, we should have divided in the previous calculations by 560 instead of 840, in linen by 300, or in single silk by 840. Warping and Sizing Calculations.In getting an order passed through a weaving shed the first point, after calculating the particulars for each piece or cut, is to get the length for warping and sizing. In the case of an order for 3750 pieces of the before-mentioned dimensions, the total length of warp is calculated thus—38 yards for one piece × 3750 = 142,500 yards, allowing nothing for waste in length, as the tension on the yarn in process will stretch it sufficiently to allow for that, and perhaps a little more. At the warping mill the length is taken in wraps of 3564 yards, subdivided into The number of back beams for the sizing machine is proportioned to the capacity of the warping mill—say five beams, the length on each beam must be 14,256 yards, and the total number of ends on the beams equal to the ends in the piece—say 5 at 456 each = 2280. To Calculate the Counts of Yarn after Warping.—Divide the length by the weight and 840. A beam weighs 301lb., carrying 504 ends, each 14,256 yards long— (14,256 × 504)/(301 × 840) = 28·41’s. Having 375 pieces to make from the set of beams, which will probably weigh about 1300lb. for 30’s twist, to this add 25 per cent. for size = (1300 × 325)/100 = 325 4lb. 5oz. being about the size required (vide page 150). Actual Size.—To find the size actually put on the yarn, subtract the weight of the unsized yarn less waste from the sized yarn—e.g., 1639 Actual sized weight. Counts after Sizing.— (14256 × 2280) / (1639 × 840) = 23·61’s To Calculate the Percentage of Waste.—Multiply the waste made by 100 and divide by the weight of yarn used. If eleven skips of twist, weighing 3189lb., make 33lb. of waste— 3189 ) 3300 ( 1·034 per cent. Wages—Standard Lists.In those towns where a uniform class of goods is made of simple weave, it is possible to formulate and adhere to a standard method of payment such as is done in Burnley, Blackburn, and other towns. In other districts, such as Bolton and Preston, the sorts are so varied and difficult to classify that at many mills a private list is adhered to with satisfaction to the employer and employed. For the benefit of some readers a typical calculation will be given, based on the 1853 Blackburn list, as in 1883 this list was adopted in Preston, Chorley, and other towns. This may be considered a list of medium position with regard to other lists—Burnley being lower for plains, Ashton list being considered a low one for fancies. The Blackburn list is based on a 40-inch loom, weaving from 36 to 41-inch cloth, 60 reed Stockport counts, 16 picks per 1/4 inch, 37-1/2 yards, from 30’s to 60’s weft, and from 28’s to 45’s twist, for 12·25d. Reeds.—A 60 reed or 30 dents, being the standard, is made the starting point, and 3/4 per cent. is deducted for every two ends or counts of reeds, from 60 to 48; but no deduction is made below 48 reed, and 3/4 per cent. is added for every two ends or counts of reed above 60. Weft.—All weft from 30’s to 60’s, both included, is considered medium, and reckoned equal, but all weft above 60’s to be allowed 1 per cent. for every 10 hanks,
Twist.—All twist from 28’s to 45’s, both included, is considered medium, and reckoned equal, but all twist above 45’s up to 60’s to be allowed 1-1/2 per cent., and all above 60’s 1 per cent. for each 10 hanks,
Additions for Picks.—All picks above 8 and up to 18 are considered proportionate, but 8 picks and all below and all above 18, to have 1 per cent. allowed for every pick over and above the proportionate difference in the number of picks. Width of Looms.—A 40-inch loom being the standard, is taken as the starting point, and all additions or deductions are made therefrom. (The reed space is measured from back board to forkgrate.)
40-inch loom (45-inch reed space) the standard—
Looms of Intermediate Width.—One per cent. per inch is to be deducted from 40 down to 30-inch loom; below 30 to 26-inch loom 5/8 per cent. per inch to be deducted. Above 40-inch and up to 45-inch loom, 1 per cent. per inch to be added, and all above 45-inch 2 per cent. per inch. Narrow Cloth in Broad Looms.—Suppose a 40-inch loom should be weaving cloth 36 to 31-1/4 inches in width, take off one-half the difference between 40 and 35-inch loom price; and if weaving cloth 31 to 27-1/4 inches wide, take off one-half the difference between 40 and 30-inch loom price; or if weaving 41-1/4 to 46-inch cloth in a 50-inch loom, take off one-half the difference between 50 and 45-inch loom, and so on with all other widths. Range of Cloths.—
Basis of Calculations.—The calculations in the Blackburn list are based upon the picks counted by the glass when the cloth is laid upon the counter. Forty yards short stick to be taken as 39 yards long stick. To find price for a 44-inch cloth in 45-inch loom = 66’s reed, 44 change pinion, 528 dividend, 75 yards long, 34’s/36’s— 12·25 Standard. or from list under heading, 45-inch loom— 66 reed, 37-1/2 yards = ·822 for 1 pick. Speeds of Shafts, Etc.In calculating the speed of a shaft driven from another by pulleys or gearing, multiply the speed of the first shaft by the driving pulley or wheel, and divide by the driven one. A shaft makes 100 revolutions per minute and carries a 40-inch drum driving a 16-inch pulley on another shaft; the speed of the second shaft would be 250, thus:— (100 × 40)/16 = 250. The same rule and calculation would apply if the first shaft had carried a 40-teeth cog-wheel, and the second a 16-teeth wheel. In taking the dimensions of a pulley for calculations the diameter is often taken; it does not matter, though, if the circumference be taken, but care must be exercised in taking the same dimension for the driven as is taken for the driver. If the diameter is taken of one, the diameter must be taken of the other. To get Speed of Loom from Engine.—Multiply the engine speed by all the driving pulleys, and divide by the driven ones. If the engine make 46 strokes per minute, spur-wheel 105 teeth, second motion pinion 52 teeth; also on same a 52 driving a 49 on line shaft in shed. Pulley on line shaft on which is a 15-inch drum driving a loom pulley on the crank-shaft of 8 inches. The driving and driven pulleys are always alternate; then as the first must be a driver— (46 × 105 × 52 × 15)/(52 × 49 × 8) = 185 nearly. The answer gives the calculated picks per minute. About 4 per cent. must, however, be allowed for slippage, reducing the 185 to an actual speed of about 177. To find the Size of Pulley for any required Speed.—Find the ratio of the given speed and arrange size of pulley accordingly. Suppose a shaft running at 100 revolutions per minute has to drive a loom-shaft at a speed of 180 picks per minute the ratio of speed is as 100 to 180 or as 5 to 9; arrange the pulleys in this proportion—say 10 inches and 18 inches, the larger pulley being on the driving shaft. To alter Speeds.—Calculate in proportion to the alteration. If a twill-shaft is driven by a 30-cog wheel, and revolves at a speed of 45 revolutions per minute for a 4-leaf twill, and it is desirable to change this to a 3-leaf twill with the twill-shaft at 60 revolutions per minute, then, as 45 is to 60, so 30: x— x = (60 × 30)/45 = 40 A 40 wheel must now drive the wheel on the twill-shaft, and the speed will be increased one-third more. Engines.The strength of a steam engine is indicated in horse-powers. A horse-power is taken as the capacity of performing 33,000 foot-pounds of work in one minute; lifting 3300lb. 10 feet high, or 10lb. 3300 feet high would be 33,000 foot-pounds of work. To obtain the Indicated Horse-power—the most usual Standard.—A diagram is taken from the engine by a small apparatus, and this diagram, when measured and averaged at different points of its length, gives the mean pressure of steam in the cylinder. Multiply this by the speed of the piston, by the area of the piston, and divide by 33,000, and the I.H.P. is to hand. 39·81 average pressure per square inch, area of piston 400 square inches, length of stroke 5-1/2 feet, strokes per minute 40 (or 11 feet both ways)— (39·81 × 400 × 11 × 40)/33,000 = 212·32 I.H.P. Nominal horse-power (condensing) = area of piston divided by 22; ditto high pressure = area of piston divided by 11. 2-1/2 to 3 looms, with preparation, are reckoned to 1 indicated horse-power. Coal.—A good quality of coal should evaporate 8lb. of water for each 1lb. burnt, and for a manufacturing concern (including sizing, which takes a great amount of steam) the consumption of coal should be about 3-1/4lb. per I.H.P. per hour. Thus 600 horse-power should use about 24 tons per week; excluding sizing, 2-3/4lb. would suffice. To find the Circumference of a Circle.—Multiply the diameter by 3·1416 or (roughly) by 3-1/7. To find the Area of a Circular Space.—Square the diameter and multiply by ·7854. To find the Cubical Contents of a Rectangular Block.—Multiply the depth, length and breadth together. Decoration |
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