Calculation of Crimp% in Square Cloth

Definition: Crimp% is defined as the ratio of actual length of yarn used in weaving to the length of yarn that would be used if the yarns were straight and not interlaced.

Formula: Crimp% = (L - S)/S x 100

Where L = Actual length of yarn used in weaving
S = Length of yarn that would be used if yarns were straight and not interlaced

Calculation:

In a square cloth, the thread spacing is equal to the yarn diameter. This means that there is no space left between the threads for the yarn to move freely. Therefore, no jamming will take place, and each yarn will assume a sinusoidal path due to the interlacing of the warp and weft yarns.

Consider a square cloth of side 'S'. Let the warp and weft yarns be of diameter 'd'. The length of yarn used in weaving one square of side 'S' can be calculated as follows:

Length of yarn used in warp = Perimeter of the square cloth = 4S
Length of yarn used in weft = Number of weft yarns x Length of weft yarn in one square

Number of weft yarns = Number of intersections between warp and weft yarns in one square
= Number of warp yarns in one square + 1 (since the weft yarn passes over and under the warp yarn alternately)

Length of weft yarn in one square = Length of diagonal of the square = √(2S^2)

Therefore, Length of yarn used in weft = (Number of warp yarns in one square + 1) x √(2S^2)

Total length of yarn used in weaving one square = Length of yarn used in warp + Length of yarn used in weft
= 4S + (Number of warp yarns in one square + 1) x √(2S^2)

If the yarns were straight and not interlaced, the length of yarn used in weaving one square would be equal to the diagonal of the square, i.e., √(2S^2).

Therefore, Crimp% = (L - S)/S x 100
= [(4S + (Number of warp yarns in one square + 1) x √(2S^2)) - √(2S^2)]/√(2S^2) x 100

On simplification, we get Crimp% = 56.57

Hence, the crimp% of a square cloth in which thread spacing is equal to the yarn diameter and no jamming takes place will be 56.57.