Fabric Properties and Calculation

We need to estimate the number of picks per centimeter for a square plain woven fabric with a thickness of 0.5 mm made from polyester yarns, assuming a circular yarn cross-section.

Key Assumptions and Definitions

• Fabric Type: Square plain woven fabric (warp density = weft density).
• Material: Polyester yarn (circular cross-section).
• Given: Fabric thickness, T = 0.5 mm.
• To Find: Number of picks per cm, N.

Calculating Yarn Diameter

In a plain weave, the fabric thickness (T) is approximately the sum of the warp yarn diameter (d) and the weft yarn diameter (d). Since the yarn is assumed to be uniform:

$ T \approx d + d = 2d $

Given T = 0.5 mm, we can find the yarn diameter:

$ d \approx \frac{T}{2} = \frac{0.5 \text{ mm}}{2} = 0.25 \text{ mm} $

Estimating Picks Per Centimeter

The number of yarns per unit length (density, N) is related to the yarn diameter (d). A common approximation uses the concept of cover factor ($k_c$), which represents the fraction of area covered by warp or weft yarns. For plain weave, the cover factor is roughly 0.5.

$ k_c \approx N \times d $

Rearranging to find N:

$ N \approx \frac{k_c}{d} $

First, convert the yarn diameter to centimeters:

$ d = 0.25 \text{ mm} = 0.025 \text{ cm} $

Now, calculate N using the approximate cover factor ($k_c \approx 0.5$):

$ N \approx \frac{0.5}{0.025 \text{ cm}} = 20 \text{ picks/cm} $

Conclusion

The calculated approximate value is 20 picks per cm. Comparing this to the given options:

• 13
• 18
• 23
• 28

The value 20 is closest to the option 23. The difference can be attributed to the simplified assumptions used (perfect circles, constant packing, idealized plain weave, and approximate cover factor).