The wale constant and course constant are 4.2 and 5.04 respectively. If the loop length is 4.2 mm, then stitch density (number/cm$^2$) is______.
Stitch Density Calculation Explained
This section provides a concise, step-by-step calculation for determining the stitch density using the given fabric constants and loop length, suitable for exam preparation.
Given Fabric Constants
| Parameter | Value |
| Wale Constant ($WC$) | 4.2 |
| Course Constant ($CC$) | 5.04 |
| Loop Length ($L$) | 4.2 mm |
Stitch Density Calculation Steps
The stitch density ($D$), measured in stitches per square centimeter (stitches/cm$^2$), is determined using a formula that incorporates the wale constant, course constant, and the square of the loop length.
Unit Conversion
First, convert the loop length ($L$) from millimeters (mm) to centimeters (cm) to match the required units for stitch density.
$ L = 4.2 \text{ mm} = \frac{4.2}{10} \text{ cm} = 0.42 \text{ cm} $
Formula Application
The formula used to calculate stitch density ($D$) is:
$ D = \frac{WC \times CC}{L^2} $
Substitute the given values into the formula:
$ D = \frac{4.2 \times 5.04}{(0.42 \text{ cm})^2} $
Final Calculation
Calculate the numerical value of the stitch density.
$ D = \frac{21.168}{0.1764 \text{ cm}^2} $
$ D = 120 \text{ stitches/cm}^2 $
Result
The calculated stitch density is 120 stitches/cm$^2$.
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