Fabric Areal Density Calculation

The areal density of a fabric is its mass per unit area. For a plain woven fabric, it can be estimated by summing the mass contribution from warp and weft yarns per square meter, neglecting yarn crimp.

Formula Derivation

The formula for areal density ($D_{area}$) is derived as follows:

• Tex ($T$) is defined as grams per 1000 meters of yarn.
• Mass per meter of warp yarn ($M_w$) = $\frac{T_w}{1000}$ g/m.
• Mass per meter of weft yarn ($M_f$) = $\frac{T_f}{1000}$ g/m.
• In 1 square meter, the total length of warp yarn is the number of ends per meter multiplied by 1 meter height.
• Ends per meter ($E_m$) = Ends per cm ($E$) $\times$ 100 cm/m.
• Total length of warp yarn in 1 $m^2$ = $E_m \times 1$ m = $(E \times 100)$ m.
• Mass of warp yarns per $m^2$ = $M_w \times (E \times 100)$ = $\frac{T_w}{1000} \times E \times 100 = \frac{T_w \times E}{10}$ g/$m^2$.
• Similarly, Picks per meter ($P_m$) = Picks per cm ($P$) $\times$ 100 cm/m.
• Total length of weft yarn in 1 $m^2$ = $P_m \times 1$ m = $(P \times 100)$ m.
• Mass of weft yarns per $m^2$ = $M_f \times (P \times 100)$ = $\frac{T_f}{1000} \times P \times 100 = \frac{T_f \times P}{10}$ g/$m^2$.
• Total Areal Density ($D_{area}$) = Mass of warp per $m^2$ + Mass of weft per $m^2$.
• $D_{area} = \frac{T_w \times E}{10} + \frac{T_f \times P}{10}$ g/$m^2$.

Applying Given Values

Given:

• Ends per cm ($E$) = 20
• Picks per cm ($P$) = 30
• Warp yarn tex ($T_w$) = 30 tex
• Weft yarn tex ($T_f$) = 25 tex

Calculate the mass contribution from each set of yarns:

• Warp yarn contribution = $\frac{30 \text{ tex} \times 20 \text{ ends/cm}}{10} = \frac{600}{10} = 60$ g/$m^2$.
• Weft yarn contribution = $\frac{25 \text{ tex} \times 30 \text{ picks/cm}}{10} = \frac{750}{10} = 75$ g/$m^2$.

Total Areal Density

Sum the contributions to find the total areal density:

• Total Areal Density = 60 g/$m^2$ + 75 g/$m^2$ = 135 g/$m^2$.

The calculated value of 135 g/$m^2$ falls within the expected range.