Cover Factor of Fibre, Yarn and Fabric

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CONCEPT OF SIMILAR CLOTH
Fibre or raw materials of the two cloths may be same but they can differ on other factors, such as:-
i) The yarn count may be different.
ii) The ratio of yarn count in warp and weft may differ.
iii) The warp ratio of yarn spacing may differ.
iv) The average of yarn spacing may differ.
v) The weave design may differ.
vi) The amount of twist in yarn may differ.

If there is similarity in COVER FACTOR of two cloths but they differ in such points as mentioned above then they are called similar cloth.

COVER FACTOR
Cover is the degree of evenness of thread spacing. Good cover gives the effect of a uniform plane surface & it can not be obtained with hard twisted yarn. In case of woven fabric cover factor is a number that indicates the extent to which the area of a fabric is covered by warp and weft threads. For any fabric by introducing suitable numerical constants its evaluation can be made in accordance with any system of counting. It is denoted by k.

Mathematically,

        k = d / p;

where, d₁ = Warp dia; d₂ = Weft dia; P₁ = Warp spacing; P₂ = Weft spacing; k₁ = Warp cover factor, and k ₂ = Weft cover factor.

     

So, k₁ = d₁/P₁    &    k₂ = d₂/P₂

Therefore, Fabric Cover Factor =  k₁ + k₂.

The ratio of yarn diameter to yarn spacing, d/p, is a measure of the relative closeness of the yarns in the warp or weft of a woven fabric. This ratio also expresses the fraction of the area of the cloth covered by the warp or weft yarns. We may therefore call it the fractional cover,  i.e.

                      Fractional cover = d / p.

Substituting Peirce’s estimate of yarn diameter, d = 1/28 √N, we have 

d / p= [1/(28√N) x1/p]

 But 1/p = n, where n = threads/in., so

 d / p= n/(28√N) ……………………………… (6)

Now d/p has a value of 1.0 when the yarns are just touching. Peirce multiplied eq.(6) by 28 to eliminate the numerical constant, 28, and defined the result as the ‘coverfactor’, K.

Cover Factor, K  = n /  √N  ……………………………………………..(7)

Because we have multiplied by 28, cover factor as defined in eq.(7) has a value of 28 when the yarns are just touching. The relative yarn spacing corresponding to various cover factors are shown below:

It is usual to calculate separate cover factors for the warp and the weft. Using the suffices 1 and 2 for warp and weft, we have

      Warp Cover Factor, K₁ = n₁ / √N₁ and

      Weft Cover Factor, K₂ = n₂ / √N₂.

The sum of the warp and weft cover factors is known as cloth cover factor, Kc.  It is customary and more informative, however, to state the warp and weft cover factors separately. Just as twist factor enables us to compare the relative hardness of twist in yarns of different counts, so cover factor enables us to compare the relative closeness of the yarns in different fabrics.

Math related to cover factor

Compare the relative closeness of the warp yarns in the following two plain cloths; (a) 16s cotton; 50 ends/in; and (b) 36s cotton; 84 ends/in.

We have the cover factor for cloth (a), K₁ = 50 / √16   = 12.5.

And for cloth (b) cover factor, K₂ = 84 / √36   = 14.0

So the ends are more closely spaced in cloth (b) than in cloth (a)

MATH:- Calculate the warp and weft cover factors for the following fabric: 60 denier nylon x 48s worsted; 96 x 72.

      60 denier = 5315/60 = 88.57s cotton count.

So, K₁ = 96 / √88.57   = 10.2

       40s worsted = 48 x 560/840 = 32s cotton count.

So, K₂ = 72 / √32   = 12.7

GENERAL FORMULA FOR CALCULATING COVER FACTORS

   Indirect systems                                              direct systems.

      K = cn/ √N                                                    K = cn √N

Where N is the yarn number in the particular system.

System                Value of c                          System          Value of c

Cotton                     1.0                                     Denier        0.01375

Worsted                  1.228                                 Tex             0.04126

Linen lea                 1.667                                 lb/spdl        0.2422

MATH: Calculate the cover factor corresponding to 80 threads/in. of 100 denier. 

From the table constant for the denier system is  0.01375.

Therefore, K  = 0.01375 x 80 x √100  = 11.0

MATH: How many threads/in. of 5 tex nylon are required to give the same cover factor as 90 threads/in. of 2/100s cotton?

Since the equivalent singles count of 2 /100s is √50 s.

Therefore,

                            K  = 90/ √50.

So, K = 12.7  = 0.04126 x n √5

 Therefore  the number of threads required

n=12.7/0.04126 x √5 = 138 threads / in.         

Thus required thread/in is 138 of 5 tex to give the same cover factor as 90 threads/in. of 2/100s cotton.

This problem can also be solved with reference to the formula for calculating cover factor.

     5 tex  = 590.5 / 5  = √118 s cotton count.

As before, K  = 12.7  = n/ √118.

Therefore n = 12.7 x   118   = 138 as before.

Wish You Good Luck..................................
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