1. Fractional Cover is defined as d/p where d is the diameter of the yarn and p is the thread spacing.
2. There are various theories for calculation of yarn diameter. According to Law yarn diameter d is equal to 1/ sqrt (Fn) where F is 500 for worsted yarn, 800 for cotton yarns, 530 for woolen n being worsted and cotton and Yorkshire count respectively. According to Ashenhurst yarn diameter d = 1/(F sqrt(N)), where F is .95, .9,.84 for cotton, worsted and woolen yarns respectively and n= yds/lb. According to Pierce, yarn diameter is 1/(28 sqrt(N) where N is the English count.
3. Ashenhurst Diameter intersection theory says that when the count of warp and weft are the same, it is assumed that an intersection takes up as much space as a thread. Then Threads/inch (T) can be determined as equal to D x W/ (W+I) where D is the diameter per inch of yarn, W is the threads in one repeat of weave and I are the intersection in one repeat of weave. For plain weave W =2, I=2 for 2/1 twill weave, W=3 and I = 2.
4. Curvature theory says that T = D x W/ ( W +.732 I), the notations being the same as in point 3.
5. Armitage Maximum Setting Theory says that cloths which are similarly built are equally firm. For regular twill weaves Threads per inch (T) = Sqrt (6 x C(F+4)) where C are the counts of worsted yarn and F is the average float of weave. For other weaves, Armitage gave the following “setting ratio” instead of (F +4). For plain weave it is 4.75, for 2/2 hopsack it is 6.25, for 4 end satin it is 6.5 for 5 end, 6 end and 8 end satin it is 7.5, 7.75 and 9.0 respectively.
6. Laws Maximum Setting suggests that T = ((D x F)/ (F+1) )+ various percentages where F is the average float and D is the diameter per inch. For common weaves like plain weave T = ( D X 1)/(F+I), for twill weave T= ((DF)/(F+1))+ 5% for each float exceeding two, for satin weave T = ((DF)/(F+1))+5.5% for each float, for hopsack weaves T= ((DxF)/(F+1))+ 4.5% for 2 floats and 9.5% for floats exceeding two.
7. Brierjey’s Maximum Setting suggests that square settings vary according to the formula T= sqrt (KC x (F)^m) where C is the average count of yarn, F is the average float, K is a constant varying according to kind of yarn and numbering system: it is 134 for worsted yarn, 200 for cotton yarn and 60 for york shire yarn. m is a constant varying according to the type of weave: For twill weaves it is 0.39, for Satin weaves it is 0.42 and for plain and hopsack weaves it is 0.45.
An amazing treatment on fabric geometry is done in this presentation.
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