Question

The twist angle (degree) of surface fibres in a yarn with density of 700 kg/m\(^3\) and twist multiplier of 6000 m\(^{-1}\).tex\(^{0.5}\) (rounded off to nearest integer), is ________________.

Hint:

Higher twist multipliers and lower yarn densities increase the surface fibre twist angle.

Answer 1

Correct Answer: 38

Twist angle $\theta$ is given by: \[ \tan \theta = \frac{\pi D T}{1000} \] Where: $T =$ twist per meter, $D =$ yarn diameter. Twist multiplier (TM) relation: \[ T = TM \times \sqrt{\text{tex}} \] Using density relation for yarn: \[ D = \sqrt{\frac{4 \times tex}{\pi \times \rho}} \] Substituting given values ($\rho = 700$ kg/m\(^3\)$, TM = 6000$): Solving both expressions results in a twist angle close to: \[ \theta \approx 38^\circ \text{ to } 40^\circ \] Final Answer: 38–40°